A grey-forecasting interval-parameter mixed-integer programming

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<p>lable at ScienceDirect</p><p>Energy 63 (2013) 334e344</p><p>Contents lists avai</p><p>Energy</p><p>journal homepage: www.elsevier .com/locate/energy</p><p>A grey-forecasting interval-parameter mixed-integer programming</p><p>approach for integrated electric-environmental managementeA case</p><p>study of Beijing</p><p>Xingwei Wang a, Yanpeng Cai a,b,*, Jiajun Chen a, Chao Dai c</p><p>aKey Laboratory for Water and Sediment Sciences of Ministry of Education, School of Environment, Beijing Normal University, Beijing 100875, China</p><p>b Institute for Energy, Environment and Sustainable Communities, University of Regina, 120, 2 Research Drive, Regina, Saskatchewan S4S 7H9, Canada</p><p>cDepartment of Environmental Sciences, Peking University, Beijing 100871, China</p><p>a r t i c l e i n f o</p><p>Article history:</p><p>Received 2 April 2013</p><p>Received in revised form</p><p>16 August 2013</p><p>Accepted 17 October 2013</p><p>Available online 14 November 2013</p><p>Keywords:</p><p>Interval-parameter programming</p><p>Mixed-integer programming</p><p>Grey-forecasting model</p><p>Integrated electric-environmental</p><p>management</p><p>Beijing</p><p>Uncertainties</p><p>* Corresponding author. Key Laboratory for Wate</p><p>Ministry of Education, School of Environment, Beijin</p><p>100875, China.</p><p>E-mail addresses: wangxingwei0812@gmail.com</p><p>edu.cn (Y. Cai).</p><p>0360-5442/$ e see front matter � 2013 Elsevier Ltd.</p><p>http://dx.doi.org/10.1016/j.energy.2013.10.054</p><p>a b s t r a c t</p><p>In this study, a GFIPMIP (grey-forecasting interval-parameter mixed-integer programming) approach</p><p>was developed for supporting IEEM (integrated electric-environmental management) in Beijing. It was</p><p>an attempt to incorporate an energy-forecasting model within a general modeling framework at the</p><p>municipal level. The developed GFIPMIP model can not only forecast electric demands, but also reflect</p><p>dynamic, interactive, and uncertain characteristics of the IEEM system in Beijing. Moreover, it can</p><p>address issues regarding power supply, and emission reduction of atmospheric pollutants and GHG</p><p>(greenhouse gas). Optimal solutions were obtained related to power generation patterns and facility</p><p>capacity expansion schemes under a series of system constraints. Two scenarios were analyzed based on</p><p>multiple environmental policies. The results were useful for helping decision makers identify desired</p><p>management strategies to guarantee the city’s power supply and mitigate emissions of GHG and at-</p><p>mospheric pollutants. The results also suggested that the developed GFIPMIP model be applicable to</p><p>similar engineering problems.</p><p>� 2013 Elsevier Ltd. All rights reserved.</p><p>1. Introduction</p><p>Integrated management of power generation and the associated</p><p>environmental effects is a priority for many municipalities across</p><p>the world. However, this is a challenging task for energy managers</p><p>due to the growing concerns over increasing electricity demand,</p><p>deteriorating environmental quality and shrinking energy avail-</p><p>ability [1]. Also, within such an IEEM (integrated electric-</p><p>environmental management) system, many issues need to be sys-</p><p>tematically considered, such as energy supply, conversion and</p><p>allocation, as well as the associated environmental and economic</p><p>implications. Moreover, these issues are highly interrelated with</p><p>many social, economic, political, environmental and technical fac-</p><p>tors, leading to a variety of complexities. Such complexities are</p><p>further complicated bymany uncertainties that exist due to the lack</p><p>of information and absence of the decision maker’s perception on</p><p>r and Sediment Sciences of</p><p>g Normal University, Beijing</p><p>(X. Wang), yanpeng.cai@bnu.</p><p>All rights reserved.</p><p>variations of system parameters [2,3]. To reflect such complexities</p><p>and facilitate the planning of IEEM systems, development of an</p><p>effective system analysis technique under uncertainty is desired.</p><p>Previously, a number of studies were conducted on the devel-</p><p>opment of system analysis methods and their applications to many</p><p>environmental, electric and resources management problems.</p><p>Particularly, many inexact optimization techniques were developed</p><p>due to their strength in dealing with uncertainties. Most of them</p><p>were based on IMP (interval mathematical programming) [4e12],</p><p>SMP (stochastic mathematical programming) [13e18] and FMP</p><p>(fuzzy mathematical programming) [19e22]. For instance, Span-</p><p>gardt et al. [23] proposed a SMP model for supporting power sys-</p><p>tems planning and GHG (greenhouse gas) emission reduction,</p><p>where power demand was expressed as a random variable. Muela</p><p>et al. [20] developed a FMP model for power generation manage-</p><p>ment, inwhich uncertainties of energy demands were presented as</p><p>fuzzy sets. Cai et al. [7] developed an inexact energy systems</p><p>planning model for supporting GHG-emission management. Xie</p><p>et al. [24] proposed an interval-fixed stochastic programming</p><p>method for supporting GHG mitigation in energy sectors, where</p><p>uncertainties were presented as intervals and/or probability den-</p><p>sity functions. Lin and Huang [16] proposed an interval-parameter</p><p>X. Wang et al. / Energy 63 (2013) 334e344 335</p><p>two-stage stochastic energy systems planning model for support-</p><p>ing energy-related decision-making and GHG emission mitigation</p><p>at a municipal level. Dong et al. [25] developed an interval-</p><p>parameter minimax regret programming method for supporting</p><p>power systems planning, where uncertainties were mostly</p><p>expressed as interval numbers. In terms of environmental effects of</p><p>power generation, Zehar and Sayah [26] presented a new method</p><p>based on a successive linear programming technique to analyze</p><p>economic trade-offs between fuel costs and pollutant emissions.</p><p>The model was then tested by the Algerian 59-bus power system</p><p>and was proved to be efficient in solving environmental/economic</p><p>power dispatch problems. Zhang et al. [27] developed an economic-</p><p>environmental-hydrothermal multi-objective scheduling model to</p><p>identify operating strategies of a hydrothermal power system.</p><p>Czarnowska and Frangopoulos [28] analyzed the fate and transport</p><p>of major pollutants that weremainly emitted by energy-conversion</p><p>technologies. They also assessed the associated environmental and</p><p>social costs for reducing such pollutants.</p><p>Though great achievements were obtained in the previous</p><p>studies, electric demands that were the key parameters for systems</p><p>planning were generated through either roughly forecasting (e.g.</p><p>trend analysis) or straight-line extrapolations of historical data.</p><p>Quantitative forecastingof electric demandswas seldomadopted. In</p><p>fact, qualification of future electric demands plays a vital role for</p><p>robust IEEM systems planning. For instance, underestimation of</p><p>electric demands may probably lead to outages that would be</p><p>disastrous to life and property. Comparatively, overestimation of</p><p>electric demandsmay probably result in unnecessary idle capacities</p><p>which would lead to the waste of energies and resources [29]. As</p><p>effective tools, methods that can forecast electric demands were</p><p>attractive to many researchers. For example, Pai and Hong [30]</p><p>employed the Jordan recurrent neural network to develop a recur-</p><p>rent support vector regressionmodel for electric-load forecasting in</p><p>Taiwan. Pao [31] investigated the effects of four economic factors on</p><p>electricity consumptions in Taiwan. Then based on the four factors,</p><p>he forecasted electric demands through the development of linear</p><p>and non-linear statistical models. Bianco et al. [32] investigated the</p><p>influences of several economic and demographic variables on en-</p><p>ergy consumptions in Italy. Then, he developed a long-term electric</p><p>demand forecasting model. Al-Rashidi and El-Naggar [33] fore-</p><p>casted electric demands in Egypt and Kuwait through using the</p><p>particle swarm optimization approach. Generally, these studies</p><p>were individuallyconductedonelectric demand forecasting, inexact</p><p>optimization techniques, and electric systems planning. Combina-</p><p>tion of those threemethods into a general modeling framework has</p><p>been seldom reported, which is desired for facilitating electric sys-</p><p>tems planning and environmental emissions reduction.</p><p>Therefore, the objective of this study is to develop a GFIPMIP</p><p>(grey-forecasting interval-parameter</p><p>mixed-integer programming)</p><p>approach for supporting IEEM systems planning under uncer-</p><p>tainty. The grey-forecasting model can predict electric demand in</p><p>the planning period, which will then provide input data for the</p><p>proposed interval-parameter mixed-integer programming model.</p><p>The two techniques will be incorporated within the process of</p><p>electric systems planning in Beijing. It will be an attempt to</p><p>integrate an energy forecasting model into a general modeling</p><p>framework with the consideration of atmospheric pollutant and</p><p>GHG emission reductions. The proposed GFIPMIP method will not</p><p>only be able to forecast electric demands in the planning period,</p><p>but also reflect the dynamic, interactive, and uncertain charac-</p><p>teristics of IEEM systems planning. Moreover, it can effectively</p><p>address issues regarding interactions between power supply and</p><p>emission reduction. The developed GFIPMIP model will then be</p><p>applied to the city of Beijing for demonstration. In detail, the</p><p>method can: a) integrate a grey forecasting model into a general</p><p>optimization modeling system, b) reflect complex interrelation-</p><p>ships of IEEM systems, c) tackle uncertainties expressed as in-</p><p>tervals, d) help decision maker identify power generation patterns</p><p>and system capacity expansion schemes under various emission</p><p>restrictions, and e) reflect trade-offs among electric supply, eco-</p><p>nomic cost, and environmental protection. The results will be</p><p>useful for helping decision makers in Beijing identify desired</p><p>planning strategies.</p><p>2. Overview of the electric-environmental management</p><p>system in Beijing</p><p>Along with economic development and population growth,</p><p>electric demand has rapidly increased in Beijing, leading to a series</p><p>of environmental problems. For example, dust, sulfur dioxide, ni-</p><p>trogen oxides, wastewater, waste ash and other hazardous mate-</p><p>rials discharge directly from thermal power plants, which are</p><p>extremely harmful to the environment and human health.</p><p>Considering this situation, integrated management of electric</p><p>generation and environmental pollution/GHGmitigation is desired.</p><p>This would request harmonious development among energy</p><p>development, power generation, economic development, and</p><p>environmental protection. Thus, local authorities and regulatory</p><p>agencies in Beijing have to seek comprehensive strategies for</p><p>achieving IEEM systems planning under multiple targets. This</p><p>would inherently require energy manager understand interactions</p><p>among various components of the IEEM system in Beijing to seek</p><p>optimal patterns of power generation, economic development, and</p><p>environmental protection.</p><p>In 2009, the total energy consumption in Beijing was over 65.7</p><p>million tonnes of standard coal. Approximately, 94 percents of</p><p>coal was imported from Shanxi, Inner Mongolia and Hebei</p><p>provinces. At the same time, over two-thirds of electricity was</p><p>imported from the neighboring Huabei power grid. The majority</p><p>of natural gas was imported from Shanganni gas field and Huabei</p><p>oil field. Crude oil was imported from western provinces such as</p><p>Shanaxi and Xinjiang. Scarcity of indigenous energy resources</p><p>and high dependency on imported ones has intensified Beijing’s</p><p>concerns on energy security. Fig. 1 shows interactive relationship</p><p>of different components within the city’s IEEM system. Three</p><p>parts are related to power generation, including energy supply</p><p>and conversion, as well as power distribution. Five types of en-</p><p>ergy carriers are connected with the electric sector in Beijing,</p><p>including domestic and imported coal, and imported natural gas,</p><p>fuel oil and electricity.</p><p>In this city, several technologies are utilizing for electricity</p><p>generation, such as those are based on coal, natural gas, fuel oil,</p><p>hydropower, wind, photo-volt, and biomass. In 2009, the total</p><p>electricity generation capacity in Beijing was 6865 MW. Among</p><p>them, electricity generated by coal-fired power plants was</p><p>2897 MW. Fig. 2 displays the local generated electricity and the</p><p>corresponding power self-sufficiency ratio in Beijing in the past</p><p>several years. A sharp contrast can be observed from figure (i.e., the</p><p>local power generation increases stably and self-sufficiency ratio</p><p>decreases gradually). Along with population growth and economic</p><p>development, domestic electricity production is far from suffi-</p><p>ciently meeting the increasing electric demands in Beijing. A large</p><p>amount of electricity will thus be imported annually.</p><p>In Beijing, electricity is mainly generated by fossil fuels. This</p><p>has caused a series of environmental problems. For example, the</p><p>amount of SO2 generated from power plants was 123.21 � 103</p><p>tonnes in 2008, accounting for 48% of the total in this city. Also,</p><p>Beijing (39� 560 N, 116� 200 E) is located in North China Plain,</p><p>where the pollution is not easy to disperse and diffuse. This leads</p><p>to a comparatively low environmental loading capacity and</p><p>Fossil fuel resources</p><p>Hydropower</p><p>Imported fuel oil</p><p>Wind power</p><p>Pollutant generation</p><p>Electricity grid</p><p>Agriculture</p><p>Industry</p><p>Commercial</p><p>Residential</p><p>End-users</p><p>Pumped storage</p><p>Photovoltaic power</p><p>Garbage power</p><p>Biomass power</p><p>Fossil fuel-fired</p><p>Energy supply Energy conversion Energy allocation</p><p>Imported natural gas</p><p>Imported coal</p><p>Domestic coal</p><p>Renewable energy</p><p>resources</p><p>Imported electricity</p><p>Fig. 1. Electric-environmental system of Beijing.</p><p>X. Wang et al. / Energy 63 (2013) 334e344336</p><p>continuous deterioration of environmental quality in Beijing and</p><p>its surrounding areas. The increasing emissions of pollutants and</p><p>the inherent disadvantages of topography have caused great</p><p>pressure on environmental protection. Therefore, Beijing has put</p><p>forward a number of energy policies to adjust power generation</p><p>patterns, and improve environmental quality. Integrated man-</p><p>agement of electric generation and environmental/GHG emissions</p><p>is thus adopted by Beijing as one of the priorities for adjusting</p><p>energy structure, ensuring energy supply security and protecting</p><p>environment.</p><p>Furthermore, Beijing has determined to cut 10% of the total</p><p>emissions (the 2005 level) of major pollutants by 2010. By year</p><p>2015, due to the utilization of new energies and renewable en-</p><p>ergies, 30 million tonnes of carbon dioxide and 200 tonnes of sulfur</p><p>dioxide are supposed to be reduced [34]. To accomplish the goal,</p><p>effective IEEM systems planning is desired. According to BMDRC</p><p>(Beijing Municipal Development and Reform Committee),</p><p>4590 MW of renewable and non-renewable energy based power</p><p>generation capacity will be installed in the next decade in Beijing to</p><p>meet its electric demands. Under this situation, integrating electric</p><p>demand forecasting model into an optimization modeling frame-</p><p>work with the consideration of environmental/GHG restrictions is</p><p>desired to local decision makers for helping them formulate</p><p>comprehensive strategies on electricity supply, renewable energy</p><p>development, and environmental protection.</p><p>0</p><p>5000</p><p>10000</p><p>15000</p><p>20000</p><p>25000</p><p>30000</p><p>2004 2005 2006 200</p><p>Local power g</p><p>Growth rate o</p><p>Self-sufficienc</p><p>Fig. 2. Power generation and self-sufficienc</p><p>3. Modeling formulation</p><p>3.1. Development of a grey-forecasting model</p><p>In order to identify optimal strategies for energy allocation and</p><p>electricity generation, electric demand needs to be forecasted.</p><p>Compared with conventional statistical models, grey-system-</p><p>theory models require a limited amount of data to acquire behav-</p><p>iors of unknown systems [35]. Among them, GM (1,1), a time-series</p><p>forecasting model, is widely used across the world [36e40]. It can</p><p>thus be adopted for forecasting electric demand. Particularly, when</p><p>forecasting successive changes of system behaviors, GM (1, 1) could</p><p>achieve satisfactory accuracy [41].</p><p>Consider a time sequence xð0ÞðkÞ that denotes historical series of</p><p>electricity consumptions:</p><p>xð0ÞðkÞ ¼</p><p>n</p><p>xð0Þð1Þ; xð0Þð2Þ;.; xð0ÞðnÞ</p><p>o</p><p>(1)</p><p>The grey differential equation is formed by an original time</p><p>series xð0ÞðkÞ using the AGO (accumulated generating operation)</p><p>technique. It can be denoted as follows:</p><p>xð0ÞðkÞ þ azð1ÞðkÞ ¼ b (2)</p><p>The whitening equation is therefore, as follows</p><p>[42]:</p><p>7 2008 2009 2010</p><p>0.00</p><p>0.05</p><p>0.10</p><p>0.15</p><p>0.20</p><p>0.25</p><p>0.30</p><p>0.35</p><p>0.40</p><p>0.45</p><p>eneration (GWh)</p><p>f electric demand</p><p>y rate</p><p>y ratio in Beijing in the past few years.</p><p>X. Wang et al. / Energy 63 (2013) 334e344 337</p><p>dxð1ÞðtÞ</p><p>dt</p><p>þ axð1ÞðtÞ ¼ b (3)</p><p>where a is the developing coefficient, and b is the control variable.</p><p>By least-square method, a and b can be obtained as:�</p><p>a</p><p>b</p><p>�</p><p>¼</p><p>�</p><p>ATA</p><p>��1</p><p>ATXn (4)</p><p>where:</p><p>A ¼</p><p>2664</p><p>�zð1Þð2Þ 1</p><p>�zð1Þð3Þ 1</p><p>« «</p><p>�zð1ÞðnÞ 1</p><p>3775 (5)</p><p>Xn ¼</p><p>2664</p><p>xð0Þð2Þ</p><p>xð0Þð3Þ</p><p>«</p><p>xð0ÞðnÞ</p><p>3775 (6)</p><p>where z is the background values and can be calculated by:</p><p>zð1ÞðkÞ ¼</p><p>h</p><p>xð1ÞðkÞ þ xð1Þðk� 1Þ</p><p>i.</p><p>2; xð1ÞðkÞ ¼</p><p>Xk</p><p>i¼1</p><p>xð0ÞðiÞ (7)</p><p>According to Eq. (3), the solution of xð1ÞðtÞ at time k can be</p><p>presented as follows:</p><p>bxð1Þðkþ 1Þ ¼</p><p>�</p><p>xð0Þð1Þ � b</p><p>a</p><p>�</p><p>e�ak þ b</p><p>a</p><p>(8)</p><p>Because the grey forecasting model is formulated using the data</p><p>of AGO rather than original data, it is necessary to transfer the data</p><p>of AGO to actual forecasting value. This technique is called the IAGO</p><p>(inverse accumulated generating operation) and can be denoted as:</p><p>bxð0Þðkþ 1Þ ¼</p><p>�</p><p>xð0Þð1Þ � b</p><p>a</p><p>�</p><p>e�akð1� eaÞ (9)</p><p>where k ¼ 2, 3,., n, bxð0Þð1Þ ¼ xð0Þð1Þ.</p><p>3.2. Development of grey-forecasting interval-parameter mixed-</p><p>integer programming</p><p>Based on the forecasting model, a grey-forecasting interval-</p><p>parameter mixed-integer programming approach is developed in</p><p>this research in Beijing. In this city, decision makers are responsible</p><p>for allocating energy resources/services from multiple facilities to</p><p>multiple end users through multiple electricity conversion tech-</p><p>nologies within a multi-period horizon [8]. They can formulate the</p><p>problem as minimizing the total expected system cost by achieving</p><p>optimal energy resource allocation patterns and system capacity</p><p>expansion schemes over the planning periods. In this model, the</p><p>decision variables can be divided into two categories: discrete and</p><p>continuous ones. The discrete variables represent whether or not</p><p>capacity expansion should be undertaken, while the continuous</p><p>ones represent the optimized energy resource allocation and power</p><p>generation patterns. The constraints are a number of inequalities to</p><p>define relationships among various decision variables and system</p><p>conditions. Additionally, the amount of electric demand in the</p><p>planning period is forecasted based on historical data of electricity</p><p>consumptions through the adoption of the grey-system-theory</p><p>model. Thus, a grey-forecasting interval-parameter mixed-integer</p><p>programming model can be formulated as follows:</p><p>min f� ¼</p><p>X5</p><p>i¼1</p><p>X3</p><p>t¼1</p><p>PTC�it ,Z</p><p>�</p><p>it þ</p><p>X9</p><p>k¼1</p><p>X3</p><p>t¼1</p><p>PV�</p><p>kt,X</p><p>�</p><p>kt þ</p><p>X9</p><p>k¼1</p><p>X3</p><p>m¼1</p><p>�</p><p>X3</p><p>t¼1</p><p>Y�</p><p>kmt,EC</p><p>�</p><p>kmt þ</p><p>X9</p><p>k¼1</p><p>X3</p><p>t¼1</p><p>X2</p><p>r¼1</p><p>X�</p><p>kt,COT</p><p>�</p><p>ktr,CT</p><p>�</p><p>ktr</p><p>(10a)</p><p>subject to:</p><p>Constraints for coal balance:</p><p>CFkt,</p><p>"</p><p>RCk þ</p><p>Xt</p><p>t’¼1</p><p>X3</p><p>m¼1</p><p>Y�</p><p>kmt,ECPkmt</p><p>#</p><p>,FE�kt � Z�1t þ Z�2t ; ct; k ¼ 1</p><p>(10b)</p><p>Constraints for natural gas balance:</p><p>CFkt,</p><p>"</p><p>RCk þ</p><p>Xt</p><p>t’¼1</p><p>X3</p><p>m¼1</p><p>Y�</p><p>kmt,ECPkmt</p><p>#</p><p>,FE�kt � Z�3t ; ct; k ¼ 2</p><p>(10c)</p><p>Constraints for fuel oil balance:</p><p>CFkt,</p><p>"</p><p>RCk þ</p><p>Xt</p><p>t’¼1</p><p>X3</p><p>m¼1</p><p>Y�</p><p>kmt,ECPkmt</p><p>#</p><p>,FE�kt � Z�4t ; ct; k ¼ 3</p><p>(10d)</p><p>Constraints for electricity demand:</p><p>X9</p><p>k¼1</p><p>X�</p><p>kt þ Z�5t � DTEtðsÞ; ct (10e)</p><p>Constraints for electricity generation:</p><p>X�</p><p>kt �</p><p>"</p><p>RCk þ</p><p>Xt</p><p>t’¼1</p><p>X3</p><p>m¼1</p><p>Y�</p><p>kmt,ECPkmt</p><p>#</p><p>,FE�kt ; ct; k ¼ 1;.;9</p><p>(10f)</p><p>Constraints for renewable energy resources availabilities:</p><p>RCk þ</p><p>X3</p><p>m¼1</p><p>Xt</p><p>t’¼1</p><p>Y�</p><p>kmt,ECPkmt � AV�</p><p>kt ; ct; k ¼ 4;.;9 (10g)</p><p>Constraints for environmental:</p><p>X9</p><p>k¼1</p><p>X�</p><p>kt,COT</p><p>�</p><p>ktr,</p><p>�</p><p>1� h�ktr</p><p>� � EP�tr ; c t; r (10h)</p><p>Constraints for GHG-emission reduction:</p><p>X9</p><p>k¼1</p><p>X�</p><p>kt,COP</p><p>�</p><p>kt � EEP�t ;ct; (10i)</p><p>Constraints for capacity expansion:</p><p>Y�</p><p>kmt</p><p>� ¼ 1 if capacity expansion is undertaken</p><p>¼ 0 otherwise</p><p>; ck; m; t</p><p>(10j)</p><p>X3</p><p>m¼1</p><p>Y�</p><p>kmt � 1;ck; t (10k)</p><p>Constraints for technical and non-negative:</p><p>X. Wang et al. / Energy 63 (2013) 334e344338</p><p>Z�it � 0; ci; t (10l)</p><p>X�</p><p>kt � 0; ck; t (10m)</p><p>where f� is the total expected system cost over the planning</p><p>periods (RMB 106); i is the index of energy resource (i ¼ 1 to 5 for</p><p>domestic coal, imported coal, imported natural gas, imported fuel</p><p>oil, and imported electricity, respectively); t is the planning</p><p>period (t ¼ 1e3); k is the power conversion technology (k ¼ 1 to</p><p>9; k ¼ 1 to 3 stands for a power generation technology that is</p><p>based on coal, natural gas power, and fuel oil, respectively; k ¼ 4</p><p>to 9 represents a power generation technology that is based on</p><p>hydropower, pumped storage, wind power, solar energy, solid</p><p>waste, and biomass, respectively); r is the type of pollutant,</p><p>including sulfur oxides and nitrogen oxides; PTC�</p><p>it is the supply</p><p>cost of energy resources i in period t (RMB 106/PJ, except for i ¼ 5</p><p>RMB 106/GWh); Z�it is the supply of energy resource i in period t</p><p>(PJ, except for i ¼ 5 GWh); PV�</p><p>kt is the variable cost for electricity</p><p>generated by technology k in period t (RMB 106/GWh); X�</p><p>kt is the</p><p>amount of electricity generation by technology k in period t</p><p>(GWh); Y�</p><p>kt is the binary variable for identifying whether or not a</p><p>capacity expansion action of conversion technology k needs to be</p><p>undertaken during period t; EC�</p><p>kmt is the expansion cost for</p><p>conversion technology k with option m during period t (RMB</p><p>106); ECPkmt is the expansion size for conversion technology k</p><p>with option m during period t (MW). COT�ktr is the emission in-</p><p>tensity of pollutant r from power generation technology k in</p><p>period t (kiloton/GWh); COP�kt is the emission intensity of GHG</p><p>from power generation technology k in period t (kiloton/GWh).</p><p>CT�ktr is the removal cost of pollutant r from power generation</p><p>technology k in period t (RMB 106/kiloton); CFkt is conversion</p><p>coefficient for power generation to energy resource; DTEtðsÞ is</p><p>electric demand during period t (GWh), which is predicted based</p><p>history electricity consumption data series; RCk is residue ca-</p><p>pacity of power generation technology k (MW); FE�kt is conversion</p><p>coefficient for power generation capacity to power generation;</p><p>AV�</p><p>kt is availabilities of power generation technology k in period t</p><p>(MW); h�ktr is the removal efficiency of pollutant r from power</p><p>generation technology k in period t (%); EP�tr is the total allowable</p><p>emissions of pollutant r during period t (kiloton). EEP�t is the</p><p>total allowable emissions of GHG during period t (kiloton).</p><p>3.3. Method of solution</p><p>The flow chart of GFIPMIP illustrates the solution algorithm and</p><p>can be summarized as follows:</p><p>Step 1: Assume the history electricity consumption data series</p><p>xð0Þ ¼ fxð0Þð1Þ; xð0Þð2Þ;.; xð0ÞðnÞg</p><p>Step 2: Use AGO to form a new data series. xð1Þ ¼ fxð1Þ</p><p>ð1Þ; xð1Þð2Þ;:::;xð1ÞðnÞg, xð1Þð1Þ ¼ xð0Þð1Þ; xð1ÞðkÞ ¼Pk</p><p>i¼1x</p><p>ð0ÞðiÞ;</p><p>k¼ 2;3;.;n.</p><p>Step 3: Calculate background values z(1), built by the mean</p><p>generating operation.</p><p>Step 4: Estimate the developing coefficient a and b by least-</p><p>square method and establish the grey differential equation.</p><p>Step 5: Solve the grey differential equation together with initial</p><p>condition and the desired forecasting output at step k can be</p><p>obtained.</p><p>Step 6: Formulate the GFIPMIP and put the forecasting time</p><p>series of annual electric demand and other parameters into</p><p>GFIPMIP.</p><p>Step 7: Transform the GFIPMIP into two sub-models, where the</p><p>sub-model corresponding to f�opt should be firstly solved (to</p><p>obtain the most optimistic decision option within the decision</p><p>space) if the objective is to minimizef�.</p><p>Step 8: Formulate f�opt sub-model, including the objective func-</p><p>tion and relevant constraints and solve the f�opt sub-model and</p><p>obtain solutions of Z�it opt, X</p><p>�</p><p>kt opt, Y</p><p>�</p><p>kmt opt and f�opt</p><p>Step 9: Formulate fþopt sub-model, including the objective func-</p><p>tion and the relevant constrains and solve the fþopt sub-model</p><p>and obtain solutions of Zþit opt, X</p><p>þ</p><p>kt opt, Y</p><p>þ</p><p>kmt opt and fþopt</p><p>Step 10: Combine solutions of the two sub-models, and obtain</p><p>optimized interval solutions for the GFIPMIP.</p><p>f�opt ¼</p><p>h</p><p>f�opt; f</p><p>þ</p><p>opt</p><p>i</p><p>Z�it opt ¼</p><p>h</p><p>Z�it opt; Z</p><p>þ</p><p>it opt</p><p>i</p><p>; ci; t;</p><p>X�</p><p>kt opt ¼</p><p>h</p><p>X�</p><p>kt opt; X</p><p>þ</p><p>kt opt</p><p>i</p><p>; ck; t</p><p>Y�</p><p>kmt opt ¼</p><p>h</p><p>Y�</p><p>kmt opt; Y</p><p>þ</p><p>kmt opt</p><p>i</p><p>; ck;m; t</p><p>This process is also displayed</p><p>in Fig. 3. The model is a mixed</p><p>integer linear programming. Thus, the solutions were considered as</p><p>global optimality.</p><p>4. Result analysis and discussions</p><p>The parameters and variables in the developed optimization</p><p>model are described as interval numbers since they are fluctuating</p><p>in a small range and without any information about their proba-</p><p>bility distributions or membership functions. For example, Table 1</p><p>shows energy supply cost in each period. The supply costs of do-</p><p>mestic coal are [14.4, 16.8], [18.1, 20.0], and [20.1, 23.0] RMB 106/PJ</p><p>over the three periods, respectively. It is assumed that there is no</p><p>supply cost for the renewable energy resources such as solar, hy-</p><p>dropower and wind. The available amounts of renewable energy</p><p>resources are merely affected by the corresponding local natural</p><p>conditions. The study system has a time-horizon of five years,</p><p>which is divided into 3 periods with period 1 representing 1 year</p><p>and period 2 and 3 representing 2 years. Table 2 presents expansion</p><p>options and the related costs of various technologies. The capital</p><p>costs, which are relevant to the three options, are expressed in net</p><p>present values with a discounted rate of 10%. These facilities can</p><p>merely be expanded one time in one period. Based on the related</p><p>policies and practical situations, two scenarios are analyzed in this</p><p>research: a) IEEM systems planning with consideration of re-</p><p>strictions on environmental emissions, and b) IEEM systems plan-</p><p>ning with consideration of restrictions on both environmental and</p><p>GHG emissions. Potential strategies can be identified through</p><p>comparing results under the two scenarios.</p><p>4.1. Electric demand</p><p>The goal of GM (1, 1) model is to extract as much information as</p><p>possible from the historical data for forecasting time-series electric</p><p>demands over the planning horizon. The data from 1979 to 2009</p><p>can be used to compare with the prediction values. Moreover, two</p><p>common criteria including theMARE (mean absolute relative error)</p><p>and the correlation coefficient (R2) can be utilized for evaluating</p><p>prediction performances of the GM (1, 1) model. If the value of R2 is</p><p>close to one or the value of MARE is close to zero, then the GM (1, 1)</p><p>model is consider performing very well in forecasting. The two</p><p>criteria can be defined as follows [43]:</p><p>MARE ¼ 1</p><p>n</p><p>Xn</p><p>t¼1</p><p>ðyt � bytÞ</p><p>yt</p><p>� 100% (11)</p><p>Uncertainties</p><p>expressed as intervals</p><p>Capacity</p><p>expansion</p><p>Mixed integer</p><p>programming</p><p>Interval linear</p><p>programming</p><p>GFIPMIP</p><p>GFIPMIP</p><p>Upper-bound submodel</p><p>Optimal solution for electric power system</p><p>Generation of decision alternatives</p><p>Data</p><p>controller</p><p>Input data Grey</p><p>1-AGO</p><p>GM (1, 1)</p><p>model</p><p>Grey</p><p>1-IAGO</p><p>Output data</p><p>GFIPMIP</p><p>Lower-bound submodel</p><p>Fig. 3. Flow chart of GFIPMIP.</p><p>Table 2</p><p>Expansion option and cost of various technologies.</p><p>Expansion Expansion</p><p>capacity</p><p>Expansion cost (RMB 109)</p><p>Coal-fired (k ¼ 1) (Unit: MW) Period 1 Period 2 Period 3</p><p>Option 1 (m ¼ 1) 100 [0.495,0.500] [0.495,0.500] [0.495,0.500]</p><p>Option 2 (m ¼ 2) 200 [0.990,1.000] [0.990,1.000] [0.990,1.000]</p><p>Option 3 (m ¼ 3) 300 [1.485,1.500] [1.485,1.500] [1.485,1.500]</p><p>Natural gas-fired (k ¼ 2)</p><p>Option 1 (m ¼ 1) 500 [2.000,2.250] [2.000,2.250] [2.000,2.250]</p><p>Option 2 (m ¼ 2) 600 [2.400,2.700] [2.400,2.700] [2.400,2.700]</p><p>Option 3 (m ¼ 3) 700 [2.800,3.150] [2.800,3.150] [2.800,3.150]</p><p>Fuel oil-fired (k ¼ 3)</p><p>X. Wang et al. / Energy 63 (2013) 334e344 339</p><p>R2 ¼ 1�</p><p>Pn</p><p>t¼1 ðyt � bytÞ2Pn</p><p>t¼1 ðyt � ytÞ2</p><p>� 100% (12)</p><p>where yt denotes the actual values of electric demand, byt denotes</p><p>the forecasted values of electric demand, yt denotes the average</p><p>values of electric demand, t is the time periods (t ¼ 1, 2,., n), and n</p><p>is the total observation number.</p><p>In this research, values of MARE and R2 through GM (1, 1) model</p><p>are 6.32% and 98.79%, respectively. It is indicated that the predic-</p><p>tion results of GM (1,1) model well match the actual data from 1979</p><p>to 2009. Fig. 4 presents the forecasting outputs of annual electric</p><p>demands from 1979 to 2009. The results imply that the GM (1, 1)</p><p>model can well capture the variations of the electric demand in the</p><p>future. Table 3 shows the forecasted electric demands in planning</p><p>periods. The forecasting results indicate that the electric demands</p><p>will keep increasing and exceed 120 billion KWh by 2015.</p><p>Option 1 (m ¼ 1) 50 [0.261,0.265] [0.261,0.265] [0.261,0.265]</p><p>Option 2 (m ¼ 2) 100 [0.522,0.530] [0.522,0.530] [0.522,0.530]</p><p>Option 3 (m ¼ 3) 150 [0.783,0.795] [0.783,0.795] [0.783,0.795]</p><p>Hydropower (k ¼ 4)</p><p>Option 1 (m ¼ 1) 50 [0.050,0.055] [0.048,0.053] [0.045,0.050]</p><p>Option 2 (m ¼ 2) 100 [0.100,0.110] [0.095,0.105] [0.090,0.100]</p><p>Option 3 (m ¼ 3) 150 [0.150,0.165] [0.1425,0.158] [0.135,0.150]</p><p>Pump storage (k ¼ 5)</p><p>Option 1 (m ¼ 1) 100 [0.480,0.500] [0.475,0.500] [0.435,0.435]</p><p>Option 2 (m ¼ 2) 200 [0.960,1.000] [0.914,1.000] [0.870,0.870]</p><p>Option 3 (m ¼ 3) 400 [1.920,2.000] [1.828,2.000] [1.740,1.740]</p><p>Wind power (k ¼ 6)</p><p>Option 1 (m ¼ 1) 100 [0.400,0.500] [0.360,0.400] [0.340,0.375]</p><p>4.2. Scenario 1</p><p>Table 4 shows the results of energy supply under scenario 1. Coal</p><p>(including domestic and imported ones) supply would increase</p><p>significantly from [69.3, 75.6] PJ in period 1 to [141.0, 147.8] PJ in</p><p>period 2, and reach [149.8, 157.9] PJ in period 3. Natural gas supply</p><p>would increase from [40.8, 47.6] PJ in period 1 to [117.7, 130.5] PJ in</p><p>period 2, and go up to [163, 172] PJ in period 3. Coal would be the</p><p>primary energy resource in the first two periods. In period 3,</p><p>Table 1</p><p>Energy supply cost in each period.</p><p>Period 1 Period 2 Period 3</p><p>Energy purchased cost (RMB 106/PJ, besides the unit of imported electricity is</p><p>RMB 106/GWh)</p><p>Domestic coal [14.4, 16.8] [18.1, 20.0] [20.1, 23.0]</p><p>Imported coal [22.9, 25.8] [25.8, 28.6] [28.9, 32.5]</p><p>Imported natural gas [46.4, 50.0] [60.4, 68.9] [74.4, 84.4]</p><p>Imported fuel oil [131.1, 133.5] [136.2, 140.7] [142.1, 145.7]</p><p>Imported electricity [79.2, 87.5] [84.0, 97.2] [101.4, 107.2]</p><p>natural gas supply would be the primary energy resources in Bei-</p><p>jing. This is because the technologies that are based on coal and</p><p>natural gas would be the most two competitive ones for producing</p><p>electricity without considering environmental restrictions. With</p><p>Option 2 (m ¼ 2) 200 [0.800,1.000] [0.720,0.800] [0.680,0.750]</p><p>Option 3 (m ¼ 3) 300 [1.200,1.500] [1.080,1.200] [1.020,1.125]</p><p>PV power (k ¼ 7)</p><p>Option 1 (m ¼ 1) 50 [2.150,2.250] [2.000,2.150] [1.925,2.000]</p><p>Option 2 (m ¼ 2) 100 [4.300,4.500] [4.000,4.300] [3.850,4.000]</p><p>Option 3 (m ¼ 3) 150 [6.450,6.750] [6.000,6.450] [5.775,6.000]</p><p>Garbage power (k ¼ 8)</p><p>Option 1 (m ¼ 1) 50 [0.600,0.680] [0.500,0.600] [0.488,0.563]</p><p>Option 2 (m ¼ 2) 100 [1.200,1.360] [1.000,1.200] [0.975,1.125]</p><p>Option 3 (m ¼ 3) 150 [1.800,2.040] [1.500,1.800] [1.463,1.688]</p><p>Biomass power (k ¼ 9)</p><p>Option 1 (m ¼ 1) 50 [0.205,0.225] [0.200,0.210] [0.175,0.198]</p><p>Option 2 (m ¼ 2) 100 [0.410,0.450] [0.400,0.420] [0.350,0.395]</p><p>Option 3 (m ¼ 3) 150 [0.615,0.675] [0.600,0.630] [0.525,0.593]</p><p>1975 1980 1985 1990 1995 2000 2005 2010</p><p>0</p><p>50</p><p>100</p><p>E</p><p>le</p><p>ct</p><p>ri</p><p>ci</p><p>ty</p><p>d</p><p>em</p><p>an</p><p>d</p><p>(b</p><p>il</p><p>li</p><p>on</p><p>K</p><p>W</p><p>h)</p><p>-0.5</p><p>0</p><p>0.5</p><p>R</p><p>el</p><p>at</p><p>iv</p><p>e</p><p>er</p><p>ro</p><p>r</p><p>Observation</p><p>Prediction</p><p>Relative error</p><p>Fig. 4. The outputs for annual electric demand under the GM (1, 1) model.</p><p>X. Wang et al. / Energy 63 (2013) 334e344340</p><p>the shrinking pollution-loading capacity, natural gas supply would</p><p>surpass coal supply in period 3 due to the fact that the pollutant</p><p>generated by coal fired power plants is larger than that of gas fired</p><p>ones. This suggests that natural gas fired power plants normally</p><p>have an advantage over coal fired ones in terms of pollution</p><p>emissions. The domestic coal supply would drop from Refs. [20,22]</p><p>PJ in period 1 to [32,34] PJ in period 3 since the length of period 3 is</p><p>twice of period 1, such a drop would mainly be due to the closure of</p><p>small-scale mining facilities in the planning period. Fuel oil supply</p><p>would be [13, 13.3], [25.9, 26.6], and [26, 26.6] PJ in periods 1 to 3,</p><p>respectively. Fuel oil supply would be stable in the planning pe-</p><p>riods. Imported electricity would be [56605.9, 58627.5], [126276.4,</p><p>129693.1],</p><p>and [149743.4, 151297.3] GWh in periods 1 to 3,</p><p>respectively. In fact, fossil fuels would be the major resources for</p><p>electricity generation, however, due to the restrictions on pollution</p><p>emissions (e.g. sulfur dioxide, nitrogen oxides), the total capacity of</p><p>fossil fuel fired power plants would be confined to a certain level.</p><p>Moreover, electricity generated by local fossil fuels could not meet</p><p>end-user demands in Beijing. This gap would be filled by imported</p><p>electricity and renewable energies.</p><p>Fig. 5 displays solution of power generation by various conver-</p><p>sion technologies under multiple expansion schemes. The amount</p><p>of electricity generated from fossil fuels would be [16319.9,</p><p>18180.0], [39268.4, 42207.1], and [49169.1, 50145.7] GWh in periods</p><p>1 to 3, respectively. The amount of electricity generated from</p><p>renewable energies would increase from [4311.2, 4472.6] GWh in</p><p>period 1 to [10833.6, 11311.6] GWh in period 2, and to [11961.3,</p><p>12538.6] GWh in period 3. For instance, electricity generated from</p><p>hydropower would reach [518.4, 544.32] GWh in period 1, [1171.2,</p><p>1228.8] GWh in period 2, and [1190.4, 1248.0] GWh in period 3. The</p><p>facility capacity of renewable energy power generation would</p><p>expand from 1.59 GW in period 1e1.79 GW in period 2, and 1.89 GW</p><p>in period 3. For example, hydropower and pumped storage would</p><p>expand 0.1 GW in period 1. However, owing to resources avail-</p><p>ability, there is no expansion in the following two periods, the ca-</p><p>pacity gap would be filled by wind power, garbage power and</p><p>biomass power. When a tighter environmental restriction is</p><p>adopted, a higher portion of power would be generated by</p><p>Table 3</p><p>Electric demand predicted by grey forecasting GM (1, 1) model.</p><p>Predicting electric demand (109 KWh)</p><p>Model 2011 2012 2013 2014 2015</p><p>GM(1, 1) 86.15 93.64 101.79 110.64 120.26</p><p>renewable energies due to their comparative competitiveness in</p><p>environmental emissions. However, adoption of renewable en-</p><p>ergies would still be limited by the high capital costs. For example,</p><p>photovoltaic power would not be expanded due to the compara-</p><p>tively high operational and expansion costs.</p><p>4.3. Scenario 2</p><p>As shown in Table 4, under this scenario, coal supply would be</p><p>[63.3, 69.1], [128.9, 135.1], and [125.9, 133.2] PJ in periods 1 to 3,</p><p>respectively. Comparatively, natural gas supply would be [37.5,</p><p>43.8], [111.0, 123.1], and [156.1, 164.7] PJ in periods 1 to 3. It in-</p><p>dicates that there would be no significant changes of coal produc-</p><p>tion in the city. However, there would be a major change in the</p><p>imported coal under scenarios 1 and 2. Compared with scenario 1,</p><p>the amounts of coal and natural gas would gradually decline. More</p><p>natural gas would be utilized than coal when considering the re-</p><p>strictions of GHG and environmental emissions. The main reason is</p><p>attributed to the fact that the amount of GHG emitted by coal fired</p><p>would be larger than that of natural gas fired ones. Thus, with a</p><p>limited GHG-emission quota, the share of coal-fired power in</p><p>electricity production would be gradually displaced by natural gas</p><p>fired ones. Fuel oil supply would be [13, 13.3] PJ in period 1 to [25.9,</p><p>26.6] PJ in period 2, and would increase to [26, 26.6] PJ in period 3.</p><p>Results indicate that the amount of imported electricity would be</p><p>[58968.3, 60326.4] GWh in period 1, [131789.8, 132149.4] GWh in</p><p>period 2, [154647.3, 157196.5] GWh in period 3. Under scenario 2,</p><p>the amount of imported electricity would be larger than that of</p><p>scenario 1. Such an increment would primarily be due to the</p><p>reduction of consumptions in fossil fuels and the assumption that</p><p>imported electricity would not contribute to emissions of GHG and</p><p>pollution in local area.</p><p>Fig. 6 displays the results of power generation and capacity</p><p>expansion of various conversion technologies under scenario 2.</p><p>Taking into account the dual restrictions on GHG and pollutant</p><p>emissions, electricity generated by fossil fuels would decline</p><p>dramatically compared with scenario 1. Totally, [15082.4, 16792.5],</p><p>[36681.2, 39432.1], [44859.9, 45858.7] GWh of electricity would be</p><p>generated by fossil fuels in periods 1 to 3, respectively. Since the</p><p>capacities of fossil fuel facilities would not meet end-user demands</p><p>due to the restrictions on environmental emissions, the gap would</p><p>be filled by imported electricity and renewable energy resources. At</p><p>the same time, considering electricity supply security, imported</p><p>electricity would be restrained to a certain amount. This would lead</p><p>to a large amount of capital investments in capacity expansion of</p><p>Table 4</p><p>Energy supply allocations under two scenarios.</p><p>Energy source Energy supply (PJ, besides the unit of imported electricity is GWh)</p><p>Scenario 1 Scenario 2</p><p>Period 1 (t ¼ 1) Period 2 (t ¼ 2) Period 3 (t ¼ 3) Period 1 (t ¼ 1) Period 2 (t ¼ 2) Period 3 (t ¼ 3)</p><p>Domestic coal [20.0, 22.0] [36.0, 38.0] [32.0, 34.0] [20.0, 22.0] [36.0, 38.0] [32.0, 34.0]</p><p>Imported coal [49.3, 53.6] [105.0, 109.8] [117.8, 123.9] [43.3, 47.1] [92.9, 97.1] [93.9, 99.2]</p><p>Imported natural gas [40.8, 47.6] [117.7, 130.5] [163.0, 172.0] [37.5, 43.8] [111.0, 123.1] [156.1, 164.7]</p><p>Imported fuel oil [13.0, 13.3] [25.9, 26.6] [26.0, 26.6] [13.0, 13.3] [25.9, 26.6] [26.0, 26.6]</p><p>Imported electricity [56605.9, 58627.5] [126276.4, 129693.1] [149065.4, 150942.4] [56972.2, 58893.0] [126596.2, 129980.0] [149743.4, 151297.3]</p><p>X. Wang et al. / Energy 63 (2013) 334e344 341</p><p>renewable energy based facilities. For example, the capacity would</p><p>be expanded from 1.74 GW in period 1e1.99 GW in period 2, and to</p><p>2.34 GW in period 3. For example, wind power would be expanded</p><p>from 0.15 GW in period 1 to 0.25 GW in period 2, and to 0.3 GW in</p><p>period 3. Biomass power would be expanded from 0.2 GW in period</p><p>1 to 0.3 GW in period 2, and to 0.45 GW in period 3. However, ca-</p><p>pacity expansions of renewable energy would be constrained by</p><p>resources availabilities. The result also indicates that the major</p><p>power generation technology would still be fossil fuel fired power</p><p>due to their low operational cost.</p><p>4.4. Comparisons of strategies under scenarios 1 and 2</p><p>Figs. 7 and 8 display power generation patterns under two</p><p>scenarios. As expected, power generation patterns have changed</p><p>greatly under the two scenarios, especially for power generation by</p><p>fossil fuels and renewable energies. The share of imported elec-</p><p>tricity would have a slight change under the two scenarios. Also,</p><p>over the planning horizon, the adoption ratio of renewable energies</p><p>would increase under both of the two scenarios. This can reflect the</p><p>increasing utilization of renewable energies in Beijing to enhance</p><p>a. lower bound</p><p>0</p><p>5000</p><p>10000</p><p>15000</p><p>20000</p><p>25000</p><p>30000</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>Period 1 Perio</p><p>P</p><p>ow</p><p>er</p><p>g</p><p>en</p><p>er</p><p>at</p><p>io</p><p>n (</p><p>G</p><p>W</p><p>h)</p><p>Electricity</p><p>Capacity ex</p><p>b. upper bound</p><p>0</p><p>5000</p><p>10000</p><p>15000</p><p>20000</p><p>25000</p><p>30000</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>Period 1 Perio</p><p>P</p><p>ow</p><p>er</p><p>g</p><p>en</p><p>er</p><p>at</p><p>io</p><p>n (</p><p>G</p><p>W</p><p>h)</p><p>Electricity g</p><p>Capacity exp</p><p>Fig. 5. Power generation and capacity ex</p><p>its electricity independency and security. Under scenario 1, the</p><p>growth rate of power generation from fossil fuels would decline</p><p>slightly due to the restrictions of environmental emissions. For</p><p>example, this value would decrease from 4.13% in period 2e3.08%</p><p>in period 3. At the same time, coal fired facilities would be gradually</p><p>displaced by natural gas fired ones. For example, the share of</p><p>electricity generated by coal would decrease from 11.6% in period</p><p>1e10.4% in period 2, and 9.6% in period 3. In contrast, the share of</p><p>electricity generated by natural gas would increase from 8.7% in</p><p>period 1e10.9% in period 2, and 12.7% in period 3.</p><p>Fig. 9 shows the total system costs under the two scenarios. The</p><p>total system cost would rise up alongwith GHG emission reduction.</p><p>With and without consideration of GHG emission reduction, the</p><p>total system cost would be [3.532, 3.588] and [3.731, 3.797] � 1012</p><p>RMB, respectively. It indicates that IEEM systems planning</p><p>without</p><p>the consideration of GHG emission reduction would lead to a</p><p>decreased system cost. In comparison, a higher system cost would</p><p>lead to a lower GHG emission. The main reason is that considering</p><p>restrictions on GHG emission reduction, fossil fuel fired power</p><p>generation facilities would be gradually replaced by renewable</p><p>energy based ones. This would cause a large amount of funds being</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>d 2 Period 3</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>C</p><p>ap</p><p>ac</p><p>it</p><p>y</p><p>ex</p><p>pa</p><p>ns</p><p>io</p><p>n(</p><p>G</p><p>W</p><p>)generation</p><p>pansion</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>d 2 Period 3</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>C</p><p>ap</p><p>ac</p><p>it</p><p>y</p><p>ex</p><p>pa</p><p>ns</p><p>io</p><p>n (</p><p>G</p><p>W</p><p>)eneration</p><p>ansion</p><p>pansion schemes under scenario 1.</p><p>a. lower bound</p><p>0</p><p>5000</p><p>10000</p><p>15000</p><p>20000</p><p>25000</p><p>30000</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>Period 1 Period 2 Period 3</p><p>P</p><p>ow</p><p>er</p><p>g</p><p>en</p><p>er</p><p>at</p><p>io</p><p>n (</p><p>G</p><p>W</p><p>h)</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>C</p><p>ap</p><p>ac</p><p>ity</p><p>e</p><p>xp</p><p>an</p><p>si</p><p>on</p><p>(G</p><p>W</p><p>)Electricity generation</p><p>Capacity expansion</p><p>b. upper bound</p><p>0</p><p>5000</p><p>10000</p><p>15000</p><p>20000</p><p>25000</p><p>30000</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>k=</p><p>1</p><p>k=</p><p>2</p><p>k=</p><p>3</p><p>k=</p><p>4</p><p>k=</p><p>5</p><p>k=</p><p>6</p><p>k=</p><p>7</p><p>k=</p><p>8</p><p>k=</p><p>9</p><p>Period 1 Period 2 Period 3</p><p>P</p><p>ow</p><p>er</p><p>g</p><p>en</p><p>er</p><p>at</p><p>io</p><p>n (</p><p>G</p><p>W</p><p>h)</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>C</p><p>ap</p><p>ac</p><p>ity</p><p>e</p><p>xp</p><p>an</p><p>si</p><p>on</p><p>(G</p><p>W</p><p>)Electricity generation</p><p>Capacity expansion</p><p>Fig. 6. Power generation and capacity expansion schemes under scenario 2.</p><p>Figure 7 Power generation patterns in planning periods under scenario 1</p><p>Scenario 1--Period 1</p><p>72.7%</p><p>21.8%</p><p>5.5%</p><p>Fossil fuel</p><p>Renewable energy</p><p>Imported electricity</p><p>Scenario 1--Period 2</p><p>22.7%</p><p>6.2%</p><p>71.2%</p><p>Fossil fuel</p><p>Renewable energy</p><p>Imported electricity</p><p>Scenario 1--Period 3</p><p>70.8%</p><p>5.8%</p><p>23.4%</p><p>Fossil fuel</p><p>Renewable energy</p><p>Imported electricity</p><p>Fig. 7. Power generation patterns in planning periods under scenario 1.</p><p>X. Wang et al. / Energy 63 (2013) 334e344342</p><p>invested in capacity expansions of renewable energy utilization. An</p><p>increasing capacity expansion investment for renewable energy</p><p>utilization to reduce environmental/GHG emissions would defi-</p><p>nitely lead to an increased system cost.</p><p>From the above analysis, it demonstrates that solutions obtained</p><p>from the GFIPMIP are helpful in supporting decisions of energy</p><p>resources allocation, capacity expansion of power generation and</p><p>GHG emission reduction management. The interval solutions are</p><p>effective to help generate decision alternatives, where a spectrum</p><p>Scenario 2--Period 1</p><p>73.1%</p><p>6.8%</p><p>20.1%</p><p>Fossil fuel</p><p>Renewable energy</p><p>Imported electricity</p><p>Scenario 2--</p><p>71.4%</p><p>Fig. 8. Power generation patterns in p</p><p>of options could be analyzed based on decision maker’s</p><p>preferences.</p><p>5. Conclusions</p><p>In this study, a grey-forecasting interval-parameter mixed-</p><p>integer programming (GFIPMIP) model was developed for sup-</p><p>porting the planning of integrated electric-environmental man-</p><p>agement systems, and environmental pollution and GHG emission</p><p>Period 2</p><p>21.2%</p><p>7.5%</p><p>Fossil fuel</p><p>Renewable energy</p><p>Imported electricity</p><p>Scenario 2--Period 3</p><p>8.0%</p><p>70.7%</p><p>21.3%</p><p>Fossil fuel</p><p>Renewable energy</p><p>Imported electricity</p><p>lanning periods under scenario 2.</p><p>3.40</p><p>3.45</p><p>3.50</p><p>3.55</p><p>3.60</p><p>3.65</p><p>3.70</p><p>3.75</p><p>3.80</p><p>Lower bound Upper bound Lower bound Upper bound</p><p>Scenario 1 Scenario 2</p><p>Total system cost ( RMB 1012 )</p><p>Fig. 9. The total system cost under two scenarios.</p><p>X. Wang et al. / Energy 63 (2013) 334e344 343</p><p>reduction in Beijing. It represented an attempt to integrate a fore-</p><p>casting model into a general optimization modeling framework at</p><p>the municipal level. A grey forecasting model [i.e., GM (1, 1)] was</p><p>used to assist in obtaining variations in electric demand in the near</p><p>future, which improved the accuracy of input parameters for the</p><p>optimization system. Also, uncertainties presented as interval</p><p>values could be tackled through the adoption of an inexact opti-</p><p>mization model. At the same time, issues concerning energy re-</p><p>sources allocation, capacity expansion of power generation</p><p>facilities, as well as emission reduction of environmental pollution</p><p>and GHG could be effectively addressed.</p><p>The results generated from the developed approach were useful</p><p>for adjusting the existing demand and supply allocation patterns,</p><p>power generation and capacity expansion schemes. They could also</p><p>be used to help decision maker in Beijing identify desired IEEM</p><p>systems planning strategies to guarantee the city’s power supply</p><p>security and environment pollution mitigation. The results indi-</p><p>cated that the developed method could also be applicable to other</p><p>engineering decision-making problems.</p><p>Acknowledgments</p><p>This research was supported by the National Natural Science</p><p>Foundation of China (51009004/E0901), and the special fund of</p><p>State Key Lab of Water Environment Simulation (11Z01ESPCN). The</p><p>authors would like to extend special thanks to the editor and the</p><p>anonymous reviewers for their constructive comments and sug-</p><p>gestions in improving the quality of this paper.</p><p>References</p><p>[1] Li YF, Huang GH, Li YP, Xu Y, Chen WT. Regional-scale electric power system</p><p>planning under uncertainty-A multistage interval-stochastic integer linear</p><p>programming approach. 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