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A Fuzzy Voltage Regulator (FVR) for a Stand-aloneSynchronous Generator

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Electric Power Components and Systems, 35:429–443, 2007Copyright © Taylor & Francis Group, LLCISSN: 1532-5008 print/1532-5016 onlineDOI: 10.1080/15325000601023688

A Fuzzy Voltage Regulator (FVR) for aStand-alone Synchronous Generator

MEHMET KUBILAY EKER

Balikesir UniversityElectrical and Electronics EngineeringBalikesir, Turkey

ISMAIL H. ALTAS

Karadeniz Technical UniversityElectrical and Electronics EngineeringTrabzon, Turkey

Abstract This study deals with terminal voltage control of a stand-alone synchronousgenerator using fuzzy logic based controller as a fuzzy voltage regulator (FVR) insteadof classical automated voltage regulators (AVR). In order to obtain the simulated be-havior of the synchronous machine more accurately, a dq axis transformation basedmodel is preferred instead of reduced and linearized small signal models widely usedin literature. A laboratory prototype experimental set-up consisting of a synchronousgenerator, a three-phase resistor box, and a three-phase induction motor representinglinear and nonlinear loads has been established in order to check the validation of thesimulation model developed. The controllers in the experimental parts of this studyare digitally implemented using a personal computer and a 12 bit PCL 818 dataacquisition card with a speed rate of 100 kS/s.

Keywords synchronous generator, excitation control, automatic voltage regulation,fuzzy voltage regulation, fuzzy logic control

1. Introduction

Power system stability problems have been the subject of continuing research for years.Because of the stability on power systems, various types of classical controller [1] andnew type of controllers [2, 3] have been designed and utilized. Among those, fuzzylogic (FL) and artificial neural network (ANN) based controllers have been getting anincreasing interest from the power system researchers.

Control parameters of the excitation systems have an important role on power systemdynamic response and stability. Therefore these control parameters are required to be setand tuned properly so that the controller ought to respond as fast as possible to meetunexpected changes in the overall system.

Received 3 March 2006; accepted 6 September 2006.Address correspondence to Dr. Mehmet Eker, Faculty of Engineering and Architecture, Dept.

of Electrical and Electronics Engineering, Campus of Cagis, Balikesir, 10145, Turkey. E-mail:kubilay@balikesir.edu.tr

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Conventional analogue automatic voltage regulators (AVRs) using linear transferfunctions of synchronous machines have been designed and utilized widely. However, asynchronous generator and its components, such as exciter and governor system, are allnonlinear in reality. Therefore, a control system designed based upon linearized models,which are valid only at a chosen set of operating conditions, results in a fixed gainAVR that is unable to respond satisfactorily over the whole range of the system and itsoperating conditions. The linearized AVR models may also introduce negative dampingthat causes stability problems in some circumstances. Therefore, many studies have beendone to develop adaptive and self-tuning AVRs in order to have a controller that gives fastand more accurate responses to the operating conditions that may cause instabilities [4].The adaptive applicability of fuzzy logic based controllers to nonlinear systems withouta linearized model requirement have started a new direction for the researchers studyingon control systems including those of used in power system control [5, 6].

As in many different areas, the use of FLC has been increased rapidly in powersystems, such as in load-frequency control, bus bar voltage regulation, stability, loadestimation, power flow analysis, parameter estimation, protection systems, and manyother fields. Fuzzy logic applications in power systems are given in [6] with a detailedsurvey.

The modeling of the proposed FL compensator is discussed and explained in thisarticle with required coverage. As it is well known, instantaneous load changes affect thebus voltage and its frequency causing their values to swing about the nominal operatingpoints. When the magnitudes of these swings are large and natural damping takes longtime, the stability of the power system may be lost resulting in damages and power outagesin the system. In order to overcome the effects of swinging voltage or/and frequency, someprecautions must be taken such as power system stabilizers (PSS), voltage regulators, andcompensators, which, based upon the detection of the changes in voltage and frequency,have been used successfully over the years [7–11]. The response time of the stabilizers andcompensators is very important to have the power system to gain control with increasedstability margins. Therefore, the proposed controller must compensate and reduce theresponse time, as well as reduce the magnitude of the swinging waves when comparedto the classical types.

Any variation on the terminal voltage of the synchronous generator is used as anegative feedback signal to the fuzzy logic controller over a rectifier. The FLC is designedto act as fast as possible to minimize and make the variations zero if any one occurs.The proposed fuzzy logic based compensator and the power system that is simulated andimplemented here is described in the following sections.

Although a mathematical model of physical systems is not required for FL controllersin real time applications, it is necessary for digital simulation in computer environments.Therefore, a power system exciter model is needed for the simulation part here. It is animportant task to obtain an accurate simulation model of the excitation system in powersystem stability studies [12]. Although reduced-order synchronous generator excitationmodels have been derived and suggested by IEEE [12–14], a dq axis model for themachine tested in this study is obtained using Park’s transformations.

2. The System Description

The operating conditions of a utility connected synchronous generator can be separatedinto two categories [15, 16]. The first one includes large generators that affect the busvoltage, which is required to be controlled. The second one includes small size generators

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Fuzzy Voltage Regulator for Synchronous Generator 431

that do not have any effect on the bus voltage but on the reactive power. In this study,the first case has been studied.

As shown in Figure 1, the implementation scheme consists of a direct current (DC)motor, a synchronous generator, two different three-phase adjustable resistive load boxes,and a three-phase induction motor load. A three-phase rectifier and a FLC are used forexcitation unit. For the transient analysis in simulation, all of these components aremodeled in time domain as explained next.

Synchronous generator in Figure 1 feeds both three-phase resistive load and/or three-phase induction motor. Voltage information of synchronous generator is converted todigital data over a three-phase transformer, a three-phase rectifier, and an analog digitalconverter (ADC) to be used to find voltage amplitude. During stable operation, the trig-gering angle of three-phase rectifier remains constant, and synchronous generator voltageis set to its nominal value. As soon as any change occurs in loads, the FLC adjusts thetriggering angles of the rectifier connected to the excitation circuit of the synchronousgenerator to a new value in order to keep terminal voltage of the synchronous generatorat the nominal value. Since the required control action is taken by the FLC as well as therequired compensation for voltage regulation without any other units as used in classicalAVR systems, the process here can be considered as a fuzzy voltage regulator (FVR).The main focus of this study is to develop and test a novel FVR to be used to operate asynchronous generator at a constant terminal voltage. A separately excited direct currentmotor is used as a prime mover, as given in Figure 1. Since the main purpose of thisstudy is to develop a FL based compensator for synchronous generator excitation sys-tems, speed and torque control of the prime mover is ignored by keeping armature andfield voltages constant.

The FLC is implemented digitally in a personnel computer and included in the sameblock in Figure 1 along with PC and PCL 818. The FLC uses membership functions anda rule base table that represent an expert’s knowledge in order to control the excitationsystem so that the synchronous generator is operated at desired terminal voltage.

As mentioned earlier, the mathematical model of the system to be controlled is notnecessarily needed in FL controller. Since FL controller adjusts the system input to yield

Figure 1. Schematic diagram of the systems.

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432 M. K. Eker and I. H. Altas

a desired output by looking at only the system output, the behavior of the componentsbetween input and output is not included in the modeling. This may be true if a real-timeapplication is the subject such as the implementation case here. However, a mathematicalmodel is required since a simulation model is to be developed.

2.1. Mathematical Modeling of the System

2.1.1. Direct Current Motor. Since a separately excited DC motor is used as the primemover instead of a turbine in laboratory prototype setup, the prime mover in simulation isrepresented by an electrical equivalent circuit, shown in Figure 2, and dynamic equationsgiven by (1)–(3), which are written in terms of field voltage, armature voltage and thetorque produced [17].

vf dc = rf dc × if dc + Lf dcpif dc (1)

ve = re × ie + Lepie + ωr × Lef × if dc (2)

Tdc = Lef × if dc × ie (3)

where p is used for the operator d/dt , vf dc and if dc are the field voltage and current,respectively. rf dc and Lf dc are the resistance and inductance of the field winding, respec-tively. Similarly, ve and ie are the armature voltage and current. re and Le are resistanceand inductance of the armature winding. Lef is the mutual inductance between armatureand field windings. Voltages are in volts, currents are in amperes, resistors are in ohms,and inductances are in henries.

2.1.2. Synchronous Generator. A three-phase four-pole synchronous generator with acylindrical rotor and one damping winding is used in this study. Electrical equivalentcircuit used in the modeling of the synchronous generator is shown in Figure 3.

An accurate model of the synchronous generator, which is the main element of thepower system studied, is important for stability and productivity. Park’s transformation,which is used as reference to derive other electric machines’ models, is also preferred hereto obtain the dynamic model of the synchronous machine. Reduced-order synchronousmachines models that are also derived using Park’s transformation is used in many ap-plications for control purposes in order to simplify the computational complexity dueto the limited capabilities of computing tools. Lots of works dealing with the modelingof synchronous generators have appeared in literature during the last few decades withincreasing interest [18]. Some researchers attempted to increase the accuracy of the syn-chronous machine models [19–21]. Some others focused on the analysis based upon theestimation of machine parameters using alternative techniques [22, 23]. Although it is

Figure 2. Electrical equivalent circuit of a separately excited direct current motor.

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Figure 3. Electrical equivalent circuit of the synchronous generator.

not an exact model, the dq axis model based on Park’s transformation is preferred in thisstudy since more accurate results are obtained compare to the reduced order models.

Park’s transformation is a well known and widely used approach in generalizedelectrical machine modeling for dynamical analysis [17]. Therefore, it is not necessary tobe repeated here. However, resultant dq axis voltage equations of a three-phase cylindricalrotor synchronous machine that is used here are given in (4)–(7).

vrqs = −rs × irqs + P × ωr × λrds + pλrqs (4)

vrds = −rs × irds − P × ωr × λrqs + pλrds (5)

v′kq = r ′kq × i′kq + pλ′

kq (6)

v′f d = r ′f d × i′f d + pλ′

f d (7)

where P is the number of pole pairs. Similarly, the flux linkage equations are obtainedand given in (8)–(11).

λrqs = −Lq × irqs + Lmq × i′kq (8)

λrds = −Ld × irds + Lmd × i′f d (9)

λ′kq = L′

kq × i′kq − Lmq × irqs (10)

λ′f d = L′

f d × i′f d − Lmd × irds (11)

The produced torque by synchronous generator can be expressed as

Te = 3

2P × (λrds × irqs − λrqs × irds) (12)

Then, the combined torque equation of the overall system is given by Eq. (13).

Tdc = J 1

Ppωr + Bm × ωr + Te (13)

The equivalent circuit of the synchronous generator obtained using the transformed equa-tions are represented as in Figure 4.

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434 M. K. Eker and I. H. Altas

Figure 4. Equivalent circuits of a three-phase synchronous machine with reference frame fixed inrotor.

3. Fuzzy Logic Controller (FLC)

As it was mentioned earlier, a FL based controller adjusts system input in order to get adesired output without any interior modeling of the system. The main principle of a FLcontroller is to act in the same way as a human operator does. Since a human operatoradjusts the system input with the amounts defined by imprecise linguistic terms such aslittle, some, a few, more, small, big, etc., the operation of a FL controller is establishedon the same basis, too. Therefore, a representation model is required for these linguisticterms. It is the fuzzy set theory that enables us to assign a degree of membership inany amount that represents its inclusion in these linguistic terms. Since the developmentof fuzzy set theory by Zadeh [24], it is possible to represent imprecise concepts anduncertainties with fuzzy sets whose elements have membership degrees between 0 and 1,not only 0 or 1 as in classical crisp set theory.

A fuzzy logic based controller is built up mainly by three parts, which are calledfuzzifier, rule base (control rules), and defuzzifier, as shown in Figure 5 [25].

Similar to classical controllers, the error signal that is defined as the differencebetween system output and reference set point is compensated by FLC. However, in

Figure 5. Operational block diagram of fuzzy logic controller.

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Figure 6. Fuzzy subsets defined in the crisp universes e and de.

addition to error, change in the error signal is also considered in FL based controllers inorder to include the information about variation speed and direction of the error signalin determining the change in control signal.

The first stage of a FL controller is called fuzzifier where the crisp values of error,e, and change in the error, de, are converted to fuzzy numbers in terms of membershipdegrees µe and µde, respectively. The fuzzy numbers that are also called fuzzy setsrepresent the linguistic terms negative large (NL), negative medium (NM), negative small(NS), zero (Z), positive small (PS), positive medium (PM), and positive large (PL). Theshapes of the fuzzy subsets used in this study are shown in Figure 6.

After the membership degrees µe and µde, of error e, and its change de, respectively,are obtained in the fuzzy subsets NL, NM, NS, Z, PS, PM, and PL, the second stageof the FL controller is processed. At the second stage, the control rules correspondingto the membership degrees, µe and µde are given to yield the membership degrees µduof the change in control signal. The control rules representing the control actions to betaken in terms of the linguistic variables NL, NM, NS, Z, PS, PM, and PL are given inTable 1 where the subscripts from 1 to 49 represent the rule numbers.

For the fuzzy values of e and de being NL, NM, NS, Z, PS, PM, and PL, the fuzzynumbers of du are obtained with an IF . . . THEN . . . ELSE algorithm as

IF e is NM AND de is PM THEN du is PS ELSEIF . . . THEN . . . ELSE...

......

IF . . . THEN . . .

Table 1Fuzzy control rule table

e de NL NM NS Z PS PM PL

NL PL1 PL2 PM3 PM4 PS5 PS6 Z7NM PL8 PM9 PM10 PS11 PS12 Z13 NS14NS PM15 PM16 PS17 PS18 Z19 NS20 NS21Z PM22 PS23 PS24 Z25 NS26 NS27 NM28PS PS29 PS30 Z31 NS32 NS33 NM34 NM35PM PS36 Z37 NS38 NS39 NM40 NM41 NL42PL Z43 NS44 NS45 NM46 NM47 NL48 NL49

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Each line of this algorithm represents a rule in Table 1, and results in the µdu membershipdegrees in the universe of discourse du. At every sampling instant two or four rules arefired and µdu membership degrees are obtained for the respective µe and µde values.After µdu values are obtained for all the effective rules at a sampling instant, the crispoutput value Du of FLC are obtained by converting these µdu membership degrees tocrisp equivalent numbers. The stage where the fuzzy membership values are converted toa crisp value is called defuzzification stage of the FL controller. At defuzzification stage,aggregated fuzzy functions are used to determine the mean of fuzzy numbers obtainedfrom all effective rules in previous step. One of these functions used in defuzzificationis called the center of area (COA) method, which is widely used in FLC systems, andis defined as:

Du =

n∑

i=1

µi(du)× duin∑

i=1

µi(du)

(14)

where n is the number of the rules, µi(du) is the membership degree of du in the fuzzysubset corresponding to ith rule, dui is the crisp value of du that corresponds to themaximum membership degree of the fuzzy subset defined by ith rule.

The error signal to the FL controller, here, is defined as the difference between theestimated voltage amplitude (Vam(k)) and reference voltage value (Vref ), which is 180volts, here. In order to have a fine control on the voltage range between 170 volts and190 volts, the error signal is normalized as

e = (Vam(k)− Vref )/β (15)

where β is a scaling factor and equal to 10 here. During the simulation, it was observedthat the variation of de was being affected by sampling period T (10 ms). Therefore,this time period, T , is used as a scaling factor for de.

de(k) = (e(k)− e(k − 1))/ T (16)

As a result of the normalization of upper and lower boundaries of the crisp universein where the fuzzy subsets NB, NM, NS, Z, PS, PM, and PB are defined, as shown inFigure 6, the resultant output du of the FL controller is also needed to be normalized as:

DU(k) = T ×Du(k) (17)

Therefore, the final control action signal is then obtained by adding the change DU tothe previous value of the control signal.

α(k) = α(k − 1)−DU(k) (18)

where α is thyristor triggering angle.

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4. Results

Both simulation and experimental results are given in this section. The system is simulatedusing the proposed simulation algorithm that is written in ANSI C.

Analog data from experimental results are transferred to a personal computer (PC)over a PCL 818 data acquisition card with a sampling rate of 100 kS/s. The rectified valueof synchronous generator terminal voltage transferred to the PC every 1 ms using withinternal timer of PCL 818 card. It is found average value of consecutive 10 samples, andthis value is normalized for phase to neutral RMS value of generator terminal voltage.Samples are stored every 1 ms, but monitored every 10 ms. After the average valueof terminal voltage is found, FLC generates triggering angle of rectifier circuit of theexcitation system within 1 ms. The experimental results monitored on PC are given asscreenshots in resultant figures.

As mentioned in Section 2, the speed and torque control of the prime mover, whichis a separately excited DC motor, is ignored by keeping armature and field voltagesconstant. Since this article focuses on the excitation control of the synchronous generator,no load-frequency control is applied on this system. On the contrary, a great amount ofattention is given for the excitation control system by developing a novel fuzzy logicvoltage regulator. Even though the speed of the prime mover is not controlled, it waskept operating around the synchronous speed of the generator. Therefore, the frequencyof the generated voltages and currents were between the tolerable limits that requiredby the loads used in testing. However, it is evident that large load changes would havecaused frequency drops or rises even if the terminal voltage is controlled and kept atreference value by the developed excitation controller.

Figure 7. A screen shot of terminal voltage and triggering angle from the experiment when theload resistor is switched from 140 ohms to 40 ohms.

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The experimental results include some oscillations that are not desirable. The sourcesof these oscillations are the loose wiring and interfacing circuitry, which are designed andassembled in a research laboratory environment that is not established for high qualitymanufacturing purposes. Therefore, during some triggering intervals, the triggering cir-cuits are affected by the noise and interferences caused by other devices being operated.A stronger rotor cage with higher inertia would have damped these oscillations. Sincethese interferences are not the issue in simulation, oscillation free results are obtainedfrom the simulation.

The system was tested by applying different experiments. First, the generator isoperated to feed a 140 ohms resistive load, and then the load is reduced to 40 ohms inorder to see the effect of increased line current on the terminal voltage. As shown inFigure 7, a voltage drop occurs in the phase to neutral value of the terminal voltage assoon as the resistive load value reduced to 40 ohms resulting in an increment in linecurrent. The amount of the voltage drop is the error between the nominal set value andthe actual output. The FLC uses this error voltage to adjust the triggering angles ofrectifier used in the exciter circuit of the generator so that the terminal voltage caches

Figure 8. Plots of terminal voltage and triggering angle from the simulation when the load resistoris switched from 140 ohms to 40 ohms: (a) terminal voltage and (b) triggering angle of three-phasecontrolled rectifier used in excitation circuit.

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up the reference value again. The response time of the FLC is approximately obtainedas 0.2 seconds from the voltage or triggering angle graphs given in Figure 7. Simulationresults for the same operating conditions are given in Figure 8. Comparison of Figures 7and 8 gives very close variations on both terminal voltage and triggering angle.

A similar process applied as a second experiment. However, this time the loadresistor is increased from 40 ohms to 140 ohms while the generator is operated under a40 ohms load resistor. Under this operating condition, the line current is decreased due toincreasing load resistor resulting in a voltage increment in the value of phase to neutralvoltage, as shown in Figures 9 and 10 for implementation and simulation, respectively.Voltage and triggering angle plots from experimental results confirm these of obtainedby simulation.

After the confirmation of the simulation algorithm and the FLC with the resistiveloads, only the experimental parts are done for the following two operating conditionswith the addition of a three-phase induction motor as an additional load to resistive one.While 140 ohms resistive load is on, a three-phase induction motor is suddenly connectedparallel to the resistive load. The screen shot from this operation is given in Figure 11.After awhile, when both 140 ohms resistive load and three-phase induction motor arein use, the switch connecting the induction motor to the circuit is suddenly turned offresulting in the screen shot given in Figure 12. The effects of the induction motor onthe generator voltage and exciter circuit during turned on and off are similar to thoseobtained with the resistive load increment and decrement in the first two tests. Whenthe induction motor is turned on, an additional current due to motor affects the terminalvoltage of the generator causing a voltage drop. On the contrary, when the inductionmotor is turned off, the line current will be reduced causing a voltage increment at theterminal of the generator. The resultant figures from Figure 7 to Figure 12 confirm that

Figure 9. A screen shot of terminal voltage and triggering angle from the experiment when theload resistor is switched from 40 ohms to 140 ohms.

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Figure 10. Plots of terminal voltage and triggering angle from the simulation when the load resistoris switched from 40 ohms to 140 ohms: (a) terminal voltage and (b) triggering angle of three-phasecontrolled rectifier used in excitation circuit.

the FLC takes the required action to keep the terminal voltage of the generator at a setvalue by adjusting the triggering angle of the rectifier supplying power to the excitationcircuit of the generator. The control action takes about 0.2 to 0.3 seconds in order tobring the terminal voltage to its set point.

5. Conclusion

A FL based excitation control scheme for a stand-alone synchronous generator is devel-oped and discussed in this article. The excitation circuit of the synchronous generator isfed through a thyristor controlled rectifier whose triggering angles are determined by afuzzy logic based controller using the difference between reference and actual terminalvoltages as the error signal to be compensated. In order to keep the actual terminal volt-age constant at a desired reference value, a FL based controller designed to act as fast aspossible to compensate the effects of the changes in loads that may vary depending onthe units being fed. FL controlled exciter system acts as a voltage regulator and regulatesthe terminal voltage of the generator similar to that of a classical AVR. Therefore, this

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Figure 11. A screen shot of terminal voltage and triggering angle from the experiment when athree-phase induction motor is suddenly connected parallel to 140 ohms resistive load.

Figure 12. A screen shot of terminal voltage and triggering angle from the experiment when thethree-phase induction motor is suddenly turned off while a 140 ohms resistive load is on.

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FL controlled voltage regulator can be considered as a fuzzy voltage regulator (FVR).Since the controller part is implemented digitally in a computer as a fuzzy logic basedcontroller, FVR becomes inexpensive as well as ineffective from the machine and excitersystem parameters.

A simulation model of the proposed FL control system is developed for the designpurposes. In order to verify this simulation model, a laboratory setup is also establishedusing a 2 kVA synchronous generator feeding a three-phase adjustable load. The proposedcontroller adjusts the triggering angles of the rectifier so that an excitation control isobtained to keep the three-phase terminal voltage of the synchronous generator at aconstant reference value. A comparison of the simulation and experimental results showedsatisfactory performance for the proposed simulation model.

The proposed FVR gives a fast and good tracking performance. It operates on thebasis of a human operator’s thoughts and executes the rules to adjust the system inputby just measuring the output.

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Appendix

Machines’ Parameters

The prime mover: (Separately excited DC motor)

Power rating: 2.94 kW, terminal voltage: 200 V,ra = 1.4 #, La = 71.3 mH, Laf = 1.076 H.

The synchronous machine: (Cylindrical rotor generator)

Power rating: 2 kVA, terminal voltage: 220 V (phase to phase), power factor: 0.8,rs = 1.0 #, Lls = 12 mH, Lmq = Lmd = 111.82 mH, r ′f d = 0.65 #, L′

lf d = 5.608 mH,r ′qr = 0.65 #, L′

lqr = 5.608 mH, p = 2 (number of pole pairs),

ns = 1500 rpm, frequency: 50 Hz, J = 0.146 kgm2, Bm = 0.018688 Nms.