No. E-13-AAA-0000

Design an Effective Controller for the AdjustableSpeed Pumped Storage Power Plants

M.Alizadeh Bidgoli, S.M.T. BathaeeKhaje Nasir Toosi University

Tehran, Iranm.alizadeh.b@ee.kntu.ac.ir

Abstract—In this study, we are trying to design an effectivecontroller for a large variable speed pumped storage power plantconnected to the grid will be provided in the generator mode. Thecontroller is designed so that the both of simplicity androbustness in during of fault and post fault condition satisfied.Main controller of variable speed power plant are consisted ofthree separate controller, speed, power and dc link will be doneby hydro turbine, Machine side and grid side converterrespectively. Both of converter controllers are designed based onstator voltage oriented vector control and PI controller is usedfor hydro turbine on the steady state condition. Grid codecompliance and fault ride through are important in pumpedstorage power plant than other renewable energy such as windturbines because of power level in these plants are several tenfoldof off-shore wind turbines. Thus, a nonlinear GCC (Grid codecompliance) is designed, added to PI controller, to two aims is tomeet. At first, increase the critical time during fault withoutdamage to the equipment, such as generators, switches andcapacitors. Secondly, improve transient and voltage stabilityduring and post fault condition. Finally, full state variableselectrical and hydro turbine will be used in matlab/simulink toverify design controller.

Keywords— Variable speed pumped storege power plant;Nonlinear control; DFIM.

NOMENCLATUREΩ∗ Speed number of turbineQ reduced discharge for a unit turbineN reduced rotation speed for a unit turbineL,A The length and area of the pipe respectivelyQ ,H base flow and base headi , i ,i , i Direct and quadrature axis stator and rotor current, , , Stator and Rotor leakage and resistance,Direct and quadrature axis rotor voltage,Direct and quadrature axis stator voltage

mutual inductance,Active and Reactive power, equivalent internal q- and d-axis voltages, , , Stator and Rotor flux linkage q- and d-axisStator flux magnitude, stator transient reactance and stator reactanceTotal inertia constantTransient open-circuit time constant, Transformer and line reactancebase angular frequency is equal to 2лfs

speed of d–q reference frame is equal to 1

I. INTRODUCTION

Nowadays, using of energy storage system (ESS) in advancedelectrical networks is inevitable in order to balance betweendemand and production in electrical energy. Pumped storagepower plants (PSPP) are the most common and best optionsamong the high power level storage that is used to frequencycontrol of power grid. Moreover, roadmap to 2020 shows asignificant increase in wind energy in advanced powernetworks. So, variable-speed pumped storage units are vital inhelping to stabilize the grid because of high penetration ofwind power in an electricity network. The great disadvantageof PSPPs is that take several years to be built and operated.The efficiency of fixed speed PSPPs could be anotherdisadvantage. According to hill diagram of chart of a hydroturbine (HT), if a variable flow discharge functioning isconsidered (± 30%), the Maximum efficiency of the turbine isreached for a variable rotation speed (±10%). AdjustablePSPPs, installed power electronic converters, can changegenerator speed range around 7-10 percent of nominal value;unlike partial scale wind turbine (WT) speed range is up to30%. In the large PSPPs, medium voltage wound rotorinduction motor-generator, back to back converter and hydropump-turbine are main component of these units, but WTsusually are low voltage, in particular in onshore wind turbineup to 10 MW. Hydro pump-turbines can convert hydraulicenergy into mechanical energy that can be controlled by guidevanes of it, but WTs can convert wind energy into mechanicalenergy that is fully not controllable and is just limited byblades pitch angle. Unlike WTs, variable speed pumpedstorage power plants do not enjoy great popularity amongresearchers. Early ASPSPPs is supplied of cycloconverter orThyristor back to back converters. Recently ASPSPPs using ofmulti level Inverter and IGCT switches have flexibility andagility to cope with the uncertainty of other renewable energysuch as wind energies.The main advantages of the new variable speed plants ingenerating mode are as follows: 1-Improve the efficiency ofthe turbine speed at various points, especially at low loads. 2-Possibility of setting up and getting the car launched when therotor magnets (start up from block out and chargedtransmission line). 3-Control of active and reactive powerinjected or absorbed through the network. 4-Improvednetwork stability with rapid injection active power (flywheel).

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A comparable study using variable speed architecture has beendone with dynamic behaviour of an actual pumped storagesystem that uses synchronous machines in [1], but it have notbeen presented the dc link voltage and other parameters ofpower plants during different faults and grid code compliancein both of it. [2] dealt with a flywheel energy storage based ondoubly fed induction machine (DFIM), variable speed pumpedstorage, comparing with conventional PSPPs. A fictitiousPSPPs with two 380 MW units are fully modeled andsimulated in both generating and pumping modes [3]. Also, anexperimental setup up was accomplished to verify thepresented results. In that paper has been explained to howderive the optimal speed and optimal guide vane in generatingand pumping mode respectively. It has never been consideredthe low voltage ride through capability of PPSPs. The start-upand synchronization procedures of a PSPP in pumping modehave been presented in [4]. Modeling and dynamic simulationsof doubly fed variable speed pumped storage Ohkawachipower station unit with cycloconverter between stator androtor is considered in [5,6]. The main advantage of thesepapers that is the experimental results of Ohkawachi powerstation unit have been verified mathematical formulations.Goldisthal power plant control system has been developed in[7].

This paper consists of four sections can describe asfollows. In the second section, a third-order model of theDFIM for stability studies is shown. Also, grid-filter modelingand a nonlinear second order model of hydroelectriccomponents are introduced in this section. In the third sectiona linear state feedback with a nonlinear auxiliary input andstator voltage oriented vector control is proposed for machineside and grid side converter respectively. The proposedcontroller is applied to the fully model of the PSPP with DFIMwhich is integrated into the power system. The simulationresults and conclusions are presented in fourth and fifthsections, respectively.

II. PROBLEM FORMULATION

In this section dynamic model of a variable speed HTDFIM-based in synchronous reference frame is presented. Inthis model, positive directions for the stator and rotor currentsare assumed into the generator. Also, all parameters andequations are given in per unit. In controller design of thispaper HT is connected a single machine infinite bus through astep up transformer and a transmission lines according to Fig.1.

RSC

InfinitBus

Xl

Xt

+ +

PIPI

PI PI

+ +

PWMPWM

S1 S3S2 S3S2S1

- -

- -

+ +

- -

Rt,Xt

+ +

PIPI

PI PI

+ +

-

-

+ +

- -

ircigc

+

- Vdc

+

DFIM

Grid SideConverter

Machine SideConverter

servomotor

+PI

Wr_pu

Wr_ref_pu-

+ +

Eq.15

++

loadfrequency

control(LFC)

TransientDroop

PermanentDroop

Fig. 1. Designed controller circuit in Matlab/Simulink

A. Hydraulic components Modeling

We consider nonlinear hydraulic components model includinga non-elastic water column with long length penstock andwithout surge tank effect [8]. State equation of hydroelectriccomponents is considered by (1). = 1 1 − = − +

(1)=In the per unit system, the water starting time of a pipe is

defined as T = . Where other parameters have been

described in Nomenclature.

The detail of hydroelectric modeling is out of scope in thispaper, thus we don’t deal with more [9]. Also, We use one-mass model for the drive train as (2).

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= 12 ( − )= −= (2)

B. Genrator modeling

The doubly fed asynchronous generator is modeled by asecond order model can be expressed by (3) where theelectromagnetic transients of the stator are neglected [10].

= ( − )− − ++ ( − ) = − + − ++ (− + )(3)

Where = −In [11] the rotor flux linkage can be obtained in terms ofE ,E described in Nomenclature. Also, the rotor circuit

dynamics is described by an equivalent circuit of DFIM fortransient stability study.

The dynamics of the rotor side converter, reduced thefourth-order model to a second-order model, and mechanicaldrive train of wind turbines, namely swing equation, can bewritten following as:

⎩⎪⎪⎨⎪⎪⎧ = − + + − = − − − + = 12 + +

(4)

Where electrical equations are:= − ′ − ′= ′ − ′= − ′ + ′= − ′ + ′

C. Grid-side Filter modeling

The grid-side filter components, as shown in Fig. 1, are aninductance Lf and resistance Rf of converter-side transformer.Its and dc link are described in d,q reference frame byfollowing equations [12].

= − + − + (5)

= − − − + = − −Where: = , =

III. CONTROLLER DESIGN

A. Maximum Efficiency point tracking (MEPT)

As can be seen in Fig. 2, for any reduced flow there is onemaximum value of efficiency corresponded to one reducedspeed of rotor, N11. In normal conditions, these values ofproduction should be achieved. Consequently, in order toproduce the maximum efficiency in generating mode,corresponding rotational speed should be considered [3]. Theproduced rotational speed is introduced as the reference valueto the speed controller in HT.The speed set point of speed control in HT is calculated by aspeed optimizer in order to maximize the turbine efficiencyaccording to efficiency hill diagram of turbine provided bymanufacture of HT. This speed optimizer is a lookup tabledefined as a surface representing the optimal speed as afunction of the power and the head.

Fig. 2. Efficency hill diagram of HT [13].

B. Hydro Turbine

The control input of hydro turbine is the voltage of servomotor adjusting the guide vanes of turbine and input water thatis coming to turbine.

Fig. 3. Block diagram of proposed hydro turbine control

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As can be seen in Fig. 3 the servomotor voltage v can bedefined as followsv = k ω _ − ω + k ∫ ω _ − ω (6)C. Grid Side

The main aim of grid side converter is to maintain voltageof dc-link constant in nominal value regardless rotor powerdirection. Methods used to design the grid side controller of adoubly fed induction generators usually are based ondecoupled d,q vector control. Its consist of two decoupledcontrollers, which each controller is comprised of two loopinner or fast loop is current regulator and outer or slow loop isdc voltage and reactive power regulator. In this study a statorvoltage oriented vector control has applied to satisfy abovementioned objectives. With aligning the d-axis of thereference frame along the stator voltage, we can write Vqs=0and Vds=Vs. As (5), the voltage of dc-link can be controlled byidg. So, with adding the term of voltage compensation as Fig.1, Vdg and Vqg can be defined as follows:= − _ − − _ −+ += − _ − − _ −− +

(7)

Where

_ = − _ + − __ = − _ + − _

D. Machine Side

Controller design of machine side converter is consisted oftwo parts. In the first part the stator voltage oriented vectorcontrol is apply to it. In the second part, a nonlinear auxiliaryinput is added to direct axis input of rotor side converter toimprove the transient stability of machine under a largedisturbance by a linear state feedback controller using statevariables such as, derivation of speed of rotor ω, speed ofrotor ω and stator output voltage V . The first part of inputs, are defined as follows.= − + −− ( − ) − + +

= _ − + _ −− ( − ) − − +(8)

Where

_ = _ − + _ −_ = _ − + _ −

Also _ = ∆ + ( ) + that is derived from load

frequency control.

As can be seen in Fig. 4 grid code requirement for PSPP, avariable speed pumped storage must be connected to networkduring a sever fault, the voltage of network drops to 0, for 150msec.

Fig. 4. Grid code requirement of a PSPP during fault [14]

Thus, In order to improve the transient stability of DFIMin the mentioned condition the following error variables aredefined:

=

− − _− _At first, state equations of machine is divided two linear

and nonlinear parts. Therefore, state equations of system,described in the section one, are rearranged asx = Ax + Bu + f(x).

Where =

A =⎣⎢⎢⎢⎢⎢⎡ 0 1 0 02 0 2 0− 0 − 0− 0 0 − ⎦⎥⎥

⎥⎥⎥⎤

(9)

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=⎣⎢⎢⎢⎢⎢⎡ 0 0 02 − 2 −− 00 − 0 ⎦⎥⎥

⎥⎥⎥⎤

( ) =⎣⎢⎢⎢⎢⎡

0( ) + 2( ) − ( ) ⎦⎥⎥⎥⎥⎤

A and B are jacobian matrixes. Also ( ) and ( ) aredescribed in Appendix A.Here, the feedback gain matrix K is obtained by applying theLinear-Quadratic Regulator (LQR) design technique toachieve desire close loop dynamic of system (4). Also, for acontinuous-time state-space model, the state-feedback law u =-K.x minimizes the cost function = ∫ ( + )where = and matrix M is found by solving thealgebraic Riccati equation. For this study system in this paper,we select the H=Diag[0.1,1,10,5] and R=Diag[1,1,0.1]matrices. So, K matrix is obtained (10)

= 2.2134 −0.0234 2.3676 −1.47690.5031 0.0367 −2.0896 −1.6768−7.4303 −6.3799 −0.4127 −0.0008 (10)The stability of closed loop system is guaranteed by selectingof the matrix K from LQR design. Thus, there exist definitepositive matrixes Q, P satisfying Lyapunov equation in stablelinear system = ′ .

Therefore, V(x) = X PX where P>0 can be a Lyapunovcandidate function for the closed-loop system. The derivativeof V is given by: ( ) = 12 + 12 = − , ′ = − (11)

( ) = ′ + ′ + ( ) +( )<0(12)

According to the Lyapunov theory, the system will remainstable under the following conditions.

′ + ′ = − , > 0( ) + ( ) = 0 (13)

If we select Q=[1,1,1,5], P matrix will obtain as (13)

= 0.6357 −0.5 0.0132 −0.0032−0.5 0.7448 −0.0057 0.00440.0132 −0.0057 0.0017 −0.0015−0.0032 0.0044 −0.0015 0.0027 (14)If V in (9) is selected as (15).== ( ) ∑ P + ( ) ∑ P + ( ) ∑ P(∑ P ) − 2 (∑ P ) (15)

The second term of (13) reaches zero value and system will bestable in all of the conditions.

IV. SIMULATION RESULTS

In order to verify the proposed controller, the model shown inFig. 1 has been developed. For this reason, simulation results,done by complete simulation model for the whole system, isused. Therefore, this model is simulated byMATLAB/Simulink. Both of converter controllers aredesigned based on stator voltage oriented vector control and PIcontroller is used for hydro turbine on the steady statecondition. Also, a nonlinear auxiliary input added to d-axisrotor voltage is designed to grid code compliance of PSPP.In order to transient stability study of the system, a solid three-phase short-circuit fault is imposed at the secondary side ofthe step-up transformer at t=65 sec which is programmed to becleared after 150 msec, as shown in Fig. 5.

Fig. 5. simulated circuit in Matlab/Simulink

Fig. 6 and 7 show the stator three phase current during severfault, occurred in terminal of machine, which is cause statorvoltage decrease to zero for 150 msec for conventional vectorcontrol and proposed controller in this paper respectively. Fig.6 shows transient response of current is similar to Fig. 7 but inpost fault the nonlinear auxiliary controller can quickly damposcillations of the stator current with lower settling time 200msec approximately.

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65 65.2 65.4 65.6 65.8

-2

-1

0

1

2

Time (sec)Fig. 6. Three phase statr current without using the auxiliary input

Thre

eph

ase

stat

orC

urre

nt(p

.u)

Fig. 7. Three phase stator current using the auxiliary input

Fig. 8 shows dc link voltage, controlled by proposedcontroller in rotor side converter, can maintain dc link voltagelower than the admissible level without any additionalcomponents such as crowbar. While, dc link over voltage withconventional controller is 2 p.u approximately. Moreover,active power injected to network during fault and 70% ofnominal power turbine increases up to 1.2 p.u when theauxiliary input is not added. It can be seen from Fig. 9 thatboth of active and reactive power of turbine have nearly 10%higher than steady state condition value. It can help to improvethe transient response of dc link in post fault.

As can be seen in Fig. 9 during the fault, the minimumactive power of the PSPP with nonlinear auxiliary input is0MW, while the minimum active power using theconventional PI controller is -1 p.u where the PSPP has beenabsorbed the active power. This reveals that the PSPP usingthe conventional PI controller may lead to a worse transientstability problem of the power system.

64 64.5 65 65.5 66 66.5 670

1000

2000

3000

4000

5000

6000

7000

8000

9000

Time (sec)

DC

link

Vol

tage

(v)

with A.Iwithout A.I

Fig. 8. DC link voltage

Act

ive

Pow

erof

Pla

nt(p

.u)

Fig. 9. Output active power of generator

Fig. 10. Output reactive power of generator

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Fig. 11. Rotor speed

V. CONCLUSION

In this paper, based on all components model of PSPP,hydroelectric, DFIM and drive train, a new rotor sideconverter controller was designed. Also, conventional vectorcontrol applied to grid side converter to maintain dc linkvoltage and exchanged reactive power between converter andnetwork. The stator voltage oriented vector control is apply torotor side controller and a nonlinear auxiliary input is added todirect axis input of it to improve the transient stability ofmachine under a large disturbance by a linear state feedbackcontroller using state variables such as, derivation of speed ofrotor ω, speed of rotor ω, output active power of PSPP P andstator output voltage V . Simulation results were shown thatnonlinear auxiliary controller improve rotor speed response,Also dc link voltage where was controlled by vector controlcan maintain dc link voltage under the admissible levelwithout any additional components such as crowbar.

Appendix A( ), ( ) and ( ) are defined as follow( ) = 12 ′ + − 1 + ( − )+ − (− + ) + − ++ 32 1 − + 22+ 2 (3)2 − + 00( ) = − ′ + + (− + )+ (− + ) − − +( ) = − 1 − + + − − 1+ ( − ) − ( − ) .Appendix B:The System Parameters under Study in Fig. 1.

1-The generator parameter values are given in P.U in below:= 60 , = 380 , = 18 .= 0.26, = 0.272, = 0.00174, = 0.002,= 4.2, = 7.7, = 1, = 2, = 0.3 , =4541 , s = 7%, = 0.589, 2P = 16,

Converter Trans impedance: Rt + jXt = 0.005 + j0.15pu.2- The hydro turbine parameter values are given in below:D = 4.41 m, N = 450 rpm, Q = 54.38 m /s, T =7.5503 × 10 , H = 709.2 m

REFERENCES

[1] A. C. Padoan, J. B. Kawkabani, A. Schwery, C. Ramirez, C. Nicolet, J.J. Simond and F. Avellan, Dynamical Behavior Comparison betweenVariable Speed and Synchronous Machines with PSS, IEEE Trans.Power. Syst. Vol. 25, No. 3, pp. 1555-1565, 2010.

[2] A. S. Abdel-Khalik, A. A. Elserougi, A. M. Massoud and Sh. Ahmed,Fault Current Contribution of Medium Voltage Inverter and Doubly-FedInduction-Machine-Based Flywheel Energy Storage System, IEEETrans. Sustainable. Energy, Vol. 4, No. 1, pp. 58-67, 2013.

[3] Y. Pannatier, B. Kawkabani, C. Nicolet, J. J. Simond, A. Schwery and P.Allenbach “Investigation of Control Strategies for Variable-SpeedPump-Turbine Units by Using a Simplified Model of the Converters”IEEE Transactions on Industrial Electronics, Vol. 57, No. 9,pp. 3039-3049, Sep 2010.

[4] Y. Pannatier, B. Kawkabani, C. Nicolet, A. Schwery, J.J. Simond “Start-up and synchronization of a variable speed pump-turbine unit inpumping mode” International Conference on Electrical Machines(ICEM), 2010.

[5] J. K. Lung, Y. Lu, W. L. Hung, and W. S. Kao “Modeling and DynamicSimulations of Doubly Fed Adjustable-Speed Pumped Storage Units”IEEE Transaction on Energy Conversion, Vol. 22, No. 2, pp. 250-258,June 2007.

[6] T. Kuwabara, A. Shibuya, H. Furuta, E. Kita, K. Mitsuhashi “Designand Dynamic Responce Characteristics of 400 MW Adjustable SeedPumped Storage Unit For Ohkawachi power station” IEEE Transactionson Energy Conversion, Vol. 11, No. 2,pp. 376-384, June 1996.

[7] K. Grotenburg, F. Koch, I. Erlich and U. Bachmann “Modeling andDynamic Simulation OF Variable Speed Pump Storage UnitsIncorporated into the German Electric Power System” 15th TriennialWorld Congress Conference (IFAC), 2002.

[8] P. Kundur, Power System Stability and Control, McGraw-Hill.NewYork, 1994.

[9] H. Fang, L. Chen, N. Dlakavu, and Z. Shen “Basic Modeling andSimulation Tool for Analysis of Hydraulic Transients in HydroelectricPower Plants” IEEE Transactions on Energy Conversion, Vol. 23, No. 3,Sep 2008.

[10] M. Rahimi and M. Parniani “Transient Performance Improvement ofWind Turbines With Doubly Fed Induction Generators Using NonlinearControl Strategy” IEEE Transactions on Energy Conversion, Vol. 25,No. 2, Jun 2010.

[11] F. Wu, X. P. Zhang, P. Ju, and M. J. H. Sterling “DecentralizedNonlinear Control of Wind Turbine With Doubly Fed InductionGenerator” IEEE Transactions on Power Systems, Vol. 23, No. 2, May2008.

[12] M. Rahimi and M. Parniani “Coordinated Control Approaches for Low-Voltage Ride-Through Enhancement in Wind Turbines With DoublyFed Induction Generators” IEEE Transactions on Energy Conversion,Vol. 25, No. 3, Sep 2010.

[13] F. Bonnet, L. Lowinsky, M. P. David, P. É. Vidal and I. E. Laplace“Doubly Fed Induction Machine Speed Drive for Hydro-Electric PowerStation” European Conference on Power Electronics and Applications,2007.

[14] A. Bocquel and J. Janming “Analysis of a 300 MW Variable SpeedDrive for Pump-Storage Plant Applications” European Conference onPower Electronics and Applications, 2005.