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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Energy Res.</journal-id>
<journal-title>Frontiers in Energy Research</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Energy Res.</abbrev-journal-title>
<issn pub-type="epub">2296-598X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">883602</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2022.883602</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Energy Research</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>A Low-Carbon Dispatch Strategy for Power Systems Considering Flexible Demand Response and Energy Storage</article-title>
<alt-title alt-title-type="left-running-head">Han et al.</alt-title>
<alt-title alt-title-type="right-running-head">Power System Flexible Resource Dispatch</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Han</surname>
<given-names>Haiteng</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1422195/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wei</surname>
<given-names>Tiantian</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1422234/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wu</surname>
<given-names>Chen</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Xu</surname>
<given-names>Xiuyan</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zang</surname>
<given-names>Haixiang</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Sun</surname>
<given-names>Guoqiang</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wei</surname>
<given-names>Zhinong</given-names>
</name>
</contrib>
</contrib-group>
<aff>
<institution>College of Energy and Electrical Engineering</institution>, <institution>Hohai University</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1533378/overview">Qinran Hu</ext-link>, Southeast University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1698072/overview">Minjian Cao</ext-link>, Tsinghua University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1698743/overview">Xin Zhao</ext-link>, Southeast University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1323463/overview">Xun Dou</ext-link>, Nanjing Tech University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Haiteng Han, <email>hanht@hhu.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Smart Grids, a section of the journal Frontiers in Energy Research</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>26</day>
<month>04</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>883602</elocation-id>
<history>
<date date-type="received">
<day>25</day>
<month>02</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>21</day>
<month>03</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Han, Wei, Wu, Xu, Zang, Sun and Wei.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Han, Wei, Wu, Xu, Zang, Sun and Wei</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>The consumption of traditional fossil energy brings inevitable environmental protection problems, which also makes the low-carbon transition in industrial development imminent. In the process of low-carbon transition, the power industry plays a very important role. However, the large-scale integration of renewable energy resources such as wind power and photovoltaic brings new characteristics to power system dispatch. How to design a dispatch strategy that considers both low-carbon demand and economic cost has become a major concern in power systems. The flexible resources such as demand response (DR) and energy storage (ES) can cooperate with these renewable energy resources, promoting the renewable energy generation and low-carbon process. Thus, a low-carbon dispatch strategy for power systems considering flexible DR and ES is proposed in this article. First, models of DR and ES based on their behavior characteristics are established. Then, a carbon emission index is presented according to China&#x2019;s Clean Development Mechanism (CDM). Finally, the low-carbon dispatch strategy for power systems is proposed through the combination of the carbon emission index and flexible resource dispatch models. The simulation results show that the proposed dispatch strategy can significantly improve wind power consumption and reduce carbon emission.</p>
</abstract>
<kwd-group>
<kwd>power system dispatch</kwd>
<kwd>flexible resources</kwd>
<kwd>demand response</kwd>
<kwd>energy storage</kwd>
<kwd>low-carbon dispatch strategy</kwd>
</kwd-group>
<contract-sponsor id="cn001">Fundamental Research Funds for the Central Universities<named-content content-type="fundref-id">10.13039/501100012226</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Energy crisis and environmental protection issues are receiving more attention worldwide. Many countries are focusing on the development of sustainable renewable energy resources. China is in the stage of energy transformation, facing the challenge of carbon neutrality target by 2060. The strategy of energy revolution has emerged, which paves the way for low-carbon industrial development. In addition, in the process of energy structure transformation, flexible resources are important to achieve low-carbon advancement in power systems.</p>
<p>The trend of clean power integration is irreversible. The uncertainties brought by large-scale integration of renewable energy resources pose a higher challenge to the secure and stable operation of power systems (<xref ref-type="bibr" rid="B17">Shan et al., 2018</xref>; <xref ref-type="bibr" rid="B34">Cheng et al., 2021</xref>). On the one hand, customers are guided to stagger power consumption and optimize the load structure through reasonable demand response (DR) (<xref ref-type="bibr" rid="B19">Shu et al., 2017</xref>). On the other hand, high-quality ES systems should be selected to match the generation dispatch of the power system (<xref ref-type="bibr" rid="B17">Shan et al., 2018</xref>; <xref ref-type="bibr" rid="B28">Zhang et al., 2018</xref>). Generally, DR in power systems refers to the electricity customer behavior of changing their electricity consumption activities according to market regulation signals (<xref ref-type="bibr" rid="B10">Hobbs et al., 1993</xref>; <xref ref-type="bibr" rid="B4">Federal Energy Regulatory Commission, 2007</xref>; <xref ref-type="bibr" rid="B29">Zhang et al., 2008</xref>). The DR in the electricity market can be classified into price-based response (PDR) and incentive-based response (IDR) according to the response mode. In addition, the electricity customers are guided to respond to the power system dispatch in long-term and short-term time scales (<xref ref-type="bibr" rid="B23">Wang et al., 2021</xref>). As an effective method for optimal dispatch of power systems, DR has been proposed in a large number of countries, helping change the electricity consumption pattern. It supports not only the grid&#x2019;s peak-shaving and valley-filling but also renewable power consuming (<xref ref-type="bibr" rid="B6">Gao et al., 2014</xref>; <xref ref-type="bibr" rid="B1">Aghaei and Alizadeh, 2013</xref>) IDR can combine with PDR to improve the reliability and flexibility of DR and make DR dispatched precisely in real time (<xref ref-type="bibr" rid="B25">Xu et al., 2019</xref>). <xref ref-type="bibr" rid="B26">Zhang et al. (2021</xref>) propose an optimal DR dispatch model considering supply&#x2013;demand balance and security constraints; the imbalance pressure caused by renewable energy is alleviated. In the study by <xref ref-type="bibr" rid="B11">Hong-Tao et al. (2018</xref>), Chen establishes a wind&#x2013;solar power consumption model, and it verifies the effectiveness of DR on reducing the curtailment of wind and solar power. In the study by <xref ref-type="bibr" rid="B7">Gao et al. (2019</xref>), Gao characterizes the uncertainty of DR participation by considering the risk attitudes. It shows that the introducing DR can improve the adequacy of generation systems including wind power. In the study by <xref ref-type="bibr" rid="B12">Li et al. (2021</xref>), Li develops an optimal DR dispatch strategy for DR dispatch coordinated with the load aggregator to achieve joint optimization of entity benefits. Furthermore, the application of automatic DR in smart grids can greatly enhance the security of power system operation (<xref ref-type="bibr" rid="B22">Taorong et al., 2020</xref>). DR can be applied in frequency modulation to balance the active power (<xref ref-type="bibr" rid="B32">Zhu et al., 2021</xref>) and ensure sufficient voltage balancing control capacity (<xref ref-type="bibr" rid="B21">Tan and Shaaban, 2020</xref>).</p>
<p>Similar to DR, energy storage (ES) also has the function of flexible regulation. The renewable power curtailment can be reduced by introducing ES into the system. Thus, the ES configuration strategy is regarded as an effective approach to enhance the friendliness of wind and solar power generation (<xref ref-type="bibr" rid="B30">Zhang et al., 2022</xref>). It is also helpful for the stability and economic efficiency of power systems (<xref ref-type="bibr" rid="B2">Ani, 2021</xref>). Dorahaki developed an optimal VPP dispatch model which contains distributed wind power and ES devices. The ES device can smooth the fluctuations caused by wind power in the study by <xref ref-type="bibr" rid="B3">Dorahaki et al. (2020</xref>). In addition, the joint operation of wind power and ES can relieve the contradiction of renewable energy supply and reprogram the tariff profit (<xref ref-type="bibr" rid="B27">Zhang J. et al., 2020</xref>). The storage duration, capacity, and charging/discharging frequency of ES are investigated in the study by <xref ref-type="bibr" rid="B8">Hargreaves and Jones, (2020</xref>) to make it suitable for renewable energy systems. The combination of DR and ES is more beneficial to promote the optimal operation of the power systems (<xref ref-type="bibr" rid="B24">Wang et al., 2016</xref>; <xref ref-type="bibr" rid="B9">He et al., 2021</xref>). The adverse impacts of wind power uncertainties on power system stability can be solved by introducing DR and ES. Su integrates DR to a hybrid Wind-PV-ES system, achieving a goal of zero-curtailment of renewable power based on the correlation analysis (<xref ref-type="bibr" rid="B20">Su et al., 2020</xref>). In the study by <xref ref-type="bibr" rid="B5">Firouzmakan et al. (2019</xref>), DR and ES are considered in comprehensive stochastic energy management system containing micro-CHP units and renewable energy to implement resource complementarity and improve integral revenue. A multi-energy microgrid with wind&#x2013;solar power generation considering DR and ES is constructed to provide a reasonable plan for multiple energy applications (<xref ref-type="bibr" rid="B18">Shen et al., 2022</xref>). In conclusion, the integration of DR and ES offers additional sources of flexibility in the system (<xref ref-type="bibr" rid="B15">Mimica et al., 2022</xref>).</p>
<p>Carbon emission trading is an effective way to promote global emission reduction through the market mechanism. In the study by <xref ref-type="bibr" rid="B13">Lou et al. (2017</xref>), Lou includes carbon emission trading cost in the objective function based on the concept of low-carbon economy. It optimizes the power generation dispatch under the random charging/discharging behavior of EVs and effectively reduces the system&#x2019;s carbon emission. At the same time, the focus on carbon emission stimulates the demand for EVs, which helps take the lead in achieving the goal of &#x201c;carbon peak&#x201d; and &#x201c;carbon neutrality&#x201d; (<xref ref-type="bibr" rid="B16">Nie et al., 2022</xref>). <xref ref-type="bibr" rid="B14">Melgar-Dominguez et al. (2020)</xref> demonstrates that implementing a carbon emission trading scheme can make reduction in costs of the supplied energy and purchase of emission allowances. By incorporating the cost of carbon emission trading into a multi-energy complementary system, the environmental factors and system operating characteristics can be fully considered. Thus, wind and photovoltaic power curtailment and load shedding are reduced while minimizing system operating costs (<xref ref-type="bibr" rid="B33">Zhu et al., 2019</xref>). In the study by <xref ref-type="bibr" rid="B31">Zhang W. et al. (2020</xref>), Zhang quantitively evaluates the operation efficiency of different carbon emission trading systems to determine whether they are profitable to the economy and environment. Flexible resources such as DR and ES can cooperate with renewable energy to optimize power system dispatch and promote renewable power consumption. In addition, the import of the carbon emission trading market model can quantify the impacts of the dispatch strategy on carbon emission.</p>
<p>The existing literature has examined the response characteristics of DR and ES from various perspectives, showing the enhancing functions of DR and ES on carbon emission reduction. However, the integrated utilization of flexible resources still needs to be further explored, especially during the low-carbon transition period of power systems. Therefore, we propose a low-carbon dispatch strategy that combines carbon emission index and flexible DR and ES resources in this study. The strategy that realizes the reasonable coupling of conventional thermal power units, flexible resources, and carbon trading can effectively reduce wind power curtailment and quantitatively evaluate the reduction of carbon emission.</p>
<p>The remainder of this study is organized as follows. First, <xref ref-type="sec" rid="s2">Section 2</xref> establishes the models of DR and ES based on their behavioral characteristics. Subsequently, <xref ref-type="sec" rid="s3">Section 3</xref> proposes a low-carbon dispatch strategy through the combination of carbon market with the flexible DR resources and ES models. <xref ref-type="sec" rid="s4">Section 4</xref> demonstrates the effectiveness of the proposed strategy with simulation results. Finally, <xref ref-type="sec" rid="s5">Section 5</xref> draws the conclusion of this work.</p>
</sec>
<sec id="s2">
<title>2 Models of Flexible Resources in Power System Dispatch</title>
<sec id="s2-1">
<title>2.1 The Response and Configuration Model of Multiple Demand Response Resources</title>
<p>We consider incentive-based DR (IDR) and price-based DR (PDR) in this study. Here, three types of IDR including interruptible load (IL), direct load control (DLC), and transferable load (TL) are modeled.</p>
<p>Generally, IL and DLC adjust the response amount and duration within a period according to a dispatch plan as there is a supply&#x2013;demand balance problem in the system.</p>
<p>The cost of IL and DLC can be expressed as<disp-formula id="e1">
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<p>The dispatch of TL can shift part of the load from the peak hours to the valley hours, releasing the load pressure and reducing thermal unit start-ups and shutdowns.</p>
<p>The cost of TL response can be expressed as<disp-formula id="e2">
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<p>The PDR participates in system dispatch according to price signals, and the response amount and cost of PDR can be expressed as<disp-formula id="e3">
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<p>When the locational marginal price is not in the threshold interval, the PDR resource can choose whether to respond and adjust to the specified load level. PDR can obtain the corresponding economic compensation from the system. The PDR acquisition response cost can be expressed as<disp-formula id="e4">
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</disp-formula>
</p>
<p>The cost model of multiple DR is introduced above. Generally, DR also requires considering the constraints such as response duration, interval time, and amount constraints. The constraints on DR resources are as follows.<list list-type="simple">
<list-item>
<p>&#x2022; Maximum response duration constraint:</p>
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<list list-type="simple">
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<p>&#x2022; Maximum response count constraint:</p>
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</list>
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<list list-type="simple">
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<p>&#x2022; Minimum response interval time constraint:</p>
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<list list-type="simple">
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</p>
</sec>
<sec id="s2-2">
<title>2.2 Energy Storage Model</title>
<p>The ES of power systems are modeled as follows. It is established based on its charging/discharging power, charging/discharging efficiency, maximum charging/discharging rate, self-discharging rate, and state of charge (SOC).<list list-type="simple">
<list-item>
<p>&#x2022; Charging and discharging power constraints:</p>
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</list>
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<label>(9)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Charging and discharging capacity constraints:</p>
</list-item>
</list>
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<list list-type="simple">
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<p>&#x2022; Self-discharging capacity constraint:</p>
</list-item>
</list>
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<list list-type="simple">
<list-item>
<p>&#x2022; Storage capacity:</p>
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</list>
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<list list-type="simple">
<list-item>
<p>&#x2022; SOC constraint:</p>
</list-item>
</list>
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</sec>
</sec>
<sec id="s3">
<title>3 The Low-Carbon Dispatch Model Considering Flexible Demand Response and Energy Storage</title>
<sec id="s3-1">
<title>3.1 A Carbon Market Model Based on Clean Development Mechanism Trading Mechanism</title>
<p>The carbon emission trading mechanism is proposed to promote CO<sub>2</sub> emission reduction. Based on the current economic situation, China participates in the Clean Development Mechanism (CDM) market. The large-scale grid integration of wind power is in accordance with the objective of the CDM. It can meet the demand of low-carbon dispatch of power systems. With the introduction of the CDM, power generation entities are pre-assigned a certain baseline of CO<sub>2</sub> emissions, and the actual carbon emission is monitored (<xref ref-type="bibr" rid="B13">Lou et al., 2017</xref>).</p>
<p>Depending on the actual situation in China, the allowance allocation method is feasible. The allowance can influence the trading scale of the emission trading market and is regarded as an important factor of carbon emission trading cost. Therefore, allowances need to be measured in advance to assess the cost.</p>
<p>Enterprises responsible for emission reduction obligations attend the initial allocation of carbon emission trading allowances. The competent department of carbon emission trading distributes carbon emission allowances to them through legal means.</p>
<p>Enterprises obtain carbon emission rights through the initial allocation of carbon emission allowances. A reasonable allocation method is conducive to the optimal allocation of resources. It can enable enterprises to produce in a low-carbon and economically efficient way (<xref ref-type="bibr" rid="B13">Lou et al., 2017</xref>). We adopt the industry baseline method to calculate the free carbon emission allowances for power producers.<disp-formula id="e14">
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<p>The amount of carbon allowances and the distribution method set by the government directly affects the effect of the supply of carbon emission rights. It further impacts the trading price in the carbon emission trading market. If an enterprise does not get enough allowances, it will enter the secondary market of trading to buy more. Conversely, when an enterprise emits less carbon than its allowances, it can earn revenue by selling the excess emission allowances. Therefore, the carbon emission of the participating carbon market in the model can be expressed as<disp-formula id="e15">
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<p>The different allocation methods lead to different amounts of allowances for each enterprise. Thus, it indirectly affects the reasonableness of the supply of allowances. As a result, the motivation of enterprises to reduce emissions also changes, which affects the trading price.</p>
<p>The cost of emission <inline-formula id="inf1">
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</sec>
<sec id="s3-2">
<title>3.2 The Dispatch Model Considering Flexible Demand Response and Energy Storage Resources.</title>
<sec id="s3-2-1">
<title>3.2.1 The Objective Function of the Dispatch Model</title>
<p>The dispatch model consists of five main parts: <inline-formula id="inf2">
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<p>&#x2022; Thermal unit dispatch cost</p>
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<p>The thermal unit dispatch process includes the start-up and shutdown cost and fuel cost.</p>
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<p>Then, the start-up and shutdown costs of thermal units in a dispatch cycle can be expressed as<disp-formula id="e19">
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<p>The fuel cost of thermal units is usually a binomial of its power output, which can be expressed as<disp-formula id="e20">
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<p>Thus, the total cost of thermal unit dispatch is expressed as<disp-formula id="e21">
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<p>&#x2022; Penalty cost for wind power curtailment</p>
</list-item>
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<list list-type="simple">
<list-item>
<p>&#x2022; DR participation cost</p>
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<list list-type="simple">
<list-item>
<p>&#x2022; ES operation cost</p>
</list-item>
</list>
</p>
<p>According to the ES model presented in 2.2, the operation cost of ES can be expressed as<disp-formula id="e26">
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<p>Through integration of the aforementioned five subobjectives, the main objective function can be expressed as<disp-formula id="e27">
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</p>
</sec>
<sec id="s3-2-2">
<title>3.2.2 The Constraints of the Dispatch Model</title>
<p>The model also includes constraints on the operation of thermal power units and relative constraints of DR and ES.<list list-type="simple">
<list-item>
<p>&#x2022; Spinning reserve constraint:</p>
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</list>
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<label>(28)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Power balance constraint:</p>
</list-item>
</list>
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<label>(29)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Upper and lower limit constraints of thermal unit output:</p>
</list-item>
</list>
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</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Minimum start-up and shutdown time constraints:</p>
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<label>(31)</label>
</disp-formula>
<list list-type="simple">
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<label>(32)</label>
</disp-formula>
<list list-type="simple">
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<p>&#x2022; Maximum start-up and shutdown power constraints:</p>
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<label>(33)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; System stability requirement:</p>
</list-item>
</list>
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<label>(34)</label>
</disp-formula>
</p>
<p>Constraints of DR resources in <xref ref-type="disp-formula" rid="e1">Eqs 1</xref>&#x2013;<xref ref-type="disp-formula" rid="e8">8</xref> (35)</p>
<p>Constraints of ES resources in <xref ref-type="disp-formula" rid="e9">Eqs 9</xref>&#x2013;<xref ref-type="disp-formula" rid="e13">13</xref> (36)</p>
</sec>
</sec>
</sec>
<sec id="s4">
<title>4 Case Study</title>
<p>To verify the effectiveness of our proposed low-carbon dispatch strategy, a modified IEEE30-bus test system is selected and shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. It has six thermal units and 41 lines. The system is assembled with three DR aggregators (named as D1, D2, and D3 in <xref ref-type="fig" rid="F1">Figure 1</xref>) containing different DR resources at Bus 5, 7, and 21, respectively. D1 and D2 each contain three IDRs, and D3 contains one PDR resource. A wind farm with a total capacity of 45&#xa0;MW is located at Bus 28. An ES module with a capacity of 500&#xa0;MW&#xb7;h is located at Bus 15. The relevant parameters of thermal power units, DR resources, ES device, system load forecast, and wind power forecast output are given in <xref ref-type="sec" rid="s11">Supplementary Material S1</xref>. The model proposed in this study is solved by GAMS on a 16-core CPU/16G RAM PC. To quantitively access the impact of flexible DR and ES resources on the wind power consumption and carbon reduction, three scenarios are designed as follows.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Modified IEEE 30-bus test system.</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g001.tif"/>
</fig>
<sec id="s4-1">
<title>Scenario 1</title>
<p>In this scenario, DR resources do not participate in the system dispatch process.</p>
<p>The outputs of thermal units are shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. The amount of wind power curtailment and daily operation costs of the system are shown in and <xref ref-type="table" rid="T1">Tables 1</xref>, <xref ref-type="table" rid="T2">2</xref>, respectively.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Outputs of thermal units at each period in Scenario 1</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g002.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Amount of wind power curtailment at each period.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Time/h</th>
<th align="center">1</th>
<th align="center">2</th>
<th align="center">3</th>
<th align="center">4</th>
<th align="center">5</th>
<th align="center">6</th>
<th align="center">7</th>
<th align="center">8</th>
<th align="center">9</th>
<th align="center">10</th>
<th align="center">11</th>
<th align="center">12</th>
</tr>
<tr>
<th align="left">Amount/MW</th>
<th align="center">31.9</th>
<th align="center">44.3</th>
<th align="center">31</th>
<th align="center">37.5</th>
<th align="center">11</th>
<th align="center">5.6</th>
<th align="center">38.7</th>
<th align="center">52.9</th>
<th align="center">30</th>
<th align="center">5.6</th>
<th align="center">0</th>
<th align="center">0</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Time/h</td>
<td align="char" char=".">13</td>
<td align="char" char=".">14</td>
<td align="char" char=".">15</td>
<td align="char" char=".">16</td>
<td align="char" char=".">17</td>
<td align="char" char=".">18</td>
<td align="char" char=".">19</td>
<td align="char" char=".">20</td>
<td align="char" char=".">21</td>
<td align="char" char=".">22</td>
<td align="char" char=".">23</td>
<td align="char" char=".">24</td>
</tr>
<tr>
<td align="left">Amount/MW</td>
<td align="char" char=".">0</td>
<td align="char" char=".">0</td>
<td align="char" char=".">10.6</td>
<td align="char" char=".">10.5</td>
<td align="char" char=".">13.4</td>
<td align="char" char=".">5.2</td>
<td align="char" char=".">36.3</td>
<td align="char" char=".">40.1</td>
<td align="char" char=".">27.1</td>
<td align="char" char=".">18.5</td>
<td align="char" char=".">26.8</td>
<td align="char" char=".">20.1</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Daily operation cost of the system in Scenario 1</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Total cost/$</th>
<th align="center">Thermal unit dispatch cost/$</th>
<th align="center">Carbon emission trading cost/$</th>
<th align="center">Wind power curtailment penalty/$</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">105,512</td>
<td align="char" char=".">87,614</td>
<td align="char" char=".">2,985</td>
<td align="char" char=".">14,913</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>It can be found from <xref ref-type="table" rid="T1">Table 1</xref> that the wind power curtailment occurs frequently in Scenario 1. In <xref ref-type="table" rid="T2">Table 2</xref>, the total cost of system operation is $105512, of which the thermal unit dispatch cost, carbon emission trading cost, and wind power curtailment penalty are $87613, $2,985, and 14913, respectively.</p>
</sec>
<sec id="s4-2">
<title>Scenario 2:</title>
<p>In this scenario, only DR resources participate in the system dispatch process.</p>
<p>The characteristic parameters of IDR and PDR resources are listed in <xref ref-type="sec" rid="s11">Supplementary Material S1</xref> and the LMP curves of PJM.</p>
<p>The outputs of thermal units, values of DR response, and amount of wind curtailment are shown in <xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref>; <xref ref-type="table" rid="T3">Table 3</xref>, respectively. The daily operation costs of the system are listed in <xref ref-type="table" rid="T4">Table 4</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Outputs of thermal units at each period in Scenario 2</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Response values of DRs at each period in Scenario 2</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g004.tif"/>
</fig>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Amount of wind curtailment at each period in Scenario 2</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Time/h</th>
<th align="center">1</th>
<th align="center">2</th>
<th align="center">3</th>
<th align="center">4</th>
<th align="center">5</th>
<th align="center">6</th>
<th align="center">7</th>
<th align="center">8</th>
<th align="center">9</th>
<th align="center">10</th>
<th align="center">11</th>
<th align="center">12</th>
</tr>
<tr>
<th align="left">Amount/MW</th>
<th align="center">3</th>
<th align="center">15.5</th>
<th align="center">2.1</th>
<th align="center">9.1</th>
<th align="center">11</th>
<th align="center">5.6</th>
<th align="center">4</th>
<th align="center">27.9</th>
<th align="center">19.3</th>
<th align="center">14.7</th>
<th align="center">0</th>
<th align="center">0</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Time/h</td>
<td align="char" char=".">13</td>
<td align="char" char=".">14</td>
<td align="char" char=".">15</td>
<td align="char" char=".">16</td>
<td align="char" char=".">17</td>
<td align="char" char=".">18</td>
<td align="char" char=".">19</td>
<td align="char" char=".">20</td>
<td align="char" char=".">21</td>
<td align="char" char=".">22</td>
<td align="char" char=".">23</td>
<td align="char" char=".">24</td>
</tr>
<tr>
<td align="left">Amount/MW</td>
<td align="char" char=".">0</td>
<td align="char" char=".">0</td>
<td align="char" char=".">20.7</td>
<td align="char" char=".">4.5</td>
<td align="char" char=".">7.5</td>
<td align="char" char=".">5.2</td>
<td align="char" char=".">30.3</td>
<td align="char" char=".">0.1</td>
<td align="char" char=".">12.1</td>
<td align="char" char=".">18.5</td>
<td align="char" char=".">26.8</td>
<td align="char" char=".">4.1</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Daily operation costs of system in Scenario 2</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Total cost<bold>/</bold>$</th>
<th align="center">Thermal unit dispatch cost/$</th>
<th align="center">Carbon emission trading cost/$</th>
<th align="center">Wind power curtailment penalty/$</th>
<th align="center">DR response cost/$</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">97418</td>
<td align="char" char=".">81,479</td>
<td align="char" char=".">2,776</td>
<td align="char" char=".">7,260</td>
<td align="char" char=".">5,902</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The wind power curtailment amount in Scenario 1 and Scenario 2 are 497.10 and 242.00 MW, respectively. Compared with Scenario 1, the participation of DR resources in Scenario 2 helps reduce the wind power curtailment by 51.32%. In addition, it is worth noting that the carbon emission trading cost before and after DR participation is $2,985 and $2,776 respectively. With DR participation in the system dispatch, the overall outputs of thermal power units decrease. In addition, the peak-to-valley gap of the system is reduced, which directly reduces carbon emission. DR provides more opportunity for wind power generation and avoids frequent start-up and shutdown actions of the thermal units. Therefore, it also helps relieving the pressure of high load peaking.</p>
</sec>
<sec id="s4-3">
<title>Scenario 3</title>
<p>In this scenario, both DR and ES participate in the system dispatch process.</p>
<p>The outputs of thermal units, values of DR response, and variation of ES capacity are shown in <xref ref-type="fig" rid="F5">Figure 5</xref>, <xref ref-type="fig" rid="F6">Figure 6</xref>, and <xref ref-type="fig" rid="F7">Figure 7</xref>, respectively. The blue curve representing energy storage capacity in <xref ref-type="fig" rid="F7">Figure 7</xref> is associated with the left <italic>Y</italic>-axis, and the green and yellow bars representing the charging and discharging capacity are associated with the right <italic>Y</italic>-axis. The daily operation costs of the system are listed in <xref ref-type="table" rid="T5">Table 5</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Outputs of thermal units at each period in Scenario 3</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Response values of DRs at each period in Scenario 3</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g006.tif"/>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Variation of ES capacity at each period in Scenario 3.</p>
</caption>
<graphic xlink:href="fenrg-10-883602-g007.tif"/>
</fig>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Daily operation costs of the system in Scenario 3</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Total cost/$</th>
<th align="center">Thermal unit dispatch costs/$</th>
<th align="center">Carbon emission trading cost/$</th>
<th align="center">Wind power curtailment penalty/$</th>
<th align="center">DR response cost/$</th>
<th align="center">ES cost/$</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">90988</td>
<td align="char" char=".">81,479</td>
<td align="char" char=".">2,776</td>
<td align="char" char=".">0</td>
<td align="char" char=".">6,189</td>
<td align="char" char=".">544</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In Scenario 3, the time distribution of wind power resources is further optimized with the participation of ES in the system operation process. The wind power here is completely consumed. The flexible dispatch strategy and superior response performance of DR resources and ES play an important role in wind power consumption and system power balance maintenance. Moreover, ES helps with relieving the pressure of peaking. In carbon emission reduction, the effect of ES is reflected in the consumption of wind power to reducing carbon emission at the source-side.</p>
<p>As can be found from <xref ref-type="table" rid="T6">Table 6</xref>, the participation of DR in the system dispatch process has optimized the operation of thermal units, reducing their peaking pressure and the costs arising from frequent start-ups and shutdowns. In addition, the increase in wind power consumption results in significant reduction in wind power curtailment penalty. The improvement of thermal unit outputs has reduced the carbon emission trading cost of the system by 7.00% with DR participation. Although the involvement of ES brings added costs to the system, it is notably less than the decrease in the wind power curtailment penalty. Thus, compared with Scenario 1 and 2, the total cost in Scenario 3 decreases by 7.67 and 13.77%, respectively.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Comparison of costs in each scenario.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Scenario</th>
<th align="center">Total cost/$</th>
<th align="center">Thermal unit dispatch cost/$</th>
<th align="center">Carbon emission cost/$</th>
<th align="center">Wind power curtailment penalty/$</th>
<th align="center">DR response cost/$</th>
<th align="center">ES cost/$</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">1</td>
<td align="char" char=".">105,512</td>
<td align="char" char=".">87,614</td>
<td align="char" char=".">2,985</td>
<td align="char" char=".">14,913</td>
<td align="char" char=".">0</td>
<td align="char" char=".">0</td>
</tr>
<tr>
<td align="left">2</td>
<td align="char" char=".">97,418</td>
<td align="char" char=".">81,479</td>
<td align="char" char=".">2,776</td>
<td align="char" char=".">7,260</td>
<td align="char" char=".">5,902</td>
<td align="char" char=".">0</td>
</tr>
<tr>
<td align="left">3</td>
<td align="char" char=".">90,988</td>
<td align="char" char=".">81,479</td>
<td align="char" char=".">2,776</td>
<td align="char" char=".">0</td>
<td align="char" char=".">6,189</td>
<td align="char" char=".">544</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s5">
<title>5 Conclusion</title>
<p>In this article, we propose a low-carbon dispatch strategy for power systems considering flexible DR and ES. First, the models of flexible DR resources and ES is established based on their behavior characteristics. Second, by combining the carbon market model with the flexible DR resources and ES model, the low-carbon dispatch strategy is proposed. Finally, the effectiveness of the proposed strategy is verified with simulations.</p>
<p>From the presented work, general conclusions can be drawn as follows:<list list-type="simple">
<list-item>
<p>1) The cooperation of DR and ES has a remarkable impact on the power system dispatch. The combined operation mode of DR and ES effectively promotes peak-shaving and valley-filling.</p>
</list-item>
<list-item>
<p>2) The combined DR&#x2013;ES dispatch has a notable function on wind power consumption. Through the dispatch of flexible resources, the wind power curtailment can be greatly reduced.</p>
</list-item>
<list-item>
<p>3) The low-carbon dispatch strategy can quantitatively evaluate the reduction of carbon emission, realizing the reasonable coupling of conventional thermal power units, flexible resources, and carbon trading. It can help design carbon reduction policies according to DR and ES activities.</p>
</list-item>
</list>
</p>
<p>In the future work, we plan to combine the uncertainties derived from power and load with our framework and make the proposed model appropriate for short-time scale dispatch environment.</p>
</sec>
</body>
<back>
<sec id="s6">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="sec" rid="s11">Supplementary Material</xref>; further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>HH conceptualized and formed the methodology. TW prepared the original draft. HH, TW, and XX reviewed and edited the article. HH, CW, and TW supervised the study. ZW, HZ and GS administered the project. HH funded the acquisition. All authors have read and agreed to the published version of the manuscript.</p>
</sec>
<sec id="s8">
<title>Funding</title>
<p>This research was funded in part by the Fundamental Research Funds for the Central Universities under Grant B200201016 and in part by the Postdoctoral Research Funding Program of Jiangsu Province under Grant 2021K622C.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s11">
<title>Supplementary Material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fenrg.2022.883602/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fenrg.2022.883602/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet1.docx" id="SM1" mimetype="application/docx" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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<sec id="s12">
<title>Glossary</title>
<def-list>
<def-item>
<term id="G1-fenrg.2022.883602">Indices</term>
</def-item>
<def-item>
<term id="G2-fenrg.2022.883602">
<bold>
<italic>t</italic>
</bold>
</term>
<def>
<p>Index of hours</p>
</def>
</def-item>
<def-item>
<term id="G3-fenrg.2022.883602">
<bold>
<italic>i</italic>
</bold>
</term>
<def>
<p>Index of thermal units</p>
</def>
</def-item>
<def-item>
<term id="G4-fenrg.2022.883602">
<bold>
<italic>l</italic>
</bold>
</term>
<def>
<p>Index of branches</p>
</def>
</def-item>
<def-item>
<term id="G5-fenrg.2022.883602">Parameters</term>
</def-item>
<def-item>
<term id="G6-fenrg.2022.883602">
<inline-formula id="inf11">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Weight factor of IL and DLC</p>
</def>
</def-item>
<def-item>
<term id="G7-fenrg.2022.883602">
<inline-formula id="inf12">
<mml:math id="m46">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>m</mml:mi>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>m</mml:mi>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum and minimum locational marginal price ($/MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G8-fenrg.2022.883602">
<inline-formula id="inf13">
<mml:math id="m47">
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mrow>
<mml:mi>w</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mrow>
<mml:mi>w</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum and minimum response amount of PDR (MW)</p>
</def>
</def-item>
<def-item>
<term id="G9-fenrg.2022.883602">
<inline-formula id="inf14">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum duration of a single DR response (h)</p>
</def>
</def-item>
<def-item>
<term id="G10-fenrg.2022.883602">
<inline-formula id="inf15">
<mml:math id="m49">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum response hours of DR in a dispatch cycle (h)</p>
</def>
</def-item>
<def-item>
<term id="G11-fenrg.2022.883602">
<inline-formula id="inf16">
<mml:math id="m50">
<mml:mi>T</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>A dispatch cycle</p>
</def>
</def-item>
<def-item>
<term id="G12-fenrg.2022.883602">
<inline-formula id="inf17">
<mml:math id="m51">
<mml:mi>G</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Number of the thermal units</p>
</def>
</def-item>
<def-item>
<term id="G13-fenrg.2022.883602">
<inline-formula id="inf18">
<mml:math id="m52">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Minimum response interval of DR (h)</p>
</def>
</def-item>
<def-item>
<term id="G14-fenrg.2022.883602">
<inline-formula id="inf19">
<mml:math id="m53">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum and minimum load response amounts of DR (MW)</p>
</def>
</def-item>
<def-item>
<term id="G15-fenrg.2022.883602">
<inline-formula id="inf20">
<mml:math id="m54">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Unit price of the compensation for TL/PDR in period <italic>t</italic> ($/MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G16-fenrg.2022.883602">
<inline-formula id="inf21">
<mml:math id="m55">
<mml:mrow>
<mml:msubsup>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>/</mml:mo>
<mml:msubsup>
<mml:mi>p</mml:mi>
<mml:mi>r</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Rated charging and discharging power of the ES (MW)</p>
</def>
</def-item>
<def-item>
<term id="G17-fenrg.2022.883602">
<inline-formula id="inf22">
<mml:math id="m56">
<mml:mrow>
<mml:msup>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Charging and discharging efficiency of the ES</p>
</def>
</def-item>
<def-item>
<term id="G18-fenrg.2022.883602">
<inline-formula id="inf23">
<mml:math id="m57">
<mml:mrow>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>/</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum charging and discharging capacity of the ES (MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G19-fenrg.2022.883602">
<inline-formula id="inf24">
<mml:math id="m58">
<mml:mi>r</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Self-discharging rate of the ES</p>
</def>
</def-item>
<def-item>
<term id="G20-fenrg.2022.883602">
<inline-formula id="inf25">
<mml:math id="m59">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>O</mml:mi>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi>S</mml:mi>
<mml:mi>O</mml:mi>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum and minimum state of charge</p>
</def>
</def-item>
<def-item>
<term id="G21-fenrg.2022.883602">
<inline-formula id="inf26">
<mml:math id="m60">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Rated capacity of the ES (MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G22-fenrg.2022.883602">
<inline-formula id="inf27">
<mml:math id="m61">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Initial allocation factor of carbon emission</p>
</def>
</def-item>
<def-item>
<term id="G23-fenrg.2022.883602">
<inline-formula id="inf28">
<mml:math id="m62">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3be;</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>C</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Actual carbon emission intensity factor of the <italic>i</italic>th unit</p>
</def>
</def-item>
<def-item>
<term id="G24-fenrg.2022.883602">
<inline-formula id="inf29">
<mml:math id="m63">
<mml:mrow>
<mml:msubsup>
<mml:mi>c</mml:mi>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>/</mml:mo>
<mml:msubsup>
<mml:mi>c</mml:mi>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Fixed start-up and shutdown costs ($/MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G25-fenrg.2022.883602">
<inline-formula id="inf30">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Fuel cost factors of the <italic>i</italic>th thermal unit</p>
</def>
</def-item>
<def-item>
<term id="G26-fenrg.2022.883602">
<inline-formula id="inf31">
<mml:math id="m65">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mi>p</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>CDM unit price and unit excess penalty ($/ton)</p>
</def>
</def-item>
<def-item>
<term id="G27-fenrg.2022.883602">
<inline-formula id="inf32">
<mml:math id="m66">
<mml:mrow>
<mml:msubsup>
<mml:mi>M</mml:mi>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum amount of allowance power systems can trade through the CDM (ton)</p>
</def>
</def-item>
<def-item>
<term id="G28-fenrg.2022.883602">
<inline-formula id="inf33">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Unit price of wind power curtailment penalty ($/MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G29-fenrg.2022.883602">
<inline-formula id="inf34">
<mml:math id="m68">
<mml:mi>&#x3b3;</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Reserve demand factor to deal with the system load forecasting error</p>
</def>
</def-item>
<def-item>
<term id="G30-fenrg.2022.883602">
<inline-formula id="inf35">
<mml:math id="m69">
<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Upper and lower limits on the output power of the <italic>i</italic>th thermal unit (MW)</p>
</def>
</def-item>
<def-item>
<term id="G31-fenrg.2022.883602">
<inline-formula id="inf36">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum and minimum continuous running time of the <italic>i</italic>th thermal unit (h)</p>
</def>
</def-item>
<def-item>
<term id="G32-fenrg.2022.883602">
<inline-formula id="inf37">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Upward and downward ramping rates of the <italic>i</italic>th unit (MW/h)</p>
</def>
</def-item>
<def-item>
<term id="G33-fenrg.2022.883602">
<inline-formula id="inf38">
<mml:math id="m72">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Maximum start-up and shutdown power of the <italic>i</italic>th unit (MW/h)</p>
</def>
</def-item>
<def-item>
<term id="G34-fenrg.2022.883602">
<inline-formula id="inf39">
<mml:math id="m73">
<mml:mi>&#x3b2;</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Minimum demand factor to meet the system stability requirement</p>
</def>
</def-item>
<def-item>
<term id="G35-fenrg.2022.883602">Variables</term>
</def-item>
<def-item>
<term id="G36-fenrg.2022.883602">
<inline-formula id="inf40">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Response cost of IL and DLC/TL/PDR in period <italic>t</italic> ($)</p>
</def>
</def-item>
<def-item>
<term id="G37-fenrg.2022.883602">
<inline-formula id="inf41">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Response amount of IL and DLC/TL/PDR in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G38-fenrg.2022.883602">
<inline-formula id="inf42">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Response state of IL and DLC/TL in period <italic>t</italic>
</p>
</def>
</def-item>
<def-item>
<term id="G39-fenrg.2022.883602">
<inline-formula id="inf43">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Response number of DR in a circle</p>
</def>
</def-item>
<def-item>
<term id="G40-fenrg.2022.883602">
<inline-formula id="inf44">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi>int</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Time interval after the last action of DR (h)</p>
</def>
</def-item>
<def-item>
<term id="G41-fenrg.2022.883602">
<inline-formula id="inf45">
<mml:math id="m79">
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Predicted day-ahead load in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G42-fenrg.2022.883602">
<inline-formula id="inf46">
<mml:math id="m80">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>LMP in period <italic>t</italic> ($/MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G43-fenrg.2022.883602">
<inline-formula id="inf47">
<mml:math id="m81">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>int</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Accumulated interval from the last action of DR in period <italic>t</italic> (h)</p>
</def>
</def-item>
<def-item>
<term id="G44-fenrg.2022.883602">
<inline-formula id="inf48">
<mml:math id="m82">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Status constraint variable of the ES in period <italic>t</italic>
</p>
</def>
</def-item>
<def-item>
<term id="G45-fenrg.2022.883602">
<inline-formula id="inf49">
<mml:math id="m83">
<mml:mrow>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Charging and discharging power of the ES in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G46-fenrg.2022.883602">
<inline-formula id="inf50">
<mml:math id="m84">
<mml:mrow>
<mml:msup>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Charging and discharging capacity of the ES in period <italic>t</italic> (MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G47-fenrg.2022.883602">
<inline-formula id="inf51">
<mml:math id="m85">
<mml:mrow>
<mml:msup>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Self-discharge energy of the ES in period <italic>t</italic> (MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G48-fenrg.2022.883602">
<inline-formula id="inf52">
<mml:math id="m86">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Storage capacity of the ES in period <italic>t</italic> (MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G49-fenrg.2022.883602">
<inline-formula id="inf53">
<mml:math id="m87">
<mml:mi>M</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Free carbon emission allowance of the system (ton)</p>
</def>
</def-item>
<def-item>
<term id="G50-fenrg.2022.883602">
<inline-formula id="inf54">
<mml:math id="m88">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Actual carbon emission of the system (ton)</p>
</def>
</def-item>
<def-item>
<term id="G51-fenrg.2022.883602">
<inline-formula id="inf55">
<mml:math id="m89">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Cost incurred by carbon trading or paying penalty for the excess ($)</p>
</def>
</def-item>
<def-item>
<term id="G52-fenrg.2022.883602">
<inline-formula id="inf56">
<mml:math id="m90">
<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Power output of the <italic>i</italic>th thermal unit in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G53-fenrg.2022.883602">
<inline-formula id="inf57">
<mml:math id="m91">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Thermal unit dispatch cost in a dispatch cycle ($)</p>
</def>
</def-item>
<def-item>
<term id="G54-fenrg.2022.883602">
<inline-formula id="inf58">
<mml:math id="m92">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Cost of carbon emission trading in a dispatch cycle ($)</p>
</def>
</def-item>
<def-item>
<term id="G55-fenrg.2022.883602">
<inline-formula id="inf59">
<mml:math id="m93">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Penalty cost of wind power curtailment in a dispatch cycle ($)</p>
</def>
</def-item>
<def-item>
<term id="G56-fenrg.2022.883602">
<inline-formula id="inf60">
<mml:math id="m94">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Cost of DR participation in a dispatch cycle ($)</p>
</def>
</def-item>
<def-item>
<term id="G57-fenrg.2022.883602">
<inline-formula id="inf61">
<mml:math id="m95">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mn>5</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Cost of ES operation in a dispatch cycle ($)</p>
</def>
</def-item>
<def-item>
<term id="G58-fenrg.2022.883602">
<inline-formula id="inf62">
<mml:math id="m96">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Start-up and shutdown state of the <italic>i</italic>th thermal unit in period <italic>t</italic>
</p>
</def>
</def-item>
<def-item>
<term id="G59-fenrg.2022.883602">
<inline-formula id="inf63">
<mml:math id="m97">
<mml:mrow>
<mml:msubsup>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msubsup>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Start-up and shutdown cost of the <italic>i</italic>th thermal unit in period <italic>t</italic>
</p>
</def>
</def-item>
<def-item>
<term id="G60-fenrg.2022.883602">
<inline-formula id="inf64">
<mml:math id="m98">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Start-up and shutdown cost in a dispatch cycle ($)</p>
</def>
</def-item>
<def-item>
<term id="G61-fenrg.2022.883602">
<inline-formula id="inf65">
<mml:math id="m99">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Fuel cost of thermal units ($)</p>
</def>
</def-item>
<def-item>
<term id="G62-fenrg.2022.883602">
<inline-formula id="inf66">
<mml:math id="m100">
<mml:mrow>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:mi>M</mml:mi>
<mml:msub>
<mml:mo>&#x2032;</mml:mo>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Allowance power systems purchased and sold through the CDM (ton)</p>
</def>
</def-item>
<def-item>
<term id="G63-fenrg.2022.883602">
<inline-formula id="inf67">
<mml:math id="m101">
<mml:mrow>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>p</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Allowance power systems obtained through penalty payment (ton)</p>
</def>
</def-item>
<def-item>
<term id="G64-fenrg.2022.883602">
<inline-formula id="inf68">
<mml:math id="m102">
<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Amount of wind power curtailment in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G65-fenrg.2022.883602">
<inline-formula id="inf69">
<mml:math id="m103">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Contract price for ES charging and discharging in period <italic>t</italic> (MW&#xb7;h)</p>
</def>
</def-item>
<def-item>
<term id="G66-fenrg.2022.883602">
<inline-formula id="inf70">
<mml:math id="m104">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>State of the <italic>i</italic>th thermal unit in period <italic>t</italic>
</p>
</def>
</def-item>
<def-item>
<term id="G67-fenrg.2022.883602">
<inline-formula id="inf71">
<mml:math id="m105">
<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Spinning reserve provided of the <italic>i</italic>th thermal unit in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G68-fenrg.2022.883602">
<inline-formula id="inf72">
<mml:math id="m106">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>l</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Active power of the branch <italic>l</italic> in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G69-fenrg.2022.883602">
<inline-formula id="inf73">
<mml:math id="m107">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Voltage phase-angle in period <italic>t</italic>
</p>
</def>
</def-item>
<def-item>
<term id="G70-fenrg.2022.883602">
<inline-formula id="inf74">
<mml:math id="m108">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Wind power output in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G71-fenrg.2022.883602">
<inline-formula id="inf75">
<mml:math id="m109">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Power supplied by the ES in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G72-fenrg.2022.883602">
<inline-formula id="inf76">
<mml:math id="m110">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Predicted load of the system in period <italic>t</italic> (MW)</p>
</def>
</def-item>
<def-item>
<term id="G73-fenrg.2022.883602">
<inline-formula id="inf77">
<mml:math id="m111">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>o</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>o</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Cumulative shutdown and start-up time of the <italic>i</italic>th unit in period <italic>t</italic> (h)</p>
</def>
</def-item>
</def-list>
</sec>
</back>
</article>