Optimal generation expansion planning via the Cross-Entropy method

Abstract

The Generation Expansion Planning (GEP) problem is a highly constrained, large-scale, mixed integer nonlinear programming problem. The objective of the GEP problem is to evaluate the least cost investment plan for addition of power generating units over a planning period subject to demand, availability, and security constraints. In this paper, a GEP model is presented and the Cross-Entropy (CE) optimization method is developed to solve the problem. The CE method is an effective algorithm for solving large combinatorial optimization problems. The main advantage of the CE method over other metaheuristic techniques is that it does not require decomposition of the problem into a master problem and operation subproblems, greatly reducing the computational complexity. This method also provides a fast and reliable convergence to the optimal solution.

The Cross-Entropy Method for Optimization

“…Each edge comes with a pre-specified cost and reliability (probability that it works). The NPP has applications in engineering (Wang et al 2009), telecommunications, transportation, energy supply systems (de Silva et al 2010, Kothari andKroese 2009), computer and social networking (Hintsanen et al 2010). The difficulty in solving this problem derives from the following aspects of the optimization.…”

“…To date, the CE method has been successfully applied to mixed integer nonlinear programming (Kothari and Kroese 2009); continuous optimal control problems (Sani 2009, Sani andKroese 2008); continuous multi-extremal optimization (Kroese et al 2006); multidimensional independent component analysis (Szabó et al 2006); optimal policy search (Busoniu et al 2010); clustering (Botev and Kroese 2004, Kroese et al 2007b, Boubezoula et al 2008); signal detection (Liu et al 2004); DNA sequence alignment Kroese 2002, Pihur et al 2007); noisy optimization problems such as optimal buffer allocation (Alon et al 2005); resource allocation in stochastic systems (Cohen et al 2007); network reliability optimization (Kroese et al 2007a); vehicle routing optimization with stochastic demands (Chepuri and Homem-de-Mello 2005); power system combinatorial optimization problems (Ernst et al 2007); and neural and reinforcement learning (Lörincza et al 2008, Menache et al 2005, Unveren and Acan 2007, Wu and Fyfe 2008.…”

Optimizing Generation Capacities Incorporating Renewable Energy with Storage Systems Using Genetic Algorithms

“…Although the addition of RES in the generation system offers many monetary and reliability benefits, the widespread use of RES by utility companies is still restricted. The main barrier which averts the large-scale use of RES is not the deficiency of adequate technology, but the higher cost of generated electricity [2]. Therefore, RES cannot compete with conventional energy resources only if the economics of both sources are taken into consideration.…”

Optimization by rare-event simulation

“…The CE method for optimization has been well studied and has been applied to a great variety of optimization problems, e.g., motion planning in robotic systems [51], multi-armed bandit problem [103], electricity network generation [52], control of infectious diseases [85], buffer allocation [3], and network reliability [53]. However, many other applications and modifications are still being developed for the CE method.…”

“…Since the appearance of the CE monograph [82] and the tutorial [20], the CE method has continued to develop and has been successfully applied to a great variety of difficult optimization problems, including motion planning in robotic systems [51], electricity network generation, [52], control of infectious diseases [85], buffer allocation [3], Laguerre tessellation [26], and network reliability [53]. An extensive list of recent work can be found in [14].…”