ROBUST LOAD FREQUENCY CONTROLLER DESIGN FOR HYDRO POWER SYSTEMS

A. Khodabakhshian (Ph.D.) N. Golbon (M.Sc.)

Abstract: This paper presents a new approach for power system load frequency control of a hydro turbine power system by means of a PID controller. Using a maximum peak resonance specification, the PID controller parameters are adjusted such that the open-loop frequency response curve follows the corresponding contour. Comparative results of this new load frequency controller and a conventional PI one show the improvement in system damping considerably.

Index Terms Power systems, load frequency control, PID controller

1. INTRODUCTIONElectric power systems consist of a number of control areas, which generate power to mach the power demand. However, poor balancing between generated power and demand can cause the system frequency to deviate away from the nominal value, and creates inadvertent power exchanges between control areas [1-2]. To avoid such a situation, load frequency controllers are designed and implemented to automatically balance generated power and demand in each control area.

The PI decentralized controller that achieves frequency regulation has been widely used in this process control because of the simplicity and the feasibility of implementation [1]. The main drawback of this result is that the selection of its gain is mainly based on a trial and error method to be able to obtain the best dynamic performance although it guarantees to have a zero steady-state error. In fact, there is no effective analytical method to determine optimal parameter quickly for real time application [3]. It is also well known that the speed governor of the hydro turbine needs to be equipped by a transient droop compensator [1]. This ensures that the system will be stable when the load changes and, as a result the frequency alters. However, this makes the system response to be comparatively sluggish [1].

With the increase in size and complexity, modern power systems have increasing risks that the system oscillation

would propagate into wide area resulting in a wide-area blackout. This has recently motivated lots of efforts devoted to developing system stabilization techniques to effectively damp oscillations. Lansberry, et.al. [3] have investigated a genetic algorithm as one possible means of adaptively optimizing the gain of a proportional-plus-integral hydro-generator governor. It is shown that the genetic algorithm can effectively follow changes in the water starting time of the hydro turbine (Tw) as the load changes, producing optimal control parameter in an adaptive environment. In [4], based on principle of anthropomorphic intelligent a novel intelligent PID controller is created. Simulation studies and field test indicate that the anthropomorphic intelligent PID control can somewhat improve the dynamic performance and stability of the hydro-turbine governing system when compared with a conventional PID controller. In control theory Poulin [5-6] introduce a new method to obtain the parameters of the PI (or PID) controller based on an optimization technique using the constant-M circles in Nichols chart. The main idea is to keep the maximum overshoot of the system response in a predetermined value following a step change in the reference input. The predetermined bandwidth and phase margin guarantee the stability of the system. This technique has been modified and applied for the first time in power systems by Khodabakhshian [7] to design a new PID load-frequency controller for a single-machine infinite bus with steam turbine model which is a minimum phase system. However, hydro power systems are inherently non-minimum phase and this technique needs to be developed and tested for such systems. As will be shown the performance of this new LFC is better than the conventional PI controller with also having the advantage of not using the transient droop compensator. It is also shown that this fixed parameter controller can easily obtain desirable performances even when the load changes.

2. SYSTEM MODELIn general, for satisfactory operation of power units running in parallel it is most desirable to have a frequency fixed on its nominal value even when the load varies. The control of system frequency and loads depends upon the governors of the prime movers and,

Amin Khodabakhshian is with Isfahan University, Faculty of Engineering, Isfahan, Iran (telephone: +98-311-793-2771, e-mail: aminkh@eng.ui.ac.ir). Navid Golbon is with NIGC, (telephone:+98-311-233-1657 e-mail: Golbon@behinehniru.com)

Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

WB5.4

0-7803-9354-6/05/$20.00 ©2005 IEEE 1510

therefore, its operation has to be included in LFC study as well as hydro turbines and generators. Since all the movements are small the frequency-power relation for turbine- governor control can be studied by a linearized block diagram [1]. This is shown in Figure 1 for a single-machine infinite-bus (SMIB) [1] where the blocks are

Hydro turbine =sT

sT

w

W

5.011

Load and machine = DHs2

1

Droop characteristics = RP1

RP is the regulation constant.

Figure 1: Block diagrams of turbine, governor, load and machine

2.1 TRANSIENT DROOP COMPENSATOR Hydro turbine transfer function is inherently non-minimum phase because of water inertia. Therefore, any step change on valve position creates negative reflex on output power of turbine. Using the nominal values for the speed governor, turbine and machine parameters implies that in order to have a stable system the permanent regulation constant of the speed governor should be 20% [1]. However, this coefficient is usually about 5% and this makes the gain margin and phase margin both to be negative and, therefore, the system response following a small change in load will be unstable [1]. A compensator is then suggested to be included in the speed governor as shown in Figure 2 to solve this problem [1]. The compensator transfer function is:

sTRR

sTsGR

PT

RC

)(1

1)(

where TR and RT are obtained using the equations given in [1].

Figure 2: Hydro power system with the transient droop compensator

3. PERFORMANCE REQUIRMENTSThe most important performance specifications that the load frequency controller has to satisfy include: 1- Stability of the power system (in the sense of stable system frequency regulation), 2- Asymptotic regulation of frequency and tie-line power (i.e., and Ptie go to zero as time goes to infinity), 3- Transient response shaping (e.g., non-oscillatory response to step changes in load).

4. CONVENTIONAL PI CONTROLLERIn order to always have the system frequency on its nominal value a supplementary control action such as a PI controller in the form of

sK I is usually required. This

is shown in Figure 3. As can be seen this supplementary controller increases the type of the system and this ensures that the steady-state error for a step change in load will be always zero [1]. The controller gain

IK has to be chosen in such a way that a good shape of the transient response be obtained. The Routh-Hurwitz criteria can be a very good initial effort to choose the range of the controller gain so that the system will be stable. Then, by a trial and error method the best value of IK is selected in order to have the best transient performance. However, this method cannot guarantee to have the most desirable response.

Figure 3: Block diagrams of Hydro turbine, governor, load and machine with PI controller

A new PID controller is then presented in the next section to ensure that all performance requirements given in Section 2.1 are satisfied.

5. DESIGNING A PID CONTROLLER USING MAXIMUM PEAK RESONANCE

SPECIFICATION (MPRS) Proportional integral (PI) and proportional integral derivative (PID) controllers are widely utilized in industries. The simplicity and ability of these controllers are the most important advantage and many methods are given in the literature to obtain their parameters. Poulin [5-6] has presented a unified approach for the design of PID controllers, based on the constant-M circles of the Nichols chart. The controller parameters are tuned such that the open-loop frequency curve

TurbineHydrorCompensatoGovernor &

sticsCharacteriDroop

MachineLoad &

ControllerPI

LP

TurbineHydrorCompensatoGovernor&

sticsCharacteriDroop

MachineLoad&

LP

refP

TurbineHydro

GovernoSpeed

refPs1

openGVX

open

GVX

closeGVX close

GVX

sticsCharacteriDroop

MachineLoad&

LP

gT1

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follows the corresponding constant-M circle using a predetermined maximum peak resonance. This approach gives the possibility of having the desirable maximum overshoot, the phase and gain margins and the bandwidth of the closed-loop system simultaneously. An optimization procedure is first introduced to show the basic idea. Then, some simplifications are given to ease the use of this method. This approach is applicable for stable, unstable and integrating processes. The main design is first given for a PI controller and then easily extended to a PID one. For example, assume the block diagram given in Figure 4.

Figure 4: Block diagram of a typical control system

The process transfer function is

)1)(1()1(

)(21

0sTsT

esTKsG

sP

P (1)

where is the time delay and is considered to be zero for the design of LFC. The PI controller is then given by

sTsTK

sGi

icc

)1()( (2)

The iT and cK parameters are obtained using the formula given in Appendix. Note that since in LFC design the open-loop transfer function is originally a stable process, the two other integrating and unstable processes discussed by Poulin are not taking into account in this paper.

6. DESIGNINIG A NEW LFC USING MPRS METHOD

Before the design procedure for a new LFC is given the following considerations must be considered. 1- In Figure 4 the control system is with a negative unity feedback and the PI controller is placed in the forward path. However, the system shown in Figure 1 indicates that the governor speed droop 1/ RP is in the feedback path. Although by some simple modifications this may be easily changed to a unity feedback, this will make the system to be very complicated for the purpose of this paper. 2- The process transfer function (

PG ) given in Figure 4 is with the degree of 2. On the other hand, by looking at Figure 1, it can be seen that the degree of the open-loop system including governor without compensator, turbine, electrical machine and load is 3. It should be noted that

in the proposed design algorithm in this paper the compensator will not be considered. 3- The PI controller is normally inserted in the forward path as shown in Figure 4 and this is also used by Poulin. However, in the LFC discussion the main purpose is to stabilize the system following a step change in load LP . Therefore, in practice, as shown in Figure 3 the PI controller will be placed in the feedback path for LP .The above-mentioned points indicate that there should be some changes for the system given by Poulin. in order that it can be utilized in LFC design. Therefore, the following procedure is proposed. 1- First it is assumed that the reference signal to be refP . Note that the poles of the closed-loop transfer

functions LP and refP are the same. 2- As shown in Figure 5, the droop characteristics 1/ RP is considered to be 1. This coefficient is taken into account after designing the PID controller.

Figure 5: PD and PI controller in forward path

3- In order to reduce the degree of the system to 2 a PD compensator in the form of 2Hs+D is inserted in the forward path of Figure 5. The reason for this selection is

that the open-loop pole HDs

21 is much closer to the

imaginary axis in comparison with the other open-loop

poles T

sw5.0

12 and

gTs 1

3. It should be also noted that

since the damping ratio D is small, even it changes, when

compared with 2H the pole HDs

21 can be considered

to be constant. 4- The compensator has been omitted and the new controller must provide a stable system. This can be easily achieved because this method has been originally designed for non-minimum phase systems (see Equation (1)). 5- A PI controller based on the transfer function

)5.01)(1(1)(

sTsTsTsG

wg

wP is designed exactly based

on the formula given in Appendix. It is known, as mentioned before, the water starting time (Tw) changes when the load varies. It is also known that if the open-loop pole (say,

Tws

5.01

2 ) is close to the origin, the

performance may be degraded considerably. Therefore,

PI

LP

DHs2 sTg11

sTsT

W

W

5.011

DHs21

refP

PGPIR C

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to make sure that the worst situation is considered for the design procedure, the maximum possible value of Tw (i.e. Tw = 4.0 sec [1]) is chosen. 6- The PID (PI +PD) controller parameters, therefore, will be:

Cd

CI

CC

DesignP

dl

DesignPC

HKKTi

DKK

DKTi

HKK

where

sKs

KK

TisTisK

DHs

2

2

)1()2(

7- The designed PID controller will then be placed in feedback path as shown in Figure 6. 8- It is evident that RKK PControllerPDesignP 1 .9- With respect to industrial considerations, in order to remove high frequency noise effects when a PD controller is used, it is imperative that sTsK dd 1 (in

which dd KT ) be used rather than sKd [8].

Figure 6: Hydro power system with PID controller

7. SIMULATION RESULTSConsider, for example, a typical power system taken from [1] with the following parameters;

Tg=0.2 TW = 4.0 2H=6.0 D=1.0 1/RP=20(RP =0.05) TR=14 RT=1.233

16.0open

GVX 16.0close

GVX 1.0openGVX

1.0closeGVX

The limiter values are in p.u. and taken from [1]. By using Routh-Hurwitz criteria it was found that the range of IK for the system to be stable was 1.70 IK . By using a trial and error method it was realized that

0.1IK was the best selection for having the best performance. By using MPRS method, the PID controller parameters would be

01.0dT 122.0IK 983.DesignPK 5.1dKIt was shown in Section 6 that there were some modifications in such a way that MPRS method could be used for LFC design. This causes the system performance not to be exactly the same as what is designed. It was

found that keeping the designed values of PK and dKunchanged and increasing the value of IK to

14.0IK (for this example) gives the most desirable response. This has been tested for other typical hydro power systems in the literature and the same result is achieved. That is, a small increase only in the value of

IK will improve the dynamic performance. Figures 7 and 8 show the frequency and valve position changes of the system following a small step change in load ..02.0 upPL respectively. The results clearly demonstrate the advantage of using the new load frequency PID controller. It has got much faster response and smaller overshoot.

Figure 7: Frequency variation following a small change in load (0.02 p.u.)

Figure 8: Governor output following a small change in load (0.02 p.u.)

The simulations are conducted for the other cases where different values for the water starting time (Tw) have been used. It should be noted that in these simulations the PID controller parameters are fixed as designed before for the maximum value of Tw. The results are shown in Figure 9, 10 and 11 for Tw =3.0, 2.0 and 1.0 respectively. As can be seen from Figures 9 to 11 the proposed PID controller can still have pleasing responses even when Twchanges.

TurbineHydro

PID

sticsCharacteriDroop

MachineLoad &Governor

LP

1513

Figure 9: Frequency variation following a change in load (0.02 p.u.)

Figure 10: Frequency variation following a change in load (0.02 p.u.)

Figure 11: Frequency variation following a change in load (0.02 p.u.)

8. FURTHER WORK Although the design of any supplementary controller on a one-machine system is logically the best place to begin an evaluation of the controller, a more through investigation has to be done with a multimachine model. This has been performed by using a decentralized controller and some preliminary and key results are shown in Figures 12 and 13 for a two-machine hydro system confirming the advantage of using this new LFC. However, since this paper will be getting too long if this section is added full results are not given.

Figure 12: Frequency variation following a small change in load in system B only ..01.02 upPL

Figure 13: Tie-line power variations following a small change in load in system B only ..01.02 upPL

9. CONCLUSIONS The load-frequency regulation characteristics of a single machine infinite bus system with hydro turbine have been studied. The proposed PID controller has been shown to enhance the damping of the power system following a step change in load and gives a better performance than the conventional PI controller. There is also no need to use the transient droop compensator. The design of the controller has been mainly based on a maximum peak-resonance specification theory with some modifications.

10. REFERENCES[1] Kundur, Prabha “Power system stability and control” McGraw-Hill, 1994 [2] Saadat, Hadi; “Power System Analysis” McGraw-Hill, 1999 [3] Lansberry, J; Wozniak, I; “Adaptive Hydrogenerator Governor Tuning With a Genetic Algorithm” IEEE Trans. on Energy Conversion, March 1994, Vol. 9, No. 1, pp: 179-185.

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[4] Cheng, Y.; Ye, L.; “Anthropomorphic Intelligent PID Control and Its Application in The Hydro Turbine Governor” Proceeding of the first international conference on machine learning and cybernetics, Beijing, 4-5 November 2002, pp: 391-395. [5] Poulin E., Pomerleau A.; “PID tuning for integrating and unstable processes” IEE Proc.-Control Theory Appl, 1996, Vol. 143, pp. 429-435. [6] Poulin E., Pomerleau A.; “Unified PID design method based on a maximum peak resonance specification” IEE Proc.-Control Theory Appl, Vol. 144, 1997, pp. 566-574. [7] A. Khodabakhshian, N. Golbon ; “Unified PID design for load-frequency control”, Proceeding of the 2004 IEEE International Conference on Control Applications, Taipei, Taiwan, September 2-4, 2004, pp. 1627-1632. [8] Eitelberg, E.; “A regulating and tracking PI(D) controller” Int. J. Control, 1987, Vol.45, No.1, pp. 91-95.

APPENDIX The PI controller transfer function is

sTsTK

sGi

icC

)1()(

The process transfer function is

)1)(1()1(

)(21

0

sTsTesTK

sGs

PP

where 021 TT .The equation of controller integral time constant is given by

22.03.035.065.0

22.03.0175.01

11122

121

11122

121

TTTTTTT

TTTTTTTTi

The proportional gain is then given by 21

1220

2420

2422

21

6221

coicoi

cococo

P

iC TTTT

TTTTKTK

where co is obtained by solving

coco

cococoi

TTTT

2

10

arctanarctanarctanarctan2

and the desired phase is given by 2101arccos 1.0 rM

Mr is the maximum peak resonance and is considered to be 0 dB in this paper.

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