The Scientific World Journal

Volume 2015, Article ID 731013, 15 pages

http://dx.doi.org/10.1155/2015/731013

## A Heuristic Ranking Approach on Capacity Benefit Margin Determination Using Pareto-Based Evolutionary Programming Technique

^{1}Committee of Research (CORE), Advanced Computing & Communication (ACC), Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia^{2}Faculty of Electrical Engineering, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia^{3}Engineering Centre, University Malaysia Perlis, Kampus Kubang Gajah, 02600 Arau, Perlis, Malaysia^{4}Centre of Excellence in Power System Management and Control, Electrical Engineering Department, Sharif University of Technology, Tehran 11365-11155, Iran^{5}Department of Energy Engineering, Sharif University of Technology, Tehran 11365-11155, Iran

Received 6 May 2014; Accepted 15 September 2014

Academic Editor: Shifei Ding

Copyright © 2015 Muhammad Murtadha Othman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper introduces a novel multiobjective approach for capacity benefit margin (CBM) assessment taking into account tie-line reliability of interconnected systems. CBM is the imperative information utilized as a reference by the load-serving entities (LSE) to estimate a certain margin of transfer capability so that a reliable access to generation through interconnected system could be attained. A new Pareto-based evolutionary programming (EP) technique is used to perform a simultaneous determination of CBM for all areas of the interconnected system. The selection of CBM at the Pareto optimal front is proposed to be performed by referring to a heuristic ranking index that takes into account system loss of load expectation (LOLE) in various conditions. Eventually, the power transfer based available transfer capability (ATC) is determined by considering the firm and nonfirm transfers of CBM. A comprehensive set of numerical studies are conducted on the modified IEEE-RTS79 and the performance of the proposed method is numerically investigated in detail. The main advantage of the proposed technique is in terms of flexibility offered to an independent system operator in selecting an appropriate solution of CBM simultaneously for all areas.

#### 1. Introduction

In a deregulated power system environment, electricity is considered as a commodity that can be traded in a free market where the generators and loads participated. The transition to a new structure of electricity market is to ensure the quality and efficient production of electrical energy that can be offered at a lower electricity price as well as maximizing the utilization of generation and transmission facilities [1, 2]. Hence, it is important for the independent system operator (ISO) to calculate and provide the information of available transfer capability (ATC) associated with the transfer paths to the open access same-time information system (OASIS) so that electricity market could be conducted in an effective manner [3, 4]. ATC is defined as the maximum amount of power that can be transferred from a selling area to a buying area without jeopardizing a system security [5]. ATC can be calculated as the total transfer capability (TTC) reduced by the transmission reliability margin (TRM), capacity benefit margin (CBM), and existing transmission commitment (ETC). CBM is one of the main components considered in the ATC calculation and is defined as the amount of transfer capability reserved by load-serving entities, which is anticipated to be used in cases of generation deficiency [5–9]. Inaccurate determination of CBM may result in either underestimation or overestimation of the ATC. Underestimating the ATC value possibility will cause an ineffective use in the transmission facility, while overestimating the ATC value will threaten a power system security [3, 7].

So far, several methods have been proposed to determine CBM [10–19]. The basic method used to compute the CBM for each area of an interconnected system is based on trial and error [10], by prescribing 5% of the maximum transfer capability [11] or the CBM value is specified as zero [12, 13]. Reference [14] has proposed an analytic model used for multiarea generation reliability assessment and then applied into the sequential quadratic programming (SQP) for determining the CBM values considering the loss of load expectation (LOLE) as the system reliability criterion. Rajathy et al. [15] use the differential evolution and Monte Carlo techniques to determine the CBM. A method that has been proposed in [16] is used to determine the CBM for each area of an interconnected system using the evolutionary programming (EP) as an accelerated search technique. Furthermore, CBM determination is formulated as an optimization problem which is solved by using the particle swarm optimization (PSO) technique [17, 18]. In order to provide a set of choices for different cases, three methods have been proposed in [17, 18] which will provide different values of CBM. It is observed that the existing CBM calculations do not provide adequate flexibility for the ISO to select a CBM value in accordance with system requirements [10–19]. In addition, tie-line availability is an influential factor which has an effect on the reliability of an interconnected system followed by the value of CBM. This imperative factor has been taken into account for CBM calculation in [19].

A novel multiobjective based optimization approach is presented in this paper to determine several optimum values of CBM using the Pareto-based EP technique that takes into account the tie-line reliability of an interconnected system. The proposed Pareto-based EP technique has several advantages compared to the methodology previously presented in [16] and it provides the ISO with several choices of optimum CBM values. The multiobjective function of EP technique is referred to as the transfer capability margin of CBM for all areas with LOLE less than a specified value at initial condition. Moreover, the CBMs of all areas are obtained simultaneously at every execution of the proposed technique. The first order sensitivity with modified Gaussian formulation is used as a new mutation technique to enhance the EP performance in searching for a new population at global maximum domain with less computational time. Then, the Pareto optimal front approach is used to select several optimal solutions of CBM values using the ranking index of total LOLE and total difference of LOLE. A modified IEEE-RTS79 is used as the numerical test bed to verify effectiveness of the proposed method in providing the solutions of CBMs [17]. The robustness of the proposed method in CBM determination is compared with that of the basic methodology used for the CBM calculation [17]. Performance comparison has also been performed which investigates the effect of tie-line reliability included in the CBM determination. Finally, the significance of CBM considered as firm and nonfirm transfers can be observed through its impact on the ATC determination.

#### 2. Multiobjective Functions of Capacity Benefit Margins Determination

A process involved in the Pareto-based EP technique used for determining the multiobjective function of CBMs is described as follows.

*Step (a)*. Establish a solved base case power flow solution.

*Step (b).* Determine the LOLE for each area of the interconnected system at the base case condition.

*Step (c).* Identify the assisting areas with LOLE less than the specified value, (e.g., 2.4 hrs/yr). It signifies that these areas conserve a certain amount of reserve generating capacity that could be used to compensate for the generation deficiency which may occur in the assisted area. LOLE associated with the assisted area is usually greater than . It is important to mention that the assisting and assisted areas are the terms used to signify the direction of power transfer based CBM () and this is different from the selling and buying areas which are the terms used to signify the direction of power transfer based ATC.

*Step (d).* Identify the assisted area with the largest LOLE above .

*Step (e).* Determine the parent or initial population for each assisting area with LOLE below . Equation (1) is used to generate the individuals , for parent or initial population using uniform random distribution. The determination of is based on either total rating of all tie-lines connecting between the assisting and assisted areas, PLIt_{asg}, or the total reserve generating capacity of the assisting area, DPGt_{asg}. The is determined based on the former condition when DPGt_{asg} exceeds the PLIt_{asg}. This means that tie-lines are the constraining factors for power transfer based CBM and, thus, are generated randomly based on PLIt_{asg}. The latter condition is used to determine when DPGt_{asg} is less than PLIt_{asg}. Each individual, , is considered as an external generating capacity, PG_{Ext}, or CBM, which is provided by the assisting area to support generating capacity deficiency in the assisted area having the highest LOLE:where or is the CBM in the case of transfer from assisting area to assisted area; is the total generating capacity; is the total peak load; is the tie-line rating; is the total number of tie-lines; is ; is ; is the population size; and is the total number of assisting areas.

*Step (f).* Calculate a new total generation capacity, , for each assisting area according to CBM or as given in (3) and (4). The generating capacity of the assisting area is reduced as it is partially assigned to the assisted area. The new generating capacity for each bus of the assisting area is obtained based on the ratio of generating capacity aswhere is the generating capacity and is the total number of generator buses.

*Step (g).* Determine the LOLE for each assisting area () considering the , hourly peak load, and cumulative probability of generation capacity outage () as discussed in [19].

*Step (h).* Determine a new total generation capacity, , for an assisted area with the largest LOLE above using (5) and (6). In (6), apportionment of the total or total to each generator is performed based on the ratio of generating capacity and total generating capacity of an assisted area. For an assisted area, there are number of individuals for the size of new total generating capacity, ,wherewhere is the number of assisted areas, 1.

*Step (i).* Calculate the fitness value , that is, as discussed in [19]. is an important parameter used to assist the determination of a new and the convergence criteria for the optimization process. This will be explained thoroughly in the following steps. or is calculated by taking into account the increased amount of obtained in Step (h).

*Step (j).* Perform the mutation to obtain an offspring for each assisting area with LOLE less than . In the proposed mutation approach, the modified Gaussian technique is used to improve the capability of global maximum search of a new population with less computational time [16]. This technique is suitable in solving the optimization problems in which considerable discrepancy does exist among the individual values. Each offspring comprising new individuals, , is originated from . The new individuals, , are obtained using a new mutation technique that incorporates the first order sensitivity, , and the modified Gaussian formulation, , as expressed in (7). The value of is varied in accordance with the changes in to the estimated LOLE limit, . Considerwherewhere and are the maximum and minimum values of for every assisting area, respectively; and are the maximum and minimum values of , respectively; and or is the maximum value of fitness, or .

The first order sensitivity is used to overcome the impediment of local maxima or minima which normally occurs in the case of large . Hence, robustness in searching for the global maxima or minima can easily be guaranteed by using the new mutation technique.

*Step (k).* Perform Steps (h) and (i) to determine or in relation to a new value of obtained according to (5) considering . This implies that the in (6) has been replaced by , yielding to a new value of . Apart from the obtained based on , determination of also requires several other parameters such as the hourly peak load and new cumulative probability of the generation capacity outage () as discussed in [19].

*Step (l).* Perform pairwise comparison to determine the next generation of population comprising the best individuals selected from and . For each assisting area, or has been used as a reference for selecting the best individuals as the next generation of . In this case, for and are obtained from Steps (h) and (j), respectively. The concept of selection is elucidated in terms of the formulation given in (9). Otherwise, when the total number of chosen individuals is not adequate for population size, , then the offspring, , is selected as the next generation of as illustrated inwhere is the best individuals selected from and having ; is the corresponding to the value of individual ; is the corresponding to the value of individual ; and is the size of .

*Step (m).* The convergence criteria for the EP optimization process is achieved when the mismatch between maximum fitness, , and minimum fitness, , is within a specified range, . and are the maximum and minimum values of , respectively, obtained based on the in Step (l):where is the minimum value of or and is the desired accuracy, 0.1 for an example [16].

Go to Step (f) for the next generation of EP optimization process when the mismatch does not reach to the desired level and the new value of obtained in Step (l) will be used to calculate a in Step (f). Otherwise, proceed to Step (n) once the mismatch has reached the predetermined limit .

*Step (n).* Record the optimized multiobjective function of CBM_{asg} for the transfer case from assisting areas to an assisted area. The optimized multiobjective CBM_{asg} will be recorded at the last iteration of the optimization process. The CBM_{asg} is obtained as the average value of or associated with the assisting area previously calculated in Step (l). This implies that the CBM_{asg} is calculated through (12). Hence, the multiobjective function (M.O.F) comprising several optimized CBM_{asg} for the case of power transferred from the assisting areas can be expressed by (13). Then, LOLE_{asg} is computed based on the CBM allocated for each assisting area, , as discussed in [19]. Consider

Therefore, CBM_{asd} for an assisted area is calculated by summing the optimum amount of CBM_{asg} transferred from all the assisting areas as given in

*Step (o).* Repeat Steps (a)–(n) several times in order to obtain numerous optimal solutions of multiobjective CBM_{asg}. These results will be applied into the Pareto optimal concept in such a way to find several superior multiobjective CBM_{asg}. Figure 1 presents the flowchart of the proposed EP optimization technique used to determine several multiobjective functions of CBMs.