Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm

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Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm

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Sumit Verma, Subhodip Saha, V. Mukherjee ∗

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Department of Electrical Engineering, IIT (ISM), Dhanbad, Jharkhand, India

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Received 30 June 2016; received in revised form 17 November 2016; accepted 5 December 2016

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Abstract This paper proposes teaching-learning-based optimization (TLBO) algorithm for congestion management (CM) in a pool based electricity market. Congestion is a principal problem that an independent system operator faces in post deregulated era. The aim of employing TLBO algorithm is to effectively relieve congestion in the line with minimum deviation in initial generation and, hence, congestion cost. Various security constraints such as load bus voltage and line loading are taken into account while dealing with this problem. Inspired by teaching–learning process of classroom, TLBO algorithm is a recent population based algorithm which does not require any algorithm specific control parameters unlike other algorithms. It only requires common control parameters like population size and number of generation. In this paper, the proposed TLBO algorithm is applied on modified IEEE 30- and 57-bus test power system for the solution of CM problem. The results obtained are compared to those reported in the recent state-of-the-art literature. The efficacy of the TLBO algorithm for obtaining higher quality solution is also established. © 2017 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Congestion management; Deregulation; Independent system operator (ISO); Optimal power flow; Price bids; Teaching-learning-based optimization (TLBO)

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1. Introduction

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1.1. General

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Deregulation and restructuring of the electricity industry have brought major shifts in the planning, operations and management of power system. Generating, transmitting and distributing companies are working as independent entities after deregulation. The increasing demand of electricity, all around the world, is giving rise to the market participants for trading in the electricity market. Transaction requires energy to be transferred from the sending end to the receiving ∗

Corresponding author. Fax: +91 326 2296563. E-mail addresses: [email protected] (S. Verma), subhodip [email protected] (S. Saha), vivek [email protected] (V. Mukherjee). Peer review under the responsibility of Electronics Research Institute (ERI).

http://dx.doi.org/10.1016/j.jesit.2016.12.008 2314-7172/© 2017 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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end. Sellers and buyers are exchanging energy by utilizing transmission network. In case, all proposed transactions are unable to accommodate simultaneously, then the network is said to be congested (Ihri, 2002). Congestion is the condition when a transmission network starts operating beyond certain permissible limits such as physical limit, voltage limit and stability limit of a line. Congestion, usually, occurs in deregulated market as selling and buying of energy may be settled without actually considering the constraints of the power system. Outage of line, inadequate reactive power support, failure of equipment, weather diversity are some of the causes of congestion causing real threat to power system security and may result in electricity price hike. Congestion management (CM) takes actions or control measures to relieve the congestion of transmission networks. The methods, usually, adopted for CM includes generation rescheduling, load shedding, line switching, market splitting, zonal pricing etc. (Lai, 2001).

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1.2. Literature review

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Various CM techniques have been reported in the literature in the recent years to represent the various ways for tackling CM problem. Researchers have proposed several methods in the literature like rescheduling of power, load curtailment, use of flexible AC transmission systems (FACTS) devices in addition to the optimization techniques for relieving the congestion of lines. The economic and cost aspect associated with transmission congestion have been highlighted by Singh et al. (1998). They have also discussed the impact of counter-flows on congestion cost in a bilateral model. The coordination of electricity transactions, based on priority along with the curtailment factors, has been introduced in Fang and David (1999) to deal with CM. An approach has been proposed by Jian and Lamont (2001) which minimizes both service and congestion cost to identify the services of reactive power support and real power loss. A new model, to generate extravaganza cuts by the independent system operator (ISO) in case of any CM infeasibility, has been proposed by Yamina and Shahidehpour (2003) and it has been implemented based on security-constraint price-unit commitment. A CM technique, based on generation rescheduling and load shedding which can alleviate the overloading of the transmission lines in a computationally efficient manner has been pointed out by Talukdar et al. (2005). Both deterministic and genetic based approaches were applied by Granelli et al. (2006) to find out the best topological network arrangement of a power transmission system with the aim of providing ISO a tool for CM. A technique of generation rescheduling, based on the concept of relative electric distance (RED), has been proposed by Yesuratnam and Thukaram (2007). RED has been applied for load alleviation based on the contribution of generator to the over loaded lines. This concept has been used to find out the players’ contribution and the divergence can be used for appropriate tariff design. Optimal power flow based constraint targeting voltage instabilities has been introduced in Conejo et al. (2006) which ensure secure operation as it incorporates online conditions and its functioning has been demonstrated on IEEE 24-bus RTS. A technique for optimum selection of generators based on generator sensitivities to the power flow on congested lines has been demonstrated by Dutta and Singh (2008). They have applied this method on 39-bus New England system, IEEE 30-bus and 118-bus system while employing particle swarm optimization (PSO) technique. An algorithm for CM in a pool based electricity market using PSO has been presented in Balaraman and Kamaraj (2011) which relieves the congestion effectively and economically with minimum shifts in generation of real power from initial clearing values. In Singh and Parida (2013), a sensitivity method has been proposed for allocation of distributed generators and its optimal capacity has been computed using genetic algorithm (GA) to minimize the system loss and voltage deviation. The generation rescheduling for CM with three block structure, offered by the generating companies (GENCOs), has been discussed in Kumar and Mittapalli (2014) and implemented for hybrid market model considering the impact of constant impedance, current and power. In Luo et al. (2014), the impact of market flow method on the electricity market operation has been presented with the help of mathematical proof which shows the equivalence of the market flow and unit dispatch flow. Unit commitment problem has been solved by using simulated annealing (SA) by Zhuang and Galiana (1990). Random search method (RSM) for solving various optimization problems was discussed in Jang et al. (1996). Rastgou and Moshtagh (2014) have addressed a methodology based on harmony search (HS) for solving transmission expansion planning while considering both congestion and security cost. The impact of third generation FACTS devices has been studied by Kumar and Sekhar (2013) for CM problem. Rao et al. (2011) have introduced a novel optimization technique and named as teaching-learning-based optimization (TLBO). It is based on the teaching–learning process in a classroom. The TLBO algorithm is used in Rao et al. (2012a) to solve continuous unconstrained and constrained optimization problems. TLBO has been found to be very efficient in Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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solving various engineering field optimization problems with very fast convergence rate and less computational time (Rao et al., 2011, 2012b; Rao and Kalyankar, 2011; Togan, 2012).

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1.3. Motivation

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Major motivation behind this work is to design a new technique for solving CM problem. Although several techniques have been adopted by the researchers to solve the CM problem as stated in literature survey but most of them are evolutionary and swarm intelligence based techniques. These techniques have some common control parameters like size of population and number of generations. Apart from these control parameters, some algorithms posses some specific control parameters like PSO have inertia weights and cognitive parameters. GA uses mutation and crossover rate. Similarly, HS requires pitch adjusting rate, memory consideration rate etc. Proper tuning of these parameters are required, otherwise, it may seriously affect the performance of the optimization algorithm and may even diverge. Keeping these facts in mind, the present paper has utilized the concept of TLBO algorithm which is independent of control parameters platform. The qualities associated with TLBO algorithm are (Rao et al., 2011): (a) it does not have any algorithm specific control parameters, (b) only common control parameters are sufficient to tune and (c) effective computational efforts, consistency and accuracy.

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The main goal of present paper is to propose an algorithm for solving CM problem for various contingency by rescheduling real power of generator with minimum cost. To accomplish this task, TLBO algorithm is proposed in this paper. Thus, the main motivation of the present work is to aid ISO to relieve the overloading of lines in an optimal manner. The proposed TLBO algorithm is applied on modified IEEE 30-bus and 57-bus test power system to solve CM problem under various considered contingency cases.

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1.4. Contribution

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The main contributions of this work are to

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(a) project a novel TLBO algorithm as an effective optimizing tool to minimize the rescheduling cost under different cases, (b) effectively remove the overloaded line caused due to various considered contingencies with minimum shift in generation, (c) minimize the total amount of rescheduling and losses for various cases and (d) demonstrate the effectiveness of the proposed TLBO algorithm over the others for this specific application.

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2. Mathematical problem formulation

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The main objective of CM is to minimize the congestion cost while satisfying the network constraints. Here, the CM problem is solved by rescheduling (increasing or decreasing) the real power output of generators. But change in real power output is associated with cost which, in turn, depends upon the price bids submitted by GENCOs. The problem may be stated as in (1) (Balaraman and Kamaraj, 2011) Minimize  + − Cc = (Ck PGj + Dk PGj ) $/h (1) jεNg

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+ − where Cc , Ck , Dk, PGj and PGj represent the total cost incurred for changing real power output ($/h), increment price bids submitted by GENCOs ($/MWh), decrement price bids submitted by GENCOs ($/MWh), real power increment of generator (MW) and real power decrement of generator (MW), respectively. The present optimization problem is subjected to the following equality and inequality constraints as stated in the two next sub-sections.

Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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2.1. Equality constraints The equality constraints of CM represent the power flow equations as stated in (2)–(5) (Kothari and Dhillon, 2011)

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P Gk − PDk = |V j ||Vk ||Ykj | cos(δk − δj − θkj ); j = 1, 2, ......, Nb

(2)

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QGk − QDk = |V j ||Vk ||Ykj | sin(δk − δj − θkj ); j = 1, 2, ....., Nb

(3)

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+ − C + PGk − PGk PGk = PGk ; k = 1, 2, ....., Ng

(4)

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C ; j = 1, 2, ....., Nd PDj = PDj

(5)

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where PGk and QGk are the generated real and reactive power at bus k, respectively; PDk and QDk are the real and reactive load power at bus k, respectively; Vj and Vk are voltages at bus j and k, respectively; δj and δk are bus voltage angle of bus j and k, respectively; θkj is admittance angle of line connected between k and j; Nb , Ng , Nd are number C C of buses, generators and loads, respectively; PGk and PDj are the real power produced by generator k and real power consumed by load bus j, respectively, as obtained by the market clearing value. It is to be noted here that (2) and (3) show real and reactive power balance at each node while (4) and (5) represent final power as a function of market clearing price.

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2.2. Inequality constraints

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The inequality constraints represent the operating and physical limit of all the transmission lines, transformers and generators and are stated in (6)–(9)

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max min ≤ P PGk Gk ≤ PGk , ∀k ∈ Ng

(6)

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max Qmin Gk ≤ QGk ≤ QGk , ∀k ∈ Ng

(7)

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min min max max (PGk − PGk ) = ΔPGk ≤ ΔPGk ≤ ΔPGk = (PGk − PGk )

(8)

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max V min n ≤ Vn ≤ Vn , ∀n ∈ Nl

(9)

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Pij ≤

Pijmax

(10)

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where the superscript min and max represent the minimum and maximum values of the respected variables and Nl represents number of lines.

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3. Proposed TLBO algorithm

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TLBO algorithm is inspired by teaching–learning process in the classroom. It is developed by Rao et al. (2011). A brief overview of this algorithm is provided in the next three sub-sections.

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3.1. TLBO: features

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TLBO algorithm is inspired by teaching–learning process, as teaching–learning process is the most powerful instrument of education to bring about desired changes in the students. Similarly, TLBO algorithm is augmented by the effect of influence of a teacher on the output of student (learner) (Rao et al., 2012b). The result of student, in terms of marks or grade, is considered to be the output of TLBO algorithm. Teacher is assumed to be highly learned person who teaches learners so that they can improve their marks or grades. Thus, if the students achieve good grades in different subjects, their learning will get enhanced. Moreover, learners also learn by interacting with each other which, in turn, help them to produce better result. TLBO is a population based algorithm. In this algorithm, a group of learners are considered as the population while subjects or courses offered to the learners are considered as different design variables. The output produced by the learners is analogous to the fitness of optimization problem. TLBO algorithm consists of two parts; one is ‘teacher phase’ while the other is ‘learner phase’. Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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3.2. Teacher phase In this phase, the teacher imparts knowledge to the learners and tries to increase the mean learning value of the class according to the quality of teaching. Let, there are ‘m’ numbers of design variables offered to ‘n’ numbers of learners. Let Ti be the result of the teacher and Mi be the mean result at any instant i. Ti will try to match the level of Mi to its own level and the new mean is defined as Mnew . The difference between the existing and the new mean is given by (11). diffrence meani = ri (Mnew − TF Mi )

(11)

where ri is random number in the range varying from 0 to 1 and TF is teaching factor that decides the value of mean to be changed whose value can either be 1 or 2. TF is defined by (12). TF = round[1 + rand(0, 1) × (2 − 1)]

(12)

The modification of existing solution owing to this difference is done according to the expression given by (13) Xnew,i = Xold,i + difference mean

(13)

3.3. Learner phase This phase consists of the mutual interaction between the learners which tends to increase the knowledge of the learner. Each learner interacts randomly with other learners which facilitates knowledge sharing. A learner learns something new if the other learner has more knowledge than him or her. The learning phenomenon of this phase is expressed below.

The flowchart for TLBO algorithm is presented in Fig. 1. 4. TLBO for CM problem In this work, each population considered has N number of design variables where N is the number of generators taking part in CM problem. Usually, the objective function is considered as the fitness function. The inequality constraints are converted to the penalty functions and these penalty functions are added to the objective function. In this paper, the equality constraints are handled effectively during Newton–Raphson power flow (Sadat, 2002) and the real power inequality constraints are handled during the course of iteration. Reactive power inequality constraints are handled during the load flow solution. Other inequality constraints such as load bus voltage and line power flow are considered as quadratic penalty functions. The fitness function of CM problem may be described as in Balaraman and Kamaraj (2011) Minimize FF = Cc + PF1 ×

ovl  i=1

(Pij − Pijmax )2 + PF2 ×

VB 

(ΔVj )2 + PF3 × (ΔPG )2

(14)

j=1

Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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S. Verma et al. / Journal of Electrical Systems and Information Technology xxx (2016) xxx–xxx Initialize the population, design variables and termination criterion Evaluate the initial population Calculate the mean of each design Variable Select the best solution Calculate the difference mean and modify the solutions based on best solution

Keep the previous solution

Is new solution better than existing?

No

Yes

Accept

Select the solutions randomly and modify them by comparing with each other

Keep the previous solution

No

Is new solution better than existing?

Yes

Accept

Is termination criterion fulfilled? Yes

No

Final value of solution

Fig. 1. Flowchart of TLBO algorithm. 181

where

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Vj =

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ΔPG =



(V min j − Vj ) ;

if Vj ≤ Vjmin

(Vj − Vjmax ) ; if Vj ≥ Vjmax  min min (P G − PG ) ; if PG ≤ PG max ) ; (PG − PG

max if PG ≥ PG

(15)

(16)

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Here, FF is fitness function which is required to be minimized in order to get minimum rescheduling cost; ovl, VB represent set of overloaded lines and voltage violated load buses, respectively, and PFi (i = 1–3) represent penalty factor which has been taken as 10,000 throughout simulation process (Balaraman and Kamaraj, 2011).

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4.1. Computational procedure of TLBO for CM

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Based on the above discussions, the procedure for applying the proposed TLBO algorithm for the solution of CM problem is given below. Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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Step 1: Initial population (the number of learners) is generated using the design variables which are the amount of rescheduling required by generators to manage congestion, (randomly within the limits). Step 2: Using the generated (new) learners, the fitness function is evaluated (teacher phase). Step 3: Mean of each design variable is computed and the best solution is identified as teacher among the learners based on their fitness value. Step 4: All other learners are modified with reference to the mean and the fitness function is evaluated using the modified learners. Any two learners are randomly selected and their fitness values are compared. The student with better fitness value is accepted while the other is rejected (learner phase). Step 5: Repeat Step 4, until all the learners participating in the test, confirms that any two learners do not repeat the test. Step 6: If maximum number of iteration is reached then the program is stopped otherwise it goes back to Step 3.

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5. Simulation results and discussion

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The TLBO algorithm for CM, as discussed in Section 4, is implemented using MATLAB (version 7.6.0) software on an Intel Core i3 Processor based system with 2.4 GHz clock speed and supported by 4 GB of RAM. Some successful application of MATLAB software is provided in Valipour (2016), Valipour (2015a), Valipour (2014), Khoshravesh et al. (2015) and Valipour (2015b). The performance of the proposed TLBO algorithm is studied on modified IEEE 30- and modified IEEE 57-bus test power systems. The performance of the proposed TLBO method is compared with three methods like PSO, RSM and SA reported in Balaraman and Kamaraj (2011). The bus data and line data for these two power networks are given in section Appendix A (Tables A1 and A2 for modified IEEE 30-bus test system and Tables A3 and A4 for modified IEEE 57-bus test system). The generator buses are numbered first followed by the load buses. Increment and decrement price bids submitted by the GENCOs to alter their scheduled transactions from initial market clearing price are also presented in section Appendix A (Tables A5 and A6 for modified IEEE 30- and 57-bus test system, respectively). Increment and decrement costs of generators are considered slightly more and less, respectively, than the corresponding marginal cost values. The proposed TLBO algorithm is executed for 30 independent trial runs, out of which the best solution set is presented here. The major observations of present work are documented below. Results of interest are bold faced in the respective tables.

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5.1. Example 1: modified IEEE 30-bus system

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The modified IEEE 30-bus test system is chosen as Example 1. It has six generator buses, twenty-four load buses and forty-one transmission lines. The total real and reactive power of load for this test system are 283.4 MW and 126.2 MVAR, respectively. Generation and load values, provided in section Appendix A, are taken as the initial market clearing values for PG and PD , respectively. Contingencies like, line outage and increase in system load are considered for simulation purpose. The two different cases considered for this example are:

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Case 1(a). Considering outage of line 1–2 and

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Case 1(b). Considering outage of line 1–7 and load at all buses is increased by 50%.

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5.1.1. Case 1 (a): considering outage of line 1–2 In this case, lines 1–7 and 7–8 get overloaded due to the outage of the line 1–2. For this case, Newton–Raphson power flow (Kothari and Dhillon, 2011; Sadat, 2002) is carried out and the amount of overload in the congested lines is tabulated in Table 1. The actual power flows in those lines are 147.463 MW and 136.292 MW, respectively, while the line flow limit is 130 MW for both the lines. So, net power violation is found to be 23.755 MW. For secure operation of the system, power flow in the transmission lines should not exceed their maximum permissible flow limits. Thus, necessary corrective actions should be taken to alleviate the overloading of the lines. In this paper, the line overloads are alleviated by optimal rescheduling of generators by minimal amount from initial market clearing values. Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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Table 1 Q9 Details of congested lines for modified IEEE 30-bus test system corresponding to Case 1(a).

Cases

Type of contingency

Congested lines

Line power flow (MW)

Case 1(a)

Outage of line 1–2

Case 1(b)

Outage of line 1–7 and load at all bus increased by 50%

1–7 7–8 1–2 2–8 2–9

147.463 136.292 310.917 97.353 103.524

% overload 13.43 4.84 139.17 49.77 59.27

Total power violation (MW) 23.755 251.794

Table 2 Comparison of results obtained from different algorithms for modified IEEE 30-bus test system corresponding to Case 1(a). Parameters

Total congestion cost ($/h) Power flow (MW) on previously congested line 1–7 Power flow (MW) on previously congested line 7–8 ΔPG1 ΔPG2 ΔPG3 ΔPG4 ΔPG5 ΔPG6 Total generation rescheduled (MW)

234 235 236 237 238 239 240 241 242 243

244 245 246 247 248 249 250 251

Techniques TLBO [proposed]

PSO (Balaraman and Kamaraj, 2011)

RSM (Balaraman and Kamaraj, 2011)

SA (Balaraman and Kamaraj, 2011)

494.66

538.95

716.25

719.861

130

129.97

129.78

129.51

120.78

120.78

120.60

120.35

−8.5876 +12.9855 +0.4598 +0.7289 −0.0093 +0.3988 23.169

−8.6123 +10.4059 +3.0344 +0.0170 +0.8547 −0.0122 22.936

−8.8086 +2.6473 +2.9537 +3.0632 +2.9136 +2.9522 23.339

−9.0763 +3.1332 +3.2345 +2.9681 +2.9540 +2.4437 23.809

The results obtained by employing the proposed TLBO for the solution of CM problem for the list case of Example 1 are tabulated in Table 2. The results obtained from RSM, SA and PSO techniques reported in Balaraman and Kamaraj (2011) are also included in the same table. It may be noted that the best solution reported in Table 2 completely relieves the overload of 23.755 MW without causing any overload to any other lines. Table 2 also presents that the cost incurred to relieve congestion is 716.25 $/h, 719.861 $/h and 538.95 $/h yielded by RSM, SA and PSO methods, respectively. However, the proposed TLBO method gives the best solution as 494.66 $/h. The total system loss before CM is found to be 16.023 MW while the same is decreased to 13.126 MW after CM. Comparative real power rescheduling (ΔPG ), yielded by the comparative algorithms for different generators, is shown in Fig. 2. The convergence profile of fitness function for this test case, as yielded by the proposed TLBO algorithm, is shown in Fig. 3. 5.1.2. Case 1 (b): considering outage of line 1–7 and load at all buses is increased by 50% In this case, outage of line 1–7 along with increase in real and reactive power of system load by 50% causes overloading in the lines 1–2, 2–8 and 2–9. The power flow in the overloaded lines are found to be as 310.917 MW, 97.353 MW and 103.524 MW, respectively, which are beyond the limits of their maximum power flow limits (130 MW for line 1–2 and 65 MW each for both the lines 2–8 and 2–9). The total power violation in this case is 251.794 MW (Table 1). To alleviate this amount of overloading, the optimum rescheduling of generators is carried out by using TLBO algorithm and presented in Table 3. The up/down adjustment of real power generated by the generators, as offered by the proposed TLBO method, is shown in Fig. 4. Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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Fig. 2. Comparative real power rescheduling of generators for modified IEEE 30-bus test system corresponding to Case 1(a).

Fig. 3. TLBO based convergence profile of fitness function value for modified IEEE 30-bus test system corresponding to Case 1(a).

Fig. 4. TLBO based real power rescheduling of generators for modified IEEE 30-bus test system corresponding to Case 1(b). 252 253 254 255 256

It is clear from the plot that the incremental change in real power generation is required for all the generators except the slack generator. The cost for CM is visibly less for the proposed TLBO method than the other methods reported. Also the total system loss is decreased to 16.38 MW after CM which was initially 37.8 MW during congestion. The convergence of fitness function, as offered by the proposed TLBO algorithm with the number of iterations, for this test case is shown in Fig. 5. Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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Table 3 Comparison of results obtained from different algorithms for modified IEEE 30-bus test system corresponding to Case 1(b). Parameters

Techniques TLBO [proposed]

Total congestion cost ($/h) Power flow (MW) on previously congested line 1–2 Power flow (MW) on previously congested line 2–8 Power flow (MW) on previously congested line 2–9 ΔPG1 ΔPG2 ΔPG3 ΔPG4 ΔPG5 ΔPG6 Total generation rescheduled (MW)

RSM (Balaraman and Kamaraj, 2011)

PSO (Balaraman and Kamaraj, 2011)

SA (Balaraman and Kamaraj, 2011)

5299.4

5335.5

5988.05

130

129.7

129.91

129.78

62.34

61.1

52.36

51.47

65

64.67

55.43

54.04

NR NR NR NR NR NR 168.03

NR NR NR NR NR NR 164.55

NR NR NR NR NR NR 164.53

−8.5876 76.33 1 52.34 13.33 17.496 168.088

6068.7

NR means not reported in the referred literature.

Fig. 5. TLBO based convergence profile of fitness function value for modified IEEE 30-bus test system corresponding to Case 1(b). 257

5.2. Example 2: modified IEEE 57-bus system

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The modified IEEE 57-bus system is taken as Example 2. It has seven generator buses, fifty load buses and eighty transmission lines. The total real and reactive power loads are 1250.8 MW and 336 MVAR, respectively. The two different cases considered for this example are:

261

Case 2(a). Overload simulation by reducing the capacity of the lines 5–6 and 6–12 and

262

Case 2(b). Overload simulation by reducing the capacity of the line 2–3.

258 259

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Table 4 Details of congested lines for modified IEEE 57-bus test system corresponding to Case 2(a). Cases

Type of contingency

Congested lines

Line power flow (MW)

% overload

Total power violation (MW)

Case 2(a)

Overload simulation by reducing the capacity of the lines 5–6 and 6–12

5–6

195 .971

11 .98

35.322

6–12

49 .351

41

Overload simulation by reducing the capacity of the line 2–3

2–3

37 .048

85 .24

Case 2(b)

17.048

Table 5 Comparison of results obtained from different algorithms for modified IEEE 57-bus test system corresponding to Case 2(a). Parameters

Techniques TLBO [Proposed]

Total congestion cost ($/h) Power flow (MW) on previously congested line 5–6 Power flow (MW) on previously congested line 6–12 ΔPG1 ΔPG2 ΔPG3 ΔPG4 ΔPG5 ΔPG6 ΔPG7 Total generation rescheduled (MW)

263 264

265 266 267 268 269 270 271 272 273 274 275 276

5981.3 174.914

35

+38.1219 +0.7801 +9.0766 −0.0179 −43.2018 −29.9082 +22.8093 143.9158

PSO (Balaraman and Kamaraj, 2011)

RSM (Balaraman and Kamaraj, 2011)

SA (Balaraman and Kamaraj, 2011)

6951.9

7967.1

141

148.4

146.60

35

34.84

34.67

+23.135 +12.447 +7.493 −5.385 −81.216 0 +39.03 168.70

+59.268 0 +37.452 −47.391 −52.125 0 0 196.23

7114.3

+74.499 0 −1.515 +9.952 −85.920 0 0 171.87

Newton–Raphson power flow (Kothari and Dhillon, 2011; Sadat, 2002) is carried out for these test cases and the details of the overloaded lines for both the cases are tabulated in Table 4. 5.2.1. Case 2(a): overload simulation by reducing the capacity of the lines 5–6 and 6–12 In this case, the power flow (Table 4) in the line 5–6 is 195.971 MW while that in line 6–12 is 49.351 MW. Under base loading, the original power flow limits of these two lines are 200 MW and 50 MW, respectively. To carry out overload simulation, the line limits are taken as 175 MW for the line 5–6 and 35 MW for the line 6–12. As a result of this, the former line gets overloaded by 11.98% while the latter by 41% and total power violation becomes 35.322 MW (Table 4). Optimum generator rescheduling is performed using the proposed TLBO algorithm to completely alleviate this overloading of 35.322 MW. The details of the results obtained by using the proposed TLBO algorithm are listed in Table 5 along with those yielded by PSO (Balaraman and Kamaraj, 2011), RSM (Balaraman and Kamaraj, 2011) and SA (Balaraman and Kamaraj, 2011). A comparison of the amount of real power rescheduling for this test case, required for CM, is presented in Fig. 6. It may be noted from Table 5 that the total cost of CM, obtained from the proposed TLBO method, is 5981.3 $/h which is the lowest among the costs obtained from the other three methods. From Fig. 6, it is also clear that the Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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Fig. 6. Comparative real power rescheduling of generators for modified IEEE 57-bus test system corresponding to Case 2(a).

Fig. 7. TLBO based convergence profile of fitness function value for modified IEEE 57-bus test system corresponding to Case 2(a). 277 278 279 280

281 282 283 284 285 286 287 288 289 290 291 292 293 294 295

decremental change in real power generation is required only for generator number four and six, while the remaining generators require an incremental change in real power generation to completely alleviate the overloading of the lines. The total system loss before CM was 21.458 MW and it is now decreased to 18.6 MW after CM. The convergence profile of fitness function, as obtained by the proposed TLBO, is shown in Fig. 7. 5.2.2. Case 2(b): overload simulation by reducing the capacity of the line 2–3 To simulate this case, the line 2–3 is made to be overloaded by reducing the capacity of the line to 20 MW from an initial value of 85 MW. Under base load condition, the power flow in this line is 37.048 MW and, hence, the line gets overloaded by 85.24% and the total power violation becomes 17.048 MW (Table 4). To relieve this much of power violation, the generators are optimally rescheduled according to the proposed TLBO method. The details of the results obtained by using TLBO are included in Table 6 along with the comparative methods like PSO (Balaraman and Kamaraj, 2011), RSM (Balaraman and Kamaraj, 2011) and SA (Balaraman and Kamaraj, 2011). From Table 6, it may be observed that the total cost of CM is 2916.4 $/h while using the proposed method and it is the lowest one as compared to the other three methods reported in the same table. The rescheduling of real power generation for the generators to overcome congestion is shown in Fig. 8. Positive rescheduling is required only in generator 3 and for the rest of the generators negative rescheduling is required. The TLBO based convergence of the fitness function for this case is shown in Fig. 9. Based on results obtained while employing TLBO algorithm, the advantage of TLBO is that it does not have any algorithm specific control parameters, only common control parameters like population size are sufficient to tune moreover results are computationally effective with consistent performance over many trail runs. However, the Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008

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Table 6 Comparison of results obtained from different algorithms for modified IEEE 57-bus test system corresponding to Case 2(b). Parameters

Techniques TLBO [Proposed]

Total congestion cost ($/h) Power flow (MW) on previously congested line 2–3 ΔPG1 ΔPG2 ΔPG3 ΔPG4 ΔPG5 ΔPG6 ΔPG7 Total generation rescheduled (MW)

2916.4 20

−1.0174 −24.6365 36.0991 −6.2282 −0.2811 −1.2540 −2.5732 72.089

PSO (Balaraman and Kamaraj, 2011) 3117.6 19.88

NR NR NR NR NR NR NR 76.314

RSM (Balaraman and Kamaraj, 2011) 3717.9 20

NR NR NR NR NR NR NR 89.320

SA (Balaraman and Kamaraj, 2011) 4072.9 18.43

NR NR NR NR NR NR NR 97.887

NR means not reported in the referred literature.

Fig. 8. TLBO based real power rescheduling of generators for modified IEEE 57-bus test system corresponding to Case 2(b).

Fig. 9. TLBO based convergence profile of fitness function value for modified IEEE 57-bus test system corresponding to Case 2(b).

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performance of algorithm in terms of convergence rate may get affected while dealing with high dimension problems of power systems.

298

6. Conclusion

296

307

This paper demonstrates a novel technique for CM in a pool based electricity market. The problem of congestion is modeled as optimization problem and is solved by using teaching-learning-based optimization algorithm. Contingencies like line outage and sudden load variation are considered in this work. The proposed method is tested on modified IEEE 30- and IEEE 57-bus system and the results are compared with simulated annealing, random search method and PSO. It is observed that the proposed TLBO algorithm effectively relieves congestion and rescheduling cost obtained is much lower than the cost reported by other approaches. Moreover, total amount of rescheduling and losses is also lower. It may be concluded that TLBO is a powerful approach for solving optimization problems with the advantage that it does not have any algorithm-specific parameters to control. Only common controlling parameters need to be tuned. Thus, TLBO offers uniform behavior for all the considered cases.

308

Appendix A.

299 300 301 302 303 304 305 306

309 310 311

Bus data and line data for modified IEEE 30-bus system are presented in Tables A1 and A2, respectively, while those for modified IEEE 57-bus system are given in Tables A3 and A4, respectively. Price bids submitted by GENCOs for modified IEEE 30- and 57-bus system are given by Tables A5 and A6, respectively. Table A1 Bus data for modified IEEE 30-bus test system. Bus no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Bus code

Voltage (V)

Angle (◦ )

Generation

MW

MVAR

MW

MVAR

1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1.06 1.043 1.01 1.01 1.082 1.071 1.0 1.01 1.0 1.0 1.802 1.0 1.071 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

138.59 57.56 24.56 35.0 17.91 16.93 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Load Qmin 0.0 50.0 37.0 37.3 16.2 10.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Generation

Qmax 0.0 21.7 94.2 30.0 0.0 0.0 2.4 7.6 0.0 22.8 0.0 5.8 11.2 6.2 8.2 3.5 9.0 3.2 9.5 2.2 17.5 0.0 3.2 8.7 0.0 3.5 0.0 0.0 2.4 10.6

0.0 12.7 19.0 30.0 0.0 0.0 1.2 1.6 0.0 10.9 0.0 2.0 7.5 6.2 2.5 1.8 5.8 0.9 3.4 0.7 11.2 0.0 1.6 6.7 0.0 2.3 0.0 0.0 0.9 1.9

−30 −30 −30 −30 −30 −30 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

100 100 100 100 100 100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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Table A2 Line data for modified IEEE 30-bus test system. Start bus

End bus

R (p.u.)

X (p.u.)

B/2 (p.u.)

Line limit (MW)

Start bus

End bus

R (p.u.)

X (p.u.)

B/2 (p.u.)

Line limit (MW)

1 1 2 7 2 2 8 3 9 9 9 9 11 11 8 13 13 13 13 14 16

2 7 8 8 3 9 9 10 10 4 11 12 5 12 13 6 14 15 16 15 17

0.0192 0.0452 0.0570 0.0132 0.0472 0.0581 0.0119 0.0460 0.0267 0.0120 0.0 0.0 0.0 0.0 0.0 0.0 0.1231 0.0662 0.0945 0.2210 0.0824

0.0575 0.1652 0.1737 0.0379 0.1983 0.1763 0.0414 0.1160 0.0820 0.0420 0.2080 0.5560 0.2080 0.1100 0.2560 0.1400 0.2559 0.1304 0.1987 0.1997 0.1923

0.0264 0.0204 0.0184 0.0042 0.0209 0.0187 0.0045 0.0102 0.0085 0.0045 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

130 130 65 130 130 65 90 70 130 32 65 32 65 65 65 65 32 32 32 16 16

15 18 19 12 12 12 12 21 15 22 23 24 25 25 28 27 27 29 4 9

18 19 20 20 17 21 22 22 23 24 24 25 26 27 27 29 30 30 28 28

0.1073 0.0639 0.0340 0.0936 0.0324 0.0348 0.0727 0.0116 0.1000 0.1150 0.1320 0.1885 0.2544 0.1093 0.0 0.2198 0.3202 0.2399 0.0636 0.0169

0.2185 0.1292 0.0680 0.2090 0.0845 0.0749 0.1499 0.0236 0.2020 0.1790 0.2700 0.3292 0.3800 0.2087 0.3960 0.4153 0.6027 0.4533 0.2000 0.0599

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0214 0.065

16 16 32 32 32 32 32 32 16 16 16 16 16 16 65 16 16 16 32 32

Table A3 Bus data for modified IEEE 57-bus test system. Bus no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Bus code

1 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Voltage (V)

1.04 1.01 0.99 0.98 1.01 0.98 1.02 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Angle (◦ )

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Generation

Load

Generation

MW

MVAR

MW

MVAR

146.39 87.55 41.97 89.67 461.21 100.0 344.95 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

55.0 3.0 41.0 75.0 150.0 121.0 377.0 0.0 13.0 0.0 5.0 0.0 18.0 10.5 22.0 43.0 42.0 27.2 3.3 2.3 0.0 0.0 6.3 0.0 6.3 0.0

17.0 88.0 21.0 2.0 22.0 26.0 24.0 0.0 4.0 0.0 2.0 0.0 2.3 5.3 5.0 3.0 8.0 9.8 0.6 1.0 0.0 0.0 2.1 0.0 3.2 0.0

Qmin −140 −40 −40 −30 −140 −30 −150 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Qmax 200.0 50.0 60.0 25 200 9 155 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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Table A3 (Continued) Bus no.

Bus code

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Angle (◦ )

Voltage (V)

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Generation

Load

Generation

MW

MVAR

MW

MVAR

Qmin

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

9.3 4.6 17.0 3.6 5.8 1.6 3.8 0.0 6.0 0.0 0.0 14.0 0.0 0.0 6.3 7.1 2.0 12.0 0.0 0.0 29.7 0.0 18.0 21.0 18.0 4.9 20.0 4.1 6.8 7.6 6.7

0.5 2.3 2.6 1.8 2.9 0.8 1.9 0.0 3.0 0.0 0.0 7.0 0.0 0.0 3.0 4.0 1.0 1.8 0.0 0.0 11.6 0.0 8.5 10.5 5.3 2.2 10.0 1.4 3.4 2.2 2.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Qmax 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Table A4 Line data for modified IEEE 57-bus test system. Start bus

End bus

R (p.u)

X (p.u)

B/2 (p.u)

Line limit (MW)

Start bus

End bus

R (p.u)

X (p.u)

B/2 (p.u)

Line limit (MW)

1 2 3 8 8 4 4 5 6 6 6 6 13 13 1 1 1

2 3 8 9 4 10 5 6 11 12 7 13 14 15 15 16 17

0.0083 0.0298 0.0112 0.0625 0.0430 0.0200 0.0339 0.0099 0.0369 0.0258 0.0648 0.0481 0.0132 0.0269 0.0178 0.0454 0.0238

0.0280 0.0850 0.0366 0.132 0.148 0.102 0.173 0.050 0.167 0.0848 0.0295 0.158 0.0434 0.0869 0.0910 0.2060 0.1080

0.0645 0.0409 0.0190 0.0129 0.0174 0.0138 0.0235 0.0274 0.0220 0.0109 0.0386 0.0203 0.0055 0.0115 0.0494 0.0273 0.0143

150 85 100 100 50 40 100 200 50 50 50 50 50 100 200 100 100

10 25 30 31 32 34 34 35 36 37 37 36 22 12 41 41 38

29 30 31 32 33 32 35 36 37 38 39 40 38 41 42 43 44

0.0 0.1350 0.3260 0.5070 0.0392 0.0 0.0520 0.0430 0.0290 0.0300 0.0192 0.0 0.2070 0.0 0.0289 0.0 0.0

0.0648 0.2020 0.4970 0.7550 0.0360 0.9530 0.0780 0.0537 0.0366 0.1009 0.0379 0.0466 0.0295 0.7490 0.3520 0.4120 0.0585

0.0 0.0 0.0 0.0 0.0 0.0 0.0016 0.0008 0.0 0.0010 0.0 0.0 0.0 0.0 0.0 0.0 0.0010

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

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Table A4 (Continued) Start bus

End bus

R (p.u)

X (p.u)

B/2 (p.u)

Line limit (MW)

Start bus

End bus

R (p.u)

X (p.u)

B/2 (p.u)

Line limit (MW)

3 8 8 9 10 11 12 7 7 7 14 18 19 21 21 22 23 24 24 24 26 27 28

15 18 18 4 5 7 13 13 16 17 15 19 20 20 22 23 24 25 25 26 27 28 29

0.0162 0.0 0.0 0.0302 0.0139 0.0277 0.0223 0.0178 0.0180 0.0397 0.0171 0.4610 0.2830 0.0 0.0736 0.0099 0.1660 0.0 0.0 0.0 0.1650 0.0618 0.0418

0.0530 0.5550 0.4300 0.0641 0.0712 0.1262 0.0732 0.0580 0.0813 0.1790 0.0547 0.6850 0.4340 0.7767 0.1170 0.0152 0.2560 1.1820 1.23 0.0473 0.2540 0.0954 0.0587

0.0272 0.0 0.0 0.0062 0.0097 0.0164 0.0094 0.0302 0.0108 0.0238 0.0074 0.0 0.0 0.0 0.0 0.0 0.0042 0.0 0.0 0.0 0.0 0.0 0.0

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

15 14 46 47 48 49 50 11 13 29 52 53 54 12 44 40 56 56 39 57 38 38 6

45 46 47 48 49 50 51 51 49 52 53 54 55 43 45 56 41 42 57 56 49 48 55

0.0230 0.0182 0.0834 0.0801 0.1386 0.0 0.0 0.1442 0.0762 0.1878 0.1732 0.0 0.0624 0.0 0.5530 0.2125 0.0 0.1740 0.1150 0.0312 0.0 0.0 0.0

0.1042 0.0735 0.0680 0.0233 0.1290 0.1280 0.2200 0.0712 0.1910 0.1870 0.0984 0.2320 0.2265 0.1530 0.1242 1.1950 0.5490 0.3540 1.3550 0.2600 0.1770 0.0482 0.1205

0.0 0.0 0.0016 0.0 0.0024 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0020 0.0 0.0 0.0 0.0 0.0 0.003 0.0 0.0

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

Table A5 Price bids submitted by GENCOs for modified IEEE 30-bus test system. Bus number

Increment ($/MWh)

Decrement ($/MWh)

1 2 3 4 5 6

22 21 42 43 43 41

18 19 38 37 35 39

Table A6 Price bids submitted by GENCOs for modified IEEE 57-bus test system.

312

313 314 315 316

Bus number

Increment ($/MWh)

Decrement ($/MWh)

1 2 3 4 5 6 7

44 43 42 43 42 44 44

41 39 38 37 39 40 41

References Balaraman, S., Kamaraj, N., 2011. Transmission congestion management using particle swarm optimization. J Electr. Syst. 7 (1), 54–70. Conejo, A.J., Milano, F., Bertrand, R.G., 2006. Congestion management ensuring voltage stability. IEEE Trans. Power Syst. 21 (1), 357–364. Dutta, S., Singh, S.P., 2008. Optimal rescheduling of generator for congestion management based on particle swarm optimization. IEEE Trans. Power Syst. 23 (4), 1560–1569.

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Please cite this article in press as: Verma, S., et al., Optimal rescheduling of real power generation for congestion management using teaching-learning-based optimization algorithm. J. Electr. Syst. Inform. Technol. (2016), http://dx.doi.org/10.1016/j.jesit.2016.12.008