Dynamics of diesel and wind turbine generators on an isolated powersystem

D. Dasa,*, S.K. Adityaa, D.P. KotharibaElectrical Eng. Dept., Indian Institute of Technology, Kharagpur721302, India

bCentre for Energy Studies, Indian Institute of Technology, New Delhi110016, India

Abstract

The paper presents dynamic system analysis of an isolated electric power system consisting of a diesel generator and a wind turbinegenerator. The 150 kW wind turbine generator is operated in parallel with a diesel generator to serve an average load of 350 kW. Timedomain solutions are used to study the performance of the power system. Optimum values of gain settings of the Proportional-Integralcontroller (P-I) are obtained by using the integral squared error (ISE) technique. A simple variable structure control (VSC) logic is alsoproposed for improvement of the dynamic performance of the system. q 1998 Elsevier Science Ltd. All rights reserved.

Keywords: Wind and diesel power system; Stability; Optimization

1. Introduction

A constantly increasing power demand has to be metthrough an adequately planned electrical power generationprogramme. Electrical energy is environmentally the mostbenign form of energy, with production routed throughconventional fossil fuel burning or through nuclear energyand wherever possible through hydro resources. All of thesein addition to other disadvantages give rise to environmentalissues of a varied nature. Therefore it is necessary toconsider the problems of electrical energy generation andenvironment jointly so that the increasing need of electricityfor industrialization will be met with minimal environmen-tal degradation. One of the solutions is to utilize windenergy in favourable sites which are remote from centralisedenergy supply systems. Since wind power varies randomlythere must be a stand-by power source to meet load demand.The diesel and wind system is one of the hybrid systemsutilizing more than one energy source. A wind and dieselsystem is very reliable because the diesel acts as a cushion totake care of variation in wind speed, and would alwaysprovide power equal to load minus the wind power.

Scott et al. [1] have investigated the dynamic interactionto quantify any increased disturbance to the Block IslandPower Company (BIPCO), on Block Island (which operatesan isolated electric power system consisting of diesel andwind turbine generators resulting from connection of theMOD-OA wind turbine generator). In this study, the

dynamic simulation of the wind turbine generator operatedin parallel with a diesel generator on an isolated powersystem is carried out. Optimum values for the gain settingsof the Proportional-Integral (P-I) controller have beenobtained using the Integral Squared Error (ISE) technique.A simple Variable Structure Control (VSC) logic is alsoproposed for the improvement of system dynamic perfor-mance.

2. Description of diesel and wind systems

The model considered in this study consists of the follow-ing sub-systems [1,3,4]:

Wind dynamics model;Diesel dynamics model;Blade pitch control of wind turbine;Generator dynamics model.

The wind model is one feature that is unique to the windturbine generator and is not required for the diesel generatorsystem in the stability programme. Anderson et al. [2] havepresented one model that can properly simulate the effect ofwind behaviour, including gusting, rapid (ramp) changesand background noise. The basic conditions for start upand synchronization are that the wind speed is to be withinan acceptable range and there must be a phase matchbetween the generator and system voltages [1].

The diesel dynamics is associated with diesel power andthe nature of the dynamic behaviour in this model is

Electrical Power and Energy Systems 21 (1999) 183189

JEPE 278

0142-0615/99/$ - see front matter q 1998 Elsevier Science Ltd. All rights reserved.PII: S0142-0615(98)00033-7

* Corresponding author; e-mail: ddas@ee.iitkgp.ernet.in.

dominated by the diesel speed governor controller. A totalpower set point is selected in which it can manually adjustedfrom zero to maximum value. The purpose of the adjustablepower set point is to allow system utility personnel to lowerthe power setting below the maximum settings of the windgenerator to prevent controlling diesel from dropping to lessthan 50% of the rated power. Operation of a diesel enginefor extended periods at two power levels could result inpossible engine damage.

Pitch control has the potential for producing the highestlevel of interaction because of the presence of both dieseland wind turbine control loops. The pitch control systemconsists of a power measurement transducer, a manualpower set point control, a proportional plus integral feed-back function, and a hydraulic actuator which varies thepitch of the blades. Turbine blade pitch control has a signif-icant impact on the dynamic behaviour of the system. Thistype of control only exists in horizontal axis machines.

Variable pitch turbines operate efficiently over a widerrange of wind speeds than fixed pitch machines. However,cost and complexity are higher.

The generator dynamics model consists of a synchronousgenerator driven by a diesel engine through a flywheel andconnected in parallel with an induction generator driven bya wind turbine. The diesel generator will act as a dummygrid for the wind generator which is connected in parallel.Variations of electrical power due to changes in wind speedshould be as small as possible; this is obtained by using theinduction generator as a wind turbine drive train. Unlikesynchronous generators, induction generators are highcompliance couplings between the machine and the electri-cal system. This is true for induction generators with slip ofat least 12% at rated power. The controlled variables areturbine speed and shaft torque. Control acts on the turbineblade pitch angle (pitch control). Since the torque speedcharacteristic of the induction generator is nearly linear in

D. Das et al. / Electrical Power and Energy Systems 21 (1999) 183189184

Fig. 1. Conceptual model of diesel and wind turbine generator system.

Fig. 2. Functional block diagram for wind and diesel systems with pitch control.

the operating region, torque changes are reflected as speedchanges. Therefore, it is possible to provide a single speedcontroller to control speed as well as torque.

3. Mathematical model of the system

A linear model is formulated for the wind and dieselturbine generator system for the purpose of identifyingand quantifying the underdamped oscillation. This objectiveis met by retaining the pertinent controller dynamics forboth the diesel unit governors and wind turbine generatorpitch controller/actuator. The conceptual model that resultsis shown in Fig. 1. The fluid coupling shown in Fig. 1transfers speed difference into power. The actual functionis nonlinear (Square law) but for the model it is linearized,resulting in a constant for the particular power set pointselected. Fig. 2 shows the functional block diagram that isobtained.

The transfer function of the hydraulic pitch actuator isgiven as:

DHSU1S

Kp21 1 STp1TkS2 1 STp2 1 11 1 S

1

But Tk is very small compared to Tp2 and hence Tk isneglected from the mathematical model. Therefore Eq. (1)can be written as

DHSU1S

Kp21 1 STp11 1 STp21 1 S 2

The transfer function Eq. (2) of the hydraulic pitch actua-tor is split into two blocks (Fig. 2) and DH1 is a dummyvariable.

The transfer function of the diesel governor (Fig. 2) is

given as:

DPfSDvrefS2 Dv2S

Kd1 1 SS1 1 ST1 3

As vref is the reference speed setting (a constant) for thediesel generator, therefore Dvref 0.0. Substituting Dvref 0.0 in Eq. (3), we getDPfS

2 Dv2S Kd1 1 SS1 1 ST1 4

The transfer function of the diesel governor Eq. (4) is splitinto two blocks and DPf1 is a dummy variable.

Appearing in a block (Fig. 2) labelled data fit pitchresponse is a simple lag which is required to match thephase/gain characteristic of the model. Other state variablesare marked in Fig. 2. The system is a linear continuous-timedynamic system and can be represented by a set of lineardifferential equations of the form:

_X AX 1 BU 1 GP 5where X, U and P are state, control and disturbance vectorsand A, B and G are constant matrices associated with themrespectively. For this system (Fig. 2), X, U and P aregiven as

X 0 DH1 DH DD Dv1 Dv2 DPf 1 DPf 6

U U1 7

P 0 DPv DPload 8where, 0 stands for transpose. A, B and G are given inAppendix 1. Data for this system are given inAppendix 2.

D. Das et al. / Electrical Power and Energy Systems 21 (1999) 183189 185

Fig. 3. Kp vs J for several values of KI.

4. Optimization of the Proportional-Integral (P-I)controller gain settings using the ISE technique

Many utilities prefer to use the P-I controller forbetter system dynamic response and in the presentstudy, the P-I controller is used. The P-I control law

is given as

U1 KpDPmax 2 DPvtg1 KIZt

0DPmax 2 DPvtg dt 9

For the study system, Pmax 150 kW is constant, there-fore DPmax 0.0. Substituting DPmax 0.0 in Eq. (9)we obtain

U1 2KpDPvtg2 KIZt

0DPvtg dt 10

An attempt is made to obtain the optimum values of P-Igain settings (Kp and KI) using the integral squared error(ISE) technique for a 1% step increase of load.

A performance index

J Zt

0DPvtg2 dt 11

is minimized to obtain the optimum values for P-I gainsettings. Note that DPvtg is also a function of Dv1 and Dv2(Fig. 2).

Fig. 3 shows the plot of J vs Kp for several values ofKI, where Kp and KI are proportional and integral gains

D. Das et al. / Electrical Power and Energy Systems 21 (1999) 183189186

Fig. 4. Plot of Kv vs J.

Fig. 5. Frequency responses with conventional and variable structure controllers.

respectively. From Fig. 3, it is seen that Kp 10:0 and KI 4:0 are more or less optimum values of P-I gain settings.

5. Variable structure control (VSC) logic

In this study, an attempt is also made to improve thesystem dynamic performance by using a simple variablestructure control (VSC) logic which is based on proportional(P) and proportional-integral (P-I) control concept. If thecontrol law applied at the first stage of the transient (aslong as error is sufficiently large) is chosen as

U1 2KvDPvtg if uDPvtgul1 12

where 1 . 0 is some constant, but when the error is smallthe control law is

U1 2KpDPvtg 2 KIZt

0DPvtg dt if uDPvtgu # 1 13

where uDPvtgul1 for t $ t1, then if the parameters Kv, Kp, KIand 1 are suitably selected, one can ensure a high-qualitytransient response, distinguished by good dynamic andsteady-state characteristics. Indeed taking the magnitudeof Kv as being sufficiently large, one can make sure thatthe speed of the system is high; thus, the error DPvtg, in

response to a step input rapidly enters the regionuDPvtgu # 1. At the instant t1, when the error has fallen to1, the structure of the controller is changed by switching to aP-I control, which eliminates the steady error remaining inthe system.

An attempt is made to obtain optimum values of Kv byusing the ISE technique. The same performance index J Eq.(11) is chosen to obtain the optimum values of Kv. Through-out this optimization process, values of Kp and KI are fixed at10.0 and 4.0, respectively. Fig. 4 shows the plot of J vs Kvfor 1 0.0004. It is worth mentioning here that severalvalues of 1 are tried out. However, 1 0.0004 gives thelowest value of J. From Fig. 4, it is seen that the optimumvalue of Kv is 2 10.0. However, any positive value of Kvdoes not minimize the performance index J Eq. (11) andperhaps this is due to excessive control action.

6. Dynamic responses

Figs. 5 and 6 show the dynamic responses for a 1% stepincrease of load with the P-I controller and variable struc-ture controller (VSC). It is seen that the activation of pitchcontrol with the conventional P-I controller results in anunderdamped response. Although this is a stable response,the low damping allows the oscillation to continue for a

D. Das et al. / Electrical Power and Energy Systems 21 (1999) 183189 187

Fig. 6. Power responses with conventional and variable structure controllers.

longer time before damping out. It is seen that with the useof VSC, damping is greatly improved. Peak wind generatorfrequency deviation (Fig. 5(a)) and peak diesel power devia-tion (Fig. 6(a)) are much less compared to the conventionalP-I controller. From Fig. 6(b), it is also seen that with the useof VSC, the wind power deviation (DPvtg) is slow andmonotonic and hence is preferred. From Figs 5 and 6, it isalso seen that with the use of VSC, settling time is much lesscompared to that of the conventional P-I controller. There-fore, it can be concluded that the variable structure control-ler improves the system damping compared to the fixedstructure P-I controller.

7. Conclusions

A linear mathematical model of the wind and diesel turbinegenerators operating on an isolated electric power system hasbeen formulated for the purpose of identifying and quantifyingthe underdamped oscillation. The simulation incorporateswind turbine pitch control and diesel governor. Optimumvalues for the gain parameters of the conventional propor-tional-integral (P-I) controller and variable structure controller(VSC) have been obtained using the integral squared error(ISE) technique. Analysis reveals that the variable structurecontroller gives better dynamic performance in terms of peak

deviations and settling time compared to that of the conven-tional fixed structure P-I controller.

It can also be concluded that wind turbine generation,even when providing a large proportion of the powerrequired by an isolated utility can be a practical optionresulting in system disturbances no greater than thosefound in a conventional diesel system.

Appendix 1

A, B and G matrices of the system (Fig. 2) are givenbelow:

Note that B is a 7 1 matrix because there is only onecontrol input.

Appendix 2

Area capacity; PR 350 kW;Hv inertia constant on machine base 3:5 s for wind system;Hd inertia constant on machine base 8:5 s for diesel system;

D. Das et al. / Electrical Power and Energy Systems 21 (1999) 183189188

A

21Tp2

0 0 0 0 0 0

Kp2 2Kp2Tp1

Tp2

!21 0 0 0 0 0

0 Kp3 21 0 0 0 0

0 0Kpc2Hv

2Kfc2Hv

Kfc2Hv

0 0

0 0 0 Kfc2Hd

2Kfc 0 1

0 0 0 0 2Kd 0 0

0 0 0 0 2KdT1

1T1

21T1

26666666666666666666666666664

37777777777777777777777777775

B

1Tp2

Kp2Tp1Tp20

0

0

0

0

26666666666666666666664

37777777777777777777775

; G

0 0

0 0

0 01

2Hv0

0 212Hd

0 0

0 0

266666666666666666664

377777777777777777775

Kfc 16:2 pu kW=Hz Kd 16:5 pu kW=Hz;

Kp2 1:25 Tp2 0:041 s;

Kp3 1:40 Tp1 0:60 s;

DPload 0:01 pu kW Kpc 0:80;

T1 0:025 s Tk 0:0009 s:

References

[1] Scott GW, Wilrekar VF, Shaltens RK. Wind turbine generator interac-tion with diesel generators on an isolated power system. IEEE TransPower Apparatus Syst 1984;PAS 103(5):933937.

[2] Anderson PM, Bose A. Stability simulation of wind turbine systems.IEEE Trans Power Apparatus Syst 1983;PAS 102(12):37913795.

[3] Hinrichsen EN. Controls for variable pitch wind turbine generators.IEEE Trans Power Apparatus Syst 1984;PAS 103(4):886892.

[4] Hinrichsen EN, Nolan PJ. Dynamics and stability of wind turbinegenerators. IEEE Trans Power Apparatus Syst 1982;PAS101(8):26402648.

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