MODELING AND SIMULATION OF A HYBRID WIND...

MODELING AND SIMULATION OF A HYBRID

WIND-DIESEL MICROGRID

VINCENT FRIEDEL

Master of Science Thesis in Electric Power Systems

at the School of Electrical Engineering

Royal Institute of Technology

Stockholm, Sweden, June 2009

—

In collaboration with the Georgia Institute of Technology

XR-EE-ES 2009:007

Abstract

Some communities in remote locations with high wind velocities andan unreliable utility supply, will typically install small diesel poweredgenerators and wind generators to form a microgrid. Over the pastfew years, microgrid projects have been developed in many parts of theworld, and commercial solutions have started to appear. Such systemsface specific design issues, especially when the wind penetration is highenough to affect the operation of the diesel plant.

The dynamic behavior of a medium penetration hybrid microgrid isinvestigated. It consists of a diesel generator set, a wind-generator andseveral loads. The diesel engine drives a 62.5 kVA synchronous generatorwith excitation control. The fixed-speed wind turbine drives a 60 kWcage rotor induction generator. The microgrid can be connected to theutility grid but can also run as an isolated system. The total load of themicrogrid is about 100 kVA which varies during the day, and consists ofstatic and dynamic loads, including an induction motor.

The excitation controller and speed controller for the diesel’s synchronousgenerator are designed, as well as the power control of the wind turbine,and the controller for capacitor banks and dump load. The system ismodeled and simulated using PSCAD.

The study evaluates how the power generation is shared between thediesel generator set and the wind generator, the voltage regulation dur-ing load connections, and discusses the need of battery energy storage,the system ride- through-fault capability and frequency control, partic-ularly at times when the utility is disconnected and the microgrid is runas an independent isolated power system. The results of several casestudies are presented.

Keywords: Power Systems, Hybrid microgrid, Wind-Diesel

system, PSCAD modeling

Acknowledgment

I wish to thank Prof. R. G. Harley for hosting my Master’s Thesis work in his lab,for his guidance and availability at every steps of this project, and for reviewingand commenting on my final report.

I am also thankful to all the members of the Power Electronics Lab at GeorgiaTech for welcoming and helping me, especially Yi Du who assisted my first stepswith PSCAD.

I would like to thank Katherine Elkington from the Royal Institute of Technol-ogy for her comments and for reviewing my report.

I am grateful for the opportunity I have been given to do this Master’s Projectin two countries, between Sweden and the United States, and I wish to thankMehrdad Ghandhari, my examiner, as well as the Royal Institute of Technology inStockholm, Sweden, and the Georgia Institute of Technology in Atlanta, USA.

List of Symbols

Diesel generator set

Vb Rated RMS Line-to-Neutral Voltage VIb Rated RMS Line Current Aωb Base Electrical Frequency rad/sH Inertia sTa Armature Time constant sXd D-axis synchronous reactance p.u.X ′d D-axis transient reactance p.u.T ′do D-axis transient open-circuit time constant sX ′′d D-axis subtransient reactance p.u.T ′′do D-axis subtransient short-circuit time constant sXq Q-axis synchronous reactance p.u.X ′′q Q-axis subtransient reactance p.u.T ′′qo Q-axis subtransient open-circuit time constant sTE Exciter time constant sKE Exciter constant related to self-excited field -SE Exciter Saturation Function -KA Voltage Regulator gain -TA Voltage Regulator amplifier time constant sVRMIN Voltage Regulator limiter p.u.VRMAX Voltage Regulator limiter p.u.KF Voltage Regulator stabilizing circuit gain -TFi Voltage Regulator stabilizing circuit time constant sτ1 Dead Time of the diesel’s speed governor sK Actuator Gain of the diesel’s speed governor p.u.τ2 Actuator time constant diesel’s speed governor sKd Droop gain diesel’s speed governor p.u.

Lines parameters

r Line resistance p.u.g Line shunt conductance p.u.l Line inductance p.u.c Line shunt capacitance p.u.R Cable resistance Ω/kmX Cable inductance Ω/km

Loads parameters

PL Power load p.u.QL Reactive power load p.u.UL Voltage magnitude p.u.TWaterPump Water pump torque p.u.ωim Water pump speed p.u.sr Induction machine rated slip p.u.ηr Induction machine efficiency at rated load p.u.

Wind turbine parameters

JRotor Rotor moment of inertia kg·m2

JBlades Blade moment of inertia kg·m2

JGenerator Generator moment of inertia kg·m2

n Gearbox ratio -Pw Wind Turbine output power p.u.ρ Air density kg/m3

U Wind speed m/sA Swept area m2

Cp Power coefficient p.u.λ Tip-speed ratio -β Blade pitch angle. deg.θp Motor angular position deg.J Inertia of the blade and the motor sB coefficient of viscous friction of the pitch mechanism -K spring constant of the pitch mechanism -k slope of the torque/voltage curve of the pitching system -v(t) voltage applied to the pitching motor terminals p.u.m slope of the torque/speed curve of the pitching motor -Qp pitching moment on the pitching system s

Dump loads parameters

PDump Active dump load p.u.PWind Active wind power p.u.PDieselMIN Minimum diesel load p.u.PLoad Active load demand p.u.

Utility grid connection parameters

VHV Voltage on the high side of the transformer p.u.SSC Short-circuit power of the utility p.u.ZHV Equivalent impedance on the high voltage side p.u.VLV Voltage on the low side of the transformer p.u.ZLV Equivalent impedance on the low voltage side p.u.RTR Resistance on the low voltage side of the transformer p.u.XTR Inductance on the low voltage side of the transformer p.u.

Contents

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose of the project . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Introduction to PSCAD . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Modeling of the system 5

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Description of the Microgrid . . . . . . . . . . . . . . . . . . 52.1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Diesel Generator Set . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 Synchronous generator . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Excitation system . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.4 Voltage and Frequency droop control . . . . . . . . . . . . . . 13

2.3 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.1 Static Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2 Dynamic Load . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Soft-Starter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.1 Building of the soft-starter . . . . . . . . . . . . . . . . . . . 202.5.2 Operating modes . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6 Wind Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6.1 Design choices . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6.2 Components of the wind turbine model . . . . . . . . . . . . 242.6.3 Estimation of the wind turbine inertia . . . . . . . . . . . . . 252.6.4 Aerodynamics of the wind turbine . . . . . . . . . . . . . . . 282.6.5 Power control . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.6.6 Wind model, gusts and turbulences . . . . . . . . . . . . . . . 34

2.7 Dump Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.7.1 Need for a dump load . . . . . . . . . . . . . . . . . . . . . . 36

2.7.2 Dump load control . . . . . . . . . . . . . . . . . . . . . . . . 362.8 Capacitor banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.9 Grid Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Simulations and Results 41

3.1 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2 Diesel Generator Set Alone . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.1 Step connection of the static loads . . . . . . . . . . . . . . . 433.2.2 Starting of the induction motor . . . . . . . . . . . . . . . . . 44

3.3 Wind turbine and Utility . . . . . . . . . . . . . . . . . . . . . . . . 483.3.1 Wind Turbine Connection . . . . . . . . . . . . . . . . . . . . 483.3.2 Step connections of loads . . . . . . . . . . . . . . . . . . . . 483.3.3 Wind Speed steps . . . . . . . . . . . . . . . . . . . . . . . . 503.3.4 High wind with stall or pitch controlled turbines . . . . . . . 503.3.5 Utility disconnection . . . . . . . . . . . . . . . . . . . . . . . 52

3.4 Wind Turbine and Diesel Generator Set . . . . . . . . . . . . . . . . 543.4.1 Wind turbine connection . . . . . . . . . . . . . . . . . . . . 543.4.2 Step connection of loads . . . . . . . . . . . . . . . . . . . . . 563.4.3 Wind speed steps . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.5 Wind turbine, Diesel Generator Set and Utility . . . . . . . . . . . . 613.5.1 Utility connection and disconnection . . . . . . . . . . . . . . 613.5.2 Step connection of loads . . . . . . . . . . . . . . . . . . . . . 62

3.6 Three-phase faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.6.1 At the diesel generator set terminal . . . . . . . . . . . . . . 653.6.2 At the wind turbine terminal . . . . . . . . . . . . . . . . . . 673.6.3 At the loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 Conclusion and Future Developments 71

4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

A PSCAD Models 73

B Particle Swarm Optimization 77

C Wind Turbine Aerodynamical Model 83

C.1 WTPerf input file example . . . . . . . . . . . . . . . . . . . . . . . 83C.2 Polynomial regression . . . . . . . . . . . . . . . . . . . . . . . . . . 85C.3 Fortran Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

D Capacitor Bank controller 91

Bibliography 95

Chapter 1

Introduction

1.1 Background

In some remote locations, or in locations of a weak utility grid, distributed gen-eration offers a higher reliability, by providing on-site generation from many smallenergy sources. Typical distributed generation (DG) sources range from a few kilo-watts to a few megawatts. The disadvantage of DG sources is usually their highercosts.

Typical DG sources include hydro power, combustion engines, small wind turbinesand photovoltaic systems.

Many hybrid wind-diesel systems are in operation around the world [1], [2]. Thesesystems offer different penetration levels, with a large choice of technical solutions.This study models a medium penetration hybrid microgrid which includes renew-able penetration of about 50 % of the load. The wind power allows a reduction ofthe diesel generator rating. Systems both with and without battery energy storageare commercially available. Different options are studied to ensure that the powerquality requirements are matched, including design options in the wind turbinepower controller, the installation of capacitor banks to correct the power factor, ordump load to ensure the power balance in the system.

1.2 Purpose of the project

This project has been carried out under the supervision of Prof. R. G. Harley, inthe School of Electrical and Computer Engineering at the Georgia Institute of Tech-nology, in Atlanta, USA.

The dynamic behavior of the medium penetration hybrid system in Figure 1.1 isstudied. The microgrid consists of a diesel generator set, a wind generator and sev-eral loads. The excitation controller for the synchronous generator of the diesel, as

1

CHAPTER 1. INTRODUCTION

Figure 1.1. Hybrid wind-diesel Microgrid

well as the power control of the wind turbine, are designed. The system is modeledand simulated using PSCAD.

The study investigates how the power generation is shared between the diesel gen-erator set and the wind generator, the voltage regulation during load connections,and discusses the need of battery energy storage, the system ride- through-fault ca-pability and frequency control, particularly at times when the utility is disconnectedand the microgrid is run as an independent isolated power system.

1.3 Literature review

This microgrid project deals with many aspects of power systems, including electricmachines, excitation systems, diesel engine, wind turbines, soft-starters and gridintegration, and more particularly the specific aspects of isolated hybrid micro sys-tems. Manufacturers’ data often omit some parameters, which are then estimatedbased on typical values. The following books and papers have served as referenceduring this project.

• Microgrids : Much work on isolated systems has already been reported, but itis often case oriented, and it is difficult to import methods from one project toanother. However, a review of studies related to isolated systems with WindPower appears in Isolated Systems with Wind Power from the Risø NationalLaboratory [2]. The most reliable systems are simple concepts, though thereis currently a tendency to include energy storage and power electronics. Moreand more systems take advantage of the surplus energy using some sort ofstorage such as water pumping, heating and cooling. The EU project “Micro-grids” [17] proposes a benchmark low-voltage network, and discusses controland safety methods in these systems.

2

1.4. INTRODUCTION TO PSCAD

• Power systems : Anderson’s [3] and Kundur’s [4] books have been used asreference books in the modeling of the synchronous generator, its exciter andspeed governor. Both provided typical parameters values and design rules.Furthermore, KTH compendiums [5], [15] and [16] gave the basis for electricalmachines and power systems analysis.

• Wind power : Wind-diesel systems [26] and Wind Energy Explained [19]present wind turbine design and a review of hybrid systems design issues.Some of the main issues are the dump load for the surplus energy in the sys-tem (because of a required minimum load of the diesel or a surplus of windenergy), the need of energy storage, the possibility to start and stop the dieselgenerator (continuous operation implies simplicity and reliability while inter-mittent operation enables fuel savings) and the need to supply reactive powerwhen the diesel engine is stopped, since wind turbines frequently use inductiongenerators.

1.4 Introduction to PSCAD

PSCAD/EMTDC is an industry standard software for studying the transient be-havior of electrical networks. EMTDC performs the electromagnetic transients cal-culations while PSCAD provides the graphical interface.

PSCAD/EMTDC offers a large database of built-in components, and allows theuser to define his own models, either using other built-in components or coding acomponent in Fortran.

Both methods are used during this study. Some components, like the electricalgenerators, are taken from the software library, while others, like the governors orthe wind turbine aerodynamical model, are user-defined.

3

Chapter 2

Modeling of the system

2.1 Introduction

2.1.1 Description of the Microgrid

This project investigates the dynamic behavior of a medium penetration hybridsystem or microgrid consisting of a diesel generator set, a wind generator and severalloads as shown in Figure 1.1. The diesel engine drives a 62.5 kVA synchronousgenerator with excitation control. The wind turbine drives a 60 kW cage rotorinduction generator. The microgrid can be connected to the utility grid but canalso run as an isolated system. The total load of the microgrid is about 100 kVAwhich varies during the day, and consists of different kinds of loads, including aninduction motor.

2.1.2 Methodology

Each component of the microgrid is modeled and tested independently in PSCAD.The first component to be modeled is the diesel generator set. This first modeling,and the first simulations with the diesel generator set connected to an infinite busare used as an introduction to PSCAD. Then, the loads and the lines are modeledby themselves while first connected to the infinite bus, and then to the diesel gen-erator set in order to check if the voltage requirements are fulfilled. A wind turbineaerodynamical model is then designed based on the blade performance in order toget closer to real small turbine performances.

Finally, the whole microgrid is assembled. A series of case studies are carried out,including the different operation modes of the system, i.e. diesel generator set only,wind turbine and diesel generator set, wind turbine and utility grid, and finallywind turbine, diesel generator set and utility grid. The results of these simulationsare presented in Chapter 3.

5

CHAPTER 2. MODELING OF THE SYSTEM

2.2 Diesel Generator Set

The modeling of the diesel generator set is the first step of the microgrid modeling.The purpose of this section is to introduce the diesel generator set and describe themodeling of each of its components.

The diesel generator set has to be controlled to maintain the frequency and voltageof the system while the microgrid is running in islanded mode. In this mode, it isalso the only reactive power supplying component, as the wind turbine, modeledwith a squirrel-cage induction generator, always consumes reactive power.

Figure 2.1. Principal components and controls of a diesel generator set.

A diesel generator set comprises a diesel combustion engine driving a synchronouselectrical generator and are often used when a general power grid is not available,as a primary or auxiliary power supply [6, 19]. The model of the diesel generator setin PSCAD thus comprises a 62.5 kVA synchronous generator, an excitation system,and a diesel engine plus governor. The diesel engine and the synchronous generatorrotate at the same mechanical speed, i.e. 1800 rpm, and no gearbox is used.

2.2.1 Synchronous generator

PSCAD Model

Synchronous machines are common in Power Systems. They are used to convertthe mechanical energy supplied by the prime mover into electrical power. Theirelectrical frequency is proportional to the mechanical speed and is obtained by:

ωe =p

2ωm (2.1)

where p is the number of poles, ωe and ωm respectively the generator’s electricaland mechanical speeds.

The dynamic model of the synchronous generator is designed using the built-insynchronous generator in PSCAD. As usual, the mathematical description of the

6

2.2. DIESEL GENERATOR SET

Table 2.1. Dynamic parameters for the Marathon make synchronous generator.

Parameters Value Unit DescriptionVb 277.1 V Rated RMS Line-to-Neutral VoltageIb 75.2 A Rated RMS Line Currentωb 377 rad/s Base Electrical FrequencyH 0.09 s InertiaTa 0.01 s Armature Time constantXd 1.875 p.u. d-axis synchronous reactanceX ′d 0.132 p.u. d-axis transient reactanceT ′do 0.68 s d-axis transient open-circuit time constantX ′′d 0.11 p.u. d-axis subtransient reactanceT ′′do 0.0096 s d-axis subtransient short-circuit time constantXq 1.875 p.u. q-axis synchronous reactanceX ′′q 0.228 p.u. q-axis subtransient reactanceT ′′qo 0.0658 s q-axis subtransient open-circuit time constant

generator is based on Park’s transformation [3], thus projecting the variables on thedirect axis of the field winding, on the quadrature axis and the neutral axis. Amongother dynamic calculations, the model determines the torque and uses the dynamicequation:

∆ω =Tm − Te −D∆ω

J(2.2)

where Tm is the mechanical torque, Te is the electrical torque, D is the damping ofthe generator, ω is the shaft speed and J the inertia.

The modeling is based on a Marathon 62.5 kVA, 4 pole machine. Its mechani-cal speed is 1800 rpm at 60 Hz and its parameters are shown in Table 2.1. It ismore convenient to normalize all the parameters, and that is done as described in[3], and explained below. Note that the rated power and voltage of the synchronousgenerator are chosen as the base values for the whole microgrid.

S1Φb = Generator rated per-phase VA = 20.8 kVA (2.3)

ULNb = Generator rated line-to neutral RMS terminal voltage = 277.1 V (2.4)

Ib =S1Φb

ULNb= 75.2 A (2.5)

Zb =ULNbIb

= 3.69 Ω (2.6)

Some of the generator’s parameters have not been provided by the manufacturer:Xq, T ′′do, X

′′

q and T ′′qo. These parameters are therefore estimated according to [7]:

7


Xq ≈ Xd (2.7)

as the generator is modeled as a round rotor generator,

T ′′do =Xd · T

′

d · T′′

d

X ′′d · T′

do

(2.8)

X ′′q = 2X2 −X′′

d (2.9)

where X2 is the negative sequence reactance, and X2 = 0.169 p.u., and

T ′′q ≈ T′′

d (2.10)

T ′′qo =XqX ′′q· T ′′q (2.11)

The inertia in seconds H is derived from the given inertia J in kg·m2 according toEquation 2.12

H =12Jω2

RVA(2.12)

where ω is the shaft speed in rad/s and RVA the synchronous generator rated ratingin VA.

2.2.2 Excitation system

The generator excitation system consists of an exciter and a voltage regulator, shownin Figure 2.2. A comprehensive description of such systems is provided in [3] and [4].

The purpose of this part of the modeling is to simulate a typical manufacturer’sexciter. Though simple excitations systems may be implemented in the PSCADsystem, the IEEE provides standardized mathematical models which are designedto represent specific commercial systems. These systems, intended for use in com-puter simulations, are described by Kundur in [4] and have been updated by theIEEE in [8].

The exciter used with the chosen Marathon generator is a rotating and brushlesssystem. It is modeled as the AC5A transfer function presented in Figure 2.2. Thetransfer function can be divided in two parts: the exciter itself and the voltageregulator. The automatic voltage regulator (AVR) contains a stabilizing feedbackloop. The description of each symbol and typical values given by the IEEE areshown in Table 2.2.

As the manufacturer’s parameters are not available, most of these typical valuesfrom Table 2.2 are used. However the stabilizing feedback loop is optimized, asdescribed by Kundur [4]. Note that according to [9], a critical selection of these

8


Figure 2.2. Transfer function of the AC5A excitation system model [8].

Table 2.2. Excitation system model parameters.

Symbol Typical Value DescriptionTE 0.8 Exciter time constantKE 1.0 Exciter constant related to self-excited fieldSE - Exciter Saturation Function

SE(EFD1) 0.86 -EFD1 5.6 -SE(EFD2) 0.5 -EFD2 4.4 -KA 400 Regulator gainTA 0.2 Regulator amplifier time constantVRMIN -7.3 -VRMAX 7.3 -KF 0.03 Regulator stabilizing circuit gain

TF1, TF2, TF3 1.0, 0, 0 Regulator stabilizing circuit time constant

parameters is not necessary, and that stability can be maintained over a significantrange even when using the typical parameter values. However, the exciter has tobe optimized to provide an acceptable steady-state error.

The optimized system, consisting of the synchronous generator set and its exci-tation system, is tested by applying a step increase in the voltage reference VREF.The stabilizing components KF, TF1, TF2 and TF3 are optimized using the ParticleSwarm Optimization algorithm, which is described in Appendix B. The simulationis computed by PSCAD, and the PSO algorithm is implemented in MATLAB. Thecost function CF of this PSO is a linear function of the overshoot (OS), the settlingtime (ST) at a 2% band and the integral of the difference between the reference andterminal voltages (Ar), as defined in Equation 2.13 and Figure 2.3.

9


Figure 2.3. Overshoot, settling time and area of voltage response.

CF = a ·OS + b · ST + C ·Ar (2.13)

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Ter

min

al V

olta

ge (

pu)

Figure 2.4. Response of the 10 particles at the sixth iteration of the PSO algorithm.

Each particle has four elements: KF, TF1, TF2, TF3. The initial values of theelements and thus the positions of these particles in the solution space have a stronginfluence on the rapidity of convergence and on the ability to find the optimalsolution. Nevertheless, these positions are chosen randomly within given limits.Table 2.3 shows the initial range and final optimal value of each element when allthe particles have converged to the same solution. The disturbance is a step changefrom 0.9 to 1.0 p.u. in the reference voltage. Figure 2.4 shows the response to thereference voltage Vref step change at the sixth iteration of the algorithm, when theresponse is assumed satisfactory. The final parameters in Table 2.3 are selected.

10


Table 2.3. Initial range and final position of the particles.

Symbol Initial Range Final ValueKF [0;0.1] 0.0683TF1 [0.5;1.5] 1.1413TF2 [0;1.0] 0.4645TF3 [0;0.5] 0.0037

2.2.3 Diesel Engine

Internal Combustion Engine Model

The diesel engine is used to provide power to the generator and control the speedof its shaft by means of a governor. An Internal Combustion Engine is available inPSCAD Library. It takes the shaft speed and the fuel intake as inputs, and suppliesa mechanical torque Tm as output. This built-in model is customizable, and theparameters of Table 2.4 are entered. The diesel engine rating is sized about 25percent larger than the electrical generator in order to support overload. It rotatesat the same speed as the synchronous generator, and thus no gearbox is needed.The PSCAD model also allows to study the effect of misfired cylinders, but thisoption is not used in this study.

Table 2.4. Input parameters of the Internal Combustion Engine.

Parameter Value UnitEngine rating 80 MW

Machine rating 62.5 MVAEngine speed rating 1800 rpmNumber of cylinders 6 -

Number of engine cycles Four stroke -Misfired cylinders No -

PSCAD generates the output mechanical torque from an input cylinder torque/anglecurve. Many diesel engines operate on a four-stroke cycle, and the typical torque-angle characteristic curve is presented in a shape as seen in Figure 2.5, [10]. Thiscurve data is entered into the PSCAD model. The four events during this cycle arethe intake, compression, power and exhaust strokes. During intake and exhaust,the torque production is negligible compared to the compression and power strokes.During compression, the torque is negative to increase the gas pressure, and theexplosion occurs during the power stroke. It corresponds to the highest peak inFigure 2.5.

Each cylinder offers the same torque-angle characteristic, with an angle differencebetween cylinders depending on the number of cylinders. Finally, the total diesel

11


−400 −200 0 200 400−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Angle (deg.)

Tor

que

(p.u

.)

Figure 2.5. Produced torque of one cylinder in a cycle.

engine torque is equal to the sum of these individual torques. Because of the sharp-ness of the power stroke, the resultant torque of a four-cylinder engine containssignificant ripples. These ripples are somewhat smoothed by the engine inertia, butare still large enough to cause vibrations. A flywheel may be added in order to in-crease the smoothing, or an engine with more cylinders offering a smoother torquemay be used. In this study, a six-cylinder engine is chosen.

The torsional effect on the shaft is neglected, as the system is small and mechanicallystiff. A rigid body diesel generator set is therefore assumed and the inertia of theengine is added to the synchronous generator’s inertia. A typical inertia of a 75 kWdiesel engine is about 1 kg·m2, which gives H ≈ 0.24 s. Adding a flywheel, a typicalinertia for the whole diesel engine and generator set is about 0.5 s [11].

Speed Controller

The diesel engine speed is controlled by its fuel intake which in turn is regulatedby a governor as shown in Figure 2.6. In this microgrid, the speed controller of thediesel generator set is responsible for the system frequency whenever the microgridis run isolated from the main grid.

Typical diesel governors are described in [11] and [12]. The dead time τ representsthe time required for each cylinder to receive the fuel, since not all the cylindersare in that position at the same time. The actuator, which produces the fuel flow,is also represented by a time constant τ2. A limiter is added, as the fuel intakecan not be negative, and also has a maximum value. The mechanical torque Tm istransmitted to the synchronous generator. The typical values used in the modeling

12


Figure 2.6. Governor model in PSCAD.

are shown in Table 2.5.

Table 2.5. Typical governor data [11], and Proportional controller gain.

Parameter Value Unit Descriptionτ 0.02 s Dead TimeK 1.0 p.u. Actuator Gainτ2 0.05 s Actuator time constantKd 50.0 p.u. Droop gain

2.2.4 Voltage and Frequency droop control

The diesel engine is responsible for the system’s frequency and voltage control. Themain task of these controllers is to take care of the active and reactive power sharingbetween the sources, using only the local information (voltage and frequency).

This is done using an active power versus frequency droop, and a reactive powerversus voltage droop [13, 14], as illustrated in Figure 2.7. Using this solution,the micro-source only uses the local information to adjust its power production.This facilitates the expansion of the microgrid, since each micro-source controls itsproduction based on the local voltage and frequency. The power setpoint of eachindividual source can be set independently, and each micro-source has the abilityto autonomously adjust its output following a disturbance.

In Figure 2.7, the frequency versus active power and voltage versus reactive powerdroops are illustrated. The power setpoints P0 and Q0 determine the power gener-ation at nominal frequency f0 and voltage V0, when the microgrid is connected tothe utility grid.

13


Figure 2.7. Frequency vs active power and voltage vs reactive power droops.

Proportional-integral (PI) or proportional-integral-derivative (PID) controllers aretypically used in governors of diesel generator sets. However, these controllers donot allow a speed droop, and a proportional (P) controller is used. The frequency isallowed to change as a function of the active power demand. When the active powerdemand increases, the diesel generator set speed decreases slightly and reaches anew steady-state. When the active power demand decreases, less kinetic energy isextracted from the generator, which accelerates.

In this microgrid, the gain of the governor is designed to allow a 4 % frequencydroop, as shown in Figure 2.7. This droop is responsible for the active powersharing between the active power sources, which are the wind turbine, the dieselgenerator set and the utility grid.

If the voltage regulator of the diesel generator set does not allow a voltage droop,then there might be reactive power circulating between the utility grid and thediesel generator set at times when both are connected to the microgrid. This re-active power flow would be caused by the difference between the reference voltageof the synchronous generator’s exciter and the actual terminal voltage set by theutility grid.

A voltage vs reactive power droop is implemented as follows [13]: the voltage refer-ence is set to be a function of the reactive power output from the diesel generator,within an acceptable percentage (in this study ± 2 %) around 1.0 p.u.

14

2.3. LINES

2.3 Lines

In a power system, electric energy is transmitted from power plants to consumersvia lines, cables and transformers [16]. A classical single-phase model of a symmet-rical three-phase line is shown in Figure 2.8.

Figure 2.8. Model of a line with distributed quantities.

This power line model has a resistance r and an inductance l, corresponding respec-tively to the resistivity of the conductor and the magnetic flux surrounding the line.The shunt parameters (shunt conductance g and shunt capacitance c) represent theleakage currents in the insulation and the electric field between the lines. Thesequantities are distributed along the line.

Figure 2.9. Lumped parameters of a medium line model.

For short and medium length lines, this distribution along the line can however beneglected, and it is possible to calculate the total resistance and inductance of theline as lumped parameters. The π-equivalent model of a medium line with lumpedparameters is shown in Figure 2.9.

Figure 2.10. Lumped parameters of a short line model.

In a microgrid, the lines are usually tens to hundreds of meters, and thus the shortline model shown in Figure 2.10 is used, neglecting the shunt capacitance, as shownin [18].

15


In this study, the wind turbine is assumed to be 500 m far from the substation,the diesel generator set connected through a 20 m cable, and the loads are 250 mfrom the substation. The voltage level throughout the microgrid is 480 V.

Typical impedance values of overhead, twisted, Al. cables are shown in Table 2.6.

Table 2.6. Impedance data for low-voltage cables [18]

Cable type R (Ω/km) X (Ω/km)Twisted cable, 4×50 mm2, Al 0.642 0.100Twisted cable, 4×120 mm2, Al 0.255 0.096Twisted cable, 4×150 mm2, Al 0.208 0.096

Note that cables offering lower resistance may be more expensive, but they maylimit losses and voltage drop. Here, 4×120 mm2 cables are chosen, and the cableparameters are:

Table 2.7. Impedance of the system’s cables.

Cable Length (m) R (p.u.) X (p.u.)Wind Turbine to Substation 500 0.0346 0.013Diesel Generator Set to Substation 20 0.0014 0.00052Substation to loads 250 0.0173 0.0065

16

2.4. LOADS

2.4 Loads

The microgrid in Figure 1.1 includes three different kinds of loads: lighting orheating, computers and a water pump. These loads are represented respectivelyby a constant impedance characteristic, a constant power characteristic, and aninduction motor. Each type of load amounts to about 33 kVA, and may vary duringthe day. The total maximum load is thus 100 kVA. The load modeling is furtherdetailed in this section and is divided between static (lighting/heating, computers)and dynamic loads (induction machine).

2.4.1 Static Loads

A description of static load models is given in Chapter 3 of [15]. A general repre-sentation of static loads, taking the frequency dependency into account is given.

PL = PZIP + κPL0

(

2∑

k=1

kpk

(

ULUL0

)mpk(1 +Dpk∆f)

)

(2.14)

QL = QZIP + κQL0

(

2∑

k=1

kqk

(

ULUL0

)mqk(1 +Dqk∆f)

)

(2.15)

Simpler models are also widely used, as the exponential and the so-called ZIP mod-els, composed of constant impedance (Z), constant current (I) and constant power(P). The exponential models for active and reactive loads are expressed as:

PL = PEXP = PL0

(

ULUL0

)mp

and QL = QEXP = QL0

(

ULUL0

)mq

(2.16)

The exponents mp and mq are the parameters of this model, and can be set asfollows:

• mp = mq = 0 : constant power characteristic

• mp = mq = 1 : constant current characteristic

• mp = mq = 2 : constant impedance characteristic

The static loads of the microgrid are represented using the exponential model ofEquations 2.16. Both the constant power and the constant impedance are repre-sented with a 0.9 power factor. Note that other loads such as a dump load may beadded, when the wind power exceeds the load demand.

Among the loads in the system, the computers are likely to have the tightest volt-age variation tolerance. The Information Technology Industry Council (ITIC) givesvoltage sag tolerance of typical computers in the ITIC Curve shown in Figure 2.11.The voltage of the microgrid will thus have to obey these clearing times, which aresummarized in Table 2.8, and this table will be taken as reference especially whenthe microgrid is islanded.

17


Figure 2.11. ITIC curve.

Table 2.8. Voltage tolerance for computers.

Voltage Sag Duration (s)V < 0.7 0.02

0.7 < V < 0.8 0.50.8 < V < 0.95 101.1 < V < 1.2 0.51.2 < V < 1.4 0.03

1.4 < V 0.01

2.4.2 Dynamic Load

The dynamic load is a 34 kW induction motor, which drives a water pump. Asquirrel-cage rotor model is used, and its parameters are entered in PSCAD usingthe so-called EMTP Type 40 format, in which the parameters are entered based onthe steady state torque-slip curve, as shown in Table 2.9. The water pump impelleris a square-law device and its torque TWaterpump is proportional to the square of itsspeed ωim, such that

TWaterpump = C · ω2im (2.17)

where the parameter C is tuned so that the motor reaches full torque at rated slip.The motor rated slip is sr = 0.233 p.u., and its efficiency at full load is ηr = 0.92.

18

2.4. LOADS

Thus, C can be calculated as follows:

C =1

(1− sr)2·

1

ηr=

1

(1− 0.0233)2·

1

0.92= 1.14 (2.18)

Table 2.9. Induction machine parameters.

Parameter Unit DescriptionRated Power kW 34Rated RMS Voltage V 277Rated speed rpm 1758Efficiency % 92Power Factor - 0.82Locked Rotor current p.u. 6.887Starting Torque p.u. 2.5043Break down Torque p.u. 2.9217

19


2.5 Soft-Starter

2.5.1 Building of the soft-starter

Although the use of power electronics is preferably avoided because of their costor harmonics they introduce, soft-starters may be used to reduce the voltage dropalong the supply feeder during induction machines’ starting. In the present system,soft-starters may be required to start the water pump, or during the connection ofthe wind turbine [28]. These applications are discussed later in this report.

A soft-starter is implemented by 6 thyristors installed in an anti-parallel config-uration, as shown in Figure 2.12. Its control circuit is shown in Figure 2.13. Asnubber RC-circuit limits the rate of change of the voltage across each thyristor.

Figure 2.12. Model of a soft-starter in PSCAD.

Here a simple current limiting soft-starter is modeled. The firing angles are con-trolled in order to limit the voltage drop. In Figure 2.12, Ea2 refers to the voltage ofphase a and its zero-crossings are taken as reference to calculate the angle at whichthe forward thyristor in phase a is triggered. The reverse and forward thyristorstriggerings have a phase difference of 180 degrees, and forward thyristor triggeringsare separated by 120 degrees.

Figure 2.14 shows the control signals determining the firing angle for Ia, governingthe forward thyristor on phase a. Different control methods may be implementedto limit the starting current. Here the firing angle is simply decreased linearly with

20

2.5. SOFT-STARTER

Figure 2.13. Control circuit of the soft-starter.

time, and the slope of this decrease is tuned to minimize the voltage drop at themotor terminals.

Figure 2.14. Control signal of the soft-starter.

2.5.2 Operating modes

Depending on the firing angle, four operating modes may take place [28]:

• Open circuit. When the firing angle is greater than 150 degrees, the thyristorswill not conduct when they are triggered, and thus the soft-starter appears asan open-circuit.

• If the firing angle is decreased, the soft-starter enters a mode where either twoor none of the thyristors are conducting.

21


• If the firing angle is further decreased, it increases the conduction interval,and either 3 or 2 thyristors are conducting.

• If the conduction interval is extended further (i.e. the firing angle is de-creased), the soft-starter will not change the voltage and will transmit all theenergy.

These operating modes are illustrated in Figure 2.15, showing the current Ia in theforward thyristor in phase a.

16.075 16.08 16.085 16.09 16.095

−1.5

−1

−0.5

0

0.5

1

1.5

Time (s)

Cur

rent

(pu

)

(a) Firing angle: 150 degrees

18.485 18.49 18.495 18.5 18.505 18.51

−1

−0.5

0

0.5

1

Time (s)

Cur

rent

(pu

)

(b) Firing angle: 135 degrees

23.94 23.95 23.96 23.97 23.98

−3

−2

−1

0

1

2

3

Time (s)

Cur

rent

(pu

)

(c) Firing angle: 90 degrees

31.45 31.46 31.47 31.48−1.5

−1

−0.5

0

0.5

1

1.5

Time (s)

Cur

rent

(pu

)

(d) Firing angle: 0 degree

Figure 2.15. Current waveform in phase a for different firing angles.

22

2.6. WIND TURBINE

2.6 Wind Turbine

2.6.1 Design choices

The wind turbine chosen in the microgrid of Figure 1.1 is a 60 kW fixed-speedturbine driving a cage-rotor induction generator. In this section, different aspectsof wind turbines are discussed.

Induction generator

The electrical generator converts mechanical power into electrical power. Differentkinds of generators may be used for wind turbines. Some small turbines use DCgenerators, but the most common types are synchronous and induction generators.Induction generators have usually a simple construction, and are relatively cheaper.They also simplify the connection and disconnection from the grid. Different typesof induction generators are used, such as a cage rotor type, a wound rotor withvariable rotor resistance type, or a doubly fed slip ring type.

However, when induction generators are used in small or isolated electrical networks,special measures must be taken in order to supply reactive power or maintain thevoltage stability.

Figure 2.16. EW50 50 kW wind turbine [23]

Operating scheme

Wind turbines with induction generators may operate at a nearly constant rotorspeed or at variable speed. In both cases, below rated wind speed, the goal is tomaximize the energy production, while power has to be limited above rated speed.However, variable speed turbines require the use of power electronics, which in-creases the cost, and may introduce harmonics in the system. In this study, a

23


constant speed turbine is chosen. Both a stall-regulated and a pitch-controlled tur-bines are modeled.

The blades of a stall-regulated wind turbine are designed to intrinsically regulatethe wind power production. They are optimized so that their efficiency drops athigher wind speeds.

In the case of a pitch-controlled turbine, the blade angle can be controlled. Be-low rated wind speed, the blade angle is kept constant and aims to maximize thepower production. Once rated wind speed is reached, this blade angle is increasedin order to limit the aerodynamical torque.

Both a stall-regulated and a pitch-controlled model are simulated in PSCAD, andthese are discussed later in the report.

Starting of wind turbines

There are mainly two methods to start a fixed-speed wind turbine. The first one isto run its generator as a motor until rated speed is reached, and then it switches togenerator mode. The second one is to release the brakes and let the aerodynamicalforce accelerate the rotor, until its speed approaches the rated speed, and thenconnect the generator to the grid. Connection methods have been described in [27].

2.6.2 Components of the wind turbine model

In PSCAD, the wind turbine model consists of an electrical machine, a wind sourceand a turbine aerodynamical model. In this study, the electrical generator is a cagerotor induction machine. The aerodynamical model takes the blades’ performanceinto account, and if pitch-control is used, another block is used to model the bladepitch control. The gearbox is not represented in PSCAD, and all the parametershave either to be transferred to the high-speed side or to be calculated in the per-unit system.

The induction generator’s modeling is based on manufacturer’s data, like the waterpump induction machine described in Section 2.4.2. Its parameters are detailed inTable 2.10, and its torque speed curve is shown in Figure 2.17.

The wind turbine used in the microgrid is a 60 kW turbine. Since the goal here isto build a realistic model, the goal is to approach the data given by manufacturers.Two turbines giving a good amount of information have been found. The first oneis a WES 80 kW turbine [22]. It is a 2-blade, variable-speed turbine with a rotordiameter of 18m, and its output power is regulated both by a power electronic con-verter and pitch angle. The second one is a EW 50 kW [23], 3 blade, stall-regulatedturbine with a rotor diameter of 15 m. Both offer similar per-unit power curves,

24

2.6. WIND TURBINE

0 600 1200 1800 2400 3000 3600−4

−3

−2

−1

0

1

2

3

4

Speed (rpm)

Tor

que

(pu)

Figure 2.17. Torque-Speed Curve of the induction machine.

with a cut-in speed (at which the wind turbine starts to generate power) of about4 m/s, rated wind speed (when it reaches its rated power) of 13 m/s and cut-outspeed (at which it is disconnected from the system) of 25 m/s. Both turbines use agearbox, offering ratios from 20 to 28. The development of the wind turbine aero-dynamical model is detailed in Section 2.6.4.

The pitch controller which regulates the wind turbine’s power and the wind sourceare explained in Section 2.6.5 and Section 2.6.6.

Table 2.10. Wind turbine induction generator parameters.

Parameter Unit DescriptionRated Power kW 60Rated RMS Voltage V 277Rated speed rpm 1758Power Factor - 0.88Locked Rotor current p.u. 6.6783Starting Torque p.u. 2.4Break down Torque p.u. 2.6Inertia kg·m2 0.52

2.6.3 Estimation of the wind turbine inertia

The inertia time constant has a strong impact on the transients of wind turbines.However, this parameter is typically not reported by manufacturers, and an estima-tion is necessary. Examples of inertia time constants are [29, 30] 3.5 s for a 150 kWturbine, 4.64 s and 5.19 s respectively for a GE 1.5 MW and a GE 3.6 MW turbine.

25


In this study the induction generator inertia is known, and a simplified model ofthe rotor is analyzed in order to estimate the mass distribution along the bladesand calculate the inertia. Note that the gearbox does not appear in PSCAD, andall values have either to be transferred to the high-speed side or to be directly cal-culated in the per-unit system.

The WES80 inertia will serve as model, since the manufacturer provides a fairamount of informations. This turbine has 2 blades. The gear ratio is 20, the gener-ator rotates at 1800 rpm, and the blades rotate at 90 rpm. The total rotor diameteris 18 m, and each blade is 7.8 m long. The rotor without the blades has a diameterof 2.4 m. Each blade weighs 86 kg, and the total rotor weighs is about 900 kg.

This rotor is illustrated in Figure 2.18.

Figure 2.18. Rotor model

The generator’s inertia is known, equal to 0.52 kg·m2 and its rotor weighs about100 kg [24]. The generator rotor is considered as the only part of this system ro-tating at 1800 rpm. So the group consisting of the blades and the rotor hub weighs900− 100 = 800 kg and is rotating at 90 rpm.

The rotor is approximated by a homogeneous cylinder with a 2.4 m diameter. Ac-cording to the previous estimations, it weighs 800− (2 · 86) = 628 kg and its inertiais calculated as

Jcyl =1

2·M ·R2 =

1

2· 628 · 1.22 = 452 kg ·m2 (2.19)

26

2.6. WIND TURBINE

Mass distribution and inertia of the blades

The blade chord varies from 500 mm at the tip to 625 mm near the center ofinertia. A much simplified model of the blade is used, considering that the chordvaries linearly (Figure 2.19) and the weight is uniform along the blades. In thatcase, the blade density is calculated as

ρSurface =86 · 2

7.8 · (0.625 + 0.5)= 19.6 kg/m2 (2.20)

Figure 2.19. Blade model.

Then, the weight w of a section at a distance r from the bottom of the blade andof length δr is estimated as

w(r, δr) = ρSurface · δr · Chord(r) = 19.6 · δr ·(

0.625−r

7.80.125

)

(2.21)

Finally, the inertia of each blade is expressed as

J1Blade =∫ 7.8

0ω(r, δr) · (r + 1.2)2 (2.22)

J1Blade = 19.6[

−0.016

4r4 +

0.5865

3r3 +

1.4779

2r2 + 0.9r

]7.8

0

(2.23)

J1Blade = 2547 kg ·m2 J2Blades = 2 · J1Blade = 5094 kg ·m2 (2.24)

Calculation of the total wind turbine inertia

To summarize, there are three components in this simplified system. Two of themare rotating at 90 rpm and their inertia is JRotor = 452 kg·m2 and JBlades =5094 kg·m2 respectively. The induction generator is rotating at 1800 rpm andits inertia is JGenerator = 0.52 kg·m2. Seen from the high speed side, the equivalentmoment of inertia of this system is

Jtotal =JRotor + JBlades

n2+ JGenerator (2.25)

where n is the gearbox ratio.

27


Jtotal =452 + 5094

202+ 0.52 = 14.38 kg ·m2 (2.26)

Finally, the inertia time constant of the whole system is

H =12Jtotalω

2

RVA=

1214.38

(

1800·2π60

)2

80000= 3.19 s (2.27)

where RVA is the rated power of the turbine, and ω is the shaft speed.

The value 3.2 s will be used in the study.

2.6.4 Aerodynamics of the wind turbine

PSCAD built-in model

Figure 2.20. Power Curves: PSCAD model (squares) and actual turbine

The prebuilt wind governor in PSCAD offers two models, one suitable for horizontal-axis turbines with two blades (called MOD 5), and the other one for horizontal-axisturbines with three blades (MOD 2), based on two papers in IEEE Transactions onPower Apparatus and Systems. Some parameters can be set: the generator ratedpower, the machine angular speed, rotor radius, air density, gear box efficiency andthe gear ratio.

The first test is to plot the power curve (Figure 2.20) of the PSCAD model in orderto validate the aerodynamic model, before studying the dynamics of the system andoptimizing the pitch-controller.

User-defined aerodynamical model

Since the power curve of the PSCAD model does not match the selected model, asecond aerodynamical model is developed. This work is based on Chapter 3 of [19].

The output power from a wind turbine is given by Equation 2.28.

28

2.6. WIND TURBINE

Pw =1

2ρU3ACp(λ, β) (2.28)

where Pw is the output power in kW, ρ is the air density in kg/m3, U the windspeed in m/s, A the swept area in m2, Cp the power coefficient in p.u., β the bladepitch angle in degrees, and λ the tip-speed ratio defined as

λ =ω ·R

U(2.29)

where ω is the rotor rotational speed, U is the wind speed and R is the rotor radius.

The National Renewable Energy Laboratory website [25] provides different codeshelping to predict rotor performances and the Cp values are found from WTPerf.This software simulates the blades’ performance based on many input parameterslike the number of blades, rotor radius, hub height, blade chord and twist distribu-tions. An example of a WTPerf input file is shown in Annex C.1.

The goal is to approach an actual turbine’s performance. This is done by “tuning”the blade chord and twist and testing the blade’s performance thanks to WTPerf.

The optimal chord distribution is given by the equation [20]

C(r) =1

n·

8

9 · CL2πR

1

λopt√

λ2opt(

rR

)2 + 49

(2.30)

where CL is the lift coefficient in p.u., R the rotor radius in m, λopt the designtip-speed ratio and n the number of blades.

For small tip-speed ratios, a large number of blades is usually recommended (8to 24 blades for a tip-speed ratio equal to 1). For ratios larger than 4, 1 to 3 bladesare recommended.

The optimal twist angle distribution can also be determined as (see [19])

φ = arctan

(

2

3λ rR

)

(2.31)

For example, the parameters in Table 2.11 are obtained for a 3-blade turbine, witha 7.5 m rotor radius, and a tip-speed ratio equal to 6.5.

The optimal distributions given by Equation 2.30 and Equation 2.31 are approx-imated by linear segments to be entered as input in WTPerf. The software thencalculates the power coefficients for different tip-speed ratios. Figure 2.21 showsCp(λ, β) curves for different blade pitch angles. Note that the highest efficienciesare obtained with the smallest angles in Figure 2.21.

29


Table 2.11. Optimal chord and twist angles.

r/R Twist Angle (deg.) Chord (m)0.1 45.73 3.230.2 27.15 2.060.3 18.87 1.460.4 14.38 1.120.5 11.59 0.910.6 9.70 0.760.7 8.34 0.650.8 7.31 0.570.9 6.50 0.511.0 5.86 0.46

Figure 2.21. Curves of power coefficient Cp(λ, β) versus tip-speed ratio, computedwith WTPerf

WTPerf provides a table of discrete values of Cp for different values of the windspeed and the blade angle. However, an approximating function is required to buildthe model in PSCAD. A two-dimensional polynomial regression (approximation)is computed (see the MATLAB code in Appendix C.2) as seen in Figure 2.22 andfinally the power coefficient as a function of the tip-speed ratio λ and the pitchangle β is obtained and used to build the aerodynamical model in PSCAD.

Final model

This aerodynamic model of the wind turbine is based on the same principles as theprebuilt model in PSCAD. It calculates the output torque and power transmittedto the electrical generator based on the wind speed Uwind, the shaft speed ω andthe blade angle β.

30

2.6. WIND TURBINE

Figure 2.22. Polynomial regression of the power coefficient function, computed withMATLAB

First, the tip-speed ratio λ is calculated based on the rotor radius R, the shaftangular velocity ω and the wind speed Uwind:

λ =ωR

Uwind(2.32)

Then the Power coefficient is estimated based on the polynomial approximationP (λ, β) previously explained:

Cp = P (λ, β) (2.33)

The wind power in the swept area is

PWind =1

2ρAU3 (2.34)

The wind mechanical power generated by the wind turbine is calculated as

Pm = Cp · PWind (2.35)

Finally, the mechanical torque transmitted to the induction generator is

Tm =Pmω

(2.36)

Two models are built: a stall-regulated turbine, taking the Power curve of EW50as reference (see Figure 2.23), and a pitch controlled turbine, taking the WES80power curve as reference (see Figure 2.24).

31


Figure 2.23. Power curve of the stall regulated turbine, model (squares) and refer-ence

Figure 2.24. Power curve of the pitch controlled turbine, model (squares) andreference

2.6.5 Power control

Stall control

In the case of a stall regulated turbine, the blades are designed to reduce their ownefficiency in high winds. The blades have a fixed pitch, and no power controller isrequired.

Pitch control

The pitch controller is of paramount importance in a pitch-controlled constant-speedwind turbine. The design of the pitch actuator is based on the proposed systemin [19], which gives the transfer function of a simple pitch mechanism driven by anAC motor. It includes moments from spring and viscous frictions. The differentialequation for this system is

32

2.6. WIND TURBINE

Jθp +Bθp +Kθp = kv(t) +mθp +Qp (2.37)

where θp is the angular position of the motor in degrees, J is the inertia of theblade and the motor in seconds, B is the coefficient of viscous friction, K is thespring constant, k is the slope of the torque/voltage curve for the motor mechanismsystem, v(t) is the voltage applied to the motor terminals in p.u., m is the slopeof the torque/speed curve and Qp is a pitching moment due to aerodynamic forcesthat disturb the system.

The differential equation leads to the following transfer function:

Θps =1

Js2 + (B −m)s+K(KΘp,ref (s) +Qp(s)) (2.38)

Reference [19] gives typical values for the parameters. J = 116

s, B −m = 14

andK = 1.

One of the main limitations of such pitch controlled turbines is the fact that thepitch mechanism is very slow. A rate limiter has thus been added, limiting theblade angle rate change to ± 5 deg/s as in [31]. Finally, the blade angle itself islimited between 1 and 25 degrees to replicate the model’s performance.

Figure 2.25. Pitch mechanism and pitch controller in PSCAD.

Typical pitch controllers are of the PI or PID type. Both are evaluated and op-timized using Particle Swarm Optimization, and a PID is finally selected as itincreases the system’s responsiveness, and its stability, especially in higher winds.

Using Particle Swarm Optimization, the power output response to a wind speedstep is optimized. The optimized parameters are the PID parameters: the propor-tional gain Kp, the integral time constant Ti and the derivative time constant Td.Starting ranges and final values are shown in Table 2.12. Figure 2.26 shows theresponse to a wind speed step after the tenth iteration of the algorithm. In thatcase, the first overshoot remains high in any case, as a result of the slow responseof the pitch mechanism.

33


Figure 2.26. Response of the particles to a wind speed step.

Table 2.12. PID parameters optimized with PSO.

Parameter Initial range Final valuesKp [0 ; 60] 13.0382Ti [0 ; 1.0] 0.0536Td [0 ; 1.0] 0.6132

Because of the rate change limiter, the first overshoot is not avoidable, even once ithas been optimized. Such a typical pitch actuator does not provide a fast enoughresponse to smooth the wind turbine output power, and as a result the pitch-controlled turbine is very sensitive to gusts.

2.6.6 Wind model, gusts and turbulences

The variations of the wind speed over time are divided into four categories: inter-annual, annual, diurnal and short-term. Inter-annual variations requires a long-termstudy. Annual and diurnal are useful for steady-state studies, as well as to designthe wind turbine. In this study, the variations of wind direction and yaw controlwill not be studied. However, it will focus on short-term wind speed variations, i.e.variations shorter than 10 minutes. These variations include gusts and turbulences.Turbulences refer to short-term variations from less than 1 second to 10 minutes.The turbulence can be studied as a stochastic phenomenon. As seen in [19], byconvention in wind engineering, a mean wind speed U as well as a standard deviationσU are determined over periods of 10 minutes. The turbulence intensity TI is givenby:

TI =σUU

(2.39)

where U is the mean wind speed in meters per second and the standard deviationσU is calculated as

34

2.6. WIND TURBINE

σU =

√

1

Ns − 1·

∑

i=1

Ns(ui − U)2 (2.40)

where Ns is the number of taken measures and ui is the instantaneous wind speedat the ith measure, in m/s.

The standard deviation σU is usually between 0.1 and 0.4. The highest turbu-lences occur at lowest wind speeds. As an example, if the mean wind speed is 10.4meters per second, then the standard deviation is about 1.63 meter per second.The probability density function is best described by a Gaussian probability den-sity function. PSCAD offers a wind model, with gusts and noise. As shown inFigure 2.28, two of these models are connected in series, in order to introduce gustsof different magnitudes and frequencies. The curve in Figure 2.27 is obtained.

Figure 2.27. Wind turbulences.

Figure 2.28. Wind Model in PSCAD.

35


2.7 Dump Load

2.7.1 Need for a dump load

The need for dump load arises with the presence of a wind turbine. It is neededonly if:

• There is no connection to the grid to export the excess power generated inthe microgrid.

• There is no pitch control or power electronic control to limit the wind turbinepower production.

When the produced wind power exceeds the power demand in the microgrid, adump load needs to be connected to ensure the power balance in the system at anytime. Another way may be to control the wind power generation by pitching theblades, but this is not available in the case of a stall-regulated turbine. Thus, allthe available wind power is typically generated and has to be consumed.

2.7.2 Dump load control

The role of the dump loads is to consume the excess power at times when windpower exceeds the load demand. A second role may also be to ensure that thediesel engine is running at a sufficient load level, to optimize its fuel consumption.Note that the diesel generator set cannot be stopped since it regulates the voltageand frequency in the microgrid.

The maximum amount of dump load that may be required in this microgrid corre-sponds to the time when the wind turbine is running at full capacity, and no loadis connected. Under such conditions, the required dump load is

PDumpMAX = PWindMAX + PDieselMIN (2.41)

where PDieselMIN is the minimum load of the diesel generator set.

When delivering its maximum output power, the stall-regulated wind turbine sup-plies about 1.12 p.u. of active power. If the diesel minimum load is 0.1 p.u., thenthere is a need for a dump load of at least 1.22 p.u., i.e. 76 kW. This dump load mayinclude air or water heating [33], an induction motor [34] or water desalinization[35]. For example if the water pump is coupled to a reservoir, its control may workas follows: the water pump would be started if the water level becomes low, or whenthere is excess energy to consume, unless the reservoir is full.

In this study the dump load is modeled as six 0.25 p.u. fixed impedance loadswith a 0.9 power factor. The output power from the wind PWind and the power

36

2.8. CAPACITOR BANKS

demand PLoad are measured, and a minimum diesel load PDieselMIN is set. Therequired dump load is calculated as

PDump = PWind + PDieselMIN − PLoad (2.42)

If PDump ∈ [0.25 · i; 0.25 · (i+ 1)[, then i loads are connected.

2.8 Capacitor banks

Capacitor banks may be connected to keep the power factor of the diesel and util-ity within an acceptable range. These banks supply reactive power to the system,which is necessary especially in the “Wind/Diesel” mode, where the diesel generatorset supplies some reactive power, but the wind turbine uses an induction machinewhich uses reactive power.

The capacitor banks are modeled as three 0.1 p.u. reactive power capacitors, whichare controlled using two integer variables: b and c.

The first variable b represents the number of capacitor banks that are connected,and varies as a function of the diesel generator set’s power factor. A hysteresiscontroller is implemented, in order to avoid the fast connection and disconnectionof the capacitor banks. When the power factor goes below pfLow, an additionalcapacitor bank is connected, and when it reaches pfHigh power factor, one capacitorbank is disconnected.

Figure 2.29. Hysteresis control for the capacitor banks connection

The second variable c disconnects some of the capacitor banks depending on thereactive power delivered by the diesel generator set. This variable ensures thatthere will not be reactive power flowing back to the synchronous generator. TheFORTRAN Code implementing this controller is given in Appendix D.

37


2.9 Grid Integration

The utility is usually modeled as a voltage source connected to the microgrid throughan impedance and a transformer. The impedance is calculated based on the short-circuit power level of the grid at the point of connection. The stronger the grid, thehigher the short-circuit power level.

Figure 2.30. Equivalent circuit for the utility

At the point of connection, the voltage level in the utility grid is VHV and the short-circuit power level is SSC at the utility grid in Figure 2.30. The equivalent utilitysystem impedance ZHV referred to as the high voltage side of the transformer canthus be calculated as

ZHV =V 2

HV

SSC

(2.43)

On the low voltage side of the transformer, this gives the following equivalentimpedance.

ZLV =V 2

LV

V 2HV

· ZHV (2.44)

The XR

ratio of the system is also usually provided by the utility, and thus theresistance and inductance are deduced as follows:

θ = arctanX

R(2.45)

RLV = ZLV · cos θ (2.46)

XLV = ZLV · sin θ (2.47)

Depending of how remote the microgrid is, the grid connection can be weak at theconnection point, and the short-circuit power will then be lower. Different short-circuit impedances are listed in Table 2.13, corresponding to different short-circuitpower level, with X

R= 3, at VLV = 480 V. The base power is 62.5 kVA and the base

voltage is 480 V.

38

2.9. GRID INTEGRATION

Table 2.13. Short-circuit impedance value at different grid capacities.

Short-Circuit Power (kVA) Resistance (p.u.) Inductance (p.u.)20,000 0.0010 0.003010,000 0.0020 0.00595,000 0.0039 0.01181,000 0.0197 0.0592500 0.0395 0.1185

Typical transformer data are given in [32], and the ohmic impedances on the lowvoltage side are determined as

RTR =%R

100

[

(VLV)2

RVA

]

(2.48)

XTR =%X

100

[

(VLV)2

RVA

]

(2.49)

where RVA is the transformer volt ampere rating. With a 4160-480Y, 500 kVAtransformer, with R = 2% and X = 6% [32], the impedances RTR and XTR are0.0025 p.u. and 0.0075 p.u. respectively.

39

Chapter 3

Simulations and Results

3.1 Case study

This microgrid offers four modes of operation, which have been simulated indepen-dently using the previously detailed model. Both normal operations and faultedconditions are simulated.

• Diesel generator set running alone. When the wind speed is too low, orwhen the wind turbine is under maintenance and the microgrid is isolated fromthe utility grid, the diesel generator set is the only generator available and isnot able to supply the maximum power demanded by the microgrid. Howeverusual diesel generator sets can be over loaded with 25% for long periods oftime. In this scenario the connection of each load is simulated, especially thestarting of the induction motor, with and without a soft-starter.

• Utility grid and Wind turbine. When the utility grid is available, thediesel generator may be stopped in order to save fuel. In that case, thefrequency and voltage are set by the utility grid. The case without windpower is not studied. The scenarios to be evaluated are the wind turbineconnection and the connection of loads.

• Diesel generator set and Wind turbine. When the wind speed is suffi-cient, the wind turbine is connected to the system, which runs in Wind-dieselmode. The wind turbine reduces the diesel load, but also provides the lackingpower at times when the power demand exceeds that of the diesel generatorset. In that case, the wind turbine connection is simulated, as well as theconnection of the loads. The dump load and capacitor banks controls are alsostudied.

• Utility grid, Diesel generator set and Wind turbine. This last case isnot economically efficient, but may be useful if a critical load is connected, andthe connection to the utility is not reliable. If a fault occurs at the utility gridin the previous case (Utility + Wind), then the grid connection is interrupted

41

CHAPTER 3. SIMULATIONS AND RESULTS

and the diesel generator is started. Then, if the utility connection comes back,these three systems (Utility, Wind and Diesel) have to run together and offera stable system. This case is one reason why the diesel generator set voltageregulator needs to allow a voltage droop.

• Short-circuit faults. Three-phase short-circuit faults are simulated, at dif-ferent locations in the microgrid, at the loads, at the diesel generator set ter-minal and at the wind turbine terminal respectively. These faults are clearedafter 150 ms, and the system’s voltage and frequency recovery patterns areevaluated.

Note that the results earlier than the dashed line in the simulation represent theinitialization transients in PSCAD and should be ignored. In the initial state att = 0 s, the components of the system are not synchronized, and this causes largetransients during the initialization, in the first seconds after the simulation starts.

42

3.2. DIESEL GENERATOR SET ALONE

3.2 Diesel Generator Set Alone

When the utility grid is disconnected and the wind turbine is not running, then thediesel generator set supplies all the load demand. In this operating mode, there isno need for dump load or capacitor banks. However, the diesel generator set hasnot been sized to supply the maximum load demand, and it can only supply 2/3 ofthe maximum load. In this study, load step changes are simulated. In reality, theload changes would be smoother.

3.2.1 Step connection of the static loads

Figure 3.1. Active and Reactive power during load connection.

First, all the static loads are disconnected. A 0.5 p.u. constant impedance (lighting)is connected at t = 6.0 s and disconnected at t = 21.0 s. The 0.5 p.u. constantpower (computers) is connected and disconnected respectively at t = 11.0 s andt = 16.0 s. The active and reactive powers are shown in Figure 3.1.

According to the frequency droop control, the frequency is supposed to be 1.02 p.u.at no load, and 0.985 p.u. at full active load. At no-load, the frequency is thusexpected to be 61.2 Hz, and to drop to 61.2−0.035 ·60 = 59.1 Hz at full active load.The actual frequency droop response of the diesel’s governor is shown in Figure 3.2.After a first transient during the initialization of the PSCAD simulation, the sys-tem reaches an initial steady-state. At no-load, the system’s frequency is 61.2 Hz,and it drops to 59.3 Hz when both loads are connected, which amounts to 0.9 p.u.

43


Figure 3.2. Voltage and Frequency at the substation.

active load. The voltage variations do not exceed the computer tolerance, and thesteady-state voltage at the loads is kept within 5 % around the nominal value.

3.2.2 Starting of the induction motor

The starting of an induction motor is supposed to be the heaviest load the microgridwill be subject to. In this microgrid, a relatively large motor amounting to half ofthe diesel generator rating is simulated. It drives a water pump as explained inSection 2.4.2. The induction motor with his shaft load is started directly on-line att = 16.0 s and disconnected at t = 35.0 s, and the large transients measured at thesubstation in Figure 1.1 are shown in Figure 3.3.

The impact of a direct on-line start is severe on the microgrid’s voltage. This volt-age drop does not match the computer voltage’s requirement, and the inductionmotor therefore has to be started by another method. The soft-starter explained inSection 2.5 is added and its starting impact on the system’s voltage and frequencyis shown in Figure 3.4.

Once the induction motor has reached its rated speed, the soft-starter is bypassed(here at t = 30.0 s). The speed and current of the induction motor during directstarting and soft-starting are shown respectively in Figure 3.5 and Figure 3.6. Thepeak current of 4 p.u. at t = 24 s in Figure 3.6 depends on the ramp time of the

44


Figure 3.3. Voltage and frequency at direct online starting of the induction motor.

Figure 3.4. Soft-starting of the induction motor.

thyristor trigger angles in the soft-starter. A slower ramp time will yield a lowerpeak value.

45


Figure 3.5. Induction motor speed during direct- (above) and soft- (below) starting.

46


Figure 3.6. Induction motor current during direct- (above) and soft- (below) start-ing.

47


3.3 Wind turbine and Utility

In this section, the wind turbine is connected to the utility grid. The diesel generatorset is not running.

3.3.1 Wind Turbine Connection

During its starting process, the wind turbine is accelerated by the wind until theinduction motor approaches its rated speed. The connection occurs once the in-duction motor approaches its rated speed. When the microgrid is connected to theutility grid, the main criteria during the connection of the wind turbine is the gridcode. The voltage maximal drop during the connection is typically required to beless than 4% [27]. This voltage change depends mostly on the grid’s short circuitcapacity. If the microgrid is connected to a weak utility grid, then a soft-startermay be required for the induction generator. In this mode, the grid codes have tobe studied further, depending on the national regulations.

3.3.2 Step connections of loads

Figure 3.7. Active and Reactive power produced by the wind and the utility, con-sumed by the load.

The mean wind speed is kept constant (though it includes gusts and turbulences),and each load is connected respectively at t = 6 s (constant power), t = 11 s (con-stant impedance) and t = 16 s (soft-starting of the induction motor), as shown inFigure 3.7. In this mode, the power balance is ensured by the utility grid, which

48

3.3. WIND TURBINE AND UTILITY

Figure 3.8. Voltage and Frequency during loads connection.

provides the difference between wind generation and load demand. The wind tur-bine supplies active power to the micro grid, and consumes reactive power, whichimplies that the wind turbine reactive power is negative in Figure 3.7. At no-load,all the wind power is transmitted to the utility grid. At t = 6 s, the constant powerload is connected, amounting to about 0.5 p.u., the wind power is consumed by theload, and the utility grid starts to supply the difference between active and reactivepower. Only one capacitor bank is connected since the reactive power level is low.At t = 11 s, the constant impedance amounting to 0.5 p.u. is connected. Since thewind power is constant, the utility grid power increases and one additional capacitorbank is connected to correct the power factor. At t = 16 s, the induction motoris started using its soft-starter. During its acceleration, it consumes first more re-active power, and one capacitor bank is thus connected (at t = 18.0 s). Once ithas reached its rated speed, this capacitor bank is disconnected (at t = 29 s). Theconnection of a capacitor bank supplies reactive power to the system. This in turndecreases the utility reactive power supply. When a capacitor bank is disconnected,the utility reactive power supply increases. When there is excess active power inthe microgrid (when the wind power exceeds the demand), it may be sold to theutility.

The voltage and frequency are regulated by the utility, and the voltage level atthe load is kept within [0.95; 1.05] at steady-state, as shown in Figure 3.8. Notethat between 16.0 s and 30.0 s the induction motor is starting, which corresponds

49


to a transient.

3.3.3 Wind Speed steps

Figure 3.9. Active and Reactive power produced by the wind and the utility, con-sumed by the load.

In this simulation, the load is constant, and steps in the wind speed are investigated.At t = 0 s, the mean wind speed is 6 m/s, and it is increased step by step to 8 m/s,10 m/s, 12 m/s, 14 m/s and 16 m/s respectively at t = 5.0 s, t = 10.0 s, t = 15.0 s,t = 20.0 s and t = 25.0 s. The active and reactive power supplied by the windturbine and the utility grid and consumed by the load is shown in Figure 3.9.At each wind speed step, the power supplied by the utility grid is reduced. Thecapacitor banks are connected at t = 1.0 s and t = 10.5 s, in order to correct thepower factor in the micro-grid. The frequency and voltage are set by the utilitygrid (Figure 3.10), and the wind speed steps do not cause significant transients. Asshown in Figure 3.10, the voltage at the substation is increased at t = 10.5 s. Thefrequency is constant.

3.3.4 High wind with stall or pitch controlled turbines

In this simulation, the pitch controlled and the stall regulated wind turbines arecompared. The mean wind speed is initially 14.5 m/s, and a wind speed step occursat t = 10.0 s from 14.5 m/s to 16.5 m/s. As shown in Figure 3.11, in the case ofthe pitch controlled turbine, the pitch mechanism is continuously acting. Becauseof the limited speed of response of the pitch actuator, the regulation is very slow,

50


Figure 3.10. Voltage and frequency at the substation during wind speed steps.

Figure 3.11. Active power from the wind, utility and load consumption (above) andblade angle (below) with the pitch-controlled model.

51


Figure 3.12. Active power from the wind, utility and load consumption with thestall-regulated model.

and the output power is finally not smoother than with stall-regulation, where theblade angle is kept constant (Figure 3.12). As a result, the stall-regulated model ischosen for this system.

3.3.5 Utility disconnection

If the connection to the grid is lost in this Wind-Utility mode, the diesel generatorset needs to be started, which typically takes a few seconds. During that time,the system’s frequency and voltage are not controlled, and the system collapses asshown in Figure 3.13. In this simulation, the micro grid is running with the windturbine, the utility grid and 1.0 p.u. load. At t = 10.0 s, the connection to theutility grid is lost, and the system’s voltage and frequency collapse.

This problem may be solved by adding short-term energy storage to the system,such as flywheels or battery storage, in order to maintain the frequency and thevoltage while the diesel engine is started.

52


Figure 3.13. Voltage and Frequency when the grid connection is lost at t = 10 s.

53


3.4 Wind Turbine and Diesel Generator Set

3.4.1 Wind turbine connection

In order to illustrate the impact of the wind turbine connection on the grid’s voltageand to investigate if a soft-starter is needed, the stall-regulated turbine is connecteddirectly to the grid, and Figure 3.14 and Figure 3.15 show how the active, reactivepower, voltage and frequency of the diesel generator and wind turbine behave.

Figure 3.14. Active and reactive power, direct connection of the stall-regulatedwind turbine to the grid, with a 5.5 m/s mean wind speed.

Grid codes differ from country to country and often from site to site, but a usuallimit is a voltage drop of 4 % during the connection process [27]. These grid codesmay be studied in future work. However, in this section the microgrid is isolatedfrom the utility grid, and the goal is to check if the direct connection of the windgenerator, without a soft-starter, could match the computers’ voltage tolerance.

The connection is supposed to occur at low wind speeds, and in this simulationthe mean wind speed is 5.5 m/s. Gusts and turbulences are unavoidable, and havebeen included, so the wind speed is actually varying between 5 and 6 m/s. Theturbine is connected at t = 10.0 s and disconnected at t = 20.0 s. The voltage andfrequency impact of the connection are shown in Figure 3.15. The disconnection hasan impact on the system’s voltage, but does not violate the voltage sag standards.The connection’s impact is heavier, because the voltage drops under 0.8 p.u. for aperiod of 0.2 s, but still matches the computers’ voltage requirements.

54

3.4. WIND TURBINE AND DIESEL GENERATOR SET

Figure 3.15. Voltage and frequency, direct connection of the stall-regulated windturbine, with a 5.5 m/s mean wind speed.

Figure 3.16. Active and reactive power, direct connection of the pitch-controlledwind turbine, with a 7.5 m/s mean wind speed.

55


Figure 3.17. Voltage and frequency, direct connection of the pitch-controlled windturbine, with a 7.5 m/s mean wind speed.

A common concept when the wind turbine is equipped with a pitch mechanism(active-stall or pitch controlled turbines) is to limit the power output from the windduring the connection process, in order to limit the impact on the microgrid’s volt-age, even in higher wind speeds. This is shown in Figure 3.16 and Figure 3.17.When the turbine is equipped with a pitch mechanism, the blade angle is controlledto limit the wind power during the connection process. Once the turbine has beenconnected to the grid, the turbine comes back to its normal operation mode, maxi-mizing its production until it reaches its rated power. In Figure 3.16 and 3.17, thepitch-controlled wind turbine is connected at t = 10.0 s and switched to maximumpower production at t = 15.0 s. Note that the wind speed in this simulation is higherthan in the case with the stall regulated turbine. It is disconnected at t = 25.0 s,and even with a higher wind, the voltage sag standards are not violated.

The impact of the wind turbine’s connection is almost the same with the stall-regulated or the pitch-controlled model, since the connection takes place when theinduction generator speed is close to synchronous speed.

3.4.2 Step connection of loads

This section investigates the power sharing between the diesel and the wind gener-ator at different load levels, while the micro grid is isolated from the utility grid.

56


The capacitor banks and the dump load controllers’ behavior are studied as well.

Figure 3.18. Active power and Dump load.

The mean wind speed is kept constant, though gusts and turbulences are includedwhich cause wind power variations. The active and reactive power of the dieselgenerator set, the wind generator and the dump load are shown in Figure 3.18 andFigure 3.19 respectively, with the capacitor banks connecting at various times. Thesystem is connected at no-load at t = 0.0 s and the dump loads are connected andconsume the excess power from the wind. One capacitor bank is connected initially,in order to correct the power factor from the diesel generator set. At t = 6.0 s, theconstant power load is connected, and as a result the dump load is disconnected. Anadditional capacitor bank is connected at t = 6.0 s and quickly disconnected, whichproves that the capacitor controller still needs to be improved to avoid chatteringon and off (Figure 3.19). At t = 11.0 s, the constant impedance load is connected,and the diesel generator set increases its generation. The diesel generator providesthe difference between the wind power and the demand from the loads, and alsosupplies the reactive power since it is the only generator able to produce reactivepower. At t = 16.0 s, the induction motor starts using its soft-starter. An addi-tional capacitor bank is connected during the starting, and disconnected once therated speed is reached. The capacitor banks are connected in order to correct thepower factor, as shown in Figure 3.19.

As shown in Figure 3.20, the substation voltage is kept within the 5 % limits around1.0 p.u. at steady-state, and within the computer’s requirement during transients.

57


Figure 3.19. Reactive power and capacitor banks connection, c1 c2 and c3 are thecapacitor breaker control variables, taking two values: open (1) or closed (0).

Figure 3.20. Voltage and Frequency during loads connection.

58


The frequency shown in Figure 3.20 obeys the 3.5 % frequency droop, setting thesystem’s frequency at 59.1 Hz when the diesel generator is supplying 1.0 p.u. activeload.

3.4.3 Wind speed steps

This section studies the power sharing between the diesel generator and the windgenerator and the dump load behavior while the stall-regulated turbine is subjectto wind speed step changes. The wind speed is initially at 6 m/s, the diesel suppliesmost of the load (Figure 3.21) and sets the substation frequency to about 59.5 Hz(Figure 3.22).

Figure 3.21. Active power production and consumption, dump load connection.

When a wind speed step occurs at t = 5.0 s, the wind turbine increases its pro-duction, and the diesel generator set speed is increased, and its power generation isdecreased. So the frequency progressively increases, as shown in Figure 3.22. Thishappens at every wind speed, at t = 10.0 s and t = 15.0 s. At t = 20.0 s, a dumpload is connected in order to ensure a minimum load of the diesel generator. Att = 25.0 s, after the wind speed increases from 14 to 16 m/s, the wind power exceedsthe demand and the dump load is increased in order to consume this excess power.The frequency set by the diesel generator is about 61 Hz.

Figure 3.23 shows the wind speed variation which takes gusts and turbulences intoaccount.

59


Figure 3.22. Substation voltage and frequency during during wind speed steps.

Figure 3.23. Wind speed during the simulation of wind speed step changes.

60

3.5. WIND TURBINE, DIESEL GENERATOR SET AND UTILITY

3.5 Wind turbine, Diesel Generator Set and Utility

3.5.1 Utility connection and disconnection

This section investigates the effect of suddenly disconnecting the utility grid andreconnecting it without correctly synchronizing it to the diesel generator set. Thesystem in Figure 1.1 is started with the diesel generator set, the wind turbine andthe utility grid and all loads connected. The utility grid is suddenly disconnectedat t = 20.0 s and reconnected at t = 30.0 s. The power supplied by the utility grid,the diesel generator set and the wind turbine are shown in Figure 3.24. The voltageand frequency at the substation and at the loads are shown in Figure 3.25.

Figure 3.24. Active and reactive power produced by the wind and the utility,consumed by the load.

When the system is running connected to the utility grid, before t = 10.0 s, thefrequency and the voltage are set by the utility grid, equal to about 1.0 p.u. and60.0 Hz. When the disconnection occurs, the diesel generator increases its powerproduction (Figure 3.24). The voltage at the loads drops under 0.95 p.u. for about1 s but still satisfies the computer’s voltage tolerance requirement. The frequencyafter the disconnection of the utility is set by the diesel’s governor, and drops toabout 59.4 Hz, which corresponds to the frequency droop.

Automatic re-closure of the connection to the utility grid is commonly used, andthis causes out-of-synchronism connection at t = 30.0 s to the substation voltagemaintained by the diesel generator. When the reconnection occurs at t = 30.0 s, the

61


Figure 3.25. Voltage and Frequency during utility connection (t = 20 s) and dis-connection (t = 30 s).

transients are much heavier than at the disconnection. The voltage drops to about0.85 p.u., which does not violate the voltage sag standards. However, the suddenreconnection of the utility causes severe transients in Figure 3.24. In this simulationthe voltage sag seems acceptable for the micro-grid, however the large power flowsshown in Figure 3.24 may damage the generation and distribution equipment.

3.5.2 Step connection of loads

This simulation investigates the behavior of the diesel generator voltage and itsgovernor when the diesel and the wind turbine are both connected to the utilitygrid. As stated in Section 2.2.4, there are two sources of reactive power in this case,and it has to be checked that the substation voltage level set by the utility grid isaccepted by the diesel voltage regulator.

In this simulation, each load is connected one after another. The mean wind speedis kept constant. The active power and the reactive power in the system are shownin Figure 3.26.

At t = 5.0 s, the fixed power load is connected, at t = 10.0 s the constant impedanceis connected, and at t = 16.0 s, the induction motor is started, with the soft-starter.The substation frequency and voltage are regulated by the utility grid, and thediesel generator’s active and reactive power are expected to be constant, according

62

3.5. WIND TURBINE, DIESEL GENERATOR SET AND UTILITY

Figure 3.26. Active and reactive power produced by the wind and the utility,consumed by the load.

Figure 3.27. Voltage and frequency during loads connection.

to the voltage and frequency droop controls. In Figure 3.26, it is shown that the

63


active power from the diesel generator set is constant at the connection of the loads,while the reactive power varies. This is explained by the voltage drops at t = 5.0 s,t = 10.0 s and the induction motor starting (Figure 3.27), which implies a variationof the diesel generator’s reactive power, while the frequency is constantly kept equalto 60 Hz.

Note that the values of the frequency and voltage droop slopes control the dieselpower production when connected to the utility grid. When the microgrid is con-nected to the utility grid modeled as an infinite bus, the voltage and the frequencyat the substation bus are almost constant, and correspond to specific points on thefrequency vs active power and voltage vs reactive power droop curves.

64

3.6. THREE-PHASE FAULTS

3.6 Three-phase faults

This section investigates if the voltage and frequency recover after specific short-circuit faults, and if the voltage sag standards are violated. The simulations mayunderline the need for a faster synchronous generator’s exciter.

Three short-circuit faults are simulated in this section. These faults are locatedat different locations in the system, and are cleared by opening circuit breakersand thus disconnecting the faulted line as well as a component of the system. Oneshort-circuit fault is simulated while the system is connected to the utility grid, andthe other ones are simulated in islanded mode. In these last two cases, the dieselgenerator set’s regulator response is of interest.

In all the faults of Section 3.6, the induction motor soft-starter is not reinserted.

3.6.1 At the diesel generator set terminal

In this section a fault is simulated at the diesel generator set connection as shown inFigure 3.28. If a short-circuit occurs at the diesel generator set terminal while themicrogrid is running isolated from the grid, then there is no frequency or voltagecontrol in the system, and as a result the voltage and frequency collapse. Hence theshort-circuit is simulated at the diesel generator’s terminal, but with the microgridconnected to the utility grid.

Figure 3.28. Network where the fault occurs at t = 10.0 s.

The fault occurs at t = 10.0 s and is cleared after 150 ms by opening circuit breakersCB3 and CB4 and thus disconnecting the faulted line and the diesel generator fromthe substation. The voltage at the substation and at the load recovers after 250 ms(Figure 3.29). The voltage drops under 0.5 p.u. for about 150 ms which respects the1547 IEEE Standard for Interconnecting Distributed Resources with Electric Power

65


Figure 3.29. Voltage and frequency response to a 3-phase short-circuit at the dieselterminal, clearing time = 0.15 s.

Figure 3.30. Induction motor speed response to a 3-phase short-circuit at t = 10.0 sat the diesel terminal, clearing time = 0.15 s.

Systems [36]. However, the computers may be disconnected because CB7 may tripdue to under voltage protection. The impact of this fault on the induction motorand the wind turbine speeds is shown respectively in Figure 3.30 and Figure 3.32.Figure 3.31 shows the current in the induction motor. In that case, the peak currentwhen the fault is cleared is far smaller than during the direct starting. However, thesoft-starter may be controlled to limit this current in the case of a fault, in order toimprove the system’s recovery.

66


Figure 3.31. Induction motor current response to a 3-phase short-circuit att = 10.0 s at the diesel terminal, clearing time = 0.15 s.

Figure 3.32. Wind Turbine speed response to a 3-phase short-circuit at t = 10.0 sat the diesel terminal, clearing time = 0.15 s.

3.6.2 At the wind turbine terminal

In this section a fault is simulated at the wind turbine connection. The system issimulated isolated from the utility grid, as shown in Figure 3.33.

A 3-phase short-circuit fault occurs at t = 10.0 s at the wind turbine connection,near the substation. It is cleared after 150 ms by opening CB1 and CB2 and isolatingthe turbine from the system. As shown in Figure 3.34, the voltage at the substationand at the load connection recovers after 500 ms. The frequency recovers too, butsince the wind turbine has been disconnected from the system, the diesel governorreduces its frequency according to the frequency droop control so that the frequencyafter the fault is cleared drops to about 59 Hz.

67



Figure 3.34. Voltage and frequency response to a 3-phase short-circuit at t = 10.0 sat the wind turbine terminal, clearing time = 0.15 s.

3.6.3 At the loads

In this section, the system is running isolated from the grid, and a short-circuitfault occurs at the load connection point as shown in Figure 3.35.

The fault occurs at t = 10.0 s. It is cleared after 150 ms by tripping CB7 anddisconnecting the faulted load, i.e. the constant power load in this case. Figure 3.36shows the voltage at the substation bus and the load bus and frequency at the

68



substation. Both voltages recover after 750 ms, and as in the previous case, thevoltage sag duration exceeds the ITIC curve’s tolerance. Since the fault is clearedby disconnecting the constant power load, the post-fault load is lower than thepre-fault load and the substation bus frequency after the fault is clear increasesslightly.

Figure 3.36. Voltage and frequency response to a 3-phase short-circuit at the loadconnection, clearing time = 0.15 s.

69


3.6.4 Conclusion

All the faults simulated in this chapter violate the voltage sag standards defined bythe ITIC curve shown in Section 2.4, stating that the load voltage should not dropunder 0.5 p.u. for more than 20 ms. Since the simulated faults are cleared after150 ms, this requirement is not fulfilled.

Different solutions may be used to improve the system’s response. Some com-munities may simply want to add a wind turbine to their existing diesel generatorset, and replacing the diesel generator or only its exciter would imply extra costs.However, the voltage recovery is mainly limited by the diesel generator set’s exciter,and replacing this component may allow to get a stronger and faster voltage con-trol. The induction motor’s soft-starter may also be controlled in order to limit itsin-rush current after the fault, in order to reduce its load demand while the systemis recovering from the fault.

70

Chapter 4

Conclusion and Future Developments

4.1 Conclusion

The main purpose of this project is to create a model of a wind-diesel hybrid mi-crogrid using PSCAD/EMTDC.

The diesel generator set is modeled from manufacturer’s and typical values, andits speed and voltage controllers are defined to allow a frequency and a voltagedroop, which facilitates the expansion of the grid and the self-synchronization ofadditional AC sources.

The wind turbine is modeled with a cage rotor induction generator and a bladeaerodynamical model is built to approach typical turbines’ performance. Both apitch-controlled fixed-speed turbine and a stall regulated fixed-speed turbine aremodeled, and the stall-regulated turbine is finally chosen, as it is more commonlyused by the manufacturers, may offer a longer lifetime, and does not offer largerpower variations during gusts.

The diesel generator set’s voltage regulator and the wind turbine pitch-control areoptimized using Particle Swarm Optimization, however these controllers’ responsesare limited respectively by the synchronous generator exciter and the pitch mecha-nism.

The induction motor load rating amounts to half of the diesel generator set, and itsstarting requires a soft-starter to limit the voltage dip, so that the voltage is keptwithin the computers’ voltage tolerance. A dump load aiming to consume the ex-cess energy is added to the system. A controller for connecting the capacitor banksis proposed, which aims to avoid the continuous connection and disconnection ofcapacitor banks.

71

CHAPTER 4. CONCLUSION AND FUTURE DEVELOPMENTS

4.2 Future Work

Different aspects of a microgrid have not been studied in this work, or would requireimprovements.

First, the capacitor banks may be deteriorated because of the harmonics introducedwhen a soft-starter is used. It has to be checked that their current and power do notexceed their tolerance. The capacitor banks’ controller may be further improved,in order to avoid chattering on and off as in Figure 3.19 at t = 6.0 s. This maybe done by using more capacitor banks of a smaller rating, or by allowing largervariations of the power coefficient. The capacitor banks’ controller may also haveto be stopped when a fault occurs in the system. If this is not the case, the systemmay become oscillatory and take a few more seconds to recover.

The possibility to shut-down the diesel engine when the microgrid is running asan island requires an additional component to supply reactive power as well as tomaintain and control the frequency and the voltage in the system. This can be doneby equipping the wind turbine with another electrical machine, or adding some sortof energy storage in the system.

The grid codes require more attention, depending on the local regulation. In thiswork only an introduction to the issue of grid integration has been given, and de-pending on the utility grid strength, some additional equipment might be required.

The induction motor soft-starter may be developed further, in order to limit itsstator current when a fault occurs in the system. The induction motor may also becontrolled as a dump load, starting water pumping in two cases: if the water levelin the water tank is low, or if there is excess energy in the microgrid.

An economical study of this system may also be carried out, in order to optimizethe steady-state load of the diesel generator set, minimize its consumption, andoptimize the use of deferrable loads such as the water pump.

72

Appendix A

PSCAD Models

All the models shown in this section are taken from the file:

\PSCAD Files\FinalMicrogrid\090406_Microgrid.psc

Figure A.1. Model for the diesel generator set.

73

APPENDIX A. PSCAD MODELS

Figure A.2. Model for the wind turbine.

74

Figure A.3. Model for the induction motor, with soft-starter.

75

APPENDIX A. PSCAD MODELS

Figure A.4. Complete Microgrid.

76

Appendix B

Particle Swarm Optimization

The algorithm

Particle swarm optimization is a stochastic optimization algorithm developed byDr. Eberhart and Dr. Kennedy in 1995 [37].

The system is initialized with a population of random solutions. The particlessearch for optima by traveling through the problem space. Each particle keepstrack of its best solution achieved so far, saving its best cost function value as wellas its position at that solution. The particle velocity is also influenced by the globaloptimum achieved so far.

At each iteration, the cost function at each particle’s position is calculated andglobal and local best solutions are updated. Then, each particle’s acceleration iscalculated, driving the particles towards their local and global best. Their velocityis randomly weighted, and an inertia can also be added, in order to tune the velocityat which this algorithm converges.

One of the main advantages of Particle Swarm Optimization is its ability to workwell in a variety of applications, requiring slight parameters changes.

The algorithm is detailed in Figure B.1. Different parameters can be personal-ized, as a, b and c in the calculation of the cost function, which give more or lessweight to specific criteria. The inertia J appearing when updating the particles’velocity and position can be tuned as well, and its result is a quicker or slowerconvergence of the algorithm.

77

APPENDIX B. PARTICLE SWARM OPTIMIZATION

Figure B.1. PSO algorithm.

MATLAB implementation

This section provides the MATLAB code implementing the particle swarm opti-mization algorithm.

The first code initiates the particle position and velocity.

clear all

% Initialize particle position and velocity

78

% Position limits:

Kf=0; Tf1=0; Tf2=0; Tf3=0;

Limits = [Kf,0,0.1

Tf1,0.5,1.5

Tf2,0,1.0

Tf3,0,0.5];

Npart = 10;

% Definition of particle position and velocity

for i = 1:Npart

for j = 1:4

X(i,j) = Limits(j,2) + (Limits(j,3)-Limits(j,2)) * rand();

V(i,j) = 0;

end

end

X

V

% Initialization of global and local best results

Gbest = inf;

for i = 1:Npart

Lbest(i) = inf;

end

Then the simulations are run under PSCAD, and the voltage response using eachparticle is saved as a MATLAB Matrix. The following code calculates the costfunction of each result.

% Read the data file

Z6 = [F1’;F2’;F3’;F4’;F5’;F6’;F7’;F8’;F9’;F10’];

OStot=[];

STtot=[];

CFtot=[];

Artot=[];

for a=1:size(Z6,1)/2

Resp_sig = Z6(2*a,:);

plot(Z6(2*a-1,:),Resp_sig)

hold on

% Calculation of the cost function

% Overshoot

OS = max(Resp_sig)-1.0; % in p.u.

79

APPENDIX B. PARTICLE SWARM OPTIMIZATION

% Settling Time

step = 250; % micro second

L = 2.0/(step*10^-6);

K = length(Resp_sig);

ST=3.0;

while K >= L

if abs(Resp_sig(K)-1.0)>0.02

ST = K*step*10^-6 - 2.0;

K = 0;

else

K=K-1;

end

end

% Area

Ar = 0;

Ar = sum(abs(1.0-Resp_sig(L:length(Resp_sig))));

% Cost Function

CF = Ar/2000 + OS + 0.1*ST;

Artot = [Artot;Ar];

OStot = [OStot;OS];

STtot = [STtot;ST];

CFtot = [CFtot;CF];

end

Artot

OStot

STtot

CFtot

Finally, the local and global bests are calculated and the particles’ new position andvelocity are updated using the following code.

% Update the local bests and their cost

for i = 1:Npart

if CFtot(i) < Lbest(i)

Lbest(i) = CFtot(i);

for j = 1:4

Xlbest(i,j) = X(i,j);

end

end

end

80

% Update of the global best and its cost

[min_CF, min_CF_index] = min(CFtot);

if min_CF < Gbest

Gbest = min_CF;

for j=1:4

Xgbest(1,j) = X(min_CF_index,j);

end

end

% Update of the particle velocity and position

for i = 1:Npart

for j = 1:4

V(i,j) = 0.2*V(i,j) + rand()*(Xlbest(i,j)-X(i,j))

+ rand()*(Xgbest(j)-X(i,j));

X(i,j) = X(i,j) + V(i,j);

end

end

Lbest’

Gbest

X

V

81

Appendix C

Wind Turbine Aerodynamical Model

C.1 WTPerf input file example

The Cp(λ, β) curves used to build the aerodynamical model of the wind turbine havebeen obtained with WTPerf [25], a software available on the National RenewableEnergy Laboratory (NREL) website. Here is an example of an input file.

—– WT Perf Input File —————————————————–Approximated 60kW turbine.Compatible with WT Perf v3.00f—– Input Configuration —————————————————-True Echo: Echo input parameters to “<rootname>.ech”?False DimenInp: Turbine parameters are dimensional?True Metric: Turbine parameters are Metric (MKS vs FPS)?—– Model Configuration —————————————————-16 NumSect: Number of circumferential sectors.5000 MaxIter: Max number of iterations for induction factor.1.0e-6 ATol: Error tolerance for induction iteration.1.0e-6 SWTol: Error tolerance for skewed-wake iteration.—– Algorithm Configuration ————————————————False TipLoss: Use the Prandtl tip-loss model?False HubLoss: Use the Prandtl hub-loss model?True Swirl: Include Swirl effects?True SkewWake: Apply skewed-wake correction?True AdvBrake: Use the advanced brake-state model?True IndProp: Use PROP-PC instead of PROPX induction algorithm?False AIDrag: Use the drag term in the axial induction calculation?False TIDrag: Use the drag term in the tangential induction calculation?—– Turbine Data ———————————————————–2 NumBlade: Number of blades.12 RotorRad: Rotor radius [length].

83

APPENDIX C. WIND TURBINE AERODYNAMICAL MODEL

0.2 HubRad: Hub radius [length or div by radius].3.5 PreCone: Precone angle, positive downwind [deg].7.0 Tilt: Shaft tilt [deg].0.0 Yaw: Yaw error [deg].3.0 HubHt: Hub height [length or div by radius].10 NumSeg: Number of blade segments (entire rotor radius).RElm Twist Chord AFfile PrntElem0.202 5.000 0.0521 1 False0.282 4.500 0.0504 1 False0.362 4.000 0.0496 1 False0.442 3.600 0.0488 1 False0.521 3.000 0.0479 1 False0.601 2.500 0.0471 1 False0.681 1.800 0.0454 1 False0.761 1.100 0.0446 1 False0.841 0.500 0.0433 1 False0.920 0.000 0.0417 1 False—– Aerodynamic Data ——————————————————-1.225 Rho: Air density [mass/volume].0.00001464 KinVisc: Kinematic air viscosity0.143 ShearExp: Wind shear exponent (1/7 law = 0.143).False UseCm: Are Cm data included in the airfoil tables?1 NumAF: Number of airfoil files.“D:/WTA/UnsteadyAeroExp/s809cln.dat” AFFile: List of NumAF airfoil files.—– I/O Settings ———————————————————–False TabDel: Make output tab-delimited (fixed-width otherwise).True KFact: Output dimensional parameters in K (e.g., kN instead on N)True WriteBED: Write out blade element data to “<rootname>.bed”?False InputTSR: Input speeds as TSRs?“mps” SpdUnits: Wind-speed units (mps, fps, mph).—– Combined-Case Analysis ————————————————-0 NumCases: Number of cases to run. Enter zero for parametric analysis.WS or TSR RotSpd Pitch Remove following block of lines if NumCases is zero.—– Parametric Analysis (Ignored if NumCases > 0 ) ————————-3 ParRow: Row parameter (1-rpm, 2-pitch, 3-tsr/speed).2 ParCol: Column parameter (1-rpm, 2-pitch, 3-tsr/speed).1 ParTab: Table parameter (1-rpm, 2-pitch, 3-tsr/speed).True OutPwr: Request output of rotor power?True OutCp: Request output of Cp?True OutTrq: Request output of shaft torque?True OutFlp: Request output of flap bending moment?True OutThr: Request output of rotor thrust?1, 25, 1 PitSt, PitEnd, PitDel: First, last, delta blade pitch (deg).10, 120, 10 OmgSt, OmgEnd, OmgDel: First, last, delta rotor speed (rpm).

84

C.2. POLYNOMIAL REGRESSION

1, 25, 1 SpdSt, SpdEnd, SpdDel: First, last, delta speeds.

C.2 Polynomial regression

MATLAB Code for the Cp(λ, β) curves.

Cp1 = Cp10; Cp2 = Cp20; Cp3 = Cp30; Cp4 = Cp40; Cp5 = Cp50;

Cp6 = Cp60; Cp7 = Cp70; Cp8 = Cp80; Cp9 = Cp90;

Cp10 = Cp100; Cp11 = Cp110; Cp12 = Cp120;

for j =2:4:18

for i =2:12

% Based on i rpm

RPM = 10*i;

Radius = 9;

RotSpeed = RPM/60*2*pi;

Wspeed = 1:1:25;

lambdai = RotSpeed*Radius./Wspeed;

plot(lambdai,Cpi(:,j));

xlabel(’Speed Ratio’)

ylabel(’Power coefficient’)

hold on

end

end

MATLAB Code for the Cp(λ, β) matrix. WTPerf gives a table of Cp as a functionof the wind speed, the rotor angular speed and the blade angle. This code calculatesthe value of Cp as a function of only λ and β.

% loop on the pitch, to put the pitch as a variable

CpLPitch = [];

for m = 1:25

% Cp as a function of lambda, and fixed pitch

X=[];

for i = 1:12

X=[X,[lambdai;Cpi(:,m+1)’]];

end

% Reordering of the X matrix

for i = 1:length(X)

for j = 1:length(X)

85


if ((X(1,i)>X(1,j))&(i<j))

A=X(:,j);

X(:,j)=X(:,i);

X(:,i)=A;

end

end

end

if m==1

CpLPitch = [CpLPitch,X’];

% To keep the value of tip-speed ratio in the first column

else

CpLPitch = [CpLPitch,X(2,:)’];

end

end

k=1;

while CpLPitch(k,1)<25

k=k+1;

end

Cp2 = CpLPitch(1:k-1,:);

The last code computes a 2-dimensional polynomial regression of the Cp matrix.This is necessary to get a function of Cp(λ, β), in order to be able to calculate Cpin real time during the simulation.

% Define X, Y and and Z=f(X,Y)

Lbd = Cp2(:,1);

Pitch = 1:15;

Z = Cp2(:,2:16);

PP = polyfitweighted2(Pitch’,Lbd’,Z,8,ones(size(Z)));

Y1 = 1:1:25; % Lambda

X1 = 1:1:15; % Pitch Angle

Z1 = polyval2(PP,X1,Y1);

%Test de validité

for i = 1:1:25

plot(Y1,Z1(:,i),’green’);

ylabel(’Power Coeffictient’)

86

C.3. FORTRAN MODEL

xlabel(’Tip-speed ratio’)

hold on

end

The function “polyfitweighted2” finds the least-square fit of 2D data. It returnsthe polynomial coefficients corresponding to this regression. The polynom has thenbeen deduced thanks to the following Maxima Code. PP contains the polynomialcoefficients determined earlier.

>> Vdm1: vandermonde_matrix([B,B,B,B,B,B,B,B,B]);

Vdm2: vandermonde_matrix([L,L,L,L,L,L,L,L,L]);

PP: matrix([0.12016,-0.037022,-0.32388,0.018859,0.083221,0.19029,

-5.38E-05,-0.056799,0.011277,-0.051902,-0.00079141,0.012275,

0.0028153,-0.003754,0.0080341,0.00011393,-0.0011029,-0.0012416,

0.00068157,9.65E-05,-0.00070144,-6.74E-06,4.80E-05,0.00010644,

2.81E-06,-5.91E-05,1.76E-05,3.35E-05,1.85E-07,-9.98E-07,-3.57E-06,

-1.71E-06,1.74E-06,1.44E-06,-1.16E-06,-8.04E-07,-1.95E-09,

7.83E-09,4.25E-08,3.64E-08,-9.04E-09,-2.92E-08,-8.80E-09,2.08E-08,

7.26E-09]);

Vdm3: Vdm1*transpose(Vdm2);

M: matrix([]);

for m: 1 step 1 thru 9 do

for j: 0 step 1 while j < m do

(i: m-j,

M: addcol(M,[Vdm3[j+1,i]]))$

M;

Poly: M.transpose(PP);

C.3 Fortran Model

Finally, the aerodynamical model, calculating the Output torque and power frombased on the wind speed Uwind, the shaft speed ω and the blade angle β, has beenimplemented in the following way.

First, the tip-speed ratio is calculated based on the rotor radius R, the shaft angularvelocity ω and the wind speed Uwind.

! Estimation of the Power and Torque of a stall-regulated Wind turbine

! Vincent Friedel

#LOCAL REAL GR

#LOCAL REAL R

#LOCAL REAL B

87


#LOCAL REAL Cp

#LOCAL REAL ro

#LOCAL REAL A

#LOCAL REAL Rva

#LOCAL REAL Pwind

#LOCAL REAL L

GR = 1

R = 7.8

A = 3.1415*R*R-3.1415*0.3*0.3

ro = 1.225

B = $Beta

L = $w*R/GR/$Vw

Cp = 7.8399999999999998E-10*L*L*L*L*L*L*L*L

Cp = Cp+3.1500000000000001E-9*B*L*L*L*L*L*L*L

Cp = Cp-1.1899999999999999E-7*L*L*L*L*L*L*L

Cp = Cp+1.05E-10*B*B*L*L*L*L*L*L

Cp = Cp-2.8000000000000002E-7*B*L*L*L*L*L*L

Cp = Cp+6.9E-6*L*L*L*L*L*L

Cp = Cp-6.24E-9*B*B*B*L*L*L*L*L

Cp = Cp+1.99E-7*B*B*L*L*L*L*L

Cp = Cp+8.3299999999999999E-6*B*L*L*L*L*L

Cp = Cp-2.0115000000000001E-4*L*L*L*L*L

Cp = Cp-4.9399999999999999E-9*B*B*B*B*L*L*L*L

Cp = Cp+6.1200000000000003E-7*B*B*B*L*L*L*L

Cp = Cp-1.56E-5*B*B*L*L*L*L

Cp = Cp-6.8300000000000007E-5*B*L*L*L*L

Cp = Cp+0.0032038*L*L*L*L

Cp = Cp+1.46E-8*B*B*B*B*B*L*L*L

Cp = Cp-5.5700000000000002E-7*B*B*B*B*L*L*L

Cp = Cp-4.6800000000000001E-6*B*B*B*L*L*L

Cp = Cp+3.1069000000000002E-4*B*B*L*L*L

Cp = Cp-6.8002000000000004E-4*B*L*L*L

Cp = Cp-0.028168*L*L*L

Cp = Cp+2.2399999999999999E-8*B*B*B*B*B*B*L*L

Cp = Cp-1.7600000000000001E-6*B*B*B*B*B*L*L

Cp = Cp+4.71E-5*B*B*B*B*L*L

Cp = Cp-4.1723999999999998E-4*B*B*B*L*L

Cp = Cp-8.1831999999999998E-4*B*B*L*L

Cp = Cp+0.0094042*B*L*L

Cp = Cp+0.12725*L*L

Cp = Cp-4.2700000000000004E-9*B*B*B*B*B*B*B*L

Cp = Cp+2.53E-7*B*B*B*B*B*B*L

Cp = Cp-4.5299999999999998E-6*B*B*B*B*B*L

Cp = Cp+3.3399999999999999E-5*B*B*B*B*L

88

C.3. FORTRAN MODEL

Cp = Cp-8.8020000000000004E-4*B*B*B*L

Cp = Cp+0.01873*B*B*L

Cp = Cp-0.093053*B*L

Cp = Cp-0.14378*L

Cp = Cp-5.4299999999999997E-9*B*B*B*B*B*B*B*B

Cp = Cp+5.9400000000000005E-7*B*B*B*B*B*B*B

Cp = Cp-2.6699999999999998E-5*B*B*B*B*B*B

Cp = Cp+6.3929999999999998E-4*B*B*B*B*B

Cp = Cp-0.0087986*B*B*B*B

Cp = Cp+0.070764*B*B*B

Cp = Cp-0.32241*B*B

Cp = Cp+0.72553*B

Cp = Cp-0.42726

Pwind = (3.1415*R*R-3.1415*0.3*0.3)/2*ro*$Vw*$Vw*$Vw/50000

$Pm = Pwind*Cp

$Tm = $Pm/$w*7.5

$Vw1 = $Vw

$w1 = $w

$Cp1 = Cp

$L1 = L

$Beta1 = B

89

Appendix D

Capacitor Bank controller

Below is shown the FORTRAN code for the capacitor banks controller.

! Capacitor banks connection control

! Vincent Friedel

#LOCAL REAL Pload

#LOCAL REAL Qload

#LOCAL REAL powfac

#LOCAL REAL b

#LOCAL REAL c

Pload = $Pld + $Pw

Qload = $Qld + $Qw

powfac = Pload / sqrt(Pload*Pload + Qload*Qload)

b = $C1i

if (b >= 3) then

if (powfac > 0.97) then

b = b - 1

end if

else if (b == 2) then

if (powfac < 0.7) then

b = b + 1

else if (powfac >= 0.975) then

b = b - 1

end if



b = b + 1

else if (powfac >= 0.98) then

b = b-1

91

APPENDIX D. CAPACITOR BANK CONTROLLER

end if



b = b + 1

end if

end if

if (b >= 3) then

$C1 = 0

$C2 = 0

$C3 = 0


$C1 = 1

$C2 = 0

$C3 = 0

else if (b ==1) then

$C1 = 1

$C2 = 1

$C3 = 0


$C1 = 1

$C2 = 1

$C3 = 1

end if

if (time < 0.5) then

$C1 = 1

$C2 = 1

$C3 = 1

b = 0

c = 0

end if

! Algorithm to switch on a number c of cap banks

c = $Bi

if (c == 0) then

if (Qload > 0.2) then

c = c + 1

end if

else if (c == 1) then


c = c + 1

else if (Qload < 0.01) then

c = c - 1

92

end if



c = c + 1

else if (Qload < 0.05) then

c = c - 1

end if


if (Qload < 0.09) then

c = c - 1

end if

end if

if (c == 0) then

$C1 = 1

$C2 = 1

$C3 = 1


$C1 = 1

$C2 = 1


$C1 = 1

end if

$A = b

$C = c

$B = powfac

93

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