SCIENTIA SINICA Informationis, Volume 48 , Issue 10 : 1450-1466(2018) https://doi.org/10.1360/N112018-00132

## Investigating the market-based operation mechanism of DR resources using the equilibrium model

• AcceptedOct 4, 2018
• PublishedNov 22, 2018
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Appendix

Proof. 对于传统发电商而言, 令${B_{~-~i}}~=~\sum\nolimits_{i~=~1}^n~{{B_i}}~+~{B_{\rm~DRA}}~-~{B_i}$, $i~=~1,\ldots,n$, 代入式(2)和(5)得到 $${p_1} = \frac{D}{{{B_i} + {B_{ - i}}}}, {Q_i} = \frac{{D{B_i}}}{{{B_i} + {B_{ - i}}}}, \tag{A1}$$ 将式(35)代入式(11), 并对${B_i}$求导, 有 $$\frac{{\partial {\pi _i}}}{{\partial {B_i}}} = \frac{{{D^2}}}{{{{({B_{ - i}} + {B_i})}^2}}}\left[ {\frac{{{B_{ - i}} - {B_i}}}{{{B_{ - i}} + {B_i}}} - \frac{{{B_{ - i}}}}{D}C_{1i}^\prime \left(\frac{{D{B_i}}}{{{B_{ - i}} + {B_i}}}\right)} \right]. \tag{A2}$$

Proof. 首先, 通过推导可以得出$f_{1,i}^{\prime~\prime~}({Q_i})~>~0$, $f_{1,{\rm~DRA}}^{\prime~\prime~}({Q_{\rm~DRA}})~>~0$, 即优化问题(23)$\sim$(26)是一个严格的凸优化问题, 并且存在唯一的最优解. 该凸优化问题的最优性条件为

### References

[1] Zhang Q, Wang X F, Wang J X, et al. Survey of demand response research in deregulated electricity markets. Autom Electron Power Syst, 2008, 32: 97--106. Google Scholar

[2] Paterakis N G, Erdin? O, Catal?o J P S. An overview of Demand Response: Key-elements and international experience. Renew Sustain Energy Rev, 2017, 69: 871-891 CrossRef Google Scholar

[3] Wang H, Xu X Y, Yan Z. Multi-objective optimization of security constrained unit commitment model and solution considering flexible load. Power Syst Technol, 2017, 41: 1904--1911. Google Scholar

[4] Deng R, Yang Z, Chow M Y. A Survey on Demand Response in Smart Grids: Mathematical Models and Approaches. IEEE Trans Ind Inf, 2015, 11: 570-582 CrossRef Google Scholar

[5] Albadi M H, El-Saadany E F. A summary of demand response in electricity markets. Electric Power Syst Res, 2008, 78: 1989-1996 CrossRef Google Scholar

[6] Zhao H T, Zhu Z Z, Yu E K. Study on demand response markets and programs in electricity markets. Power Syst Technol, 2010, 34: 146--153. Google Scholar

[7] Carreiro A M, Jorge H M, Antunes C H. Energy management systems aggregators: A literature survey. Renew Sustain Energy Rev, 2017, 73: 1160-1172 CrossRef Google Scholar

[8] Gkatzikis L, Koutsopoulos I, Salonidis T. The Role of Aggregators in Smart Grid Demand Response Markets. IEEE J Sel Areas Commun, 2013, 31: 1247-1257 CrossRef Google Scholar

[9] Liu X F, Gao B T, Luo J, et al. Non-cooperative game based hierarchical dispatch model of residential loads. Autom Electron Power Syst, 2017, 41: 54--60. Google Scholar

[10] Parvania M, Fotuhi-Firuzabad M, Shahidehpour M. ISO's Optimal Strategies for Scheduling the Hourly Demand Response in Day-Ahead Markets. IEEE Trans Power Syst, 2014, 29: 2636-2645 CrossRef ADS Google Scholar

[11] Henriquez R, Wenzel G, Olivares D E. Participation of Demand Response Aggregators in Electricity Markets: Optimal Portfolio Management. IEEE Trans Smart Grid, 2018, 9: 4861-4871 CrossRef Google Scholar

[12] Guo H Y, Chen Q X, Xia Q, et al. Flexible ramping product in electricity markets: basic concept, equilibrium model and research prospect. Proc CSEE, 2017, 37: 3057--3066. Google Scholar

[13] Lee W J, Quilumba F L, Shi J, et al. Demand response -- an assessment of load participation in the ERCOT nodal market. In: Proceedings of IEEE Power and Energy Society General Meeting, San Diego, 2012. Google Scholar

[14] Nguyen D T, Negnevitsky M, de Groot M. Pool-Based Demand Response Exchange-Concept and Modeling. IEEE Trans Power Syst, 2011, 26: 1677-1685 CrossRef ADS Google Scholar

[15] Wu H, Shahidehpour M, Alabdulwahab A. Demand Response Exchange in the Stochastic Day-Ahead Scheduling With Variable Renewable Generation. IEEE Trans Sustain Energy, 2015, 6: 516-525 CrossRef ADS Google Scholar

[16] Heydarian-Forushani E, Moghaddam M P, Sheikh-El-Eslami M K. Risk-Constrained Offering Strategy of Wind Power Producers Considering Intraday Demand Response Exchange. IEEE Trans Sustain Energy, 2014, 5: 1036-1047 CrossRef ADS Google Scholar

[17] Parvania M, Fotuhi-Firuzabad M, Shahidehpour M. Optimal Demand Response Aggregation in Wholesale Electricity Markets. IEEE Trans Smart Grid, 2013, 4: 1957-1965 CrossRef Google Scholar

[18] Schachter J A, Mancarella P. Demand response contracts as real options: a probabilistic evaluation framework under short-term and long-term uncertainties. IEEE Trans Smart Grid, 2016, 7: 868-878 CrossRef Google Scholar

[19] Faria P, Spinola J, Vale Z. Aggregation and Remuneration of Electricity Consumers and Producers for the Definition of Demand-Response Programs. IEEE Trans Ind Inf, 2016, 12: 952-961 CrossRef Google Scholar

[20] Asadinejad A, Tomsovic K. Optimal use of incentive and price based demand response to reduce costs and price volatility. Electric Power Syst Res, 2017, 144: 215-223 CrossRef Google Scholar

[21] Yang Y, Zhang Y, Li F. Computing All Nash Equilibria of Multiplayer Games in Electricity Markets by Solving Polynomial Equations. IEEE Trans Power Syst, 2012, 27: 81-91 CrossRef ADS Google Scholar

[22] Li G, Shi J, Qu X. Modeling methods for GenCo bidding strategy optimization in the liberalized electricity spot market-A state-of-the-art review. Energy, 2011, 36: 4686-4700 CrossRef Google Scholar

[23] Wang Y L, Zhao J H, Wen F S, et al. Market equilibrium of multi-energy system with power-to-gas functions. Autom Electron Power Syst, 2015, 39: 1--10. Google Scholar

[24] Liu L G, Liu H X, Liu Z F, et al. Cooperation capacity optimization of wind power and thermal power based on Cournot model. Sci Sin Technol, 2016, 46: 467--474. Google Scholar

[25] Liu L G, Liu H X, Liu Z F, et al. Analysis of tripartite asymmetric evolutionary game among wind power enterprises, thermal power enterprises and power grid enterprises under new energy resources integrated. Sci Sin Technol, 2015, 45: 1297--1303. Google Scholar

[26] Feuerriegel S, Neumann D. Measuring the financial impact of demand response for electricity retailers. Energy Policy, 2014, 65: 359-368 CrossRef Google Scholar

[27] Li N, Chen L, Dahleh M A. Demand Response Using Linear Supply Function Bidding. IEEE Trans Smart Grid, 2015, 6: 1827-1838 CrossRef Google Scholar

[28] Xian W, Yuzeng L, Shaohua Z. Oligopolistic Equilibrium Analysis for Electricity Markets: A Nonlinear Complementarity Approach. IEEE Trans Power Syst, 2004, 19: 1348-1355 CrossRef ADS Google Scholar

[29] Wang Y, Wang S, Wu L. Distributed optimization approaches for emerging power systems operation: A review. Electric Power Syst Res, 2017, 144: 127-135 CrossRef Google Scholar

[30] Hong Y G, Zhang Y Q. Distributed optimization: algorithm design and convergence analysis. Control Theory Appl, 2014, 31: 850--857. Google Scholar

[31] Kamyab F, Amini M, Sheykhha S. Demand Response Program in Smart Grid Using Supply Function Bidding Mechanism. IEEE Trans Smart Grid, 2016, 7: 1277-1284 CrossRef Google Scholar

[32] Cheng Y C. Dual gradient method for linearly constrained, strongly convex, separable mathematical programming problems. J Optim Theor Appl, 1987, 53: 237-246 CrossRef Google Scholar

[33] Bertsekas D P, Tsitsiklis J N. Parallel and Distributed Computation: Numerical Methods. Englewood Cliffs: Prentice-Hall, 1989. 210--219. Google Scholar

[34] Bertsekas D P. Nonlinear Programming. Belmont: Athena Scientific, 1999. 192--209. Google Scholar

• Figure 1

Trading framework of the electricity market

• Figure 2

Solution algorithm flow chart of the equilibrium model

• Figure 3

(Color online) Evolution of price in the day-ahead market

• Figure 4

(Color online) Evolution of DRA and generators' bidding strategies in the day-ahead market

• Figure 5

(Color online) Evolution of price in the DRX market

• Figure 6

(Color online) Evolution of 4 DR customers' bidding strategies in the DRX market

• Figure 7

(Color online) The impacts of compensation coefficient on retailers' revenues and compensation amounts

• Figure 8

(Color online) The impacts of DR resources and day-ahead market demand on the price of day-ahead market

• Table 1   The impacts of the compensation coefficient on equilibrium results
 Item Compensation coefficient 0 (without DR) 0.1 0.3 0.5 0.7 0.9 3*G1 Supply function (MW$^{2}$h/) 0.293 0.293 0.277 0.284 0.289 0.293 Bid output (MW) 24.00 24.00 20.04 19.51 19.08 18.71 Profit (/h) 1256 1256 887 799 733 683 3*G2 Supply function (MW$^{2}$h/) 0.285 0.285 0.269 0.275 0.280 0.283 Bid output (MW) 23.33 23.33 19.48 18.94 18.49 18.12 Profit (/h) 1200 1200 848 762 698 649 3*G3 Supply function (MW$^{2}$h/) 0.277 0.277 0.262 0.267 0.271 0.274 Bid output (MW) 22.68 22.68 18.94 18.38 17.92 17.54 Profit (/h) 1148 1148 811 727 665 617 3*DRA Supply function (MW$^{2}$h/) – 0 0.021 0.046 0.068 0.088 Bid output (MW) – 0 1.54 3.17 4.51 5.63 Profit (/h) – 0 36 120 231 360 Price of day-ahead market (/MWh) 81.94 81.94 72.29 68.74 66.07 63.97 Price of DRX market (/MWh) – – 86.76 88.65 90.20 91.49 Total profit of DR customers (/h) – 0 8 20 33 45 Increase in retailers' revenue (/h) – 0 193 366 485 573 Net increase in retailers' revenue (/h) – 0 135 183 146 57
• Table 2   The impacts of the day-ahead market demand on equilibrium results
 Item Demand of day-ahead market (MW) 40 50 60 70 80 3*G1 Supply function (MW$^{2}$h/) 0.213 0.250 0.284 0.314 0.341 Bid output (MW) 13.63 16.66 19.51 22.28 24.99 Profit (/h) 525 666 799 937 1082 3*G2 Supply function (MW$^{2}$h/) 0.208 0.244 0.275 0.304 0.329 Bid output (MW) 13.33 16.23 18.94 21.55 24.10 Profit (/h) 506 638 762 890 1023 3*G3 Supply function (MW$^{2}$h/) 0.204 0.237 0.267 0.294 0.317 Bid output (MW) 13.04 15.81 18.38 20.85 23.26 Profit (/h) 488 612 727 846 969 3*DRA Supply function (MW$^{2}$h/) 0 0.019 0.046 0.075 0.104 Bid output (MW) 0 1.30 3.17 5.31 7.65 Profit (/h) 0 43 120 227 365 3*Price of day-ahead market (/MWh) With DR (/MWh) 63.98 66.63 68.74 70.97 73.29 Without DR (/MWh) 63.98 69.97 75.96 81.94 87.93 Price drop (%) 0 5.0 10.5 15.5 20.0 Price of DRX market (/MWh) – 86.48 88.65 91.12 93.83 Total profit of DR customers (/h) 0 7 20 41 70 Net increase in retailers' revenue (/h) 0 68 183 334 522
• Table 3   The impacts of the retail price on equilibrium results
 Item Retail price (/MWh) 70 90 110 130 150 3*G1 Supply function (MW$^{2}$h/) 0.290 0.284 0.278 0.272 0.293 Bid output (MW) 19.00 19.51 20.00 20.45 24.00 Profit (/h) 721 799 880 964 1256 3*G2 Supply function (MW$^{2}$h/) 0.281 0.275 0.270 0.264 0.285 Bid output (MW) 18.40 18.94 19.44 19.91 23.33 Profit (/h) 686 762 840 923 1200 3*G3 Supply function (MW$^{2}$h/) 0.272 0.267 0.262 0.257 0.277 Bid output (MW) 17.84 18.38 18.90 19.38 22.68 Profit (/h) 654 727 804 884 1148 3*DRA Supply function (MW$^{2}$h/) 0.073 0.046 0.023 0.003 0 Bid output (MW) 4.76 3.17 1.67 0.26 0 Profit (/h) 182 120 62 9.74 0 Price of day-ahead market (/MWh) 65.58 68.74 71.99 75.30 81.94 Price of DRX market (/MWh) 90.49 88.65 86.91 85.28 – Total profit of DR customers (/h) 35 20 9 1 0 Net increase in retailers' revenue (/h) 301 183 87 12 0
• Table 4   The impacts of the number of DR customers on equilibrium results
 Item Number of DR customers 5 10 20 40 80 800 3*G1 Supply function (MW$^{2}$h/) 0.293 0.279 0.284 0.287 0.288 0.290 Bid output (MW) 24.00 19.91 19.51 19.28 19.14 19.01 Profit (/h) 1256 864 799 762 742 723 3*G2 Supply function (MW$^{2}$h/) 0.285 0.271 0.275 0.278 0.279 0.281 Bid output (MW) 23.33 19.35 18.94 18.69 18.55 18.42 Profit (/h) 1200 826 762 726 707 688 3*G3 Supply function (MW$^{2}$h/) 0.277 0.263 0.267 0.270 0.271 0.272 Bid output (MW) 22.68 18.80 18.38 18.13 17.99 17.85 Profit (/h) 1148 789 727 692 674 655 3*DRA Supply function (MW$^{2}$h/) 0 0.027 0.046 0.058 0.065 0.072 Bid output (MW) 0 1.94 3.17 3.90 4.32 4.73 Profit (/h) 0 73 120 148 164 181 Price of day-ahead market (/MWh) 81.94 71.38 68.74 67.25 66.44 65.64 Price of DRX market (/MWh) – 95.37 88.65 84.82 82.73 80.67 Total profit of DR customers (/h) 0 25 20 10 7 2 Net increase in retailers' revenue (/h) 0 119 183 217 235 252

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