IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005 485

Tuning a PID Controller for a DigitalExcitation Control System

Kiyong Kim, Member, IEEE, and Richard C. Schaefer

Abstract—Some of the modern voltage regulator systems areutilizing the proportional, integral, and derivative (PID) controlfor stabilization. Two PID tuning approaches, pole placement andpole–zero cancellation, are commonly utilized for commissioninga digital excitation system. Each approach is discussed includingits performance with three excitation parameter variations. Theparameters considered include system loop gain, uncertain excitertime constants, and forcing limits. This paper is intended for var-ious engineers and technicians to provide a better understandingof how the digital controller is tuned with pros and cons for eachmethod.

Index Terms—Excitation system, loop gain, pole placement,pole–zero cancellation, proportional, integral, and derivative(PID) control, voltage overshoot, voltage response.

I. INTRODUCTION

TODAY’S digital excitation systems offer numerous bene-fits for performance improvements and tuning over their

analog voltage regulator predecessors. The days of potentiome-ters, screwdrivers, and voltmeters for tuning are replaced witha laptop computer and a table and chair. Unlike the past, whenexcitation systems were tuned by analog meters, today’s exci-tation can be tuned very precisely to desired performance andrecorded into a file for future performance comparison in theform of an oscillography record.

II. PROPORTIONAL, INTEGRAL, AND DERIVATIVE

(PID) CONTROL

The present-day digital regulator utilizes a PID controller inthe forward path to adjust the response of the system [1]. Formain field-excited systems, the derivative term is not utilized.The proportional action produces a control action proportionalto the error signal. The proportional gain affects the rate of riseafter a change has been initiated into the control loop. The in-tegral action produces an output that depends on the integral ofthe error. The integral response of a continuous control systemis one that continuously changes in the direction to reduce theerror until the error is restored to zero. The derivative actionproduces an output that depends on the rate of change of error.For rotating exciters, the derivative gain is used which measures

Paper PID-04-19, presented at the 2004 IEEE Pulp and Paper Industry Con-ference, Vancouver, BC, Canada, June 27–July 1, and approved for publicationin the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Pulp and PaperIndustry Committee of the IEEE Industry Applications Society. Manuscript sub-mitted for review July 1, 2004 and released for publication November 16, 2004.

The authors are with Basler Electric Company, Highland, IL 62040 USA(e-mail: kiyongkim@basler.com; richschaefer@basler.com).

Digital Object Identifier 10.1109/TIA.2005.844368

Fig. 1. Simplified block diagrams of automatic voltage regulators.

the speed of the change in the measured parameter and causesan exponentially decaying output in the direction to reduce theerror to zero. The derivative term is associated with the voltageovershoot experienced after a voltage step change or a distur-bance. The basic block diagram of a PID block utilized in theautomatic voltage regulator control loop is shown in Fig. 1. Inaddition to the PID block, the system loop gain providesan adjustable term to compensate for variations in system inputvoltage to the power converting bridge. When performance ismeasured, the voltage rise time is noted at the 10% and 90%levels of the voltage change. The faster the rise time, the fasterthe voltage response [5].

The benefits of a fast excitation controller can improve thetransient stability of the generator connected to the system, orstated another way, maximize the synchronizing torque to re-store the rotor back to its steady state position after a fault. Afast excitation system will also improve relay tripping coordi-nation due to the excitation systems’ ability to restore terminalvoltage quickly, and providing more fault current to protectiverelays for optimum tripping time.

III. CHARACTERISTIC OF EXCITATION CONTROL SYSTEMS

An optimally tuned excitation system offers benefits inoverall operating performance during transient conditionscaused by system faults, disturbances, or motor starting [5].During motor starting, a fast excitation system will minimizethe generator voltage dip and reduce the heating losses ofthe motor. After a fault, a fast excitation system will improve

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486 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005

Fig. 2. Generator saturation curve illustrating generator gain.

Fig. 3. Phase shift of the exciter field, the generator field, and the sum of thetwo.

the transient stability by holding up the system and providingpositive damping to system oscillations.

A fast excitation system offers numerous advantages, im-proved relay coordination and first swing transient stability,however an excitation system tuned too fast can potentiallycause megawatt instability if the machine is connected to avoltage-weak transmission system. For these systems a powersystem stabilizer may be required to supplement machinedamping.

The evaluation of system performance begins by performingvoltage step responses to examine the behavior of the excitationsystem with the generator. It is performed with the generatorbreaker open, since the open-circuited generator representsthe least stable condition, i.e., the highest gain and the leastsaturation (see Fig. 2). Fig. 3 represents a Bode plot of thegenerator and exciter field for a sweep frequency from 0 to10 Hz. The frequency plot represents the potential voltageoscillation frequency after a disturbance. The time constantof the generator field and the exciter field is plotted andillustrated to show that as the frequency increases, the phaseangle becomes more lagging. The phase angle of the generatorfield adds directly with the phase angle of the exciter field. Asthe phase angles add to 150 , the system will most likely becomeunstable because of the combined gain of the generator andthe excitation system. Unless compensated properly through

Fig. 4. One-line diagram.

the PID controller, the synchronous machine may becomeoscillatory after a fault [8].

Besides the open-circuit voltage step test, another test per-formed is the voltage step test with the generator breakerclosed. When voltage step tests are performed with the gen-erator breaker closed, very small percentage voltage steps areintroduced to avoid large changes in generator vars. In thiscase, a 1%–2% voltage step change is typical [7].

IV. TUNING OF PID CONTROLLER

The controller parameters are determined with several excita-tion system parameters, such as voltage loop gain and open-cir-cuit time constants [1]. These parameters vary with not only thesystem loading condition but also gains dependent on the systemconfiguration, such as the input power voltage via power poten-tial transformer (PPT) to the bridge rectifier as shown in Fig. 4.Commissioning a new automatic voltage regulator (AVR) canbe a challenging task of checking excitation system data in ashort time, without any test data, and with no other link to theactual equipment, except for an incomplete manufacturer’s datasheet, or some typical data set.

To tune the digital controller, two methods are predominantlyused, one being the pole-placement method and the other beingthe cancellation approach [1], [2]. To simplify the design of thePID controller, we assume in Fig. 1.

Every PID controller contains one pole and two zero termswith low-pass filter in the derivative block ignored. For gen-erators containing rotating exciters, the machine contains twoopen-loop poles, one derived from the main field and the otherderived from the exciter field. A pole represents a phase lag inthe system while the zero tends to provide a phase lead compo-nent. The location of poles and zeros with relation to the exciterand generator field poles determines the performance of the ex-citation control system.

Root locus is used to describe how the system responds basedupon gain in the system. Using the pole-placement methodand referencing Fig. 5(a), the poles of the generator main fieldand exciter field are located on the real axis. The generatormain field pole is located close to the origin while the exciterfield pole is typically tens times the distance, the distancedepending upon the time constant of the exciter field versus

KIM AND SCHAEFER: TUNING A PID CONTROLLER FOR A DIGITAL EXCITATION CONTROL SYSTEM 487

Fig. 5. Root locus and voltage response with two different systemgains ((K )). (a) Root locus of different loop gains gains: K =90;K = 70;K = 25. (b) Step responses performance gains:K = 90;K = 70;K = 25.

the main field. The smaller the exciter field time constant,the greater the distance. The PID controller consists of onepole and two zeros.

Fig. 5(a) shows how the closed-loop poles move as theloop gain increases. The loop gain represents the totalizedgain that includes the generator, field forcing of the excitationsystem, and PID controller. The open-loop zeros becomes theclosed-loop zeros and do not depend on the loop gain. Onthe other hand, the poles of the closed-loop system (exciter,generator, and controller) are moving toward zeros in a certainpath as the loop gain increases. The path of the closed-looppoles depends on the relative location of poles and zeros basedupon its time constants. With fixed PID gains, a certain systemgain determines the closed-loop poles. Two cases of theclosed poles are shown in Fig. 5(a), one for system gain 1.0 andthe other for system gain 0.13.

In general, the poles nearest to the origin determine thesystem responses. When the poles become a conjugate pair,

Fig. 6. 5% Voltage step response using pole-placement method.

the system response will be oscillatory. The conjugate pairrepresents the ratio of the imaginary to real value of poles todetermine the voltage overshoot. The absolute value of thepole determines the frequency of voltage oscillation. The fastervoltage response can be achieved by moving the poles from theorigin and the less oscillatory response with the smaller ratio(see Fig. 5(b)).

A. Pole Placement

In the pole-placement method, the desired closed-loop polelocations are decided on the basis of meeting a transient re-sponse specification. The design forces the overall closed-loopsystem to be a dominantly second-order system. Specifically,we force the two dominant closed-loop poles (generator andcontroller) to be a complex conjugate pair resulting in an un-derdamped response. The third pole (exciter) is chosen to be areal pole and is placed so that it does not affect the natural modeof the voltage response. The effect of zeros on the transient re-sponse is reduced by a certain amount of trial and error and en-gineering judgment involved in the design.

The pole-placement method generally requires specific infor-mation of the exciter field and main generator field time con-stants to determine the gains needed for the digital controllerfor adequate response. Voltage overshoot of at least 10%–15%is anticipated with the pole-placement method with a 2–3-s totalvoltage recovery time, although its voltage rise time can be lessthan 1 s.

Fig. 6 illustrates the generator terminal voltage performanceof a 100-MW steam turbine generator when a 5% open-cir-cuit voltage step change has been introduced. Generator voltageovershoot is 20% with a total voltage recovery time of 2.5 s. ThePID gains are as follows: , and .

The excitation system bandwidth is used to characterize theresponse of the generator with the voltage regulator. The widerthe voltage regulator bandwidth, the faster is the excitationsystem.

To derive the voltage regulator bandwidth, the gain and phaseshift is plotted over a range of frequencies, typically, 0–10 Hz

488 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005

Fig. 7. Root locus for 100-MW generator using pole-placement method gains:K = 90;K = 70;K = 29;K = 15.

Fig. 8. Closed-loop Bode diagram of pole-placement method.

by applying a signal oscillator into the voltage regulator sum-ming point. The input signal is compared to the generator outputsignal by measuring the phase and gain of the frequency rangeof 0–10 Hz, which represents the potential oscillating frequencyof the generator interconnected to the system. For these Bodeplots, information of the generator and exciter time constantalong with the excitation system gains are used to determine thebandwidth of the generator excitation system.

A typical root locus with pole-placement method is shown inFig. 7. Notice how the closed-loop poles move along the circlewith increasing gain. Fig. 8 shows the phase lag, 59.1 at 3dB. The decibel rise prior to roll-off confirms the voltage over-shoot noted during the voltage step response in Fig. 6.

The ideal excitation system will maintain high gain with min-imum phase lag. The point of interest is the degree of phase lagand gain at 3 dB, the bandwidth of the excitation system. Theless phase lag with higher gain gives the better performance ofthe excitation system. Fig. 9 highlights the open-loop responseof the excitation system. It shows the phase lag of 105 at 0dB, crossover frequency.

Fig. 9. Open-loop Bode diagram of pole-placement method.

Fig. 10. Root locus for 100-MW generator using pole–zero cancellationmethod gains:K = 80;K = 20;K = 40;K = 15.

B. Pole–Zero Cancellation

The cancellation method offers the benefit of performancewith minimum voltage overshoot. This method uses the factthat the dynamic behavior of the pole is cancelled if the zerois located close to the pole. The PID controller designed usingpole–zero cancellation method forces the two zeros resultingfrom the PID controller to cancel the two poles of the system.The placement of zeros is achieved via appropriate choice ofthe PID controller gains. Since exciter and generator poles areon the real axis, the controller has zeros lying on the real axis.Unlike the pole-placement method that uses high integral gain,a proportional gain is set to be at least four times greater thanthe integral term.

A typical root locus with inexact cancellation is shown inFig. 10. The zeros are selected to cancel the poles correspondingto exciter and generator time constants. Thus, the closed-loopsystem will be dominantly first order.

The exciter and generator time constants vary with thesystem condition. The exact pole–zero cancellation is not

KIM AND SCHAEFER: TUNING A PID CONTROLLER FOR A DIGITAL EXCITATION CONTROL SYSTEM 489

Fig. 11. Voltage response using pole–zero method.

practical. However, the exciter time constant is much smallerthan generator time constant in rotary excitation controlsystems. As the loop gain increases, the poles move towardthe corresponding zeros. Since the two time constants arewell separated, the effect of nonexact pole–zero cancellationis not detrimental.

The cancellation method provides for an extremely stablesystem with very minimum voltage overshoot and the fieldvoltage remains very stable even with high loop gains

. Fig. 11 shows thevoltage response of a 100-MW steam turbine generator usingpole–zero cancellation gains.

The closed- and open-loop Bode plots are, respectively, il-lustrated in Figs. 12 and 13 when the pole–zero cancellationmethod is used. The gain remains high and the phase lag is com-pensated for a wide frequency. Again using the 3-dB point thatrepresents the bandwidth of the excitation system, the phase lagis 46.3 —a very fast excitation system. Notice the gain re-mains very flat before it begins to roll off. The flat response il-lustrates a very stable system with little to no voltage overshoot.Fig. 13 shows the phase lag of 91 at crossover frequency of0 dB.

V. EFFECT OF PARAMETER VARIATIONS

The performance of two methods is conducted using com-puter simulation in the presence of parameter variations. Theparameters considered include system loop gain and uncertainexciter time constant.

Since, in general, the calculation of loop gain requires severalexcitation system parameters that are generally not availableduring commissioning, specifically, the machine time constant,this lack of information can make the use of the pole-placementapproach more time consuming for setup than cancellation ap-proach.

Fig. 12. Closed-loop Bode diagram of pole–zero cancellation method.

Fig. 13. open-loop Bode diagram of pole–zero cancellation.

A. Variation Due to Uncertainty in the Loop Gain

Variation due to uncertainty in the loop gain is consideredby variations in from the values of 0.1, 0.3, and 1.0. Allthe other parameters remain unchanged. Fig. 14 illustrates theresponses of the two methods described, pole placement andpole–zero cancellation, while changing the loop gain ( ) ofthe digital controller. Note that both Fig. 14(a) and (c) displaysimilar rise time but voltage overshoot only occurs using thepole-placement method in this example. The pole–zero cancel-lation method provides a means to quickly and accurately tunethe generator excitation system. Faster voltage response can beachieved by simply increasing the loop gain.

B. Uncertainty in the Knowledge of the Exciter Time Constant

Uncertainty in the knowledge of the exciter time constant isconsidered from the values of 0.2, 0.6, and 1.0 s (see Fig. 15).All other parameters remain unchanged. The comparisonof Fig. 15(a) and (c) indicates the superiority of the perfor-mance resulting from pole–zero cancellation design over the

490 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005

Fig. 14. Step responses with loop gains, (a) Generator voltages for poleplacement. (b) Control outputs for pole placement. (c) Generator voltages forpole–zero cancellation. (d) Control outputs for pole–zero cancellation.

pole-placement design. The root locus of each method is, re-spectively, shown in Fig. 16(a) and (b). For the pole-placement

Fig. 15. Step responses with exciter time constants. (a) Generator voltages forpole placement. (b) Control outputs for pole placement. (c) Generator voltagesfor pole–zero cancellation,. (d) Control outputs for pole–zero cancellation.

design, the exciter pole at pushes the root locus to theright with small loop gain . On the other hand, the root

KIM AND SCHAEFER: TUNING A PID CONTROLLER FOR A DIGITAL EXCITATION CONTROL SYSTEM 491

Fig. 16. Root locus with exciter time constant 1 s. (a) Pole placement—lessstable system, more voltage overshoot. (b) Pole–zero cancellation—more stablesystem.

locus is moved to the left for the pole–zero cancellation design,providing a more stable system.

VI. SOME TIPS FOR TUNING THE PID CONTROLLER

A. Main Field-Excited Excitation Systems

For main field-excited systems, since only one field exists,the derivative term is not used, however, the same gains ratiobetween the proportional term and the integral term is used withno derivative term applicable [3].

B. Applying Suitable Gains

The ratio between the integral term and the proportional termneeds to be a minimum of four for good performance. Hence,with an integral gain of 20, the proportional gain will be 80.It has been found that it works best to have an integral gainof not more than 20 in most cases to obtain satisfactory per-formance [8], [9]. The derivative term will affect the voltageovershoot, and here, a value of 20 will generally be adequate.For faster voltage rise time, the proportional term is increased.

Fig. 17. 5% voltage step response, 0.976-s voltage recovery, and 0.8% voltageovershoot.

On slow-speed hydro machines where the generator and excitertime constant tend to be quite large due the slow speed of the tur-bine. Often the term is increased to 150 to help overcomethe large inductive lag of the machine’s field which will nor-mally slow the voltage reaction time of the machine’s response.Fig. 17 illustrates the performance of a 70-MW hydro machinethat has a 9-s main field time constant and a 2-s exciter fieldtime constant. Notice the voltage overshoot and settling time[6]. Fig. 17 utilizes a , and .

Where the generator, such as a hydro, has a large field timeconstant as mentioned above, and the exciter field ratio to mainfield becomes less, an additional damping factor may be re-quired to make the field voltage more damped or stable, knownas . It is an additional filter that affects the derivative termused with rotating exciter applications to reduce the effect ofnoise. For these systems where the field voltage may require ad-ditional damping, the gain value should be applied. Valuesof 0.01–0.08 can be used to reduce the noise content of the fieldvoltage.

C. Gain for Nonnegative Forcing Systems

For systems where negative field forcing is not used, the loopgain of the controller should be reduced to achieve best re-sponse as compared to systems having negative forcing. Noticein Fig. 18 how voltage overshoot is affected by the same gainterms with and without negative field forcing. To get a properresponse for nonnegative forcing system, gain is reduced with

from 5 to 1.

VII. CONCLUSION

The pole-placement and the pole–zero cancellation methodsfor designing PID controllers for excitation systems have been

492 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005

Fig. 18. Voltage step responses with and without negative field forcing. (a)K = 5 with negative field forcing. (b)K = 5 with no negative forcing. (c)K = 1 with no negative forcing.

presented. The sensitivity of the two designs to various uncer-tainties and parameter variations are presented. Using the can-cellation method of tuning PID gains, commissioning can beaccomplished very quickly with excellent performance results.

REFERENCES

[1] K. Kim, M. J. Basler, and A. Godhwani, “Design experience with PIDcontrollers for voltage regulation of synchronous generator,” IEEETrans. Energy Convers., submitted for publication.

[2] K. Kim, A. Godhwani, M. J. Basler, and T. W. Eberly, “Commissioningexperience with a modern digital excitation system,” IEEE Trans. En-ergy Convers., vol. 13, no. 2, pp. 183–187, Jun. 1998.

[3] R. C. Schaefer, “Application of static excitation systems for rotating ex-citer replacement,” in Proc. IEEE Pulp and Paper Industry Tech. Conf.,1997, pp. 199–208.

[4] R. C. Schaefer, “Steam turbine generator excitation system moderniza-tion,” in Proc. IEEE Pulp and Paper Industry Tech. Conf., 1995, pp.194–204.

[5] IEEE Guide for Identification, Testing, and Evaluation of the DynamicPerformance of Excitation Control Systems, IEEE Std 421.2-1990.

[6] R. C. Schaefer, “Voltage versus var/power factor regulation on hydrogenerators,” presented at the IEEE PSRC, 1993.

[7] IEEE Guide for Specification for Excitation Systems, IEEE Std 421.41990.

[8] R. C. Schaefer, “Voltage regulator influence on generator stability,” pre-sented at the Basler Electric Power Control and Protection Conf., St.Louis, MO, 2003.

[9] R. C. Schaefer, K. Kim, and M. J. Basler, “Voltage regulator with dualPID controllers enhance power system stability,” presented at the HydroVision Conf., Portland, OR, Jul./Aug. 2002.

Kiyong Kim (M’97) received the B.S. degreefrom Hanyang University, Seoul, Korea, in 1979,the M.S.E.E. degree from the University of SouthFlorida, Tampa, in 1991, and the D.Sc. degree fromthe Systems Science and Mathematics Department,Washington University, St. Louis, MO, in 1995.

From 1979 to 1988, he was a Research Engineerwith the Agency for Defense Development, Korea,working in the areas of system modeling, analysis,design, and simulation. He is currently with BaslerElectric Company, Highland, IL. His current interests

are stability analysis of power systems, design of excitation control systems, andlarge-scale computational methods.

Richard C. Schaefer (M’91–SM’01) receivedthe A.S. degree in engineering technology fromBelleville Area College, Belleville, IL, in 1972.

He is Senior Application Specialist in ExcitationSystems for Basler Electric Company, Highland, IL.Since 1975, he has been responsible for excitationproduct development, product application, and thecommissioning of numerous plants. He has authoredtechnical papers for conferences sponsored bythe IEEE Power Engineering Society (PES), thePulp and Paper Industry Committee of the IEEE

Industry Applications Society (IAS), Society of Automotive Engineers, Water-power, Power Plant Operators, and for the IEEE TRANSACTIONS ON ENERGY

CONVERSION and IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS.Mr. Schaefer is a past IEEE 421.4 Task Force Chairman for modification of

Preparation of Excitation System Specifications and is involved in committeework for the PES and IAS.