Bi-level two-stage stochastic SCUC for ISO day-ahead scheduling considering uncertain wind power and demand response

Transcription

1 The 6th International Conference on Renewable Power Generation (RPG) October 2017 Bi-level two-stage stochastic SCUC for ISO day-ahead scheduling considering uncertain wind power and demand response Naiwei Gong, Xianjue Luo, Danyang Chen Department of Electrical Engineering, Xi an Jiaotong University, Xi an, , People s Republic of China nwgong@stu.xjtu.edu.cn Published in The Journal of Engineering; Received on 12th October 2017; Accepted on 2nd November 2017 Abstract: This study considers ISO day-ahead (DA) scheduling under uncertain conditions with demand response (DR). Two kinds of DR, incentive-based DR (IDR) and price-based DR (PDR) are both incorporated according to their response characteristics. A bi-level two-stage stochastic security-constrained unit commitment (SCUC) model is proposed for this programme to minimise the ISO cost considering uncertain wind power output and uncertain price elasticity. The upper level is a two-stage stochastic programme. The first stage determines unit commitment and contract capacity of IDR programme while the second stage determines economic dispatch, wind power utilisation and actual dispatch power of IDR programme in the real-time (RT). A chance-constraint is used to ensure wind power utilisation. In the lower level, a priority method is used to select successful bidders based on the calculated contract capacity from the upper level. Results on the revised IEEE 118-bus system show that, the ISO would avoid frequent rescheduling and economic loss with uncertain PDR incorporated into the model. Besides, with IDR flexibly mitigating uncertainty and volatility from wind power and PDR, the ISO would have lower cost and avoid frequent rescheduling of thermal units. Also, this model could ensure wind power utilisation, thus promoting wind power integration. Nomenclature G B N T SU i F(P it ) t on,i T off,i U i L i UR i W bt L bt p I bt ε t,t (ξ) Δ(ξ) R t R curt t R trans t R c t p P, bt (ξ) DR i Decision variables u it x it p c i,bt set of thermal generators set of buses number of scenarios time horizon start-up cost fuel cost minimum on time minimum off time maximum generation power maximum generation power maximum ramp up rate wind power generation load power power consumption price elasticity (self) forecast error of price elasticity electricity price payment to the IDR users for curtailment payment to the IDR users for transfer payment to the IDR users for capacity uncertain PDR maximum ramp down rate generator state number of periods in one state continuously IDR contract capacity p w bt() j wind power consumption p it (ξ) thermal generation P (ξ) actual scheduled IDR p trans p transt j () j net transferred IDR power () j transferred IDR power to other time () curtailed IDR power 1 Introduction Traditionally, the ISO day-ahead scheduling focuses on the generation side. The ISO gets the forecast load curve and executes the security-constrained unit commitment (SCUC) one day ahead to meet the load demand [1]. However, with the rapidly increasing renewable energy integration, like wind power, the ISO finds it difficult to accommodate the large-scale volatile and uncertain renewable energy just relying on the thermal generators. The smart grid, which enables two-way communication between the generation side and the user side, provides opportunity for increasing the adjustment capability of the ISO. The user side can be integrated into the ISO scheduling actively through demand response (DR). There are mainly two kinds of DR, price-based DR (PDR) and incentive-based DR (IDR) [2]. PDR changes the load profile through electricity price such as time-of-use price and real-time price (RTP) [2]. The relationship between the electricity price and power consumption is expressed by price elasticity [3]. The IDR shapes the load profile through signing contract with the users in the day-ahead market. In the real time, the ISO could schedule the load power within the contract capacity [4]. The payment includes two parts: the contract capacity payment and the actual scheduled power payment. The IDR includes DLC, IL, demand side bidding (DSB) etc. [4]. Tumuluru et al. [5] incorporates DR into the traditional deterministic unit commitment (UC) model, illustrating that DR could improve wind power utilisation. Madaeni and Sioshansi [6] combines stochastic UC with PDR, validating that PDR could lower the economic cost caused by uncertain wind power. Most existing papers propose to incorporate just one kind of DR into the UC problem, ignoring different kinds of DR and their characteristic complementary. Liu et al. [7] proposes to

2 consider both IDR and PDR into the stochastic UC model. IDR is considered in real time while PDR is considered in day ahead to accommodate wind power. This paper incorporates both IDR and PDR according to their characteristics into the bi-level two-stage stochastic model for ISO day-ahead scheduling. The uncertain PDR under RTP would reshape the load curve based on the uncertain users price elasticity. This impact is incorporated into the second stage of the stochastic SCUC model. The IDR is flexible and schedulable resource. It is incorporated in both stages in the stochastic SCUC model to mitigate the volatility and uncertainty from the wind power and PDR in the real time. This paper provides a way for the ISO to consider both kinds of DR according to their characteristics to minimise the cost and utilise wind power to the most extent. ( where, Qu, x, p C I, j ) is equal to subject to min T + T F p it () j ( R curt t ()+R j trans t p transt () j ) u i,t = 1, i [ G, 1 x i,t 1 t on,i t [ T (6) (7) 2 Mathematical formulation A bi-level two-stage stochastic model is used for the ISO day-ahead scheduling. The upper level is a two-stage stochastic SCUC model to determine UC and contract capacity with the IDR users. In the lower level, the ISO determines successful IDR bidders by a priority method based on the contract capacity calculated from the upper level. 2.1 Upper level The upper level involves a two-stage stochastic SCUC programme. The uncertainty comes from the forecast wind power and price elasticity. A chance constraint is adopted to ensure wind power utilisation in the whole day. We assume there are three kinds of loads: industrial, commercial and residential loads. The PDR is a random variable based on the uncertain price elasticity, as shown in the following equations: 1 I t,t()= j DPI t /PI t + D I (), j t [ T (1) DR t /R t 1 C t,t()= j DPC t /PC t DR t /R t 1 R t,t()= j DPR t /PR t DR t /R t + D C (), j t [ T (2) + D R (), j t [ T (3) p P,bt ()= j DR ( t 1 I t,t() P j t I + 1 C t,t() P j t C + 1 R t,t() P j t R ) R t Once the IDR participants sign contract with the ISO, the ISO could schedule the load power within the contract capacity, including curtailment and transfer. The capacity payment used in the upper level is forecast contract price. The final capacity payment would be the result of DSB from the lower level, which would be explained in details in the next part. The first stage is to determine UC and IDR contract capacity. After the scenarios of wind power and price elasticity are realised, the second stage is to decide economic dispatch, wind power utilisation, actual curtailed IDR power and shifted IDR power, respectively. The objective function is shown in (5) and (6) while constraints are shown in (7) (30) as below min T SU i u it + T R C t (4) p C + EQu, [ ( x, pc I, j )] (5) i=1 = B p trans u i,t = 0, i [ G, t off,i x i,t 1 1 t [ T x i,t+1 = x i,t + 1, u i,t = 1&x i,t. 0 x i,t+1 = x i,t 1, u i,t = 0 & x i,t, 0 x i,t+1 = 1, u i,t = 1 & x i,t, 0 x i,t+1 = 1, u i,t = 0 & x i,t. 0 (8) (9) (10) (11) (12) u i,t [ { 0, 1}, x i,t [ Z, (13) p C 15% L bt, t [ T, b [ B (14) L i u it p it () j U i u it, (15) p i,t () p j i,t 1 () UR j i, (16) p i,t 1 () p j i,t () DR j i, (17) p it ()+ j B p j L bt B p w bt() j p () j B ()= ()+p j trans ()=p j transt j p transt p transf () p trans T p trans t=1 p P,bt (), j t [ T (18) (), j t [ T, b [ B (19) (), j t [ T, b [ B (20) ()=0, j b [ B (21) () 0, j t [ T, b [ B (22) () 0, j t [ T, b [ B (23) () 0, j t [ T, b [ B (24) ()+ j p transt () j p C, t [ T, b [ B (25) ()+p transt j t [ T, ()+p j p,bt () L j bt, b [ B (26) p w bt() W j bt (), j t [ T, b [ B (27)

3 Pr T p w bt() b j T W bt () j t=1 1 t (28) U ij B p w kij b bt()+ j p it () j i[l b U ij, L bt + p () p j P,bt () j (29) i, j [ V, t [ T i=1 U i p i,t () j a B (30) L bt p () p j P,bt () j, t [ T The objective function (5) is to minimise the ISO cost. The first term of the (5) is thermal generators start-up costs. The second term is IDR payment. These two parts are the first-stage cost while the third part of (5) is the second-stage cost shown in details in (6). The second-stage cost shown in (6) contains two parts: thermal generators fuel cost and actual scheduled IDR cost. Constraints (7) (14) are the first-stage constraints while (15) (30) are second-stage constraints. Constraints (7) and (8) are minimum up/down time constraints to ensure that once the unit is on/off, it should hold on/off for a defined time. Constraints (9) (12) are operation status limits to indicate the relationship between operation status and operation time. Constraint (13) ensures the unit status is binary. Constraint (14) limits the IDR capacity within 15% total load for about 10 15% DR is enough to be effective [8]. Constraint (15) limits the thermal generation capacity in any time. Constraints (16) and (17) are ramp rate constraints to restrict the power change in adjacent time slot to a defined range. Constraint (18) is power balance limit to ensure that the thermal power generation and actual utilised wind power is equal to the load consumption considering PDR and IDR. Constraint (19) shows the relationship of actual scheduled IDR with curtailed power and transferred power. Constraint (20) shows the net transferred load power in any time slot. Constraint (21) ensures that the net transferred load power in any time slot in the whole day is 0. Constraints (22) (24) ensure that the curtailed and transferred load power is positive. Constraints (25) and (26) limit the actual scheduled IDR within the IDR capacity and the sum of actual scheduled IDR and PDR within the original load power. Constraints (27) and (28) are wind power limitations, which ensure the utilised wind power is less than wind power generation and is no less than times wind power generation with the probability more than 1 t. Constraint (29) is transmission capacity constraint. Constraint (30) ensures the reserve requirement. 2.2 Lower level The DSB method is adopted for the IDR programme. The users bid their maximum capacity and corresponding price in the market for the ISO to select. It is assumed that the total IDR bidding capacity is always more than the ISO required. A priority method is used for the ISO to select successful bidders as described below: Step 1: In the upper level, the ISO obtains the optimal contract capacity based on forecast IDR contract price. Then the ISO issues the required IDR contract capacity and corresponding contract price to the demand side bidders one day ahead. Step 2: The IDR bidders bid their capacity and price to the ISO according to the issued contract capacity and price. It is assumed that each bidder is intent to bid successfully. So the bidders bidding prices would be close to the issued contract price as a balance of their own profits and willingness to be selected. This assumption is important for the next steps. Step 3: The ISO sorts the bidders based on the bidding price from the smallest to biggest. Then the ISO signs contract with the bidders orderly until the contract capacity reaches the calculated required IDR capacity. Note that we assume that the contract capacity with a bidder could be less than the bidder s maximum bidding capacity. Step 4: The last successful bidder s bidding price would be the final uniform contract capacity price. The final IDR contract price would equal to or slightly greater than or slightly less than the forecast IDR contract price as explained in Step 2. Note that the ISO contract capacity is fixed. The final ISO cost would be recalculate based on the final IDR contract price. 3 Methodology The adopted sample average algorithm (SAA) contains three parts: scenario generation, convergence analysis and solution validation. The readers can refer to [9] for details. We first use Monte Carlo sampling to generate a number of scenarios (e.g. N scenarios) of the uncertain parameters with the same probability 1/N. Then we reformulate our true problem in (5) (30) based on the generated scenarios as follows: min T N + 1/N SU i u it + T j=1 T + T R C t ( ( F p it j )) p C ( R curt t ( j ) + R trans t p transt ( j )) Subject to (8) (15) and (7), (16) (27), (29) and (30) j N b T (31) W bt () j p w bt() M j z j, j [ N (32) N 1/N z j t (33) j=1 z j [ { 0, 1}, j [ N (34) The convergence analysis is similar to [10]. The first stage of our problem is a mixed-integer LP while the second stage involves a chance constraint. First, the convergence of the chance constraint can be proved convergence according to [11]. After the chance constraint (28) is converted to (32) (34), the second stage of the problem is a mixed-integer linear programme (MILP). According to [9], the SAA for this problem will eventually converge to its true solution. Thesolutionvalidationprocesscanbereferredto[9, 10]. 4 Case study As demonstrated earlier, the uncertainties in the model come from wind power generation and price elasticity. We double the wind power data from the 118-bus case in [10] to adapt to our system. We assume the wind power forecast error obeys N(0,10) normal distribution. The distribution can be other forms not to lose generality. Similarly, we assume the price elasticity forecast error obeys N(0,1) normal distribution. The wind power data are paired with price elasticity to form a total set of samples. The price data is adopted from the PJM market and is revised correspondingly. The price elasticity for industrial, commercial, residential users are 0.4, 0.35, 0.25, respectively. The proportion of the three kinds of load is 3:1:2 derived from [8] with the base commercial load being 400 MW.

4 Table 1 Forecast electricity price in 24 hours Time Price, $ Time Price, $ Time Price, $ 00: : : : : : : : : : : : : : : : : : : : : : : : Table 2 Demand side bidding capacity and price Users Bidding amount, MW Bidding price, $/MW The forecast price data is shown in Table 1. The thermal generator and load data are derived from [10]. The DSB capacity and price are shown in Table 2. The problem is solved by CPLEX 12.1 at default settings on a computer workstation with 6 Intel Cores and 64 GB RAM. 4.1 Optimal results The optimal results concerning UC, cost, contract capacity are shown in Tables 3 and 4. The forecast contract capacity price is $10/MW. The curtailment and transfer payment are $8/MW and $6/MW, respectively. We can see from Table 4 that G (10, 11, 20, 21, 24, 25, 27, 28, 29, 39, 40, 43, 44, 51) are committed while the rest is not used. It is because these units have the lowest marginal costs among the 54 units. Further, G (11, 20, 21, 24, 25, 39, 40) are committed all along. Their start-up costs are Table 3 Optimal results for the revised IEEE 118-bus system Cost, $ Committed units Optimal IDR capacity, MW 1,160, ,926 Table 4 Optimal unit commitment for starting-up generators Fig. 1 Impact of PDR on the load curve relatively high compared to other units. Frequency status changing would bring economic loss. The impact of PDR and IDR on load curve is shown in Figs. 1 and 2, respectively. It can be seen from Fig. 1 that the PDR has considerable influence on the load curve. During 9:00 12:00 and 15:00 20:00, the load variation is obvious. It is because the influence is determined by the electricity price and price elasticity. The rising electricity price results in the less load consumption. The electricity price varies dramatically during these moments, resulting in the obvious load consumption variation. It can be seen from Fig. 2 that IDR plays an important role in smoothing the load curve. The load consumption increases during valley periods and decreases substantially during peak periods. The peak load decreases about 15%. The IDR shares the adjustment responsibility of thermal generators and provides a chance for wind power consumption during load valley periods. Fig. 3 shows the load curve considering both IDR and PDR. It is obvious that the load curve is smoother than only including one kind of DR. The IDR mitigates the volatility and uncertainty from PDR and wind power, exempting thermal generators from frequent adjustments and promoting wind power integration. After the ISO determines the contract IDR capacity to be 12,926 MW in the upper level, the ISO ranks the five bidders from the smallest bidding price to biggest as shown in Table 2. According to the priority method, the ISO signs contracts with Bidder 1, 2, 3 with contract capacity equalling to their maximum bidding capacity, i.e. 2000, 4000, 5000 MW, respectively. Then the ISO signs contract with Bidder 4 with contract capacity being 1926 MW which is less than the bidder s maximum bidding capacity. Since the bidding price of the last successful bidder (Bidder 4) is 10 $/MW, the final uniform IDR capacity price the ISO paid to each bidder is 10 $/MW which is equals to the forecast contract Generator no. Unit commitment in 24 h Fig. 2 Impact of incentive-based DR on the load curve

5 Fig. 3 Impact of PDR and IDR on the load curve Fig. 5 Thermal generation curve under different IDR price Table 5 Different results under different IDR price IDR price, $ Cost, $ IDR capacity, MW Wind power utilisation, % Committed units Table 6 Different results for four cases Case Cost, $ Committed units Wind power utilisation, % IDR capacity, MW (7,5,3) 1,076,000 14, (10,8,6) 1,160,000 12, (15,15,10) 1,178, price. Note that the final capacity price could be slightly less or more than the forecast value, which depends on the specific case. 4.2 Results under different IDR contract price The results under different IDR capacity price and scheduled price are shown in Table 5, Figs. 4 and 5. It can be seen from Table 5 that with higher IDR contract price, the contract capacity is lower and the ISO cost is higher. The wind power utilisation is higher with lower IDR capacity and more scheduled IDR. The scheduled IDR can not only lower the ISO cost, but also promote wind power utilisation. The load curve with the lowest IDR price is the smoothest as shown in Fig. 4. The generation power with the lowest IDR price is the fewest and smoothest as exhibited in Fig Results for four typical cases We give four typical cases: DR not included, only IDR included, only PDR included, both PDR and IDR included. We name the four cases as case 1, 2, 3, 4, respectively. The results for four cases are shown in Table 6. It vividly shows that with both PDR and IDR considered, the ISO obtains the lowest cost and the least 1 2,385, ,238, , ,349, ,160, ,926 Table 7 Optimal solution under different SAA samples and scenarios (Samples K, scenarios N) Objective value, $ Gap, % (5,10) 1,160, (10,20) 1,160, (20,50) 1,160, committed thermal generators. With the proposed chance constraint ensuring wind power utilisation, the actual wind power acceptance is almost equals to the wind power generation. With Case 1 compared with Case 2, we can see that with IDR included, the ISO cost decreases distinctly and the committed units are less. It is because the IDR flattens the load curve, exempting thermal generators from frequent ramping and status switching. With Case 1 compared with Case 3, we can conclude that the PDR imposes non-negligible impact on the system. Note that the impact might be beneficial or vice versa, which is determined by the change of electricity price. The impact would be more significant with increased absolute value of price elasticity. 4.4 Solution validation The objective values and the corresponding estimated optimality gaps under different SAA sample and scenarios are shown in Table 7. It is observed that the optimality gaps are small, validating the obtained optimal solution. It also illustrates that with more SAA samples and scenarios, the gap would be smaller and the results would be more precise. By increasing samples and scenarios, the results with satisfactory accuracy could be obtained. Fig. 4 Load curve under different IDR price 5 Conclusion This paper incorporates both IDR and PDR according to their characteristics into the bi-level two-stage stochastic model for ISO day-ahead scheduling. Results show that the PDR has considerable impact on the load curve. The ISO decisions would be more

6 precise with PDR considered, thus avoiding rescheduling and economic loss. Besides, with IDR flexibly mitigating uncertainty and volatility from wind power and PDR, the ISO would have lower cost and avoid frequency rescheduling of thermal units. The wind power utilisation can be ensured by the chance constraint, providing a way for the ISO to promote wind power integration. Future work would be developing optimal RTP in the PDR programme for the ISO to conduct the users to shape the load curve and increase wind power consumption during load valley periods. 6 References [1] Fu Y., Shahidehpour M., Li Z.: Security-constrained unit commitment with AC constraints, IEEE Trans. Power Syst., 2005, 20, pp [2] Qin Z., Wang X., Wang J., ET AL.: Survey of demand response research in deregulated electricity markets, Autom. Electr. Power Syst., 2008, 32, pp [3] Kirschen D.S., Strbac G., Cumperayot P., ET AL.: Factoring the elasticity of demand in electricity prices, IEEE Trans. Power Syst., 2000, 15, pp [4] Sioshansi R., Short W.: Evaluating the impacts of real-time pricing on the usage of wind generation, IEEE Trans. Power Syst., 2009, 24, pp [5] Tumuluru V.K., Huang Z., Tsang D.H.K.: Integrating price responsive demand into the unit commitment problem, IEEE Trans. Smart Grid, 2014, 5, pp [6] Madaeni S.H., Sioshansi R.: The impacts of stochastic programming and demand response on wind integration, Energy Syst., 2013, 4, pp [7] Liu X., Wang B., Yang L.I., ET AL.: Stochastic unit commitment model for high wind power integration considering demand side resources, Proc. CSEE, 2015, 35, pp [8] Jin S., Botterud A., Ryan S.M.: Impact of demand response on thermal generation investment with high wind penetration, IEEE Trans. Smart Grid, 2013, 4, pp [9] Kleywegt A.J., Shapiro A., Homem-De-Mello T.: The sample average approximation method for stochastic discrete optimization, SIAM J. Optim., 2001, 12, pp [10] Wang Q., Wang J., Guan Y.: Price-based unit commitment with wind power utilization constraints, IEEE Trans. Power Syst., 2013, 28, pp [11] Pagnoncelli B.K., Ahmed S., Shapiro A.: Sample average approximation method for chance constrained programming: theory and applications, J. Optim. Theory Appl., 2009, 142, pp