1 Fuzzy Logic Approach to Curtail Number of Controllers for Voltage Control in Grid Connected Wind Farms Mohammed Shareeq M.T., Tukaram Moger, Member, IEEE, Thukaram Dhadbanjan, Senior Member, IEEE. Abstract—In the past few years, the penetration of wind energy to the grid has been drastically increased. However, the variable nature of wind speed has an impact on power quality. Therefore, the voltage and reactive power control are necessary in a grid connected wind farms due to stochastic nature of wind speed. The wind connected system may consist of large number of voltage controllers i.e. on-load tap changing transformer (OLTC), generator voltage and switchable var compensator (SVC). As per an operator’s point of view, it is difficult to move so many controllers in a short period of time. Hence, it is important to optimize not only the reactive power dispatch for voltage control also the total number of controllers to reduce the complexity of the problem. A technique using fuzzy logic inference system is used to curtail the number of controllers in wind connected power system is presented. In this approach load bus voltage deviations are minimized by changing the controllers according to their sensitivity. 20-bus radial wind system and 163-bus equivalent of Indian southern grid wind system are considered for illustration. The results are compared with linear programming optimization technique and encouraging conclusions are drawn. Index Terms—voltage control, renewable energy, wind power system, fuzzy logic controller. I. I NTRODUCTION Wind energy is one of the most promising and fast growing renewable energy sectors in the world. Wind energy is readily available and is an inexhaustible energy source, which can be considered as an alternative to fossil fuels. Wind energy is clean, widely distributed, environmental friendly and uses no fuel. Due to the intermittent nature of wind, wind farms adversely affect the voltage and frequency of the grid. It is necessary to control the bus voltages and reactive power in the system so that the power quality of grid connected wind farms is maintain within the acceptable limits. So a suitable reactive power optimization technique has to be employed. Reactive power optimization and voltage control in power system has received greater attention from researchers. Several methods/approaches have been proposed in the literature [1]– [5] for optimally dispatching reactive power to improve the voltage profile in wind farms. In [2], the authors propose a trust region framework for co-coordinating the reactive power output of grid connected wind generators for voltage stability enhancement with full set of controllers. It is desirable to use minimum number of controllers to reduce the complexity of the problem and operating time of The authors are with the Department of Electrical Engineering, Indian Insti- tute of Science, Bangalore, INDIA, 560012 e-mail: {[email protected]} the control action. Many of the existing optimal power flow (OPF) methods [6]–[8] use all of the controllers in solving the reactive power optimization problem. But selecting most effective controllers precisely could be an elusive task if we consider the complex and varying nature of the large power system network. In [9], the authors stated that there is no way to select a subset of the most important control actions from the total set of control actions in an OPF solution since the actions are not ranked and importance of an action is not necessarily related to its magnitude. So we have to select the controllers in such a way that the final solution is close to optimum. Artificial intelligence techniques like fuzzy logic would be appropriate for this purpose. Hence, fuzzy logic controller (FLC) is used to curtail the number of controllers. There have been many applications of fuzzy systems to reactive power control problem. A fuzzy rule base system is used in [10], [11] to select the controllers, their movement direction and step size. In [12], author proposed a fuzzy linear programming (LP) approach to the reactive power and voltage control problem. Here, the objective and constrains are mod- eled using fuzzy sets and corresponding linear membership functions are defined and solved using LP technique. In this paper, instead of modeling the system parameters rigidly like in conventional optimization methods, they are mapped to corresponding fuzzy set notations. That is, voltage deviation of load buses and sensitivity of control variables are translated in to fuzzy domain. Controllers are given priorities according to their sensitivity (controlling ability) towards the voltage at the critical buses. That will ensure, only the significant controllers are used in system operation. Therefore, the complexity of the problem is reduced and also the voltage control operation is fast, which are the desirable features of a real time power system operation. II. METHODOLOGY Consider n bus grid connected wind system with g gen- erators, s switchable var compensators (SVCs), t on-load tap changing transformers (OLTC) and r remaining buses. Here, we assume that wind generators are modeled as variable speed doubly fed induction generator (DFIG), which can either inject or consume reactive power according to the system requirements. DFIG can be operated under constant power factor mode or constant voltage mode. In this paper, it is assumed that DFIG is operating under constant voltage control mode, where it can be considered as PV node if reactive power 978-1-4799-5141-3/14/$31.00 c ⃝ 2014 IEEE
Transcript
1
Fuzzy Logic Approach to Curtail Number ofControllers for Voltage Control in Grid Connected
Abstract—In the past few years, the penetration of wind energyto the grid has been drastically increased. However, the variablenature of wind speed has an impact on power quality. Therefore,the voltage and reactive power control are necessary in a gridconnected wind farms due to stochastic nature of wind speed.The wind connected system may consist of large number ofvoltage controllers i.e. on-load tap changing transformer (OLTC),generator voltage and switchable var compensator (SVC). Asper an operator’s point of view, it is difficult to move so manycontrollers in a short period of time. Hence, it is important tooptimize not only the reactive power dispatch for voltage controlalso the total number of controllers to reduce the complexity ofthe problem. A technique using fuzzy logic inference system isused to curtail the number of controllers in wind connected powersystem is presented. In this approach load bus voltage deviationsare minimized by changing the controllers according to theirsensitivity. 20-bus radial wind system and 163-bus equivalent ofIndian southern grid wind system are considered for illustration.The results are compared with linear programming optimizationtechnique and encouraging conclusions are drawn.
Index Terms—voltage control, renewable energy, wind powersystem, fuzzy logic controller.
I. INTRODUCTION
Wind energy is one of the most promising and fast growingrenewable energy sectors in the world. Wind energy is readilyavailable and is an inexhaustible energy source, which canbe considered as an alternative to fossil fuels. Wind energyis clean, widely distributed, environmental friendly and usesno fuel. Due to the intermittent nature of wind, wind farmsadversely affect the voltage and frequency of the grid. It isnecessary to control the bus voltages and reactive power inthe system so that the power quality of grid connected windfarms is maintain within the acceptable limits. So a suitablereactive power optimization technique has to be employed.Reactive power optimization and voltage control in powersystem has received greater attention from researchers. Severalmethods/approaches have been proposed in the literature [1]–[5] for optimally dispatching reactive power to improve thevoltage profile in wind farms. In [2], the authors propose atrust region framework for co-coordinating the reactive poweroutput of grid connected wind generators for voltage stabilityenhancement with full set of controllers.
It is desirable to use minimum number of controllers toreduce the complexity of the problem and operating time of
The authors are with the Department of Electrical Engineering, Indian Insti-tute of Science, Bangalore, INDIA, 560012 e-mail: {[email protected]}
the control action. Many of the existing optimal power flow(OPF) methods [6]–[8] use all of the controllers in solvingthe reactive power optimization problem. But selecting mosteffective controllers precisely could be an elusive task if weconsider the complex and varying nature of the large powersystem network. In [9], the authors stated that there is noway to select a subset of the most important control actionsfrom the total set of control actions in an OPF solution sincethe actions are not ranked and importance of an action is notnecessarily related to its magnitude. So we have to select thecontrollers in such a way that the final solution is close tooptimum. Artificial intelligence techniques like fuzzy logicwould be appropriate for this purpose. Hence, fuzzy logiccontroller (FLC) is used to curtail the number of controllers.
There have been many applications of fuzzy systems toreactive power control problem. A fuzzy rule base system isused in [10], [11] to select the controllers, their movementdirection and step size. In [12], author proposed a fuzzy linearprogramming (LP) approach to the reactive power and voltagecontrol problem. Here, the objective and constrains are mod-eled using fuzzy sets and corresponding linear membershipfunctions are defined and solved using LP technique.
In this paper, instead of modeling the system parametersrigidly like in conventional optimization methods, they aremapped to corresponding fuzzy set notations. That is, voltagedeviation of load buses and sensitivity of control variables aretranslated in to fuzzy domain. Controllers are given prioritiesaccording to their sensitivity (controlling ability) towardsthe voltage at the critical buses. That will ensure, only thesignificant controllers are used in system operation. Therefore,the complexity of the problem is reduced and also the voltagecontrol operation is fast, which are the desirable features of areal time power system operation.
II. METHODOLOGY
Consider n bus grid connected wind system with g gen-erators, s switchable var compensators (SVCs), t on-load tapchanging transformers (OLTC) and r remaining buses. Here,we assume that wind generators are modeled as variablespeed doubly fed induction generator (DFIG), which can eitherinject or consume reactive power according to the systemrequirements. DFIG can be operated under constant powerfactor mode or constant voltage mode. In this paper, it isassumed that DFIG is operating under constant voltage controlmode, where it can be considered as PV node if reactive power978-1-4799-5141-3/14/$31.00 c⃝ 2014 IEEE
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of the wind generator is well within the limits otherwise PQnode.
The main objective of this work is to reduce the voltagedeviations of the load buses. It can be stated in mathematicalform as,
V e =n∑
j=g+1
[V d
j − V aj
]2(1)
where V dj is the desired voltage at load bus j considered as
nominal voltage (1.0 p.u) and V aj is the actual voltage at load
bus j.The control variables are transformers tap setting, generators
voltage setting and SVCs setting, and the dependent variablesare reactive power of generators and voltage magnitude of theload buses (including SVC buses). Both control variables anddependent variables have upper and lower limits. These limitshave to be honored during the process.
A. Calculation of Controlling Ability of the Controllers
Let X be the row vector of the controllers in the followingorder. 1,2,...,t are OLTCs, t+1,t+2,...,t+g are generators andt+g+1,...,t+g+s are SVCs. Let Cjm be the controlling abilityof the controller Xm on jth load bus where m is the controllerindex. Cjm can be defined as,
Cjm = Hjm ×Mm (2)
where Mm is the margin available for the controller Xm andHjm is the sensitivity of controller Xm with respect to jth
load bus.Hjm can be calculated as follows.
Hjm =∂V e
j
∂Xm= 2
(V dj − V a
j
)(−Sjm) (3)
where j=g+1,g+2,...,n; m=1,...,t,...t+g,...,t+g+s; V ej is the
voltage error to be corrected at jth load bus and Sjm bethe linearised sensitivity factor of load bus j with respect tocontroller Xm.
The relationship between the net reactive power change atany node due to change in the transformer tap settings andvoltage magnitudes can be written as, ∆Qg
∆Qs
∆Qr
=
A1 A2 A3 A4
A5 A6 A7 A8
A9 A10 A11 A12
∆Tt
∆Vg
∆Vs
∆Vr
(4)
The sub-matrices A1 to A12 are the corresponding terms ofthe partial derivatives ∂Q/∂T and ∂Q/∂V , where
∂Qk
∂Tkm=
2
a3V 2k ykmsin αkm+
1
a2ykmVkVmsin (δk−δm−αkm)
(5)∂Qm
∂Tkm=
1
a2ykmVkVmsin (δm − δk − αkm); k : tap side bus
(6)∂Qr
∂Tkm= 0, r ̸= k,m (7)
and∂Qk
∂Vk=
Qk
Vk−BkkVk (8)
∂Qk
∂Vm= YkmVksin (δk − δm − θkm) (9)
Then, transferring all the control variables to the right handside and the dependent variables to the left hand side, andrearranging the equations.∆Qg
∆Vs
∆Vr
=[S] ∆Tt
∆Vg
∆Qs
(10)
where [S] is the linearised sensitivity matrix relating dependentand control variables. The detailed mathematical formulationof the sensitivity matrix [S] is discussed in [7].
B. Fuzzy Logic Controller (FLC)
A large wind farm consists of several widely distributedwind generators and on-load-tap-changing (OLTC) transform-ers for voltage control. The conventional reactive power opti-mization technique considers all the controllers in wind farmsto improve the voltage profile. And it keeps on changingthe position of these controllers from time to time. This isnot feasible in an operator point of view. Also it will makethe system more complex. Fuzzy logic technique is used toreduce the number of controllers in the proposed approach.A FLC has to select certain number of controllers from thelarge collection of voltage controllers in a wind farms. But thisselection should be done in an effective way, so that the voltageimprovement can be achieved by varying the positions of theselected controllers settings. And the remaining controllerswill be considered as non-controlling type.
A FLC is designed to select the controllers, their move-ment direction and step size. The input variables are voltagedeviations (∆V ) of the load buses and controlling ability(C) of the controllers in the system. These input parametersare transformed in to fuzzy set notations with the help ofmembership functions. The membership functions for the inputvariables are shown in Fig. 1 and 2. The voltage deviation
Fig. 1. Membership function for the voltage deviation
(∆V ) for a load bus j is calculated by
∆Vj = V aj − V d
j (11)
A rule base system consisting of 49 rules is developed is givenin Table I. The meaning of the linguistic variables in Table Iis: NL (negative large), NM (negative medium), NS (negativesmall), Z (zero), PS (positive small), PM (positive medium),
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Fig. 2. Membership function for the controlling ability
TABLE IFUZZY RULES
∆VjControlling ability (Cjm)
NL NM NS Z PS PM PLNL PL PM PS Z NS NM NLNM PM PS PS Z NS NS NMNS PS PS Z Z Z NS NSZ Z Z Z Z Z Z Z
PS PS PS Z Z Z NS NSPM PM PS PS Z NS NS NMPL PL PM PS Z NS NM NL
PL (positive large). These 7 terms are used to describe theinput variables (i.e. voltage deviation and controlling ability).
The output parameter of the FLC system is the new settingsof the OLTCs tap, generators voltage and SVCs. The outputparameter also includes 7 terms. These terms with their impli-cation are given in Table II. The output membership functionfor the controller settings is shown in Figure 3. The controllers
Fig. 3. Output membership function for the controller settings
TABLE IIIMPLICATION OF FUZZY OUTPUT PARAMETERS
Output parameter ImplicationPL 3 positive stepsPM 2 positive stepsPS No changeZ No change
NS No changeNM 2 negative stepsNL 3 negative steps
are given priorities (weights) according to their controllingabilities towards the critical load buses. These weights will
affect the final settings of the controllers. If a controller ishaving highest sensitivity towards a load bus where voltagedeviation is large then FLC will suggest 2 steps change (PM orNM) or 3 steps change (PL or NL). But if a controller is havingno significant influence on critical buses or there is not enoughmargin available for a controller, then FLC will suggest Z,PS or NS. If the control action suggested by the FLC is Z,PS or NS then no change is made in the controller setting.Thus only significant controllers are changed to improve thevoltage profile. In this way controllers and their movementsare curtailed.
C. Giving Priorities to the Controllers
For illustrative purpose, let us consider a sample systemwith three generators G1, G2 and G3, five OLTC T1,...,T5 andfour SVCs S1,. . . ,S4. Let 5 load buses L1,. . . ,L5 are violatingthe voltage limit (0.95− 1.05) p.u. For each of this criticalload buses the highest sensitive generator, OLTC, SVC can befound. Let us consider a sample as follows.
TABLE IIIMOST SENSITIVE CONTROLLERS FOR SAMPLE SYSTEM
Load Most sensitive controllers
Bus Generator OLTC SVCL1 G1 T1 S1L2 G1 T1 S3L3 G3 T3 S3L4 G3 T1 S3L5 G3 T3 S1
The idea of giving weights to the controllers according totheir controlling ability towards the critical/violated buses canbe understood from Table III. We can see that generator G2,transformers T2,T4,T5 and SVCs S2,S4 are not in the list ofmost sensitive controllers. So these controllers are given lowerpriorities compared to the most sensitive controllers. Also itshould be noted that, since we are considering the magnitudeof the voltage deviation of the load buses as one of theinput membership functions, it (voltage deviation magnitude)also will have significant effect on the final settings of thecontrollers.
From Table III, it is clear that for a particular controller, theproposed FLC approach may suggest different control actions.For example, in the above sample system, generator G1 isthe highest sensitivity generator for load buses L1 and L2.Let the control action for G1 suggested by FLC is 3 positivesteps for L1 and 2 positive steps for L2. In that case, thehighest setting for generator (G1) is selected to decide thefinal control setting of the generator. Similar method is alsoused SVC settings. For OLTC adjustment, the algebraic sum ofthe column elements of the H matrix from (3) correspondingto the transformer under consideration is found and the signis observed. A positive sign indicates that the reduction in tapimproves the voltage and a negative sign suggests that increasein tap will improve the voltage. So, if the suggested controlaction by FLC is matching with this sign, then the correctionis made, otherwise no correction is made.
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III. COMPUTATIONAL PROCEDURE
Following steps are executed in the proposed FLC approachto curtail the number of controllers for improvement in thesystem voltage profile.
1) Read input data and perform load flow analysis.2) Check for voltage violations.3) Advance fuzzy iteration count.4) Compute the sensitivity matrix [S] using (10).5) Calculate voltage deviation sensitivity [H] for all con-
trollers using (3).6) Compute controllability matrix [C] using (2).7) Design FLC as defined in Section II B.8) Feed the input parameters (voltage deviations and con-
trolling abilities of the controllers) to the FLC andproduce fuzzy output.
9) Transform fuzzy output to discrete controller settingsusing Table II.
10) Using the new control variable settings, again performthe load flow analysis.
11) Check for voltage violations. If yes go to Step 3.Otherwise go to Step 12.
12) Print the results and terminate the program.
IV. RESULTS AND DISCUSSIONS
A. 20-bus wind system
A 20-bus wind system is considered to illustrate the pro-posed approach. The single line diagram of the wind systemis shown in Fig. 4. The system consists of 9 generators (out ofwhich 8 are wind generators of same power rating), 9 OLTCsand one SVC at bus 10. Hence, total number of controllers is19 (9T, 9G, 1SVC). The system is considered on 100 MVAbase. System line data is taken from [13] and the remainingdata is given in the Appendix. The power rating of each windgenerator is obtained from the power curve, which is normallyprovided by the manufacturer. For system studies, it is assumedthat the wind speed is such that the output power of each windgenerator is 2.3 MW. Initially, it is assumed that all transformertaps are at 1.0 (nominal value), the generator voltage at 1.0p.u and zero SVC compensation.
Based on the initial load flow results, 19 buses wereviolating the lower voltage limit (0.95 p.u). Also the reactivepower output of the wind generators was hitting the upper limit(0.775 MVAr) as shown in Table IV. Total active power losswas 0.259 MW. Then fuzzy computations were carried out todetermine the new settings of the controllers with the desiredobjectives. Again load flow analysis is carried out with the newcontroller settings, it is observed that all bus voltages are wellwithin the limits. There is a considerable power loss reductionand overall system performance is improved (as shown inTable V). The proposed FLC approach changed the setting ofonly 12 controllers (5T, 6G, 1SVC) out of 19 to achieve thedesired voltage improvement. FLC approach is compared withthe conventional linear programming (LP) technique and theresult of comparison is presented in Table IV-VII. From theseTables, it can be inferred that the results of the FLC approachis closely matching with LP based optimization approach.
Fig. 4. Single line diagram of 20-bus wind system
TABLE IVREACTIVE POWER OUTPUT OF GENERATORS FOR 20-BUS WIND SYSTEM
A 24-bus, 400/220kV practical equivalent system, which is apart of southern region power grid along with 3 wind farms (A,B and C) is considered to test the proposed approach. The wind
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TABLE VIITRANSFORMERS TAP SETTING FOR 20-BUS WIND SYSTEM
farms A, B and C are connected at buses 76 (HOODY), 74(SALEM) and 81 (SOMANAHALLI) respectively. The windfarms are connected to the grid through the power transformersof rating 220/33 kV, 100 MVA. The system consists of 4conventional grid generators, 11 grid transformers out of which7 are OLTCs and 4 SVC buses. In wind farm A, there are twogroups of 10 wind generators, wind farm B consists of twogroups of 12 wind generators and wind farm C comprising ofthree groups of 8 wind generators. Totally, there are 68 windgenerators (all are of the same power rating of 2.3 MW forthe given wind speed) along with 68 OLTC wind transformersof 33/0.69 kV, 2.7 MVA. Single line diagram is shown in Fig.5 and the system data is taken from [13].From the initial load flow results, it has been observed that
Fig. 5. Single line diagram of 163-bus wind system
77 buses are violating the lower voltage limit (0.95 p.u) andtotal active power loss was 58.745 MW. After applying theFLC approach all bus voltages are well within the limitsand considerable power loss reduction is obtained as shownin the Table VIII. In this case, from the proposed approachonly 105 controllers (50T, 51G, 4SVC) out of 151 controllers
(75T, 72G, 4 SVC) are utilized to achieve the desired voltageimprovement. Again, the FLC approach is compared withthe conventional LP technique. The comparative result of thereactive power output of grid generators and SVCs, and thesystem performance parameters are given in Table VIII.
The comparative analysis of the reactive power output of
-0.4
-0.2
0
0.2
0.4
0.6
0.8
5 10 15 20 25 30 35
Rea
ctiv
e po
wer
(MV
Ar)
Wind generators
InitialLP
FLC
Fig. 6. Reactive power output of wind generators (Bus 5-38)
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
40 45 50 55 60 65 70
Rea
ctiv
e po
wer
(MV
Ar)
Wind generators
InitialLP
FLC
Fig. 7. Reactive power output of wind generators (Bus 39-72)
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
5 10 15 20 25 30 35
Vol
tage
mag
nitu
de (p
.u.)
Wind generator bus
InitialLP
FLC
Fig. 8. Voltage magnitude of wind generator (Bus 5-38)
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
40 45 50 55 60 65 70
Vol
tage
mag
nitu
de (p
.u.)
Wind generator bus
InitialLP
FLC
Fig. 9. Voltage magnitude of wind generator (Bus 39-72)
wind generators from the proposed approach and LP technique
6
is shown in Fig. 6 and 7. The voltage profile of wind generatorsis shown in Fig. 8 and 9. From the above results, it canbe observed that the voltage profiles from the FLC approachwith less number of controllers is in close agreement withthe results of conventional LP technique with all controllers.Hence, the FLC approach is very effective for improving thevoltage profile in large wind farms and it makes sure that thecomplexity in the controlling procedure is reduced.
TABLE VIIIRESULT SUMMARY OF 163-BUS INTER-CONNECTED WIND SYSTEM
In the paper, an approach has been proposed using fuzzylogic inference system to improve the voltage profile of windconnected system with reduced number of controllers. Theproposed approach is tested on the 20-bus radial and 163-bus interconnected wind systems, and encouraging results areobtained. The results are compared with the conventionallinear programming optimization technique with all controllersand it is found that the results of the FLC approach is closely
in agreement with the LP based technique even though theFLC approach is not an optimization based approach. Theadvantage of the proposed approach is that it used only fewcontrollers of high sensitivity to achieve the desired objectivesso that the reduction in complexity of the problem is ensuredand also the voltage control operation is fast, which are thedesirable features of a real time power system operation.
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