Evaluation of different initial solution algorithms to be used in the heuristics optimization to solve the energy resource scheduling in smart grids
Graphical abstract
Introduction
Presently, the planning and operation of the power systems deal with diversity of distributed energy resources, due to the increasing use of distributed generation (DG) units, mainly based on renewable sources [1]. In the future, the integration of storage units, demand response (DR) programs on the consumers side and namely the increasing penetration of electric vehicles (EVs) will also influence the power systems planning and operation [2]. The integration of these new distributed resources in power systems will require specific technical conditions to be satisfied. The introduction of new players in a smart grid context [3] is expected to help in the fulfilment of those conditions. The smart grid and all its related elements are the adequate environment to deal with the new changes in the power system and new uncertainties related with the distributed energy resources [4]. Smart grids are intended to co-ordinate the needs and capabilities of resources, network operators, consumers, aggregator player and electricity market stakeholders to operate the power system as efficiently as possible, minimizing costs and environmental impacts while maximizing the power system reliability, resilience and stability [5].
The intermittent power generation of renewable sources based DG units is one of the problems that affects more the planning and operation of the power systems [6]. The integration of EVs with vehicle-to-grid (V2G) technology [7] (i.e. ability to discharge from the EV battery to the network) can help to deal with this intermittent behaviour of the renewable sources [8]. EVs are parked approximately 96% of the time and in only 4% of the time the vehicles are travelling [7]. Thus, EVs can be used most of the time to store in their batteries the surplus of energy produced by renewable sources. In the following periods, EVs can use this extra stored energy to inject in the network, which will compensate the intermittency of the renewable sources. On the other hand, the network operators must guarantee a minimum amount of stored energy in the EVs batteries with the goal of supporting their daily trips [9].
In future scenarios of intensive distributed resources penetration (e.g. DG and EVs), the power system is expected to have a more complex planning and operation, in which the day-ahead optimal resource scheduling problem is of utmost importance. The optimal resource scheduling is characterized by obtaining the optimal dispatch of the available resources considering a certain objective function while satisfying the forecasted consumer demand. Typically, the minimization of the operation cost is used as objective function [10]. The increasing number of energy resources makes the optimal resource scheduling a large dimension and complex problem with several local optima, in which the task of obtaining the global optimum will be more difficult [11]. For these large dimension and complex problems, a deterministic technique can take several hours or even days to determine the optimal dispatch [12]. Therefore, artificial intelligence (AI) techniques, mainly metaheuristics, have been applied to deal with large dimension and complex optimization problems. Metaheuristics like tabu search, simulated annealing (SA), genetic algorithm (GA), particle swarm optimization (PSO) and artificial immune system have been used to solve many power system problems, as it is discussed in Ref. [13]. In Refs. [14], [15] the use of PSO to handle unit commitment related to EVs penetration is proposed. Ghanbarzadeh et al. [16] also applied PSO for dealing with the resource scheduling problem (based on a unit commitment perspective) with EVs penetration in the network. On the other hand, authors in Ref. [17] implemented GA to optimize the EVs charging considering the minimization of the operation cost while taking into account the network constraints. Although these techniques cannot ensure finding the global optimum [18], they use less memory and execution time than deterministic approaches. However, these metaheuristic techniques can be conveniently improved by adjusting the different parameters of each technique and, most importantly, by using good initial solutions in order to reduce the convergence effort of the optimization methods [19]. Proper initial solutions can provide solutions near the optimal one with a low execution time, solving some of the drawbacks of the metaheuristics [20]. In the initial solution, it is possible to incorporate other techniques (AI or deterministic) leading to a hybrid metaheuristic, which combines the best features of both techniques, therefore providing better results than traditional metaheuristics used to solve individually the optimization problem [21].
The main contribution of this paper is the evaluation of the SA algorithm effectiveness and efficiency considering different initial solution algorithms. Five different algorithms are developed to find the initial solution namely: (1) random solution (base case); (2) Ant colony optimization; (3) Naive-scheduling heuristic; (4) Pre-scheduling heuristic; (5) Mixed-integer linear programming. The pre-scheduling and mixed-integer linear programming heuristics are two new algorithms applied for this optimization problem that are proposed in this paper. The second and fifth algorithms turn the SA algorithm into a hybrid heuristic. This aspect of incorporating good strategies in the initial solutions is even more important in local-based metaheuristics, like the SA algorithm. In fact, these techniques do not have the same characteristics as population-based algorithms (e.g. GA and PSO) which use several individuals searching different areas of the search space in the same iteration. The local metaheuristic algorithms would benefit from an initial solution near to the optimal one, in order to use the rest of the iteration process in searching for new solutions near the optimal one. Nevertheless, the population-based methods can use one of these algorithms to obtain a good solution for an individual of the initial population, therefore allowing the algorithm to start the searching process with an individual that is better than the rest of the population. This strategy could help the population based algorithms to show a faster convergence than starting from a random initial population. In the paper, the proposed algorithms (pre-scheduling and mixed-integer linear programming) were also tested in GA and PSO to evaluate their performance in population-based metaheuristics and to compare with the SA results.
The above mentioned five algorithms are tested and validated in a very complex optimization situation concerning the day-ahead optimal resource scheduling problem considering an intensive penetration of distributed resources, mainly EVs. This problem is particularly interesting due to the high number of constraints and problems variables including the binary ones. To improve the applicability of the proposed methods, an alternating current (AC) power flow has been included in the constraints, therefore allowing to guarantee the voltage limits in the buses and the lines thermal limits. These constraints are particularly hard to guarantee due to the cosine and sine functions included in the AC power flow [22]. Other important aspect concerning the development of the proposed initial solution algorithms is their adaptability to other heuristics, like particle swarm optimization or genetic algorithms, among others. The algorithms are implemented in a module structure, therefore allowing their use independently of the following heuristic. Additionally, the modular implementation allows to run the initial solution algorithms in parallel, so that the behaviour of each one in different networks or different operational conditions can be assessed. The proposed algorithms are tested in a case study concerning a distribution network with 37 buses, 25 DG units and 1908 consumers. In the case study, a EVs penetration of up to 2000 vehicles is considered.
This paper is structured with the following sections: after this introductory section, Section 2 presents a mathematical formulation of the day-ahead optimal resource scheduling problem. Section 3 focuses on the proposed initial solution algorithms. A case study is presented in Section 4, and the last section presents the conclusions.
Section snippets
Optimal resource scheduling with intensive use of EVs
In the smart grid paradigm, the aggregation of distributed energy resources will be an important asset to the management and control of these resources. Therefore, some aggregators, like the virtual power player (VPP) [23] are being considered to aggregate distributed energy resources, mainly the ones connected at the distribution level. VPP will need to perform an optimal resource scheduling of the aggregated resources [3], and the SA algorithm with the different heuristics will be used for
Energy resource scheduling method
The proposed initial solution algorithms are explained in this section, including the implementation of these algorithms in the SA technique. Subsection 3.1 explains the reasons behind the application of SA in this paper and discusses about the application of SA to other optimization problems. The SA algorithm used in this paper is described in subsection 3.2. The decision variables used in the SA algorithm are described in subsection 3.3. Subsection 3.4 presents the initial solution algorithms
Case study
In the present subsection, the different initial solution algorithms are tested and the obtained results are compared. The results for the operation cost and the execution time are discussed in detail and the energy resource scheduling solution is evaluated for each algorithm. This section is divided into three subsections. Subsection 4.1 presents the information and input data used in the case study of this paper. Subsection 4.2 presents the results of the initial solution and the robustness
Conclusions
The paper presented two new algorithms to generate initial solutions in metaheuristics: (1) pre-scheduling heuristic (PERS2A algorithm) and (2) mixed-integer linear programming heuristic (SADT algorithm). One idea for improving the solution quality without affecting too much the execution time of a metaheuristics is the incorporation of a heuristic to generate a good initial solution. These proposed heuristics are independent from the SA, GA and PSO algorithms, thus they can be applied in other
Acknowledgements
This work is supported by FEDER Funds through the “Programa Operacional Factores de Competitividade—COMPETE” program and by National Funds through FCT “Fundação para a Ciência e a Tecnologia” under the projects FCOMP-01-0124-FEDER: UID/EEA/00760/2013, and SFRH/BD/81848/2011 (Tiago Sousa PhD), and by the SASGER-MeC, project n° NORTE-07-0162-FEDER-000101, co-funded by COMPETE under FEDER Programme. Hugo Morais is supported by the SOSPO project has received funding from the Danish Council for
Tiago Sousa received the B.Sc. and Master degrees in Electrical Engineering from the Polytechnic Institute of Porto (ISEP/IPP), Portugal in 2009 and 2011 respectively. He is an Assistant Researcher at GECAD – Knowledge Engineering and Decision-Support Research Center and is pursuing the Ph.D. degree at IST Instituto Superior Técnico – University of Lisbon (Portugal). His research interests include smart grids and heuristic optimization in power and energy systems.
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Tiago Sousa received the B.Sc. and Master degrees in Electrical Engineering from the Polytechnic Institute of Porto (ISEP/IPP), Portugal in 2009 and 2011 respectively. He is an Assistant Researcher at GECAD – Knowledge Engineering and Decision-Support Research Center and is pursuing the Ph.D. degree at IST Instituto Superior Técnico – University of Lisbon (Portugal). His research interests include smart grids and heuristic optimization in power and energy systems.
Hugo Morais (S’08–M’11) received the M.Sc. degree in Power Systems in Polytechnic of Porto and the Ph.D. degree in Electrical Engineering from the University of Trás-os-Montes e Alto Douro (Portugal). He is currently holding a position as postdoctoral researcher at the Technical University of Denmark (DTU), Automation and Control Group (AUT). His research interests include distributed energy resources management, virtual power players, smart grids, and future power systems, agents technology and power systems visualization.
Rui Castro received the Electrical Engineering degree and the M.Sc. and Ph.D. degrees from IST Instituto Superior Técnico—University of Lisbon, Lisbon, Portugal, in 1985, 1989, and 1994, respectively. In 1985, he joined University of Lisbon, where he is currently a Professor in the Power Systems Section and a Senior Researcher at INESC-ID. His research interests are in the areas of power systems transients and control, renewable energies, energy pricing, and open markets.
Zita Vale is the director of GECAD and a professor at the Polytechnic Institute of Porto. Her research interests include artificial intelligence applications to power system operation and control, electricity markets, and distributed generation. Vale has a PhD in electrical and computer engineering from the University of Porto.
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