Information exchange based clustered differential evolution for constrained generation-transmission expansion planning

Abstract

Proper investments for expansion of generation, transmission and distribution systems in an electric grid is a very important issue that rely on optimal expansion planning of the grid resources. Investments on transmission network influence those in generation and distribution side which motivates a co-optimization of all these different resources of a grid. The co-optimization based Generation - Transmission Expansion planning is a large scale, constrained, hard bound optimization problem. This research article proposes an Information exchange based Clustered Differential Evolution algorithm (IE-CDE) for solving the problem of expansion planning of generation and transmission resources in an electric grid. The proposed algorithm is first tested extensively on the CEC 2017 constrained optimization benchmark problems and the results are compared with those obtained by state-of-the art algorithms to investigate the efficiency of the proposed algorithm in solving challenging constrained optimization problems. Then the proposed algorithm IE-CDE is used to solve the challenging Generation-Transmission expansion planning problem (GT) on a test system called Garver system. The implementation is also extended to incorporate the expansion planning of demand management resources along with generation and transmission resources (GTD) on the same test system mentioned before as well as an additional one called IEEE 24 bus system. The results obtained by proposed IE-CDE on the GT and GTD expansion planning problems are compared with state of the art algorithms in the literature and the comparison reveal that the proposed method is able to find better solutions than the other algorithms yielding lower cost of expansion for the electric grid. The claim for superiority of the proposed method over others is also substantiated by statistical significance tests on the obtained results.

Introduction

Generation, transmission and distribution-demand management are three main sections of a typical power system or an electric grid which aims a seamless and reliable delivery of electricity to end users. While it is important to operate different parts of the grid optimally to ensure reliable and economical delivery of energy everyday, it is also important to plan future expansion of these different resources of a grid to ensure the same in a future scenario with an elevated demand that is projected to grow at a rate greater than 30% till 2040 across the globe [1]. Thus optimal expansion planning of power system resources has become a very important problem for all the parties involved in power system along with the widely studied power system operation problems like unit commitment, economic load dispatch, etc.

Expansion planning of the resources in an electric grid is modeled as optimization problem. Traditionally in a vertically integrated system, the generation resources are planned first followed by the transmission resources i.e. the optimization problem is solved sequentially. On the other hand, in co-optimization models of planning both the generation and transmission resources are planned simultaneously to discover potentially better solutions that may be overlooked in sequential planning [2]. In conventional grid planning models the load is assumed to be constant over time which is no longer valid with recent advances in the area of Demand Side Management (DSM) [3,4] and Demand Response (DR) [5]. Investments in form of Internet of Things (IOT) based DSM/DR controllers in the distribution side [6] are making the dispatchable load possible. Such flexible loads can bring down the peak demand levels across the grid, which makes investment in demand management resources are cheaper alternative to investing in generation resources [7]. A co-optimization model with generation, transmission and demand management resources being planned simultaneously is an important problem for the following reasons:

• Generation, transmission and demand management resources are complementary. The load can be met by a local generator unit, or by supplying power through transmission lines, or controlled with demand management tools.

• Investing in demand management tools are cheaper alternative to the same in generation side.

Co-optimization models have been investigated by researchers [8] and also by Independent System Operators (ISO) who mandate considering the interaction between resources in long term expansion planning [9]. In a vertically integrated system co-optimization is used to expand the scope of planning problem to capture the trade offs by generation, transmission and demand management resources. In restructured power system, co-optimization model is used by transmission planners for anticipative planning [2]. Many off the shelf softwares for planning have used co-optimization models like COMPETES, ReEDS and LIMES but they do not consider the fuel transportation infrastructure to add into the cost [2]. Although consideration of the fuel transportation infrastructure cost while doing a co-optimization based generation-transmission expansion planning could be found in Refs. [10,11]. Some of the recently developed co-optimization softwares like NETPLAN and Prism 2.0 also consider the cost contribution by fuel transportation infrastructure [2]. Recent works on generation-transmission expansion planning have also considered co-optimization with generation-transmission and demand management resources keeping the current trend of smart grid technologies in consideration [12]. Although the authors in Ref. [12] did not consider any cost from the fuel transportation infrastructure in the model. This paper solves a co-optimization problem with generation-transmission and demand management resources while including the cost incurred for new fuel transport infrastructure investment also.

The co-optimization expansion planning of the grid is a complex, large scale, constrained cost minimization problem with many hard constraints like line flow limits, power balance at each node of the grid, corridor limits, etc [10]. Classical solution techniques for solving co-optimization planning problems includes Bender's decomposition [12], backward-forward search [11], Mixed Integer Linear Programming (MILP) [13], etc. Classical techniques have fast convergence and simple form of representation. However, classical techniques suffer from poor quality (PL approach), problems with system dimensionality (linear and dynamic programming), and their execution time for classical techniques may increase exponentially with increase in system dimentionality (branch and bound) [14]. These drawbacks inspired the application of many bio-inspired meta-heuristic techniques to the expansion planning problem. Meta-heuristic techniques are easy to implement as they do not need to convert variables into optimization programming set [15].

Bio-inspired meta-heuristic techniques are developed by imitating natural processes and a large number of works have been reported in literature solving different power system problems using these techniques. Use of such metaheuristic techniques in solving expansion planning problem can also be found in literature e.g. Particle Swarm Optimization [16,17], Bee colony optimization [18], Genetic Algorithm [19], Differential Evolution [20], NSGA-II [21]. It is evident from recent literature surveys [[22], [23], [24], [25]] that improvisation and hybridization in meta-heuristic algorithms can help them achieve better performance. Studies like [[26], [27], [28], [29], [30]] reveal that specially designed heuristics are always welcome and better performing for large scaled, hard-constrained optimization problems.

Differential evolution is a very popular bio-inspired metaheuristic tool used in a large number of works for solving constrained Variants of Differential Evolution (DE) are very successful in solving the constrained optimization problems, which is evident from the fact that most of the entries in competition for constrained optimization benchmarks in IEEE Congress on Evolutionary Computation (CEC) 2010 and 2017 were DE variants. One class of such DE variants is based on clustering techniques and is popular for multi-modal and constrained optimization problems [22,25].

This paper proposes an Information Exchange based Clustered Differential Evolution (IE-CDE) which is mainly inspired by ensemble strategies [31] and refresh gap techniques [32]. The proposed algorithm is tested on CEC 2017 benchmark functions for constrained optimization problem and extensively compared with state-of-the-art algorithms proposed in CEC 2017 [[27], [28], [29], [30]]. IE-CDE is also tested on co-optimization expansion planning problem on a 6-bus and 24-bus system. IE-CDE was also tested on 87 bus North-North Eastern Brazilian system to show the scalability of the proposed algorithm to real systems. The main contributions of this paper are listed below:

• A novel IE-CDE optimizer for constrained optimization problems has been proposed

• A co-optimization model for generation-transmission-demand management resource expansion has been developed along with consideration of fuel infrastructure cost.

• Above mentioned co-optimization model based generation-transmission-demand management resource expansion has been solved with the proposed IE-CDE algorithm.

• IE-CDE has been tested on CEC 2017 constrained optimization benchmark problems and its performance on the same has been done with top algorithms of the constrained optimization competition of CEC 2017.

• Statistical significance analysis of IE-CDE has been conducted on co-optimization problem and comparison with state-of-art meta-heuristic algorithms has also been done.

The rest of paper is organized in the following sections: 2. Problem Definition and Formulation, 3. Proposed Algorithm: IE-CDE, 4. Analysis on CEC 2017 benchmark functions, 5. Test system for co-optimization problem, 6. Simulation results and discussion, 7. Conclusion.