Adjustable robust optimization in enabling optimal day-ahead economic dispatch of CCHP-MG considering uncertainties of wind-solar power and electric vehicle

Xianbang Chen; Yang Liu; Bin Li

doi:10.3934/jimo.2020038

Article Contents

2021, Volume 17, Issue 4: 1639-1661. Doi: 10.3934/jimo.2020038

This issue Previous Article Worst-case analysis of Gini mean difference safety measure Next Article Time-consistent multiperiod mean semivariance portfolio selection with the real constraints

Adjustable robust optimization in enabling optimal day-ahead economic dispatch of CCHP-MG considering uncertainties of wind-solar power and electric vehicle

College of Electrical Engineering, Sichuan University, Chengdu, China

^* Corresponding author: Yang Liu
^* Corresponding author: Yang Liu

Received: June 30, 2019

Revised: September 30, 2019

Early access: February 2020

Published: July 2021

Abstract Full Text(HTML) Figure(9) / Table(11) Related Papers Cited by

Abstract

At present, electric vehicles (EVs), small-scale wind power, and solar power have been increasingly integrated into modern power system via the combined cooling heating and power based microgrid (CCHP-MG). However, inside the microgrid the uncertainties of EVs charging, wind power, and solar power significantly impact the economy of CCHP-MG operation. Therefore to improve the economy deteriorated by the uncertainties, this paper presents a two-stage adjustable robust optimization to achieve the minimal operational cost for CCHP-MG. Before the realizations of the uncertainties, the day-ahead stage as the first stage decides an operational strategy that can withstand the worst-case uncertainties. As long as the uncertainties are observed, the real-time stage as the second stage adjusts the operational units to compensate the errors caused by the day-ahead operational strategy. Due to the difficulties of the model solution, this paper further adopts the duality theory, Big-M method, and column-and-constraint generation (C & CG) decomposition to convert the model into two tractable mixed integer linear programming (MILP) problems. Further, C & CG iteration algorithm is also employed to solve the MILPs, which can ultimately provide an optimal economic day-ahead dispatch strategy capable of handling uncertainties. The experimental results demonstrate the effectiveness of the presented approach.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

Full Text(HTML)

Figure 1. CCHP-MG system structure

Download: Full-size image PowerPoint slide

Figure 2. Details of data

Download: Full-size image PowerPoint slide

Figure 3. Intervals and stochastic scenarios of uncertainty sets with 30% prediction error

Download: Full-size image PowerPoint slide

Figure 4. Day-ahead dispatch decision of D-DED

Download: Full-size image PowerPoint slide

Figure 5. Day-ahead dispatch decision of S-DED

Download: Full-size image PowerPoint slide

Figure 6. Day-ahead dispatch decision of R-DED

Download: Full-size image PowerPoint slide

Figure 7. Day-ahead dispatch decision of A-DED

Download: Full-size image PowerPoint slide

Figure 8. RESs utilization results of A-DED with different budgets

Download: Full-size image PowerPoint slide

Figure 9. RESs utilization results of A-DED with different prediction errors

Download: Full-size image PowerPoint slide

Table 1. Steps of C & CG iteration algorithm

C & CG Iteration Algorithm
Step 1 (Initialization): Set an initial scenario ${\boldsymbol{u}_1} $ and convergence gap $\delta $. Initialize upper bound $ U_0=+\infty$, lower bound $L_0=-\infty $, and iteration number $ k = 1$.
Step 2 (Solve MP): Input the scenario set $ \boldsymbol{u}_1$ into (95) to solve MP. Record the optimal solution ($\boldsymbol{x}_k $, $\boldsymbol{y}_l $), the optimal value $ \alpha$ of objective, and $\boldsymbol{c}^{\top}\boldsymbol{x}$. Update the lower bound $ L_k = \alpha$, $l = 1, 2, \ldots, k $.
Step 3 (Solve SP): Input $\boldsymbol{x}_k $ into (98) to solve SP. Record the optimal solution ($\boldsymbol{u}_{k}^{0}$, $\boldsymbol{y}_{k}^{0} $) and the optimal value $\beta $ of objective. Set the worst scenario $\boldsymbol{u}_{k+1} $ to $\boldsymbol{u}_{k}^{0} $. Update the upper bound $ U_k=\beta +\boldsymbol{c}^{\top}\boldsymbol{x}$.
Step 4 (Check Convergence): If $U_k - L_k\leq d $, terminate the algorithm and record the optimal value $\nu$ as the expected cost. Otherwise, add constraints (99) and real-time adjustment variables $\boldsymbol{y}_{k+1} $ correspondingly to $ \boldsymbol{u}_{k+1}$; return to Step 2 and set $k = k+1 $.

| Show Table

DownLoad: CSV

Table 6. CGs parameters

CG	$P^{min}$	$P^{max}$	$R^{Up}$	$R^{Dn}$	$a$	$b$	$\lambda^{Up}$	$\lambda^{Dn}$
CG	(kW)	(kW)	(kW/min)	(kW/min)	(＄/kWh)	(＄/kWh)	(＄/kWh)	(＄/kWh)
MT	50	550	6	6	0.67	0	2.5	1.5
FC	50	240	2	2	0.60	0	2.5	1.5
EB	20	500	5	4	-	-	0.5	0.5

| Show Table

DownLoad: CSV

Table 7. Penalty prices

$\lambda_{Wind}$ (＄/kWh)	$\lambda_{Solar}$ (＄/kWh)	$\lambda_{Load}$ (＄/kWh)
0.536	0.536	5

| Show Table

DownLoad: CSV

Table 8. Electricity market prices

Hour	Day-ahead stage		Real-time stage
Hour	$\lambda_{Buy}^{DA}$	$\lambda_{Sell}^{DA}$	$\lambda_{Buy}^{RT}$	$\lambda_{Sell}^{RT}$
	(＄/kWh)	(＄/kWh)	(＄/kWh)	(＄/kWh)
(00:00-08:00)	1.35	1.04	2.70	0.11
(08:00-09:00, 12:00-19:00)	0.90	0.69	1.80	0.07
(09:00-12:00, 19:00-24:00)	0.50	0.39	1.00	0.04

| Show Table

DownLoad: CSV

Table 9. Energy storage system parameters

$P_{Cha}^{min}/P_{Cha}^{max}$	$P_{Dis}^{min}/P_{Dis}^{max}$	$\eta_{ESS}^{Cha}/\eta_{ESS}^{Dis}$	$\delta_{ESS}$	$E_{ESS}^{max}$	$E_{ESS}^{min}$	$E_{ESS}(0)$
(kW)	(kW)	$\eta_{ESS}^{Cha}/\eta_{ESS}^{Dis}$	$\delta_{ESS}$	(kWh)	(kWh)	(kWh)
0/200	0/200	0.9/0.9	0.001	480	120	120

| Show Table

DownLoad: CSV

Table 10. Heat storage system parameters

$Q_{Cha}^{min}/Q_{Cha}^{max}$	$Q_{Dis}^{min}/Q_{Dis}^{max}$	$\eta_{HSS}^{Cha}/\eta_{HSS}^{Dis}$	$\delta_{HSS}$	$E_{HSS}^{max}$	$E_{HSS}^{min}$	$E_{HSS}(0)$
(kW)	(kW)	$\eta_{HSS}^{Cha}/\eta_{HSS}^{Dis}$	$\delta_{HSS}$	(kWh)	(kWh)	(kWh)
0/200	0/200	0.9/0.9	0.01	600	0	0

| Show Table

DownLoad: CSV

Table 2. Comparison of efficiencies and costs of different methods

Method	Time (s)	Day-ahead Cost(＄)			Expected	Actual (＄)
Method	Time (s)	$C_{MT}$	$C_{FC}$	$C_{DA}$	Cost (＄)	RT	SUM
D-DED	6.52	5422.48	2251.42	5972.69	5972.69	613.25	6585.95
S-DED	1695.69	5336.95	2099.66	6011.19	6449.07	566.70	6577.90
R-DED	6.92	5425.33	1146.89	6503.61	10916.15	457.79	6961.91
A-DED	8.37	5422.83	1796.67	6203.84	8305.34	367.47	6571.81

| Show Table

DownLoad: CSV

Table 3. Comparison of electricity transactions of different methods

Method	Day-ahead Transaction			Actual Transaction
Method	Revenue (＄)	Loss (＄)	State	Revenue (＄)	Loss (＄)	State
D-DED	1701.19	-	Profit	1303.22	-	Profit
S-DED	1425.36	-	Profit	1051.32	-	Profit
R-DED	-	68.61	Loss	-	275.65	Loss
A-DED	1015.67	-	Profit	671.63	-	Profit

| Show Table

DownLoad: CSV

Table 4. Comparison of A-DED with different budgets

$\Gamma $	Iteration	Time (s)	Day-ahead Cost (＄)				Expected	Actual
$\Gamma $	Number	Time (s)	$C_{MT}$	$C_{FC}$	$C_{Grid}^{DA}$	$C_{DA}$	Cost (＄)	SUM (＄)
4	1	17.5	5422.8	1945.8	-1249.8	6118.6	7580.2	6568.5
8	2	28.7	5422.8	1596.3	-715.1	6304.1	8975.5	6753.4
12	3	36.2	5422.8	1332.3	-323.9	6431.6	9981.2	6880.8
16	5	37.1	5422.8	1237.5	-203.4	6457.3	10594.5	6900.3
20	6	42.0	5422.8	1180.7	-118.4	6485.0	10809.4	6928.3

| Show Table

DownLoad: CSV

Table 5. Comparison of A-DED with different budgets

Error	Iteration	Time	Day-ahead Cost (＄)				Expected	Actual (＄)
Error	Number	(s)	$C_{MT}$	$C_{FC}$	$C_{Grid}^{DA}$	$C_{DA}$	Cost (＄)	RT	SUM
10%	1	15.3	5422.5	2098.4	-1500.2	6020.2	7152.4	103.5	6123.7
20%	3	36.3	5422.8	1715.5	-914.3	6224.8	8562.3	235.7	6460.5
30%	3	29.2	5422.8	1332.7	-323.9	6431.4	9987.2	449.4	6880.8
40%	4	30.3	5409.2	1050.6	176.8	6636.0	11425.6	479.9	7385.9
50%	8	36.4	5306.4	937.1	752.9	6996.3	13021.7	1023.3	8019.6

| Show Table

DownLoad: CSV

Table 11. Energy conversion coefficients

$\eta_{MT}^{EH}$	$\eta_{EB}^{EH}$	$\eta_{MT}^{HC}$	$\eta_{EB}^{HC}$	$\eta_{HSS}^{HC}$
0.8	0.8	0.8	0.8	0.8

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

[1]	A. Ben-Tal, A. Goryashko, E. Guslitzer and A. Nemirovski, Adjustable robust solutions of uncertain linear programs, Math. Program., 99 (2004), 351-376. doi: 10.1007/s10107-003-0454-y.
[2]	A. Ben-Tal and A. Nemirovski, Robust convex optimization, Math. Oper. Res., 23 (1998), 769-1024. doi: 10.1287/moor.23.4.769.
[3]	C. Chen, Simulated annealing-based optimal wind-thermal coordination scheduling, IET Generation, Transmission & Distribution, 1 (2007), 447-455. doi: 10.1049/iet-gtd:20060208.
[4]	C. M. Correa-Posada and P. Sánchez-Martín, Integrated power and natural gas model for energy adequacy in short-term operation, IEEE Transactions on Power Systems, 30 (2015), 3347-3355. doi: 10.1109/TPWRS.2014.2372013.
[5]	C. Duan, L. Jiang, W. Fang and J. Liu, Data-driven affinely adjustable distributionally robust unit commitment, IEEE Transactions on Power Systems, 33 (2018), 1385-1398. doi: 10.1109/TPWRS.2017.2741506.
[6]	C. Duan, L. Jiang, W. Fang, J. Liu and S. Liu, Data-driven distributionally robust energy-reserve-storage dispatch, IEEE Transactions on Industrial Informatics, 14 (2018), 2826-2836. doi: 10.1109/TII.2017.2771355.
[7]	F. Fang, Q. H. Wang and Y. Shi, A novel optimal operational strategy for the CCHP system based on two operating modes, IEEE Transactions on Power Systems, 27 (2012), 1032-1041. doi: 10.1109/TPWRS.2011.2175490.
[8]	F. Farmani, M. Parvizimosaed, H. Monsef and A. Rahimi-Kian, A conceptual model of a smart energy management system for a residential building equipped with CCHP system, Internat. J. Electrical Power Energy Systems, 95 (2018), 523-536. doi: 10.1016/j.ijepes.2017.09.016.
[9]	H. Gao, J. Liu, L. Wang and Z. Wei, Decentralized energy management for networked microgrids in future distribution systems, IEEE Transactions on Power Systems, 33 (2018), 3599-3610. doi: 10.1109/TPWRS.2017.2773070.
[10]	W. Gu, S. Lu, Z. Wu, X. Zhang, J. Zhou, B. Zhao and J. Wang, Residential CCHP microgrid with load aggregator: Operation mode, pricing strategy, and optimal dispatch, Appl. Energy, 205 (2017), 173-186. doi: 10.1016/j.apenergy.2017.07.045.
[11]	Y. Guo, J. Xiong, S. Xu and W. Su, Two-stage economic operation of microgrid-like electric vehicle parking deck, IEEE Transactions on Smart Grid, 7 (2016), 1703-1712. doi: 10.1109/TSG.2015.2424912.
[12]	Z. Guo and X. Xiao, Wind power assessment based on a WRF wind simulation with developed power curve modeling methods, Abstract Appl. Anal., 2014 (2014), 1-15. doi: 10.1155/2014/941648.
[13]	N. Haouas and P. R. Bertrand, Wind farm power forecasting, Math. Probl. Eng., 2013 (2013), 5pp. doi: 10.1155/2013/163565.
[14]	R. Hashemi, A developed offline model for optimal operation of combined heating and cooling and power systems, IEEE Transactions on Energy Conversion, 24 (2009), 222-229. doi: 10.1109/TEC.2008.2002330.
[15]	S. Jin, Z. Mao, H. Li and W. Qi, Dynamic operation management of a renewable microgrid including battery energy storage, Math. Probl. Eng., 2018 (2018), 19pp. doi: 10.1155/2018/5852309.
[16]	Y. Lee and R. Baldick, A frequency-constrained stochastic economic dispatch model, IEEE Transactions on Power Systems, 28 (2013), 2301-2312. doi: 10.1109/TPWRS.2012.2236108.
[17]	B. Li, X. Qian, J. Sun, K. L. Teo and C. Yue, A model of distributionally robust two-stage stochastic convex programming with linear recourse, Appl. Math. Model., 58 (2018), 86-97. doi: 10.1016/j.apm.2017.11.039.
[18]	B. Li, J. Sun and K. L. Teo, A distributionally robust approach to a class of three-stage stochastic linear programs, Pac. J. Optim., 15 (2019), 219-236.
[19]	B. Li, J. Sun, H. Xu and M Zhang, A class of two-stage distributionally robust games, J. Ind. Manag. Optim., 15 (2019), 387-400. doi: 10.3934/jimo.2018048.
[20]	G. Li, G. Li and M. Zhou, Model and application of renewable energy accommodation capacity calculation considering utilization level of inter-provincial tie-line, Protection and Control of Modern Power Systems, 4 (2019), 1-1. doi: 10.1186/s41601-019-0115-7.
[21]	G. Li, R. Zhang, T. Jiang, H. Chen, L. Bai, H. Cui and X. Li, Optimal dispatch strategy for integrated energy systems with cchp and wind power, Appl. Energy, 192 (2017), 408-419. doi: 10.1016/j.apenergy.2016.08.139.
[22]	G. Li, R. Zhang, T. Jiang, H. Chen, L. Bai and X. Li, Security-constrained bi-level economic dispatch model for integrated natural gas and electricity systems considering wind power and power-to-gas process, Appl. Energy, 194 (2017), 696-704. doi: 10.1016/j.apenergy.2016.07.077.
[23]	Y. Liu, Y. Liu, J. Liu, M. Li, T. Liu, G. Taylor and K. Zuo, A MapReduce based high performance neural network in enabling fast stability assessment of power systems, Math. Probl. Eng., 2017 (2017), 1-12. doi: 10.1155/2017/4030146.
[24]	Y. Liu and N. C. Nair, A two-stage stochastic dynamic economic dispatch model considering wind uncertainty, IEEE Transactions on Sustainable Energy, 7 (2016), 819-829. doi: 10.1109/TSTE.2015.2498614.
[25]	C. Marino, M. Marufuzzaman, M. Hu and M. D. Sarder, Developing a CCHP-microgrid operation decision model under uncertainty, Comput. Industrial Eng., 115 (2018), 354-367. doi: 10.1016/j.cie.2017.11.021.
[26]	M. H. Sarparandeh and M. Ehsan, Pricing of vehicle-to-grid services in a microgrid by Nash bargaining theory, Math. Probl. Eng., 2017 (2017). doi: 10.1155/2017/1840140.
[27]	X. Shen, Y. Liu and Y. Liu, A multistage solution approach for dynamic reactive power optimization based on interval uncertainty, Math. Probl. Eng., 2018 (2018), 10pp. doi: 10.1155/2018/3854812.
[28]	R. Shi, C. Sun, Z. Zhou, L. Zhang, and Z. Liang, A robust economic dispatch of residential microgrid with wind power and electric vehicle integration, Chinese Control and Decision Conference (CCDC), 2016, 3672–3676. doi: 10.1109/CCDC.2016.7531621.
[29]	J. Soares, B. Canizes, M. A. F. Ghazvini, Z. Vale and G. K. Venayagamoorthy, Two-stage stochastic model using benders' decomposition for large-scale energy resource management in smart grids, IEEE Transactions on Industry Appl., 53 (2017), 5905-5914. doi: 10.1109/TIA.2017.2723339.
[30]	Y. Tan, Y. Cao, C. Li, Y. Li, J. Zhou and Y. Song, A two-stage stochastic programming approach considering risk level for distribution networks operation with wind power, IEEE Systems Journal, 10 (2016), 117-126. doi: 10.1109/JSYST.2014.2350027.
[31]	L. Tian, S. Shi and Z. Jia, A statistical model for charging power demand of electric vehicles, Power System Technology, 11 (2010), 126-130. doi: 10.13335/j.1000-3673.pst.2010.11.020.
[32]	T. A. Victoire and A. Jeyakumar, Hybrid PSO–CSQP for economic dispatch with valve-point effect, Electric Power Systems Research, 71 (2004), 51-59. doi: 10.1016/j.epsr.2003.12.017.
[33]	D. C. Walters and G. B. Sheble, Genetic algorithm solution of economic dispatch with valve point loading, IEEE Transactions on Power Systems, 8 (1993), 1325-1332. doi: 10.1109/59.260861.
[34]	J. Wang, J. Wang, C. Liu and and J. Ruiz, Stochastic unit commitment with sub-hourly dispatch constraints, Appl. Energy, 105 (2013), 418-422. doi: 10.1016/j.apenergy.2013.01.008.
[35]	P. Wei and Y. Liu, The integration of wind-solar-hydropower generation in enabling economic robust dispatch, Math. Probl. Eng., 2019 (2019), 12pp. doi: 10.1155/2019/4634131.
[36]	H. Wu, X Hou, B. Zhao and C. Zhu, Economical dispatch of microgrid considering plug-in electric vehicles, Automation of Electric Power Systems, 38 (2014), 77-84. doi: 10.7500/AEPS20130911002.
[37]	T. Wu, Q. Yang, Z. Bao and W. Yan, Coordinated energy dispatching in microgrid with wind power generation and plug-in electric vehicles, IEEE Transactions on Smart Grid, 4 (2013), 1453-1463. doi: 10.1109/TSG.2013.2268870.
[38]	W. Wu, J. Chen, B. Zhang and H. Sun, A robust wind power optimization method for look-ahead power dispatch, IEEE Transactions on Sustainable Energy, 5 (2014), 507-515. doi: 10.1109/TSTE.2013.2294467.
[39]	Y. Xiang, J. Liu and Y. Liu, Robust energy management of microgrid with uncertain renewable generation and load, IEEE Transactions on Smart Grid, 7 (2016), 1034-1043. doi: 10.1109/TSG.2014.2385801.
[40]	L. Xie, Y. Gu, X. Zhu and M. G. Genton, Short-term spatio-temporal wind power forecast in robust look-ahead power system dispatch, IEEE Transactions on Smart Grid, 5 (2014), 511-520. doi: 10.1109/TSG.2013.2282300.
[41]	P. Xiong, P. Jirutitijaroen and C. Singh, A distributionally robust optimization model for unit commitment considering uncertain wind power generation, IEEE Transactions on Power Systems, 32 (2017), 39-49. doi: 10.1109/TPWRS.2016.2544795.
[42]	P. Xiong and C. Singh, Distributionally robust optimization for energy and reserve toward a low-carbon electricity market, Electric Power Systems Res., 149 (2017), 137-145. doi: 10.1016/j.epsr.2017.04.008.
[43]	Y. Yang, Practical robust optimization method for unit commitment of a system with integrated wind resource, Math. Probl. Eng., 2017 (2017), 13pp. doi: 10.1155/2017/5208290.
[44]	J. Yu, Q. Feng, Y. Li and J. Cao, Stochastic optimal dispatch of virtual power plant considering correlation of distributed generations, Math. Probl. Eng., 2015 (2015). doi: 10.1155/2015/135673.
[45]	B. Zeng and L. Zhao, Solving two-stage robust optimization problems using a column-and-constraint generation method, Oper. Res. Lett., 41 (2013), 457-461. doi: 10.1016/j.orl.2013.05.003.
[46]	Y. Zhang, J. Meng, B. Guo and T. Zhang, An improved dispatch strategy of a grid-connected hybrid energy system with high penetration level of renewable energy, Math. Probl. Eng., 2014 (2014), 18pp. doi: 10.1155/2014/602063.
[47]	Y. Zhao, C. Li, M. Zhao, S. Xu, H. Gao and L. Song, Model design on emergency power supply of electric vehicle, Math. Probl. Eng., 2017 (2017), 6pp. doi: 10.1155/2017/9697051.