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Adaptive PI Controller for Voltage Regulation in Power Systems

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Static synchronous compensator (STATCOM) provides the means to improve quality and reliability of a power system as it has the functional capability to handle dynamic disturbances, such as transient stability and power oscillation damping as well as to providing voltage regulation. In this paper, a robust adaptive PI-based optimal fuzzy control strategy is proposed to control a STATCOM used in distribution systems. The proposed intelligent strategy is based on a combination of a new General Type-II Fuzzy Logic (GT2FL) with a simple heuristic algorithm named Teaching Learning Based Optimization (TLBO) Algorithm. The proposed framework optimally tunes parameters of a Proportional-Integral (PI) controller which, similar to most of other researchers regarding control of STATCOM, are in charge of controlling the device. The proposed controller guaranties robustness and stability against uncertainties caused by external disturbances or ever-changing nature of the power systems. The TLBO optimizes the parameters of the controller as well as the input and output membership functions. To validate the efficiency of the proposed controller, the obtained simulation results are compared with those of the two most recent researches applied in this field, namely, conventional Proportional Integral (PI) controller and Optimal Fuzzy PI (OFPI) controller. Results demonstrate the successfulness and effectiveness of the proposed online-TLBO General Type-2 Fuzzy PI (OGT2FPI) controller and its superiority over conventional approaches.

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Adaptive PI Controller for Voltage Regulation in Power Systems

  1. 1. Research article Adaptive PI controller to voltage regulation in power systems: STATCOM as a case study Mohammad Reza Tavana, Mohammad-Hassan Khooban n , Taher Niknam Department of Electrical Engineering, Shiraz University of Technology, Iran a r t i c l e i n f o Article history: Received 1 January 2016 Received in revised form 18 August 2016 Accepted 29 September 2016 Available online 25 November 2016 Keywords: Online intelligent control General Type-2 Fuzzy Logic Control Static synchronous compensator (STAT- COM) Teaching Learning Based Optimization (TLBO) Voltage regulation a b s t r a c t Static synchronous compensator (STATCOM) provides the means to improve quality and reliability of a power system as it has the functional capability to handle dynamic disturbances, such as transient stability and power oscillation damping as well as to providing voltage regulation. In this paper, a robust adaptive PI-based optimal fuzzy control strategy is proposed to control a STATCOM used in distribution systems. The proposed intelligent strategy is based on a combination of a new General Type-II Fuzzy Logic (GT2FL) with a simple heuristic algorithm named Teaching Learning Based Optimization (TLBO) Algorithm. The proposed framework optimally tunes parameters of a Proportional-Integral (PI) controller which, similar to most of other researchers regarding control of STATCOM, are in charge of controlling the device. The proposed controller guaranties robustness and stability against uncertainties caused by external disturbances or ever-changing nature of the power systems. The TLBO optimizes the parameters of the controller as well as the input and output membership functions. To validate the efficiency of the proposed controller, the obtained simulation results are compared with those of the two most recent researches applied in this field, namely, conventional Proportional Integral (PI) controller and Optimal Fuzzy PI (OFPI) controller. Results demonstrate the successfulness and effectiveness of the proposed online-TLBO General Type-2 Fuzzy PI (OGT2FPI) controller and its superiority over conventional ap- proaches. & 2016 ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Over the recent decades, power systems are experiencing rapid changes caused by deregulation of the power industry as well as fast growing demand. As a result, new considerations should be taken into account to ensure stability and reliability of the power systems [1]. Accordingly, new apparatuses are introduced to handle such problems and, consequently, improve the perfor- mance of the power grids. Flexible Alternative Current Transmis- sion Systems (FACTS) devices are one of the possible solutions to the above-mentioned issues. FACTS devices are able to enhance the controllability of both active and reactive power. If used alongside with proper controllers, FACTS devices will be able to improve the dynamic reaction of the system while facing transient, small signal and voltage stability [1]. Static synchronous compensator (STATCOM) is a shunt FACTS device that takes advantage of power electronics to control the flow of power to enhance transient stability of power grids [2]. To regulate voltage at its terminals, a STATCOM device controls the volume of reactive power that is injected into or absorbed from the grid. When the voltage of the grid is lower than desired, the STATCOM generates reactive power (capacitive STATCOM) to in- crease the voltage. Inversely, when system voltage is higher than expected, it absorbs proper amount of reactive power (inductive STATCOM) to decrease the voltage. So far, many different control methods have been proposed to control STATCOM dynamic [3–11]. The majority of the presented approaches in the literature include some sort of linearization of equations of the voltage source converters (VSC) average value model at a specific equilibrium [3–11]. A STATCOM based on pro- portional-integral (PI) controller was first proposed in [3]. Since then, several different PI controllers have been presented in the literature. Results reported in the literature indicate that satisfac- tory performance will be obtained from PI based STATCOM if the parameters are tuned properly, no matter if a two-level converter [4–6] is used or a multilevel converter is applied [7–11]. The main drawback of PI based STATCOM is that its performance might decline gravely if operating conditions changes from the assumed Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/isatrans ISA Transactions http://dx.doi.org/10.1016/j.isatra.2016.09.027 0019-0578/& 2016 ISA. Published by Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: khooban@sutech.ac.ir, mhkhoban@gmail.com (M.-H. Khooban). ISA Transactions 66 (2017) 325–334
  2. 2. situations, especially in the case of a large disturbance like sudden load variation or a short-circuit fault nearby. So far, a few researches have addressed assigning gains of the STATCOM PI controller to enhance voltage stability and to decrease the time required to tune the gains. In [3,6,12–16], linear quadratic regular (LQR) based linear optimal controls are presented. Such approaches highly rely on the expertise of the designer to assign optimal parameters. On the other hand, in [4], an STATCOM state feedback framework is presented which is based on a zero set concept. Again, similar to pervious works such as [12–14], gains of the state feedback controller are heavily relied on the designer's choice and experience. In [14–16], a fuzzy based PI controller is introduced to properly tune the gains of the PI controller. How- ever, the proposed approach still depends on designer's initial choices of the actual and deterministic gains. In [17], a population- based optimization algorithm is presented to optimally choose and tuning the gains of the PI controller. However, the method will have difficulties for being applied in the real-world applications as it usually takes a long time to calculate the gains of the controller. It seems that a tradeoff between performance and the variety of possible operation conditions still should be struck during the process of designer's decision-making. Therefore, efficient perfor- mance may not be always obtainable in a certain operating condition. Fuzzy Logic is widely applied in different applications such as system identification, control and modeling of nonlinear dynamic systems [18,19]. In researches such as [20,21], several controllers based on combination of fuzzy logic with PI or PID controllers are presented and different approaches are proposed to improve the performance of the resulted hybrid controller. It should be noted that tuning coefficients of PID controllers might be a difficult, time consuming and costly procedure [22,23]. In fact, a proficient gainer regularly tries to control the process by adjusting different gains of controller according to output error and/or rate of error. Lately, a large number of researchers pay attention to general type-2 fuzzy sets and systems because they have the capacity to deal with uncertainties [24–27]. The first one who presented Type- 2 fuzzy sets as a development of type-1 fuzzy sets was Zadeh in 1975 [26]. Since then, type-2 fuzzy logic systems especially IT2FLSs due to their calculation simplicity have been successfully applied to engineering areas. This illustrates that when IT2FLSs face with different uncertainties such as dynamic uncertainties, rule un- certainties, external disturbances and noises, they do better in comparison with type-1 fuzzy logic systems (T1FLS). See [27]. The rules which are made in a fuzzy logic system by the use of ac- cessible information may be uncertain. Unlike interval type-2 fuzzy sets (IT2FS) and type-1 fuzzy sets (T1FS), General type-2 fuzzy sets can deal with rule uncertainties usefully. As general type-2 fuzzy sets and systems are computationally complex, just IT2FLSs have been mainly used in literatures so far. But, Liu [28] proposed a useful way to compute centroid and type reduction of GT2FLS by using a newly introduced plane representation theorem. In this paper an online TLBO based General Type 2 Fuzzy Tuning PI (OGT2FPI) controller is presented. The proposed fra- mework is simple and does not have complexities of the pre- viously presented methods in the literature. The parameters of input and output membership functions of the fuzzy controller's coefficients are optimized simultaneously by TLBO. The proposed framework can be easily utilized in PI controllers of STATCOM in power systems. Performance of the proposed controller is eval- uated on a test case power system owning a ±100-MVAR STAT- COM with a 48-pulse VSC and connected to a 500-kV bus. Simu- lation results demonstrate the superiority of the proposed con- troller compared to OFPI and conventional PI controller. 2. The dynamic model of STATCOM 2.1. Advantages of STATCOM in power systems With the ongoing deregulation of the electric utility industry, numerous changes are continuously being introduced to a once predictable business. With electricity increasingly being con- sidered as a commodity, transmission systems are being pushed closer to their stability and thermal limits while the focus on the quality of power delivered is greater than ever. In addition, dy- namic reactive power support is becoming more important, especially in urban areas where local (i.e., at the load) generation is being reduced or eliminated. In the deregulated utility environ- ment, financial and market forces will demand a more optimal and profitable operation of the power system with respect to genera- tion, transmission, and distribution. Now, more than ever, ad- vanced technologies are paramount for the reliable and secure operation of power systems. Power electronic based equipment, such as FACTS controllers, with their capability to rapidly respond to system events, increase power transfer limits, and improve the quality of power delivered, constitute one of the most-promising technical advancements to address the new operating challenges being presented today [1,2]. This paper focuses on one such FACTS controller for voltage support as a dynamic reactive power (var) source, namely the static compensator (STATCOM). Typically, the first step in providing voltage/var support in a power system is with the application of shunt capacitors, shunt reactors, and transformer on-load-taps (OLT). Therefore, combined control of this discrete-acting existing equipment with a continuously con- trolled dynamic device, such as a STATCOM, becomes important for the overall technical and economic operation of the system [10]. 2.2. STATCOM description Fig. 1 demonstrates the equivalent circuit of a STATCOM. In this scheme, the series resistance Rs represents the sum of the inverter conduction losses and the transformer winding resistance losses. The leakage inductance of the transformer is represented by Ls. The resistance Rc which is in shunt with the capacitor C also de- note for the losses related to the switching of the inverter as well as the losses of the capacitor. Vas, Vbs and Vcs also denote the three- phase output voltages of STATCOM; moreover, Val, Vbl and Vcl re- present voltages of the three- phase bus; and, ias, ibs and ics are the output currents of the three-phase STATCOM [2,6]. 2.3. The dynamic model of STATCOM Mathematical model of a three-phase STATCOM can be given as follows [2,4,6]: = − + − ( ) L di dt R i V V 1s as s as as al = − + − ( ) L di dt R i V V 2s bs s bs bs bl = − + − ( ) L di dt R i V V 3s cs s cs cs cl ( ) ( )= − + + − ( ) ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡⎣ ⎤⎦ d dt CV t V i V i V i V t R 1 2 4 dc as as bs bs cs cs dc c 2 2 Taking advantage of abc/dq transformation, Eqs. (1) to (4) can be simplified as follows: M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334326
  3. 3. ω α ω α α α = − − − − − − − ( ) ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ d dt i i V R L K L R L K L K C K C R C i i V L V V cos sin 3 2 cos 3 2 sin 1 1 0 5 ds qs ds s s s s s s c ds qs ds s dl ql where ids and iqs respectively represent the currents of d and q corresponding to ibs, ibs, and ics; the relation between the dc vol- tage and the peak phase-to-neutral voltage on the ac side is de- noted by factor K; Vds represents the voltage of the dc-side; α denoted the phase angle at which the voltage of the STATCOM leads the bus voltage; speed of the rotating angle of the voltage vector is denoted by ω; and Vdl and Vql are respectively the d and q axis voltage corresponding to Val,Vbl and Vcl. Since Vql is assumed to be 0, considering the definition of the instantaneous active and reactive power, (6) and (7) can be obtained as bellow [2,4]: = ( ) dl V i 3 2 6dl ds = ( ) ql V i 3 2 7dl qs Given to the above mentioned equations, the traditional control strategy can be obtained, and accordingly, the control block dia- gram of the STATCOM is shown in Fig. 2 [2]. As demonstrated by Fig. 2, the phase-locked loop (PLL) is in charge of providing a synchronizing signal that will be used as the reference angle for the measurement system. Measured voltage of the bus line Vm is compared to the reference voltage Vref, and accordingly reactive reference current Iref will be provided by the voltage regulator. The allowable voltage error at the rated reactive current flow is denoted by droop factor Kd. The reactive current of the STATCOM Iq is compared with reference current Iqref, and the output of the current regulator is calculated using the the angle phase shift between the inverter voltage and the the system vol- tage. Given the upper bound for reactive power that can be gen- erated by the STATCOM, a limit will be imposed on the value of control that is denoted by the value of limiter. 3. General Type-II Fuzzy Logic Control A GT2FS in a universal set X can be defined as ∫μ̃= ( ) ∈ ( ) ̃ A x x x X / 8 A ∫μ ( )= ( ) ∈ ∈[ ] ( ) ̃ x f u u u J J, 0, 1 9 A x x x where in this formula μ ( )̃ xA is called a secondary membership function (MF) and ( )f ux is called secondary grade; Jx is the domain of the secondary MF which is called primary membership and u is a fuzzy set in [0, 1]. Fig. 3 illustrates a GT2FS where the upper and lower MFs are triangular and its secondary MF is also triangular. When ( )=f u 1x IT2FS is obtained that demonstrate a uniform un- certainty in the primary membership function and is simply Fig. 1. The general scheme of STATCOM. Fig. 2. The block diagram of PI controller for STATCOM. M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334 327
  4. 4. described by its lower μ̲ ( )˜ xA and upper μ¯ ( )˜ xA MFs. Because of calculation simplicity, especially in the type reduction, many re- searchers use interval type-2 fuzzy sets instead of general type-2 fuzzy sets [25,28,29] (Fig. 3). Lately, Liu [28] presented a new method for GT2FSs which is theoretically and computationally effective. Because this method resembles the α-cut for type-1 fuzzy sets, it is named a α-plane for type-2 fuzzy sets. ̃αA is the denotation of An α-plane representa- tion for a GT2FS ̃A. It is the union of all primary MFs whose sec- ondary grades are greater than or equal to the special value α: ∫μ̃ = ( ) ∈ ( ) α ̃αA x x x X / 10 A ∫μ α ( )= ( )≥ ∈ ∈[ ] ( ) ̃α x f u u u J J, 0,1 11 A x x x Then a GT2FS ̃A based on α-plane representation theorem can be demonstrated in the following form: α̃= ⋃ ̃ ( )α α ∈[ ] A A/ 120,1 It is a beneficial representation because α ̃αA/ can be seen as an IT2FS with the secondary grade of level α. As a result, several IT2FSs may be made from the decomposition of a general type-2 fuzzy set with a corresponding level of α for each, where α = { … ( − ) }K K K0,1/ , , 1 / , 1 . In simpler terms, a general type-2 fuzzy logic system can be seen as a huge collection of IT2FLSs with one IT2FLS for each value of α. However, Liu [30] showed that using only 5 to 10 α-plane can get the required accuracy for cen- troid calculation. Fig. 4 illustrates the new designing for a general type-2 fuzzy system based on α-plane representation. In general, a GT2FLS is made of a fuzzifier; fuzzy rule-based; fuzzy inference engine; type reducer and defuzzifier. Fuzzifier maps real values into fuzzy sets. Singleton fuzzifier whose output is a single point of a unity membership grade is used in this paper because it is simple. Fuzzy rule base includes fuzzy IF-THEN rules. In the following The jth rule in the GT2FLS is shown: ̃ ̃ … ̃ ̃ = … ( ) R If x is F and x is F and x is F Then y is G j M : 1, 2, 13 j j j n n j j 1 1 2 2 where xi for = …i n1, , and y are the input and output of the GT2FLS, ̃Fi j and ̃G j are general type-2 antecedent and the con- sequent sets. A mapping from input GT2FSs to output GT2FSs is given by the inference engine that merges rules. Because α-plane representation for fuzzy set is used, the firing set for each related IT2FS is shown as following: ( ) ( ) ( )= ̲ ¯ ( )α α α ⎡ ⎣⎢ ⎤ ⎦⎥F X f X f X, 14 j j j ( ) μ μ μ̲ = ̲ * ̲ *…* ̲ ( )α ˜ ˜ ˜ α α α f X 15 j F F F j j n j 1 2 ( ) μ μ μ¯ = ¯ * ¯ *…* ¯ ( )α ˜ ˜ ˜ α α α f X 16 j F F F j j n j 1 2 Here ( )̲ α f Xj and ( )¯ αf X j are the lower and upper MFs of the jth rule with level of α, and * indicates product t-norm. a type reducer changes the output of the inference engine which is a type-2 fuzzy -3 -2 -1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 x (x) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 (x) f() Fig. 3. a general type-2 fuzzy set with triangular upper and lower MFs where the secondary MF is triangular. Fig. 4. Architecture for a general type-2 fuzzy Logic system. M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334328
  5. 5. set into into a type-1 fuzzy set before defuzzification. Five kinds of reducers which are based on calculating the centroid of an IT2FS are demonstrated in [31]. The output of the type reduction in IT2FLS is defined with its left-end point yl and right-end point yr due to uniformly secondary grade of IT2FLS. KM iterative algorithms, introduced two algorithms for calcu- lating these two end points in [32], is presented by Mendel and Karnik. In comparison to the other type reduction methods, center of sets (COS) is used a lot because of its computation simplicity by the KM iterative algorithm [33]. If singleton fuzzifier is used, product inference engine and COS type reducer, left and right end points for each part of GT2FLS based on α- representation theorem can be shown as follows (Fig. 5). θ θ ξ= ∑ ¯ + ∑ = + ∑ ¯ + ∑ ̲ = ( ) α α α = = + = = + α α αy f j L f f 1 17 l j L j l j j L M j L j j L M j l T l 1 1 1 1 a where in this formula θ αl j is the left-end point of jth consequent set with level of α, θ θ θ= …α α α ⎡ ⎣ ⎤ ⎦, ,l l l M T1 , ξ = ̲ ¯ α α α α α ⎡ ⎣ ⎢ ⎤ ⎦ ⎥,l j f D f D j l j l , = ∑ ¯ + ∑ ̲α α= = +αD f fl j L j j L M j 1 1 and ξ ξ ξ= …α α α ⎡ ⎣ ⎤ ⎦, ,l l l M T1 . In addition, θ θ θ ξ= ∑ ¯ + ∑ ̲ ∑ ¯ + ∑ ̲ = ( ) α α α α = = + = = + α α αy f f f f 18 r j R j r j j R M j r j j R j j R M j r T r 1 1 1 1 a a where θ αr j is the right end point of jth consequent set with level of α, θ θ θ= …α α α ⎡ ⎣ ⎤ ⎦, ,r r r M T1 , ξ = ̲ ¯ α α α α α ⎡ ⎣ ⎢ ⎤ ⎦ ⎥,r j f D f D j r j r , = ∑ ¯ + ∑ ̲α α= = +αD f fr j R j j R M j 1 1 and ξ ξ ξ= …α α α ⎡ ⎣ ⎤ ⎦, ,r l l M T1 . Meanwhile, performing KM iterative al- gorithm can specify R and L for each individual IT2FLS of level α. From the combination of all of these obtained intervals into a type- 1 fuzzy set like Fig. 5, a crisp output can be obtained using centroid defuzzification as: ∑ α α α α= = ∑ ( + ) ∑ = ( + ) + = … − ( ) α α α α α α ⎪ ⎪ ⎪ ⎪ ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ U y y y y y K K K K 2 / 1, 0. 1 , , 1 , 1 19 Fuzzy l r a l r where Kþ1 shows the number of the α-planes or in other words it determines the number of individual IT2FLSs. 4. Teaching Learning Based Optimization (TLBO) TLBO algorithm, originally developed by Rao et al. [34,35], is a population-based optimization algorithm. In TLBO algorithm a population of solutions is utilized to proceed to the global solution. The two elementary components of this algorithm are Teacher and Learners. Based on two basic modes of the learning, through tea- cher (known as teacher phase) and interacting with the other learners (known as learner phase), the procedure of TLBO is di- vided into two parts, 1) Teacher phase and 2) Learner phase. 4.1. Teacher phase The first part of the algorithm is teacher phase where learners learn through the teacher. During this phase, a teacher endeavors to increase the mean result of the class room from any value. Since it is practically impossible, a teacher can improve the mean of the class room to other better value depending on the class capability. Consider Mi be the mean and Ti be the teacher at any iterationi. Ti will try to enhance existing mean Mitowards it so the new mean will be Ti designated as Mnew. The solution is updated according to the difference between the existing and the new mean given by [34] _ = ( − ) ( )Difference Mean r Mean T M 20i i new F i where TF is the teaching factor which decides the value of mean to be changed, and ri is the random number in the range [0, 1]. The teaching factor TF is generated randomly during the algorithm in the range of 1–2, in which 1 corresponds to no increase in the knowledge level and 2 corresponds to complete transfer of knowledge. The value of TF is randomly opted with equal prob- ability as ( ){ }= [ + − ] ( )T round rand1 0, 1 2 1 21F According to this _Difference Mean, the existing solution is up- dated as follows: = + _ ( )X X Difference Mean 22new i old i j, , 4.2. Learner phase In this phase, the Learners can enhance their knowledge via interaction among themselves randomly. A learner learns new things if the other learner has more knowledge than him or her. The learning phenomenon of this phase at any iteration i for two different learners Xi and Xj where ≠i j are given by ( ) ( )( )= + − < ( )X X r X X f X f X, If 23new i old i j i j i j, , ( ) ( ) ( )= + − < ( )X X r X X f X f X, If 24new i old i j j i j i, , The pseudo-code of TLBO algorithm can be summarized as follows: Step 1: Determine the optimization problem in hand and in- itialize the optimization parameters. Step 2: Initialize the population (i.e. learners’) with random generation and evaluate them. Step 3: Choose the best learner of each subject as a teacher for that subject and calculate mean result of learners in each subject. Step 4: Evaluate the difference between current mean result and the best mean result according to Eq. (20) using the teaching factor TF given in Eq. (21). Step 5: Update the learners' knowledge by the help of teacher's knowledge according to Eq. (22). Step 6: Update the learners' knowledge by the knowledge of some other learner according to Eqs. (23) and (24). Step 7: Stop if a stopping criteria is achieved, else go to Step 3. Fig. 5. Output of each individual IT2FLSs. M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334 329
  6. 6. When a stopping criterion occurs, the result is the best answer for the problem in hand (the best estimated parameters). Generally speaking, in order to guide their search for optimum solutions, heuristic algorithms, including TLBO, do not require any information about the status of the system and control variables; instead, they only need to check and measure the cost function corresponding to the status of control variables. [36–40]. So, in this paper, the cost function is considered as follows: ( )∑= ( ) CostFunction N e 1 25i where ei is the trajectory error of ith sample for the object, N is the number of sample and i is the iteration number. All parameters of the GT2FPI are updated at every final time (tf). The General opti- mization procedure for optimum General Type-II Fuzzy con- trollers' coefficients determination with TLBO is presented in Fig. 6. As stated earlier, this paper proposes an online adaptive con- troller using GT2FL and TLBO, for the objective of voltage regula- tion in Power Systems. Fig. 7 displays the overall control frame- work for online adjusting of membership functions of the fuzzy rules, based on the TLBO technique. Table 1 gives the applied optimal GT2FPI rules. The member- ship functions corresponding to the input and output variables are collocated as Negative Small (NS), Negative Medium (NM), Nega- tive Large (NL), Positive Small (PS), Positive Medium (PM), and Positive Large (PL). They have been collocated based on triangular membership function which is the most famous and popular membership function. The antecedent parts of each rule are composed using AND function (with interpretation of minimum). Here, Mamdani fuzzy inference system is also utilized. As will be displayed in Section 6, the OGT2FPI controller has appropriate efficiency in comparison to the classical techniques. 5. Advantages of the proposed method Generally speaking, this paper proposes a novel kind of Fuzzy Logic, General Type-II, in order to optimally tune parameters of a Proportional-Integral (PI) controller. The main disadvantage of type-2 fuzzy set is that type-2 fuzzy sets have three dimensions and this new third dimension of type-2 fuzzy sets provides extra degrees of freedom that facilitate control of uncertainties. To overcome above mentioned problem, the paper introduces an application of bio-inspired algorithms. Based on this, the authors employ TLBO algorithm which is one of the recently proposed population based algorithms. This algorithm does not require any algorithm-specific control parameters. In the core of this method, TLBO algorithm is utilized for evolving the parameters of the controller and the parameters of input and output membership functions. The proposed method is very simple. So, briefly it can be written: 1. The proposed adaptive PI controller based on General type-2 fuzzy logic approach is easy to implement and can be applied to a reasonably wide class of nonlinear systems. 2. The proposed method is based only on the available plant input/ output information and can be calculated on-line. 3. This proposed method is free of undesirable chattering phe- nomena. Moreover, it can handle both structured and un- structured uncertainties. 4. Another benefit of the suggested controller approach is its light burden of computations which is an important figure in prac- tical implementation and online control cases. 5. The proposed method is a free-model controller. 6. Simulation results Fig. 8 illustrates the diagram of the case study system. In the Fig. 6. General optimization procedure for optimum General Type-II Fuzzy con- trollers' coefficients determination with TLBO. Fig. 7. General scheme of proposed online TLBO-Fuzzy PI controller. Table 1 The OGT2FPI rule set. ∆P ∆f NL NM NS PS PM PL S NL NM NS PS PS PM M NL NL NM PS PM PM L NL NL NL PM PM PM M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334330
  7. 7. case study system, a ±100MVAR STATCOM is installed having a 48- pulse VSC that is connected to a 500-kV bus. This is the standard sample STATCOM system in Matlab/Simulink library, and all ma- chines used in the simulation are dynamical models [2,41]. Here, the attention of the analysis is focused on the control performance of STATCOM in bus voltage regulation mode. It should be noted that in the conventional model, in both voltage and the current regulator, the regulation rate as well as the amount of injection of the compensating reactive power are lar- gely affected by parameters of the PI controller. The conventional control scheme will be later compared to the proposed OGT2FPI controller. Assume that at the beginning, the steady-state voltage Vss equals 1.0 p.u. As a disturbance, it is assumed that a voltage drop of 0.002 p.u. (from 1.0 to 0.989 p.u.) happens at the source (substa- tion A) at time 0.2 s. It should be noted that, here, 0.989-p.u. voltage at substation A actually denotes the lowest voltage that the case study STATCOM device is able support because of its capacity limit. After the fault is cleared, the voltage is assumed to gets high back to about 1.0 p.u. In all simulations reported here, the STAT- COM is assumed to start operating immediately right after the disturbance, expecting that it will be able to bring the voltage back to 1.0 p.u. The proposed control, OFPI, ∞H and the original PI control are studied and compared. 6.1. Response of the Original Model In the original model, Kp-V ¼ 12, Ki-V ¼ 3000, Kp-I ¼ 5, Ki-I¼ 40. Here, all of the parameters are kept similar to the original model. The initial voltage source, shown in Fig. 8, is 1 p.u., with the vol- tage base being 500 kV. Observations are summarized in Table 2. It can be inferred from Table 2 that that the proposed controller is able to provide a quicker response compared to the original conventional one. It should be noted that although necessary re- active power amount is the same for both the proposed and ori- ginal approaches, the proposed OGT2FPI approach responds faster, as the voltage does. Fig. 9 shows the response of proposed control method and H-Infinity with comparison with two other methods. For the sake of simplicity, we may assume that the sensitivity (ΔVar/ΔV) is a linear function. According to Fig. 10, when the voltage error is 0.00001 p.u.Δ , Var is 0.0912MVar, which is in the same range as the 0.12-MVar mismatch. Thus, it is reasonable to conclude that the slight Var difference in Table 2 is due to round off error in the dynamic simulation which always gives tiny ripples beyond 5th digits even in the final steady state. 6.2. Change of PI control gains In this scenario, the gains of the PI controller of the original control are changed to Kp-V ¼ 1, Ki-V ¼ 1, Kp-I ¼ 1, Ki-I¼ 1 while all other parameters of the system are kept the same as before. The dynamic control gains depend on the post fault conditions; It should be noted that they are independent of the initial condi- tions of the system before the disturbance. Output results of ap- plying the proposed methods based on proposed controller shown in Fig. 10, respectively. As illustrated in Fig. 11(a,c)., one can simply observe that when the PI control gains of the original method are changed from their original tuned values, the original control approach becomes un- able to work properly and get the voltage back to 1 p.u., i.e. the STATCOM demonstrates a poor response. More precisely, the re- active power generated by the STATCOM is not enough to get the voltage increased to a desirable value to meet the needs of the system under disturbance. However, if the OGT2FPI control is applied, the STATCOM becomes able to respond to the disturbance Fig. 8. The general scheme of Case Study system. Table 2 Performance comparison for the original system parameters. Original Ctrl TLBO method 1 H-Infinity TLBO method 2 Lowest Voltage after disturbance 0.9938p.u. 0.9938p.u. 0.9938p.u. 0.9938p.u. Time(sec) when V¼1.0 0.1695 s 0.1445 s 0.1308 s 0.1278 s Var Amount at stea- dy state 79.6MVar 79.46MVar 89.38Mvar 79.32MVar Time to reach steady state Var 0.1695 s 0.1445 s 0.1308 0.1278 s Fig. 9. Output reactive power to the response of the Original Model. Fig. 10. the voltage ripples of the system. M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334 331
  8. 8. perfectly, i.e. the system voltage gets back to 1 p.u. quickly within only 0.1 s. Fig. 11(b,d). also shows that the reactive power injection cannot be continuously increased in the original control approach to support system voltage, while the OGT2FPI control successfully performs as desired. 6.3. Change of load In this case, the original PI controller gains are kept the same as originally designed, which means that Kp-V ¼ 12, Ki-V ¼ 3000, Kp-I ¼ 5, Ki-I¼ 40. However, the load at Bus B1 changes from 300 to 400 MW. The results are shown in Fig. 12. It can be simply inferred that the proposed method based on OGT2FPI can be successfully de- signed and used to automatically react to a change in loads of the system properly. Table 3 shows a few key observations of the performance. From the data shown in Table 3 and Fig. 12, it is obvious that the OGT2FPI control can achieve a quicker response compared to the original approach. 6.4. Change of transmission network In this case, the gains of PI controller again remain unchanged, i.e. they are similar to the original design. However, line 1 is switched off at 0.2 s to represent a change in the grid which may (c) (a) (b) OGT2FPI (d) Fig. 11. The effect of changes PI control gains on output reactive power and Voltages. Fig. 12. The effect of load changes on output reactive power. Table 3 Performance comparison with a change of load. Original Ctrl TLBO method 1 H-Infinity TLBO method 2 Lowest Voltage after disturbance 0.9949p.u. 0.9949p.u. 0.9949p.u. 0.9949p.u. Time(s) when V¼1.0 0.1695 s 0.1445 s 0.1308 s 0.1278 s Var Amount at stea- dy state 93.08MVar 92.95MVar 0.9277Var 92.67MVar Time to reach steady state Var 0.1695 s 0.1445 s 0.1308 s 0.1278 s Fig. 13. The effect of a change of transmission network. M.R. Tavana et al. / ISA Transactions 66 (2017) 325–334332
  9. 9. correspond to scheduled transmission maintenance. The results are shown in Fig. 13. Key observations are sum- marized in Table 4. Observations support the idea that the pro- posed method based on OGT2FPI can be designed to automatically react to changes in the transmission network. It should be noted that, in this case, the STATCOM absorbs VAR from the power system. Here, the disturbance should cause a voltage rise at (substation A) from 1.0 to 1.01 p.u.; however, on the other hand, due to loss of a line in the grid, the voltage tends to drop. If the STATCOM is not activated, the combinational impact causes the steady state voltage to rise to higher than 1.0 p.u. at the controlled bus As a result of overvoltage, the STATCOM should absorb VAR in the final steady state so that 1.0 p.u. voltage is ob- tained at the controlled bus. As shown in Fig. in case of using the original control method, initial transients immediately after 0.2 s has led to an undesired over absorption of reactive power by the STATCOM; while, on the other hand, when the OGT2FPI control is used, a much smoother and quicker response is obtained. 6.5. Summary of the simulation study It can be simply inferred from the abovementioned case studies that the proposed method based on OGT2FPI control can achieve faster and more consistent response compared to the original control approach. Interestingly, the response time and the output curve of the proposed OGT2FPI control are almost identical under various disturbances such as a change in (initial) control gains, a change in load, and also a change in network topology. In contrast, when the original control method is applied, the response curve of the system varies greatly under different change of system oper- ating condition and more importantly, the STATCOM may some- time not be able to modify the voltage to the desired value. Of course, it was already expected that the proposed controller would outperform the original control method as it dynamically and autonomously adjusts controller's gains during the voltage cor- rection process; therefore, the desired performance can be achieved adaptively. Remark 1. The target audience of this paper is not only intended for students and researchers but will also be valuable for execu- tives, managers, marketing experts and project leaders who would like to apply fuzzy logic control to industrial applications such as the control of power systems and electronics, Robotics and so on. The manuscript presents a set of new fuzzy methods, case studies and optimization algorithm which together make it possible to improve the efficiency and effectiveness of PI control. 7. Conclusion This paper presents a novel online intelligent strategy for controlling Voltage Regulation in Power Systems. The proposed framework applies a combination of a simple heuristic algorithm, named Teaching Learning Based Optimization (TLBO), and a new General Type-II Fuzzy Logic to optimally and adaptively tune gains of a proportional-integral controller which is used widely in STATCOM devices. Conventionally, implementing general type-2 fuzzy systems imposes high computational burden; however, by using a recently introduced plane representation, GT2FS can be regarded as a combination of several interval type-2 fuzzy logic systems (IT2FLS) each one of which has its own corresponding level of α. Linguistic rules are directly incorporated into the con- troller. In addition, an H1 compensator is corrupted to attenuate external disturbance and fuzzy approximation error. The proposed control methodology is evaluated on a test case power system owning a ±100-MVAR STATCOM with a 48-pulse VSC and con- nected to a 500-kV bus, which represents a large power system. Simulation results indicate that the simple TLBO algorithm is able to successfully determine optimal parameters of the controller as well as the parameters of input and output membership functions. The proposed technique is straightforward and free of computa- tional complexity. To evaluate the performance of the proposed framework, simulation results of the proposed method are com- pared with those of the conventional PI controller and OFPI con- troller, which are the latest researches in the problem in question. Results indicate the superiority of the proposed framework. 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