Congestion Management in a Stochastic Dispatch Model for Electricity Markets

Transcription

1 Congestion Management in a Stochastic Dispatch Model for Electricity Markets Endre Bjørndal 1, Mette Bjørndal 1, Kjetil Midthun 2, Golbon Zakeri 3 Workshop on Optimization and Equilibrium in Energy Economics UCLA, January 2016 Supported by the Norwegian Research Council 1 NHH/SNF 2 SINTEF 3 University of Auckland 1 / 33

2 Congestion management and balancing Delivery hour (e.g. 08:00-08:59) Spot market with congestion avoidance e.g. - Nodal pricing - Zonal pricing - (Uniform price) Congestion alleviation e.g. - Counter-purchase - Re-dispatch auction - Use of reserves list time Reasons for inadequate congestion handling: Congestion within areas not considered (in full) «Loop-flow» not included in market clearing Inadequate representation of capacity constraints 2 / 33

3 Nordic electricity market 3 / 33

4 Nordic electricity market 4 / 33

5 Nord Pool Spot /01/12, NO SE FRE RU NO SE FI NO NO NO SE EE DK SE LV LT DK BLR EIRE GB DE PL 5 / 33

6 Towards Single European Market: Next Steps Markets included in PCR - over 2800 TWh of yearly consumption Markets associate members of PCR Markets that could join next as part of an agreed European roadmap 6 / 33

7 Nordic market Pre-delivery markets Elspot (12:00) Zonal pricing Elbas (Until 1 hour Before delivery) Feasible trade Bidding regulating power market (20:00) Delivery hour (e.g. 08:00-08:59) Special Real-time regulation balancing using regulating using regulating power list power and ancillary services time Markets and systems for: Real-time balancing (Regulating power market, and other ancillary services) Congestion alleviation 7 / 33

8 Flexibility costs and uncertainty 8 / 33

9 Stochastic market clearing Literature: Wong and Fuller (2007); Bouard et al. (2005b,a); Pritchard et al. (2010); Khazaei et al. (2012); Morales et al. (2012); Khazaei et al. (2013, 2014a,b); Morales et al. (2014); Zugno and Conejo (2013)... Our paper: Energy-only stochastic market clearing as in Pritchard et al. (2010) How should the day-ahead part of the market be modeled? Eects of day-ahead network ow and balance constraints Compare to a sequential market clearing model with myopic clearing of the day-ahead part of the market 9 / 33

10 Outline 1 Introduction 2 Model 3 Day-ahead formulations 4 Numerical examples 5 Conclusions 10 / 33

11 Model Day-ahead and real-time generation ( 0) and load ( 0) quantities: x i Ci 1 X iω Ci 2 (ω, x i ) i I i I, ω Ω Upregulation Xiω u = max{x iω x i, 0} or downregulation Xiω d = max{x i X iω, 0} for exible entities. 11 / 33

12 Generator cost functions Price b i u a i + b i x i a i u a i a i a i d b i a i b i d X i ω1 x i X i ω2 Gen. d X i ω1 u X i ω2 12 / 33

13 Load benet curves Price a i b i u b i a i + b i x i a i a i d a i u a i b i d X i ω1 x i X i ω2 Con. u X i ω1 d X i ω2 13 / 33

14 Objective function Cost of real-time quantity at day-ahead parameters: Flexibility cost: c i (X iω ) = a i X iω + 0.5b i (X iω ) 2 c i (x i, X iω ) =(a u i a i )X u iω + 0.5(b u i b i )(X u iω) 2 +(a i a d i )X d iω + 0.5(b d i b i )(X d iω) 2 14 / 33

15 Stochastic market clearing model min x,f,x,f s.t. E [ i I ( c i (X i ) + c i (x i, X i )) ] (1a) x i C 1 i i I (1b) X iω C 2 i (ω, x i ) i I, ω Ω (1c) τ n(f ) + x i = 0 n N [π n] (1d) i I (n) τ n(f ω) τ n(f ) + (X iω x i ) = 0 n N, ω Ω [p ωλ nω] (1e) f U 1 i I (n) (1f) F ω U 2 ω Ω (1g) 15 / 33

16 Myopic market clearing model - day-ahead part min x,f s.t. c i (x i ) i I (2a) x i C 1 i i I (2b) τ n(f ) + x i = 0 n N [π n] (2c) f U 1 i I (n) (2d) 16 / 33

17 Myopic market clearing model - real-time part, scenario ω min X ω,f ω s.t. i I ( ) c i (X iω ) + c i (x i, X iω ) (3a) X iω C 2 i (ω, x i ) i I (3b) τ n(f ω) τ n(f ) + (X iω x i ) = 0 n N [p ωλ nω] (3c) F ω U 2 i I (n) (3d) 17 / 33

18 Day-ahead constraints We assume that U 2 represents the network constraints in a DC load ow model without losses What should U 1 represent? 18 / 33

19 Alternative day-ahead network representations 1 Nodal model, i.e., U 1 = U 2 2 Zonal model No loop ow Aggregate ow capacities set by system operator(s) 3 Unconstrained ow, i.e., U 1 = R L 4 Unconstrained ow and balance min[vnodal stoch, v zonal stoch ] v bal stoch vunc stoch 19 / 33

20 Example 1 ω = ω = P(1) = P(2) = 0.5 Real-time quantities X ω are given above All cost parameters equal zero, except a u 1 = au 2 = 1 and a u 3 = 0.25 All lines have identical impedances Capacity of line (2,3) is / 33

21 Example 1 - stochastic model min ([30 x 1 ] + + [0 x 1 ] + + [0 x 3 ] + + [60 x 3 ] +) ([ 30 x 3 ] + + [ 60 x 3 ] +) s.t. x 1 + x 2 + x 3 = 0 40 x 2 x / 33

22 Example 1 - optimal day-ahead schedules x x x (30,0, 30) (30,0, 30) (0,60, 60) (30,0, 30) (0,60, 60) (30,0, 30) (0,60, 60) xbal = (30,60, 90) (30,0, 30) (0,60, 60) xbal = (30,60, 90) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xnodal = (30,45, 75) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xnodal = (30,45, 75) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xunc = (30,60, 30) xnodal = (30,45, 75) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xunc = (30,60, 30) xnodal = (30,45, 75) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xunc = (30,60, 30) xnodal = (30,45, 75) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xunc = (30,60, 30) xnodal = (30,45, 75) (30,0, 30) (0,60, 60) xbal = (30,60, 90) xunc = (30,60, 30) xnodal = (30,45, 75) (30,0, 30) v stoch unc = 0 v stoch bal = 0.5 ( 30 ( 90)) ( 60 ( 90)) 0.25 = v stoch nodal = 0.5 ( 30 ( 75)) [ (60 45) 1 + ( 60 ( 75)) 0.25 ] = / 33

23 0 Example 2 Node 2: Nuclear + Thermal Euros/MWh MWh/h 150 Node 1: Wind (scen. 2) Consumption Node 3: Hydro Euros/MWh b = 0.01 Euros/MWh b = MWh/h MWh/h 23 / 33

24 Wind scenarios Wind = 0 p 1 = 0.2 p 2 = 0.5 Wind = 7000 p 3 = 0.3 Wind = / 33

25 Cost and benet parameters Entity Node Intercept (a) Slope (b) Flexible? Flex. cost up Flex. cost down Wind Partly - - Load Yes b u = 30b - Nucl No - - Therm Yes a u a = 6 - Hydro Yes b u = 10b - 25 / 33

26 Example 2 - optimal values, stochastic model Model Value (1000 es) Wait-and-see Unconstrained Balanced Nodal Zonal (cap {1},{2,3} = 3000) Zonal (cap {1},{2,3} = 5000) / 33

27 Example 2 - optimal schedules, stochastic model Nodal model Real-time adj. Entity Day-head Low Medium High Wind Nucl Therm Hydro Load Total Unconstrained model Real-time adj. Entity Day-head Low Medium High Wind Nucl Therm Hydro Load Total Power ow - nodal model ( 42) (438) ( 42) (0) 800 (42) 2000 (0) 320 ( 438) 800 ( 1200) 400 (1158) ( 42) (42) 3600 (83) (438) ( 438) 2640 ( 877) (3558) ( 2358) 0 ( 3517) 27 / 33

28 Example 2 - cost and benet eects, stochastic model Nodal model Flex. costs ( c) Entity E[ c] Low Medium High E[ c c] Wind Nucl Therm Hydro Load Total Unconstrained model Flex. costs ( c) E[ c] Low Medium High E[ c c] / 33

29 Myopic model Infeasibility issue, e.g. due to scheduling of non-exible nuclear in day-ahead market 29 / 33

30 Myopic / nodal model - eect of day-ahead wind capacity Total surplus Wind capacity 30 / 33

31 Myopic / balanced model - eect of day-ahead wind capacity Total surplus Wind capacity 31 / 33

32 Conclusions and further research Too restrictive constraints in the day-ahead stage of a stochastic market clearing model may hinder exibility and yield sub-optimal solutions Examples of such constraints are DC load ow capacitites, European-style zonal capacities, and even nodal balance constraints Further research: Pricing Investigate relevance for deterministic (sequential) market clearing models 32 / 33

33 References Bouard, F., Galiana, F. D., and Conejo, A. J. (2005a). Market-clearing with stochastic security-part i: formulation. Power Systems, IEEE Transactions on, 20(4): Bouard, F., Galiana, F. D., and Conejo, A. J. (2005b). Market-clearing with stochastic security-part ii: Case studies. Power Systems, IEEE Transactions on, 20(4): Khazaei, J., Zakeri, G., and Oren, S. (2012). Single and multi-settlement approaches to market clearing mechanisms under demand uncertainty. Khazaei, J., Zakeri, G., and Oren, S. (2013). Deterministic vs. stochastic settlement approaches to market clearing mechanisms under demand uncertainty. Khazaei, J., Zakeri, G., and Oren, S. S. (2014a). Market clearing mechanisms under uncertainty. Khazaei, J., Zakeri, G., and Pritchard, G. (2014b). The eects of stochastic market clearing on the cost of wind integration: a case of new zealand electricity market. Energy Systems, 5(4): Morales, J., Conejo, A., Liu, K., and Zhong, J. (2012). Pricing electricity in pools with wind producers. Power Systems, IEEE Transactions on, 27(3): Morales, J. M., Zugno, M., Pineda, S., and Pinson, P. (2014). Electricity market clearing with improved scheduling of stochastic production. European Journal of Operational Research, 235(3): Pritchard, G., Zakeri, G., and Philpott, A. (2010). A single-settlement, energy-only electric power market for unpredictable and intermittent participants. Operations Research, 58(4-part-2): Wong, S. and Fuller, J. D. (2007). Pricing energy and reserves using stochastic optimization in an alternative electricity market. Power Systems, IEEE Transactions on, 22(2): Zugno, M. and Conejo, A. J. (2013). A robust optimization approach to energy and reserve dispatch in electricity markets. Technical report, Technical University of Denmark. 33 / 33