Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 1876934, 10 pages

https://doi.org/10.1155/2017/1876934

## Multiobjective Optimization Model for Wind Power Allocation

^{1}National University of Rio Cuarto, Rio Cuarto, Argentina^{2}IFF Fraunhofer, Magdeburg, Germany

Correspondence should be addressed to Juan Alemany; ra.ude.crnu.gni@ynamelaj

Received 16 November 2016; Revised 14 February 2017; Accepted 1 March 2017; Published 19 March 2017

Academic Editor: Jian G. Zhou

Copyright © 2017 Juan Alemany 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

There is an increasing need for the injection to the grid of renewable energy; therefore, to evaluate the optimal location of new renewable generation is an important task. The primary purpose of this work is to develop a multiobjective optimization model that permits finding multiple trade-off solutions for the location of new wind power resources. It is based on the augmented -constrained methodology. Two competitive objectives are considered: maximization of preexisting energy injection and maximization of new wind energy injection, both embedded, in the maximization of load supply. The results show that the location of new renewable generation units affects considerably the transmission network flows, the load supply, and the preexisting energy injection. Moreover, there are diverse opportunities to benefit the preexisting generation, contrarily to the expected effect where renewable generation displaces conventional power. The proposed methodology produces a diverse range of equivalent solutions, expanding and enriching the horizon of options and giving flexibility to the decision-making process.

#### 1. Introduction

Finding improvements in the operational conditions of a power system is an important task because many transmission networks still run inefficiently. For example, one of the current problems that most of the transmission systems face is that a great percentage of the branches are underused. In addition, for some electrical systems, the capacity to supply the load is even less than the total generation capability. Nowadays, this important fact is emphasized in power systems with high penetration of renewable resources (RR). Due to the stochastic nature of the RR, they have a significant share of unused power capacity. There are different options to increase the energy injection from renewable sources in order to exploit at a maximum the remaining renewable power capacity, for example, the addition of new transmission lines that could help delivering the extra energy, the increased participation of the consumers on the grid by using demand response programs [1, 2], the strategic location of energy storage systems that contribute to absorbing the renewable energy surpluses [3, 4], and the placement of new distributed generation that helps maximizing the load supply [5].

In addition, due to environmental concerns, the installation of distributed generation, especially renewable, is becoming a priority in many electrical systems. In those power systems where the massive integration of renewable resources is starting or planned, it is necessary to have an efficient strategy to select the best placement and proper capacity of these resources. The decision can be made based on an economic point of view (minimization of investment costs) only. However, it is better to formulate the problem as a multiobjective optimization problem to evaluate additional operational conditions of the system. The location of renewable generation constitutes a decision-making process that can be designed and influenced by different planning perspectives. For example, the placement of new wind farms, in addition to economic factors, can also take into account the minimization of wind generation intermittency [6] or the maximization of supplying load to exploit already existent generation in the grid. Formulating the problem as a multiobjective one permits placing new generation in network regions that could benefit from the injection of new energy resources and, on the other hand, helps the existent generation to increase the share on the load. Thus, evaluating alternative sites for new generation sources is crucial and determining the optimum level of distribution of generating capacity in a multiobjective framework is more advantageous.

Multiobjective methodologies have been applied in different power system applications. Regarding generation expansion, [7] proposes the implementation of the normal boundary intersection method applied to a multiobjective generation and transmission expansion problem. The problem is modeled as a mixed-integer linear programming problem suitable for application in large-scale systems. The optimization problem is aimed at minimizing four objective functions and minimizes total costs, environmental impact, and fuel price risk while maximizing the system reliability. The study performed in [8] presents a mixed-integer linear programming model for multiyear transmission expansion planning. The study considers two objectives, the uncertain capital costs and the electricity demand, competing to occupy the permissible uncertainty budget. The authors employ the augmented -constraint method to solve the multiobjective optimization problem maximizing the robust regions against the uncertain variables centered on their forecasted values. Reference [9] represents a distant wind farm integration using a multiobjective framework. The proposed method includes two main objectives; the first one embraces the annual operational and investment costs, whereas the second one minimizes the expected not served energy. The expansion planning method uses a mixed-integer optimization problem, and a fast elitist multiobjective nondominated sorting genetic algorithm. The article [10] presents a multiobjective planning framework for the integration of stochastic and controllable distributed energy resources (DER). Multiobjective optimization is based on a strength Pareto evolutionary algorithm. The objectives are to minimize annual line losses, the annual DER dispatched energy for local ancillary services, the annual DER curtailed energy, CO2 emissions, voltage quality index, and DER penetration level. A genetic based algorithm is presented in [11]. The model considers two objectives. The first objective is the minimization of investment cost and the second one is the maximization of system reliability. However, this work does not consider the network constraints. A linear programming based multiperiod expansion considering the transmission network is presented in [12]. Based on a weighting method, the objectives are the minimization of investment, operation and transmission costs, environmental impact, imports of fuel, and fuel prices risks. An interactive mixed-integer linear programming (MILP) approach is presented in [13]. The model considers three objective functions which quantify the total expansion cost, the environmental impact associated with the installed power, and the environmental impact associated with the energy generation. They do not consider the network. These ideas can be applied to improve the operational conditions of power systems, in particular with high penetration of RR, focusing on the system ability to supply more load. To accomplish this task, it is necessary to develop new models, evaluate different operative options, and consider extended planning strategies.

The aim of the work is to develop a multiobjective optimization model that permits finding multiple trade-off solutions for the location of new wind power resources. The proposed model uses a multiobjective framework based on the augmented -constrained methodology [14, 15]. Three competitive objectives are considered: the maximization of preexisting energy injection and the maximization of new wind energy injection, both embedded in the maximization of load supply.

The paper is organized as follows: Section 2 describes and formulates the improvement of the load supplying with the placement of new wind farms under a multiobjective perspective. Section 3 presents the numerical results and the discussion about them; finally, Section 4 resumes the main conclusions of this work.

#### 2. Load Supplying Improvement with Wind Farms Placement

The capacity of delivering energy from the generation to the load demands can be measured solving a well-structured problem [16]. The main task of this optimization problem is to stress the network to the maximum without causing line overloads. Different expansion alternatives can be compared, and as a result the system operational conditions are improved. The result of this type of problems seems to be trivial: including generation where the load is located. However, under a multiobjective perspective, the results present a more diverse spectrum of solutions, giving the decision maker (DM) a broad range of possibilities to take the final decision. Therefore, the DM can put into consideration different alternatives, equally valid, giving the same results. For example, given an expected level of load supplying, several power capacities and placements can accomplish the same goal.

##### 2.1. Multiobjective Perspective

The aim of a Multiple-Objective Optimization Problems (MOOP) is not to find a solution but a set of solutions. The set of nondominated solutions (Pareto optimal) has the condition that none of them can be improved without deteriorating at least one of the rest.

According to [14] the methods for solving MOOP can be classified into three main categories: a priori, interactive, and generation methods. In a priori method, the DM expresses preferences before the solution process. The drawback of this methodology is that the DM needs to know and quantify the preferences beforehand accurately. In the interactive method, the DM interchanges information with the algorithm and progressively drives the search towards the preferred solution. The drawback is that the entire set of efficient solutions is never observed; therefore, the preferred solution is biased to the last solution found. In generation method, the set of efficient solutions is created before any DM decisions. The main advantage is that the DM can analyze a diverse universe of solutions and take a decision based on them.

The disadvantage of the generation method is the high computational cost that requires getting efficient solutions. The most widely used generation methods are the weighting and the -constrained methods. The weighting method optimizes the weighted sum of the objective functions. By varying the weights, it is possible to obtain different efficient solutions. In the -constrained method, one of the objective functions is optimized using the other objective functions as constraints. The efficient solutions are obtained by parametric variation of the right-hand side of the constrained objective functions. The augmented -constrained method presented in [15], which is an improved version of the conventional -constrained method, has several advantages over the weighting method. The method can be used with multiobjective MILPs; the scaling of the objective functions is not necessary; the number of generated solutions can be user-controlled; it avoids the generation of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations.

Therefore, the aim of this paper is to apply the augmented -constrained method to explore the different placement alternatives for new wind farm generation that lead to a more efficient exploitation of the power network and improve the energy injection of preexisting generation, while maximizing the energy injection from renewable resources.

##### 2.2. Model Formulation

The proposed model formulation considers three objective functions: maximization of the load supplying, maximization of energy injected by preexisting generation, and maximization of energy provided by the installation of the new generation. Further details about the load supplying problem can be found in [16]. The model considers three different types of constraints: the linearized representation of the network, the limits of the preexisting generation and transmission elements, and the relationship between the wind power injection at each bus of the grid and the integer nature of the variable that represents the number of turbines to be installed. The following assumptions are considered:(i)There is fixed budget to install new wind generation.(ii)All the possible wind farm placement locations have the same capacity factor.(iii)All the new wind generations are installed at the same single period.(iv)The load participation factors are constant.(v)The reserve requirement for reliability is not considered.

Based on these assumptions, the proposed model formulation is as follows:

The description of each equation is as follows.

Equation (1) is first objective function and represents the maximization of the load supplying in the power system. Equation (2) is second objective function and represents the maximization of the energy injection from the preexisting generation. Equation (3) is third objective function and represents the maximization of the energy injection from the new generation to be installed. Equation (4) is linear power flow. Equation (5) represents branch flow limits. Equation (6) is maximum bound for wind generation and establishes the relationship between the wind power injection by bus, continuous variable, and the integer number of turbines. Equation (7) is maximum number of turbines to be installed. Equation (8) is maximum power of wind generation to be installed. Equation (9) represents power limits of preexisting generation. Equation (10) represents integer nature of installed turbines.

This set of equations form a MILP problem which combined with the multiobjective -constrained method can jointly be solved with any general-purpose solver that deals with MILP models. It is important to note that the model can be easily extended to consider multiperiod planning framework, nonconstant load participation factors, and different wind capacity factors at each location of the grid.

#### 3. Numerical Results

This section illustrates the proposed methodology using practical examples. We assume that the decision variables of the problem become more important than the objective values, because the objective functions and mimic a competitive electricity market environment. Therefore, we do not produce graphics representing Pareto frontiers; instead, we put the emphasis in representative variables of the problem.

The model represented by (1)–(10) and the algorithm described by [15] are implemented in GAMS, using GUROBI as the numerical solver [17]; the stop criteria are based on the gap which is set to zero.

First, the method is explained using a small example to illustrate the methodology practically. The system data is shown in Figure 1. The planned new wind generation is set to 100 turbines, each one with a 2 MW capacity. This power is allowed to be installed equally in all the buses, except for the cases indicated with “” where only that bus is allowed.