Optimal Fuzzy Inference System incorporated with stability index tracing: An application for effective load shedding

Expert Systems with Applications 41 (2014) 1095–1103

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Optimal Fuzzy Inference System incorporated with stability index tracing: An application for effective load shedding Zulkiffli Abdul Hamid ⇑, Ismail Musirin Electrical Engineering Department, Universiti Teknologi MARA, Shah Alam, Selangor, Malaysia

a r t i c l e

i n f o

Keywords: BX-CACO FVSI-LT IFIS OFIS

a b s t r a c t The application of fuzzy logic as a decision maker has been widely implemented for solving various engineering problems, especially in the field of voltage stability improvement. Because of this sophisticated tool is very suitable for non-linear system and easy for implementation, many researchers have taken initiative to formulate it according to their point of view. In the meantime, the electricity tracing techniques have also been developed through various theories, nevertheless, only transmission service pricing and electricity deregulation become the subjects of discussion when implementing it. In virtue of that, this paper proposes a new technique for locating the suitable load buses for the purpose of load shedding considering multi-contingencies, that is, by means of stability index tracing. The amount of load power to be shed is determined via a modified version of fuzzy system, which consists of improved membership functions by optimization algorithm. Experiment on IEEE 57-bus and 118-bus reliability test systems (RTS) validates the feasibility of the proposed technique for real system application. Crown Copyright Ó 2013 Published by Elsevier Ltd. All rights reserved.

1. Introduction Severity of disturbances like sudden line and generator outages, extreme demand increase as well as failure of Flexible Alternating Current Transmission System (FACTS) devices affects the capability of a power system to maintain its performance. Maintaining the voltage magnitude at load buses within acceptable range is a compulsory objective when confronting with such phenomena; however, this can only be achieved provided that the reactive power support is adequate (Devaraj & Roselyn, 2010). Further insufficient reactive power support will bring the operating point on Q–V curve close to saddle node bifurcation (SNB) point, or to be more precise, the load margin and voltage magnitude are extremely reduced. When this happens, the power system experiences voltage collapse, which means the cascaded voltage drop from one area to another will dominate or in the worst case, it is referred as ‘total black-out’ (Pinceti, 2002). Blackout incidents that happened in Tokyo, July 1987, Western Interconnection System in the United States, 1996, the Brazilian power system in March 1999, Northeastern United States and Canada in August 2003 and Spain in July 2007 are the worst case scenarios regarding on power system disturbances. Providing reactive power support via generators power scheduling, tap changer transformers setting, FACTS devices and

⇑ Corresponding author. Tel./fax: +60 3 5543 5044. E-mail addresses: [email protected], [email protected] (Z.A. Hamid), [email protected], [email protected] (I. Musirin).

capacitor banks installation may be necessary for preventing voltage collapse. Nonetheless, if those countermeasures are exhausted, load shedding will be the last resort for fast mitigation technique. Designing a load shedding scheme necessitates for fast decision making process, since the voltage collapse occurs very fast. The application of fuzzy logic as a decision maker suits for a system that requires fast response against disturbances. In a good load shedding scheme, prior to determining the amount of shed load, identification of suitable load buses for shedding purpose is obligatory as this will affect the performance of the system during post contingency. This can be realized by means of stability indices calculation and sensitivity analysis. Various researches concerning under voltage load shedding have been performed with the aim of providing improvement in terms of voltage magnitude, or sometimes together with losses reduction concurrently (Amraee, Ranjbar, Mozafari, & Sadati, 2007; Arya, Pande, & Kothari, 2005; Echavarren, Lobato, & Rouco, 2006). In Haidar, Mohamed, and Hussain (2010), the technique for vulnerability control of a power system using fuzzy logic based load shedding has been proposed considering various contingencies. The fuzzy membership functions were designed based on intuition. However, the technique did not consider the behavior of system’s non-linearity as the load buses were selected based on their voltage magnitude. Two load shedding schemes have been proposed by Sasikala and Ramaswamy (2011), in which the stability index Risk of Voltage Instability (RVI) was utilized for identifying the suitable load buses to be shed. The results revealed that the proposed technique was able to improve the system performance with

0957-4174/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2013.07.105

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Nomenclature Amf,k, Bmf,k, Cmf,k graph points of k-th membership function for input and output AI Artificial Intelligence BX-CACO Blended Crossover Continuous Ant Colony Optimization EP Evolutionary Programming FACTS Flexible Alternating Current Transmission System FIS Fuzzy Inference System FVSI Fast Voltage Stability Index FVSIl FVSI on l-th line FVSIil FVSI on l-th line contributed by i-th load FVSI-LT FVSI-Load Tracing FVSImax maximum FVSI FVSITh threshold FVSI IFIS Intuitive Fuzzy Inference System LBmf,k lower boundary of k-th membership function LS load shedding np number of points required for each membership function nload number of loads in the power system OFIS optimization assisted Fuzzy Inference System PSP proportional sharing principle Ploss real power losses Qr receiving end reactive power

reasonable amount of load shedding. Determination of load shedding for voltage stability improvement was proposed in Fu and Wang (2011). The proposed technique divided the load shedding algorithm to two sub-problems; restoring solvability and improving voltage stability margin. To implement this, linear optimization based optimal power flow was employed considering both technical and economical aspects. The results justified that the method was effective and fast for system recovery. Article Amraee, Ranjbar, and Feuillet (2011) proposed an adaptive under voltage load shedding scheme via model predictive control. To determine the criticality of the system, the scheme calculated it based on voltage magnitude and reactive power measurement. After that, the designed model predictive load shedding will be triggered to counteract voltage collapse. After considering severity of contingencies during experiment, it was justified that the method was able to provide protection against voltage instability phenomenon. In the meantime, the development of power tracing technique is vigorously performed for solving electricity deregulation problems, which is fair and non-discriminatory transmission service pricing in deregulated environment. Most of researchers develop their methods only for solving this problem. Because of that, there is no research tries to apply the technique for stability index tracing. The existing methods are only intended for tracing the magnitude of power contributed by loads or generators, not the stability index. Article Bialek (1996) is considered as the pioneer of power tracing techniques as it has introduced the concept of proportional sharing principle (PSP); an assumption used for electricity tracing theory. In Teng (2005), the application of circuit theory has been adopted to formulate a power tracing that is based on Ohm’s Law. However, the negative sharing of traced powers still being the main problem when implementing the proposed technique. Optimization assisted power tracing has been formulated by Abhyankar, Soman, and Khaparde (2006), with various consideration of constraints have been discussed in the topic of formulation technique. The proposed algorithm is rather burdensome since lots of constraints ought to be considered during coding task. Alternative power tracing development has been promoted via (Hamid, Musirin, Othman, & Rahim, 2011a; Sulaiman, Mustafa, Shareef, & Khalid,

Q ir QLi RTS RVI SA, SB, SC St SNB SO SOO SVM Tip, Top UBmf,k Vs Vmin VMS xir Xl Zl k

receiving end reactive power contributed by i-th load i-th load reactive power reliability test system Risk of Voltage Instability input and output control variables vector vector of t-th individual in BX-CACO population saddle node bifurcation system operator single objective optimization Support Vector Machine input and output membership function type (Gaussian, triangular, and trapezoidal) upper boundary of k-th membership function graph sending end voltage minimum voltage magnitude voltage magnitude based selection receiving end power fraction contributed by i-th load l-th line reactance l-th line impedance contingency level

2012; Sulaiman, Mustafa, Shareef, Khalid, & Aliman, 2010) by means of Artificial Intelligence (AI) tools. Evolutionary Programming (EP) has been implemented in Hamid et al. (2011a) to perform generation tracing, whereas Support Vector Machine (SVM) has been implemented in Sulaiman et al. (2010, 2012) with the assistance of optimization algorithm. This paper proposes a new technique for corrective load shedding considering multi-contingencies, that is, via Fast Voltage Stability Index – Load Tracing (FVSI-LT) and Fuzzy Inference System (FIS). The FVSI-LT will be used as an identifier for load buses selection, whereas the FIS will be a decision maker for deciding the amount of shed load powers. To provide optimal performance of FIS, optimization approach has also been adopted for tuning the shape of membership functions so as to provide reliable fuzzy logic-based-load shedding scheme. 2. Stability index tracing This section demonstrates the proposed stability index tracing in determining the suitable load buses for load shedding. The way how to enhance the existing power tracing methods in the context of stability index tracing is briefly explained. 2.1. Fast Voltage Stability Index (FVSI) The Fast Voltage Stability Index (FVSI) has been proposed by Musirin and Rahman (2005) for the purpose of voltage stability assessment. The use of this index is to indicate the line stability of a power system, or in some cases, as an indicator for voltage collapse point. The reliability of this index has been justified in Musirin and Rahman (2003, 2005), which becomes the main reason for this research to utilize it as the index to be traced via the developed algorithm. However, as it is a type of line based index, there is a need to modify FVSI for indicating the most sensitive bus in the system, that is, by implementing power tracing technique. The FVSI of an l-th line can be represented in (1).

FVSIl ¼

4 Z 2l Q r V 2s X l

ð1Þ

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For a stable power system, the value of FVSI shall not exceed unity. Otherwise, the voltage collapse phenomenon will dominate. 2.2. Modification of FVSI for Load Tracing In the field of power tracing, the term ‘Load Tracing’ means a task to trace the powers contributed by individual load in the system, in which the powers to be traced are the generators’ power, line flows, and losses. So, for tracing the stability index FVSI contributed by each load, the technique is referred to as FVSI-Load Tracing (FVSI-LT). The purpose of performing FVSI-LT is to identify the most sensitive bus; which will be recognized as the most suitable bus for any preventive and corrective actions, or in other words, to rank the load buses according to their priority. Based on the power tracing concept, the FVSI of l-th can be expressed as a summation of individual FVSI contributed by each load, as in (2).

FVSIl ¼ FVSI1l þ FVSI2l þ    þ FVSIi;l nload

ð2Þ

Substituting (1) into (2) in the context of Load Tracing:

FVSIl ¼

FVSIl ¼

4 Z 2l Q 1r V 2s X l 4 Z 2l V 2s X l

) FVSIl ¼

þ

ðQ 1r

4 Z 2l Q 2r V 2s X l þ

Q 2r

þ  þ

þ  þ

4 Z 2l Q i;nload r V 2s X l

Q i;nload Þ r

X i 4 Z 2l nload Qr 2 V s X l i¼1

Fig. 1. IEEE 6-bus system with single line outage.

ð3Þ

ð4Þ

ð5Þ

According to Abhyankar, Soman, and Khaparde (2006), the participation of a load with power QLi in receiving end line flow can be expressed as in (6).

Q ir ¼ xir  Q Li

ð6Þ

Thus, substituting (6) into (5):

) FVSIl ¼

load 4 Z 2l nX xir : Q Li V 2s X l i¼1

ð7Þ

It can be deduced that from (7), the FVSI of l-th line contributed by ith load of power QLi can be mathematically represented as in (8).

FVSIil ¼

4 Z 2l V 2s X l

ðxir  Q Li Þ

ð8Þ

Eventually, it is revealed that an FVSI of l-th line contributed by i-th load can be calculated by determining the receiving end power fraction, xir via any power tracing techniques, as proposed in Bialek (1996), Hamid et al. (2011a) and Sulaiman et al. (2010, 2012). Article Hamid, Musirin, Othman, and Rahim (2012) provides a brief and detail explanation on how to perform FVSI-LT using the existing power tracing techniques. 2.3. The use of FVSI-LT in load shedding problem For a clear illustration about the application of FVSI-LT in load shedding viewpoint, let consider a simple IEEE 6-bus power system with single line outage between bus 4 and 6, as in Fig. 1. In the figure, the line between bus 5 and 6 has the highest value of FVSI, which is 1.00 and followed by the line between bus 3 and 4 with FVSI value of 0.90. The traced FVSI on a particular line contributed by individual load are also given in the figure, for instance, the traced FVSI on line between bus 5 and 6 contributed by load at bus 6 is given by FVSI6–5(L6). From these traced FVSI’s, a system operator (SO) of the system will be able to rank the load buses according to

Table 1 Bus and line ranking based on FVSI-LT. Rank

Lines

Buses

Traced FVSI

1 2 3 4

6–5 3–4, 6–5 3–4, 6–5 3–4, 6–5

5 3, 4, 6 4, 5 3, 6

0.40 0.30 0.20 0.10

their priority, i.e., based on their magnitude of the traced FVSI. Table 1 provides the ranking list of load buses to be used for preventive and corrective actions by the SO. It is obvious that load at bus 5 is the most suitable location for the SO to take any actions against disturbances. This is followed by the load at bus 3, 4, and 6. Hence, based on this information the SO is now able to decide intelligently when determining the exact location for load shedding without requiring intuitive decision anymore. 3. Fuzzy logic-based-load shedding Identification of the suitable load buses for load shedding is performed using the ranking list of FVSI-LT. However, determining the amount of load powers to be shed is rather critical as this will affect the system performance in terms of voltage stability improvement and economy. Because of its easiness and reliability, this research prefers to implement fuzzy logic as a tool for deciding the amount of load powers to be shed based on the value of maximum FVSI and minimum bus voltage. In addition, two methods for designing Fuzzy Inference System (FIS) are also presented, which are intuitive FIS (IFIS) and optimization-assisted-FIS (OFIS). 3.1. Fuzzy logic concept Fuzzy logic is one of the Artificial Intelligence (AI) tools, which was proposed by Zadeh in 1965 as fuzzy set theory. Contrary to binary logic which takes only two values (0 and 1), fuzzy logic can have the value in between and this is the main reason that makes it more preferable to be implemented for solving various engineering problems. In a Fuzzy Inference System (FIS), the input part (or antecedent) is related to the output part (or consequent)

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through a rule known as fuzzy decision rule or if–then rule. Each input and output has their own levels or quality, which is called as linguistic variable. The range of an input value (or input space) is called the universe of discourse and the linguistic variables are plotted to a graph form, that is, membership function for determining how each input from the universe of discourse is mapped between 0 and 1. A fuzzy decision rule consisting of two-inputs antecedent and one-output consequent is as follows:

In addition, there are seven linguistic variables for each input and output, as follows.  FVSImax: Very low (VL), low (L), medium (M), high (H), very high (VH), stress (S), very stress (VS).  Vmin: Extremely low (EL), very low (VL), low (L), medium (M), stable (S), very stable (VS), extremely stable (ES).  LS: Extremely low (EL), very low (VL), low (L), medium (M), high (H), very high (VH), extremely high (EH).

Ri : IF x1 IS A AND x2 IS B; THEN y IS C where Ri is the i-th rule, x1 and x2 are the inputs, y is the output, A, B, and C are the linguistic values specified within the input and output space. Fundamentally, the decision making process of a FIS is divided by five steps, as follows (Ross, 2009). i. Fuzzify inputs: the input values from the universe of discourse are mapped between 0 and 1 via the designed membership functions. ii. Apply fuzzy operator: in this case, the antecedent that has more than one part (two or more inputs) is constructed by adding a logical operator, such as AND or OR. Different logical operators used in the design process will affect the performance of FIS in terms of the output quality. iii. Apply implication method: implication process responsible for determining the resultant output membership function as a result of the logical operator. iv. Aggregate all outputs: all of the resultant output membership functions will be aggregated (or summed) to obtain the net shape of membership function. v. Defuzzification: at this stage, there are five methods of defuzzification for obtaining the actual output value, which are centroid, bisector, middle of maximum, largest of maximum, and smallest of maximum.

Determination for the number of linguistic variables has been performed via heuristic experiment, which is not discussed in this paper. The membership functions for inputs and output are shown in Fig. 2. For simplicity and easiness during coding task, the trapezoidal and triangular membership functions have been selected. According to Sasikala and Ramaswamy (2011) and Mingchui, Chinwang, and Chikong (2008), the maximum percentage of allowable load power to be shed is 60–80%. Since IFIS performs the load shedding procedure iteratively, that is, stage-by-stage, it is necessary to limit the allowable percentage to a certain value, in this case, 20% or 0.2 per stage, as depicted in LS’s membership function in Fig. 2. For the algorithm, the iterative strategy for performing load shedding using IFIS is illustrated in Fig. 3. First of all, contingencies are initiated in the system, and subsequently a load flow program is run to observe the effect of the contingencies in terms of FVSI, losses, and voltage magnitude. Later, the priority of load buses to be shed is determined by means of the proposed FVSI-LT. Next, the amount of load power to be shed is determined iteratively using IFIS, and the whole steps as depicted in Fig. 3 are performed repeatedly until the condition of the system is satisfactory, i.e., the resulted FVSI, losses, and voltage magnitude are within the acceptable range. 3.3. Optimization-assisted-Fuzzy Inference System (OFIS)

3.2. Intuitive Fuzzy Inference System (IFIS) Membership function design based on intuition requires strong knowledge about the system’s behavior. As for example, if one is needed to design a FIS for a power system under disturbances, then the responses in terms of dynamic or static stability for the system ought to be well known by the designer. Otherwise, the FIS will provide bad decision making process which affects the system performance. Because of its simplicity during design process, especially when determining the shape of the membership functions, intuitive FIS (IFIS) is widely implemented for solving various problems regarding on decision making process. In this research, the maximum value of FVSI (FVSImax) and minimum voltage magnitude (Vmin) will be treated as the inputs to the FIS, while the amount of complex load powers or MVA load powers to be shed in percentage (LS) being the output. The fuzzy rules are constructed based on the decisions as tabulated in Table 2.

This section describes the method for adopting optimization algorithm into a FIS with the intention to produce optimal shape and type of membership functions. Contrary to the previous proposed technique, which is IFIS, optimization-assisted-FIS (OFIS) requires optimization technique to find the best shape and type of membership function in accordance with the formulated problem. According to Aziz (2009), Salinas, Aguirre, Cordón, and Silvente (2008), Zhuang and Wu (2001), one of the crucial factors that affect the performance of a FIS is the designed membership functions,

Table 2 Fuzzy decision table. Vmin

FVSImax

VL L M H VH S VS

EL

VL

L

M

S

VS

ES

L M H H VH EH EH

L M M H H VH EH

L L M M H VH EH

VL L M M H VH VH

VL VL L M M H VH

EL VL L L M H H

EL EL VL L L M H

Fig. 2. Proposed membership functions for IFIS.

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(i) Control variable: the membership function shape depends on the graph points and each type of membership function has their respective number of points. For example, the number of points for Gaussian, triangular and trapezoidal membership function are two, three, and four respectively. Vector St represents a t-th individual of BX-CACO population that consists of three sub-vectors; where, each of them represents the details of membership function of the first input, SA (FVSImax), second input, SB (Vmin) and output, SC (LS). In the sub-vectors, the variable T represents the type of membership function to be used, whereas the variables A, B, and C are the points to be used for plotting the membership functions. Since there are seven membership functions to be used, the length of each sub-vector is 1 + 7np.

3T 3T 2 T ip2 T op 6 mf 1 7 6 mf 1 7 6 B1 7 6 C1 7 6 mf 1 7 7 7 6 6 6 A1 7 6 . 7 6 . 7 7 6 7 6 6 . 7 . 6 . 7 . . 7 7 6 6 6 .. 7 6 mf 1 7 6 mf 1 7 7 6 6B 7 6C 7 7 6 np 7 np 7 6 6 . 6 1. 7 7 7 6 SA ¼ 6 Amf . 7 ; SB ¼ 6 6 .. 7 ; SC ¼ 6 .. 7 6 np 7 6 . 7 6 . 7 6 mf 7 7 7 7 6 6 6 A1 7 6 mf 7 7 6 mf 7 7 7 6 6 B1 7 6 C1 7 6 . 7 7 7 6 6 6 .. 7 6 . 7 6 . 7 5 4 6 .. 7 6 .. 7 7 5 5 4 4 Amf np 7 7 C mf Bmf np np 2

Fig. 3. Load shedding strategy via IFIS.

which are the shape and type. In term of shape, the curvature of each membership function in a specified range plays a significant role in providing reliable mapping process during input fuzzification and output defuzzification. In addition, the types of membership function to be utilized are another factor. Selection between triangular, trapezoidal, and Gaussian membership function for input and output are to be considered during optimization process. For efficient implementation of optimization, the Blended Crossover Continuous Ant Colony Optimization (BX-CACO) that has fast convergence property and good solution optimality is applied. The depth knowledge of BX-CACO is not discussed in this paper as the main topic is about fuzzy logic-based-load shedding and stability index tracing. However, for a brief explanation and performance of this algorithm, article (Hamid, Musirin, Othman, & Rahim, 2011b; Hamid, Musirin, & Rahim, 2012) are recommended. For the formulation technique, the control variables, constraints, and objective function are explained as follows.

T ip1

St ¼ ½ SA

2

3T

SB

SC 

ð9Þ

ð10Þ

(ii) Constraints: the constraints to be utilized during the optimization process are as follows. In (11), each membership function type is treated with an integer code, that is, 1 for Gaussian, 2 for triangular, and 3 for trapezoidal. Whereas in (12), a k-th membership function graph is plotted based on the points that are specified between their respective lower (LB) and upper bound (UB). Lastly which is (13), each t-th individual (St) in BX-CACO population must have fuzzy membership functions that will cause FIS to produce FVSImax less than a specified threshold value, FVSITh.

1 6 T ip1; T ip2; T op 6 3 8 T is integer

ð11Þ

LBmf ;k 6 Amf ;k ; Bmf ;k ; C mf ;k 6 UBmf ;k

ð12Þ

Fig. 4. Algorithm for OFIS via BX-CACO.

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0 6 FVSImax 6 FVSITh

ð13Þ

(iii) Objective function: for the purpose of this research, the objective of optimization is to reduce the system’s FVSI. However, based on the fact that as the improved stability (FVSI) will cause consistent enhancement of voltage magnitude and reduction of losses (Abdullah, Musirin, & Othman, 2010), this research intends to formulate the algorithm as single objective optimization (SOO), with the fitness is FVSI itself. The algorithm of OFIS via BX-CACO is illustrated in Fig. 4. In the figure, the load shedding subroutine is the subprogram as depicted in Fig. 3. 4. Results and discussion The performance of IFIS and OFIS are tested on two test systems, which are IEEE 57-bus and 118-bus reliability test system (RTS). Both proposed FIS techniques applied FVSI-LT as the ranking method for identifying the suitable load buses committed for shedding. The one that utilized OFIS is noted as FVSI-LTA, whereas the other one is FVSI-LTB for IFIS. Comparative study between other ranking methods was also conducted, which are Voltage Magnitude-based-Selection (VMS) and Risk of Voltage Instability (RVI) index as proposed by Haidar et al. (2010) and Sasikala & Ramaswamy, 2011 respectively. Contrary to IFIS and OFIS, the load buses selected for shedding via VMS are based on their voltage magnitude, whereas for RVI, the priority for shedding is based on stability index RVI. Both VMS and RVI utilized their respective designed FIS for determining the amount of load powers to be shed. Table 3 summarizes all the ranking methods involved in the experiment with their corresponding FIS. To observe the reliability of all ranking methods and FIS techniques, four levels of contingency (noted as k) are initiated in the systems and the responses in terms of maximum FVSI (FVSImax), losses (Ploss), and minimum voltage magnitude (Vmin) after load shedding are analyzed. Each contingency level from k = 1 to k = 4 increases in the number of contingent lines and contingent generators; which means that the severest contingency condition happens at k = 4. For a fair comparison, firstly, the proposed FVSI-LTA is run until the stopping criteria are met, in this case, the desired FVSImax, Ploss, and Vmin after shedding. After that, the required amount of load powers for shedding in MVA percentage is recorded. Next, other methods (FVSI-LTB, VMS, and RVI) are run until their MVA percentage reaches the recorded percentage of FVSI-LTA and the corresponding FVSImax, Ploss, and Vmin are recorded. In addition, the used threshold FVSI, FVSITh as in (13) is 0.9. 4.1. Performance evaluation on IEEE 57-bus reliability test system (RTS) As for an example, the resulted membership functions of OFIS after tuning at contingency k = 4 are depicted in Fig. 5. Besides that, the performance of all methods in terms of FVSImax, Ploss, and Vmin with respect to contingency level are illustrated in Figs. 6–8

Table 3 Ranking methods with their respective fuzzy systems for solving load shedding. Ranking method

Utilized fuzzy system

Abbreviated as

FVSI-Load Tracing FVSI-Load Tracing Voltage magnitude based selection Risk of Voltage Instability index

OFIS IFIS FIS proposed by Haidar et al. (2010) FIS proposed by Sasikala and Ramaswamy (2011)

FVSI-LTA FVSI-LTB VMS RVI

Fig. 5. OFIS’s membership functions at contingency k = 4.

Fig. 6. FVSI distribution for 57-bus system.

respectively. The result details are tabulated in the Appendix, Table A1. In the figures, the condition before performing load shedding under contingency is marked by the dotted line and abbreviation ‘pre’. Firstly, by inspection from Fig. 6, FVSI-LTA is considered to be the best method as the FVSI reduction is the lowest, especially between k = 2 and k = 4. The FVSI-LTB is also good as this method results in comparable FVSI at k = 3 and k = 4. Meanwhile, both VMS and RVI result in equivalent FVSI reduction as their line trends are similar. However, their reduction is not as good as FVSI-LTA. Secondly is about the losses reduction, as in Fig. 7. It is obvious that again, FVSI-LTA reflects the best performance for all contingency levels, and followed by FVSI-LTB. The VMS and RVI provide equivalent losses reduction as their line trends overlie to each other and still, both methods are not better than FVSI-LTA and FVSI-LTB. Eventually, the corresponding voltage magnitude improvement is illustrated in Fig. 8. As can be seen, FVSI-LTB, VMS, and RVI are approximately in similar trend of voltage magnitude improvement, which varies between 0.89 and 0.9 p.u. However, further improvement is resulted from FVSI-LTA in which the voltage magnitude is above than 0.9 p.u. for all contingency levels. From the whole results, it is revealed that FVSI-LTB has great capability to be applied in load shedding problem as this method

Z.A. Hamid, I. Musirin / Expert Systems with Applications 41 (2014) 1095–1103

Fig. 7. Losses distribution for 57-bus system.

Fig. 8. Voltage magnitude distribution for 57-bus system.

1101

Fig. 9. OFIS’s membership functions at contingency k = 3.

Fig. 10. FVSI distribution for 118-bus system.

has comparable performance with other non-FVSI-LT techniques, which are VMS and RVI. Another approach known as FVSI-LTA is a comprehensive and improved version to FVSI-LTB in providing further improvement on power system performance. This finding has also justified the ability of FVSI-LT to be a reliable ranking method for identifying the suitable load buses before committing load shedding. 4.2. Performance evaluation on IEEE 118-bus reliability test system (RTS) The next evaluation is on IEEE 118-bus RTS, with the resulted membership functions of OFIS after tuning is depicted in Fig. 9. Firstly, the resulted FVSI distribution as in Fig. 10 shows the proposed technique, FVSI-LTA being the best approach for all contingency levels, followed by FVSI-LTB, VMS, and RVI. In average, all methods except RVI are capable to provide reliable system stability after load shedding, especially at k = 4. At this contingency level, only RVI results in the worst FVSI as the value exceeds unity; which is the maximum value of FVSI before the voltage collapse occurrence. Secondly, the losses distribution as in Fig. 11 illustrates a comparable reduction for all methods. It is obvious that at k = 1 and k = 3, the three methods; FVSI-LTA, FVSI-LTB, and VMS have the line trends that overlie to each other, indicating that their performance

Fig. 11. Losses distribution for 118-bus system.

are equivalent. However, FVSI-LTA is still able to provide the lowest reduction, as can be observed at k = 2 and k = 4. Lastly, the performance in terms of voltage magnitude is illustrated in Fig. 12. For the first three contingency levels, the

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5. Conclusion In brief, a new method to create a ranking list of load buses for the purpose of load shedding under contingencies has been proposed, namely FVSI-LT. The method applies power tracing approach for tracing the stability index FVSI contributed by system’s loads using the modified version of FVSI equation. It is justified that FVSI-LT provides reliable information regarding the load buses priority since the voltage stability improvement after load shedding is satisfactory and consistent regardless of contingency levels. In addition, two load shedding schemes via Fuzzy Inference System (FIS) for deciding the amount of MVA load powers to be shed have also been promoted, which are intuitive and optimal FIS. Contrary to other methods which are only workable on certain condition, the proposed FIS techniques (OFIS and IFIS) exhibit a potential performance in the voltage stability viewpoint regardless of severity of the disturbances. Fig. 12. Voltage magnitude distribution for 118-bus system.

Acknowledgments FVSI-LTB, VMS, and RVI are approximately in the same trend of improvement. However, it is observed that at the last contingency level, VMS is the best among the three methods as the resulted voltage magnitude is the highest. Roughly, FVSI-LTA is the only method that can provide further improvement for all contingency levels with the voltage magnitude varies between 0.9 and 0.95 p.u. So, from this point, it is revealed that the proposed FIS designs (OFIS and IFIS) have proven their capability to be applied for real-systems-load-shedding with consistent enhancement of static stability. It is also justified that FVSI-LT is considered to be a potential ranking method for future applications concerning suitable load buses identification besides other existing techniques like VMS and RVI.

k

Method

Load buses (according to priority)

1

Pre FVSI-LTA FVSI-LTB VMS RVI

– 30, 30, 30, 30,

31, 31, 31, 31,

57, 57, 25, 25,

25, 25, 33, 33,

50, 50, 32, 32,

33, 33, 23, 23,

18, 18, 57, 57,

23, 23, 20, 35,

42, 42, 35, 20,

Pre FVSI-LTA FVSI-LTB VMS RVI

– 30, 30, 30, 30,

31, 31, 31, 31,

50, 50, 25, 25,

25, 25, 33, 33,

33, 33, 32, 32,

18, 18, 35, 35,

53, 53, 57, 57,

Pre FVSI-LTA FVSI-LTB VMS RVI

– 31, 31, 31, 31,

57, 57, 30, 33,

33, 33, 33, 30,

25, 25, 32, 32,

30, 30, 25, 25,

50, 50, 57, 57,

Pre FVSI-LTA FVSI-LTB VMS RVI

– 31, 31, 31, 31,

30, 30, 30, 30,

57, 57, 25, 33,

25, 25, 33, 32,

33, 33, 32, 25,

50, 50, 57, 57,

2

3

4

The authors would like to acknowledge The Research Management Institute (RMI) UiTM, Shah Alam and Ministry of Higher Education Malaysia (MOHE) for the financial support of this research. This research is jointly supported by Research Management Institute (RMI) via the Excellence Research Grant Scheme UiTM with project code: 600-RMI/ST/DANA 5/3/Dst (164/2011) and MOHE under the Exploratory Research Grant Scheme (ERGS) with project code: 600-RMI/ERGS 5/3 (14/2011). Appendix A Table A1. Post load shedding results for IEEE 57-bus RTS with 15 load buses selected for load shedding.

MVAShed (%)

FVSImax

Vmin (p.u.)

PLoss (MW)

6, 2, 32 6, 2, 32 27, 38, 44 38, 27, 53

– 12.0 12.0 12.0 12.0

1.260 0.132 0.145 0.147 0.161

0.469 0.900 0.868 0.871 0.862

40.487 10.930 11.568 15.104 15.760

42, 42, 56, 56,

2, 56, 49, 57, 32, 20, 41 2, 56, 49, 57, 32, 20, 41 42, 23, 20, 27, 38, 53, 19 42, 23, 20, 53, 19, 38, 27

– 14.0 14.0 14.0 14.0

1.360 0.098 0.162 0.204 0.164

0.471 0.937 0.900 0.872 0.894

57.840 13.242 17.927 31.987 30.067

18, 18, 35, 35,

42, 42, 23, 20,

53, 53, 20, 23,

56, 56, 19, 19,

32, 32, 56, 56,

2, 49, 3, 20 2, 49, 3, 20 38, 42, 44, 49 38, 42, 44, 47

– 15.0 15.0 15.0 15.0

1.000 0.115 0.134 0.214 0.213

0.328 0.933 0.905 0.905 0.904

171.35 24.907 33.797 55.587 54.727

18, 18, 23, 23,

23, 23, 35, 35,

42, 42, 20, 20,

53, 53, 19, 19,

2, 56, 32, 49, 3 2, 56, 32, 49, 3 56, 42, 38, 44, 49 56, 42, 38, 44, 49

– 14.0 14.0 14.0 14.0

1.180 0.100 0.117 0.171 0.164

0.390 0.917 0.876 0.880 0.901

91.246 14.070 19.189 33.678 30.428

53, 53, 19, 56,

56, 56, 56, 19,

49, 49, 42, 42,

1103

Z.A. Hamid, I. Musirin / Expert Systems with Applications 41 (2014) 1095–1103

Table A2. Post load shedding results for IEEE 118-bus RTS with 20 load buses selected for load shedding. k

Method

Load buses (according to priority)

MVAShed (%)

FVSImax

Vmin (p.u.)

PLoss (MW)

1

Pre FVSI-LTA FVSI-LTB VMS RVI

– 118, 79, 26, 53, 45, 86, 101, 78, 44,13, 82, 56, 95, 61, 33, 1, 116, 62, 105, 96 118, 79, 26, 53, 45, 86, 101, 78, 44,13, 82, 56, 95, 61, 33, 1, 116, 62, 105, 96 118, 75, 76, 53, 74, 2, 50, 1, 57, 52,117, 3, 56, 70, 58, 16, 43, 44, 51, 55 118, 117, 114, 115, 110, 112, 111, 107, 113, 106, 105, 108, 109, 104, 116, 103, 102, 101, 75, 100

– 22.0 22.0 22.0 22.0

1.150 0.242 0.311 0.438 0.349

0.472 0.927 0.893 0.875 0.883

398.166 129.556 133.648 119.419 161.774

2

Pre FVSI-LTA FVSI-LTB VMS

– 118, 105, 106, 55, 45, 82, 86, 95, 44, 40, 110, 1, 98, 54, 32, 15, 41, 39, 96, 19 118, 105, 106, 55, 45, 82, 86, 95, 44, 40, 110, 1, 98, 54, 32, 15, 41, 39, 96, 19 118, 75, 76, 95, 74, 96, 99, 94, 98, 106, 82, 100, 97, 101, 105, 83, 104, 108, 93, 70 118, 117, 110, 115, 114, 106, 105, 104, 108, 112, 109, 111, 113, 95, 103, 107, 116, 96, 99, 94

– 25.0 25.0 25.0

1.422 0.232 0.325 0.350

0.474 0.892 0.862 0.874

581.192 118.727 136.935 175.483

25.0

0.260

0.873

191.983

Pre FVSI-LTA FVSI-LTB VMS RVI

– 118, 118, 118, 118, 103,

– 22.0 22.0 22.0 22.0

1.175 0.263 0.443 0.452 0.485

0.473 0.918 0.874 0.864 0.888

439.167 124.659 133.060 124.376 185.941

Pre FVSI-LTA FVSI-LTB VMS RVI

– 118, 105, 106, 45, 82, 40, 44, 53, 1, 95, 86, 98, 33, 41, 39, 43, 59, 110, 96, 2 118, 105, 106, 45, 82, 40, 44, 53, 1, 95, 86, 98, 33, 41, 39, 43, 59, 110, 96, 2 118, 75, 33, 38, 53, 39, 95, 40, 98, 44, 96, 94, 99, 37, 2, 43, 41, 97, 100, 52 118, 117, 95, 110, 98, 106, 105, 96, 94, 114, 115, 104, 99, 108, 112, 100, 111, 97, 109, 101

– 25.0 25.0 25.0 25.0

1.320 0.320 0.344 0.481 1.186

0.600 0.924 0.872 0.922 0.856

990.680 183.411 237.809 291.828 393.973

RVI 3

4

40, 79, 34, 1, 45, 53, 78, 86, 101, 44, 56, 82, 41, 33, 39, 95, 61, 43, 62 40, 79, 34, 1, 45, 53, 78, 86, 101, 44, 56, 82, 41, 33, 39, 95, 61, 43, 62 75, 2, 76, 1, 53, 74, 40, 43, 39, 50, 33, 41, 44, 57, 3, 52, 34, 37, 117 117, 114, 115, 110, 112, 111, 107, 113, 106, 116, 105, 108, 109, 104, 102, 101, 100, 99

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