Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 236958, 17 pages

http://dx.doi.org/10.1155/2015/236958

## Environmental and Economic Optimization Model for Electric System Planning in Ningxia, China: Inexact Stochastic Risk-Aversion Programming Approach

^{1}Research Institute of Technology Economics Forecasting and Assessment, School of Economics and Management, North China Electric Power University, Beijing 102206, China^{2}Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, SK, Canada S4S 0A2^{3}MOE Key Laboratory of Regional Energy Systems Optimization, S&C Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China

Received 10 June 2014; Accepted 23 August 2014

Academic Editor: Carsten Proppe

Copyright © 2015 L. Ji 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

The main goal of this paper is to provide a novel risk aversion model for long-term electric power system planning from the manager’s perspective with the consideration of various uncertainties. In the proposed method, interval parameter programming and two-stage stochastic programming are integrated to deal with the technical, economics, and policy uncertainties. Moreover, downside risk theory is introduced to balance the trade-off between the profit and risk according to the decision-maker’s risk aversion attitude. To verify the effectiveness and practical application of this approach, an inexact stochastic risk aversion model is developed for regional electric system planning and management in Ningxia Hui Autonomous Region, China. The series of solutions provide the decision-maker with the optimal investment strategy and operation management under different future emission reduction scenarios and risk-aversion levels. The results indicated that pollution control devices are still the main measures to achieve the current mitigation goal and the adjustment of generation structure would play an important role in the future cleaner electricity system with the stricter environmental policy. In addition, the model can be used for generating decision alternatives and helping decision-makers identify desired energy structure adjustment and pollutants/carbon mitigation abatement policies under various economic and system-reliability constraints.

#### 1. Introduction

In recent years, with more concern on environmental aspects, achieving sustainable social development is an important challenge faced by many countries around the world. In particular, for China, haze weather, mainly caused by coal-fired power plants, heavy industry, and vehicles, is responsible for respiratory illness, stroke, heart disease, cancer, and birth defects. The amount of sulfur dioxide (SO_{2}) and nitrogen oxide (NO_{x}) emission from thermal power industry accounts for more than 40% of the national emissions in China. Electricity industry has been one of the main contributors to environment degradation with a larger amount of SO_{2}, NO_{x}, and particle pollution (PM) emission and ever-growing power demand [1]. Many researches have been done to seek the trade-off between energy system and environment system [2]. Although various emission control schemes have been pushing forward in order to meet even stricter air pollution standards, the actual environmental quality has not been improved duo to many challenges in the processes of environment-friendly energy systems management. Firstly, energy systems are complicated with uncertainties that may exist in many system parameters (e.g., power load demand, energy prices, and available resources) [3]; their interrelationships would intensify the competitive issue of energy system planning and environmental quality management. Secondly, regional decision-makers are facing difficulties in dealing with the inevitable conflicts between economic and environmental goals under the stricter pollution control policy [4]. Therefore, reasonable and effective regional electricity system planning constrained by environmental quality under uncertainty is desired.

Previously, a number of inexact optimization methods were developed for reflecting the uncertainties/complexities and managing energy and environmental planning under uncertainty, including included fuzzy mathematical programming (FMP), stochastic mathematical programming (SMP), chance-constrained programming (CCP), and interval parameter programming (IPP) [5–11]. For example, Guo et al. (2008) developed an interval chance-constraint semi-infinite programming for regional energy system planning under uncertainties, where energy sources allocation, fuel prices, environmental regulations, and regional energy structure were desired [12]. Xie et al. (2010) proposed an interval fixed-mix stochastic programming model for greenhouse gas emissions reduction management in a regional energy system under uncertainties [13]. Li and Huang (2012) proposed a scenario-based multistage interval-stochastic integer programming model for electric-power system planning with environmental emission management under uncertainty [14]. Dong et al. (2013) developed a fuzzy radial interval linear programming model for robust planning of energy management system, in which the uncertainties were expressed as fuzzy sets and regular and radial intervals [15]. Cai et al. (2009) developed a fuzzy-random interval programming model for energy management systems strategy optimization under multiple uncertainties [16]. Ji et al. (2014) proposed a two-stage stochastic inexact robust optimization model for residential microgrid energy management, where combined cooling, heating, and electricity technology were introduced to satisfy various energy demands [17]. Among these techniques, inexact two-stage stochastic programming (ITSP) with recourse, integrated interval-parameter programming, and two-stage stochastic programming (TSP) could deal with uncertainties expressed as probability distributions and discrete intervals and received extensive attentions over the past years [18–20]. In the ITSP model, an initial energy-related decision is first undertaken before the random events happen; after the random information associated with the stochastic nature of emission-reduction targets is known, a second-stage decision can be made in order to minimize “penalties” that may appear due to any infeasibility. In general, ITSP is effective for problems where an analysis of policy scenarios is desired and was successfully applied in many fields. A remarkable limitation of the methods is their incapability in reflecting the risk of failing to limit a cost target (or reach an income target) and enhancing the system stability in regional energy system management with multiple power-generating technologies, due to considering the minimum cost or maximum net benefit as the system optimization objective [21].

Failure to consider the risk would lead to unrealistic expectations in investment profits and even investment losses. Since the construction of electricity facilities is irreversible and extremely expensive, it is imperative to deal with investment and operation risk cautiously [22]. In order to reflect such risk aversion in energy system management, downside risk was proposed to measure the system variability for a risk-averse energy system manager. The downside risk methods consider any cost above the fixed investment as a risk, measure risk below a certain point, and take all deviations below a target level into consideration [23, 24]. Downside risk has been applied in many risk management studies, like investment portfolio, water quality management, and energy market [25–27]. Nevertheless, few studies have been found in developing an inexact two-stage stochastic downside risk-aversion (ITSDP) model for supporting regional electric-power systems planning under a general regional pollutants emission mitigation and electricity demand management framework.

Therefore, considering the recent liberalization of the electricity markets and the long-term electricity system planning with maximum profits and risk-aversion from the manager’s perspective, the objective of this study is to developed an inexact two-stage stochastic downside risk-aversion model for electricity system planning and environmental pollution reduction management over a long-term planning horizon in Ningxia Hui Autonomous Region (Ningxia), China. This objective entails the following: (i) combination of interval parameter programming, two-stage stochastic programming, and downside risk method into a general planning framework for reflecting the uncertainties/complexities in regional energy-environmental systems; (ii) development of a regional energy-environmental systems management model to address interactions among energy supply, power generation, and load demand and air pollutants emissions; (iii) application of the developed method for regional electric-power systems planning with different emission mitigation level and risk-aversion attitudes in Ningxia Hui Autonomous Region (Ningxia), China. The proposed model will help obtain multiple power generation schemes under different environmental requirements, income targets and risk levels, which are valuable for creating an eco-friendly society and maintaining the sustainable development of regional energy system.

#### 2. Methodology

Two-stage stochastic programming (TSP) could provide feasible solutions for programming problems under uncertainties. In TSP, the uncertain parameters are usually expressed as probability distribution functions (PDFs) [28, 29]. In TSP, decision variables are divided into two subsets: those that must be determined before the realizations of random variables are known and those (recourse variables) that are determined after the realized values of the random variables are available. A general TSP model can be formulated as follows [30]: subject to

where is vector of first-stage decision variables; is first-stage benefits; is random events after the first-stage decisions are made; is the scenario of the happening of random events; is probability of event ; , , are model parameters with reasonable dimensions (random parameters); is system recourse at the second stage under the occurrence of event ; is expected value of the second-stage system penalties.

Although the TSP models could deal with probabilistic uncertainties in the model’s right-hand sides which are often related to resources availability, they have difficulties in handling independent uncertainties of the model’s left-hand sides and cost coefficients. Interval-parameter programming is an alternative for handling uncertainties in the model’s left- and/or right-hand sides as well as those that cannot be quantified as membership or distribution functions, since interval numbers are acceptable as its uncertain inputs [31]. Assume to be a set of intervals with crisp lower bound (e.g., ) and upper bounds (i.e., ), without information about distribution. Thus, a set of closed and bounded interval numbers could be denoted as [32]: Introducing interval parameters into conventional ITSP model, the models (1a)–(1d) could be further modified as follows [33]: subject to

On the other hand, the goal of the ITSP model could be maximizing the total expected profit (or minimizing the total expected cost). While considering risk management, it fails to provide appropriate strategies to achieving minimum profits (or controlling maximum costs) over the different scenarios. Thus, risk management theory should be added to increase the feasibility and reliability of the programming system.

According to previous research on risk management, downside risk theory is a successful approach to assess and manage risk. It can assist to incorporate risk concern (i.e., the tradeoff between the expected value and variability of the expected value) into optimization models. To present the concept of downside risk, we define as the positive deviation from a profit target for design and as the benefit during the planning horizon; that is, Downside risk is then defined as the expected value of To incorporate the concept of downside risk in the framework of two-stage stochastic models, let present the positive deviation from the profit target for design and scenario defined as follows [34]: Because the scenarios are probabilistically independent, the expected value of (i.e., downside risk) can be expressed as the following linear function of : Based on the definitions of downside risk, it is found that downside risk is an expectation in income/cost, which is quite different from the definition of other risk measures that represents a probability value. Moreover, is a continuous linear measure because it does not require the use of binary variables in the two-stage stochastic formulation [35]. This is a highly desirable property to potentially reduce the computational requirements of the models to manage risk. If the decision-maker is risk averse, he/she would prefer the lower risk. In this case, we can introduce a downside risk into the ITSP model to averse the risk. The schematic diagram of the proposed inexact two-stage stochastic down-side risk-aversion programming is illustrated in Figure 1. Therefore, an inexact two-stage stochastic downside risk-aversion programming can be formulated as follows: subject to where is the expected downside risk value that calculates through the solution of the ITSP model and is a control factor to acquire a more stringent limitation of risk, . By computing the objective function for different values of , we can obtain a series of solutions with the consideration of manager’s risk tolerance.