Transmission capacity allocation in zonal electricity markets

Transcription

1 Transmission capacity allocation in zonal electricity markets Anthony Papavasiliou (UC Louvain) Collaborators: Ignacio Aravena (LLNL), Yves Smeers (UC Louvain) Workshop on Flexible Operation and Advanced Control for Energy Systems, Isaac Newton Institute for Mathematical Sciences, University of Cambridge. January 7 th -11 th, INI Workshop

2 Outline 1. Introduction 2. Day-ahead zonal electricity market models 3. Policy analysis using 4-node, 3-zone network 4. Cutting-plane algorithms for robust day-ahead zonal electricity markets 5. Simulation results for the Central Western European network 6. Conclusions INI Workshop

3 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Introduction Appendix INI Workshop

4 Zonal electricity markets European electricity market organized as a zonal market, EC 714/2009 Two types of export/import limits: Limits on the bilateral exchange between neighbouring zones, Available-Transfer-Capacity Market Coupling (ATCMC) Limits on the net position configuration of zones, Flow-Based Market Coupling (FBMC) Both methodologies should be N-1 robust (Critical Branches/Critical Outages), Amprion et al. (2017) FBMC used to clear day-ahead electricity market at the Central Western European system since May 2015 Other markets might implement FBMC in the near future (e.g. Nord Pool, Energinet et al. (2017)) INI Workshop

5 Flow-Based Market Coupling (FBMC) Preferred methodology for electricity market operations of the EC, EU 2015/1222:... a method that takes into account that electricity can flow via different paths and optimizes the available capacity in highly interdependent grids... Increases in day-ahead market welfare of 95Me/year with respect to ATCMC, Amprion et al. (2013) Congestion management and balancing costs not included in studies. They amounted to 945Me in 2015, ENTSO-E (2015). Questions: Do FBMC or ATCMC correctly account for physical flows? Why do they/do they not? Does FBMC significantly improve the overall welfare of the market with respect to ATCMC? INI Workshop

6 Literature Jensen et al. (2017), and many references therein, study ATCMC and conclude that its performance is significantly worse than that of a nodal market Waniek et al. (2009), Waniek et al. (2010) study the accuracy of the approximation of flows in FBMC at cross-border lines Marien et al. (2013) study how discretionary aggregation parameters (for export/import limits) affect the outcome of FBMC Van den Bergh et al. (2015) summarize the concepts and methodology used for FBMC at the Central Western European system Dierstein (2017) analyzes the impacts of discretionary aggregation parameters on welfare, exchanges, prices and counter-trading costs INI Workshop

7 Contributions 1. We propose a new framework for modelling ATCMC and FBMC in which we derive export/import limitations directly from the physics of the real network. (the proposed models do not depend on discretionary aggregation parameters) 2. We present cutting-plane algorithms to systematically account for the N-1 security criterion on day-ahead markets. 3. We perform numerical simulations using an industrial-scale instance of the Central Western European system considering 100 years of operating conditions. Vast similarities between ATCMC and FBMC in all aspects. Zonal market designs fail at allocating transmission capacity and are outperformed by a nodal market. INI Workshop

8 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Day-ahead electricity market models Conclusions Appendix INI Workshop

9 Assumptions 1. All energy trades take place at the day-ahead auction 2. Bids are price-quantity pairs, associated with a node/zone 3. Participants bid truthfully 4. System operator knows: Topology of the network Susceptance and thermal limits of lines Installed production capacity at each node 5. Consumers have an infinite valuation (only for simplicity) INI Workshop

10 Nodal electricity market min bids, flows production cost s.t. fractional bids net production = outgoing flows, at each node line thermal limits n 2 l 12 n 1 l 23 l 41 B n 3 l 34 n 4 power-angle constraints INI Workshop

11 Nodal electricity market min v,f,θ g G P g Q g v g s.t. 0 v g 1 g G Q g v g Q n = g G(n) l L(n, ) f l l L(,n) F l f l F l l L f l n N [ρ n ] f l = B l ( θm(l) θ n(l) ) l L n 2 l 12 n 1 l 23 l 41 B G = {1,2,3,4}, G(n 1 ) = {1},... N = {n 1,n 2,n 3,n 4 } n 3 l 34 n 4 P,Q: price and quantity F l,b l : capacity and susceptance line l L = {l 12,l 23,l 34,l 41 }, L(n 1,n 2 ) = {l 12 },... INI Workshop

12 Zonal network organization B n 3 l 23 n 2 l 12 l 34 n 1 A l 41 C n 4 G = {1,2,3,4}, G(A) = {1,2},... N = {n 1,n 2,n 3,n 4 }, N(A) = {n 1,n 2 },... INI Workshop

13 Flow-Based Market Coupling with Approximation (FBMC-A) 1. Select a base case (p 0,f 0 ) (net positions, flows on branches) p B p 0 B f 0 l 23 f 0 l 12 f 0 l 34 f 0 l 41 p 0 A p A p 0 C p C INI Workshop

14 Flow-Based Market Coupling with Approximation (FBMC-A) 1. Select a base case (p 0,f 0 ) (net positions, flows on branches) 2. Compute zone-to-line Power- Transfer-Distribution-Factors, PTDF l,z, so that f l z Z PTDF l,z p z f 0 l 12 f l12 f 0 l 23 f l23 f fl 0 l34 34 f l34 p B p 0 B f 0 l 41 p 0 A p A p 0 C p C INI Workshop

15 Flow-Based Market Coupling with Approximation (FBMC-A) 1. Select a base case (p 0,f 0 ) (net positions, flows on branches) p B p 0 B 2. Compute zone-to-line Power- Transfer-Distribution-Factors, PTDF l,z, so that f 0 l 12 f l12 f 0 l 23 f l23 f fl 0 l34 34 f l z ZPTDF l,z p z f l34 3. Define flow-based { domain: P FB A := p R Z p z = 0, z Z p 0 A p A f 0 l 41 p 0 C p C F l z ZPTDF } l,z (p z p 0 z)+fl 0 F l l L INI Workshop

16 Flow-Based Market Coupling with Approximation (FBMC-A) 4. Clear day-ahead market by solving: min v,p g G P g Q g v g s.t. 0 v g 1 g G Q g v g g G(z) p z = 0 z Z n N(z) Q n = p z z Z [ρ z ] F l z ZPTDF l,z (p z p 0 z)+f 0 l F l l L Circular definitions: base case (p 0,f 0 ), market clearing point Discretionary parameters: zone-to-line PTDF (among others) INI Workshop

17 Zonal electricity market min v,p g G P g Q g v g s.t. 0 v g 1 g G Q g v g g G(z) n N(z) p z z Z [ρ z ] p P Q n = P should include all feasible cross-border trades, EC 714/2009, Annex I, Art. 1.1 P should not include configurations that can harm security, EC 714/2009, Annex I, Art. 1.7 n 2 l 12 n 1 A l 23 l 41 B C G = {1,2,3,4}, G(A) = {1,2},... N = {n 1,n 2,n 3,n 4 }, N(A) = {n 1,n 2 },... n 3 l 34 n 4 INI Workshop

18 Deriving P directly from physics: an example Physics: n 2 r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 n 1 A B l 12 l 31 l 23 n 3 Zonal net positions: p A = r 1 p B = r 2 +r 3 G = {1,2,3} Q 1 = 200, Q 2 = 200, Q 3 = 50 N = {n 1,n 2,n 3 } L = {l 12,l 23,l 31 }, F 12 = MW demand per node INI Workshop

19 Deriving P directly from physics: an example Physics: r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 Are these zonal net positions feasible? p A = 0 p B = 0 p A = 200 p B = 200 p A = 100 p B = 100 p A = 50 p B = 50 Zonal net positions: p A = r 1 p B = r 2 +r 3 INI Workshop

20 Deriving P directly from physics: an example Physics: r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 Are these zonal net positions feasible? p A = 0 p B = 0 Yes p A = 200 p B = 200 p A = 100 p B = 100 p A = 50 p B = 50 Zonal net positions: p A = r 1 p B = r 2 +r 3 INI Workshop

21 Deriving P directly from physics: an example Physics: r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 Are these zonal net positions feasible? p A = 0 p B = 0 Yes p A = 200 p B = 200 No p A = 100 p B = 100 p A = 50 p B = 50 Zonal net positions: p A = r 1 p B = r 2 +r 3 INI Workshop

22 Deriving P directly from physics: an example Physics: r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 Are these zonal net positions feasible? p A = 0 p B = 0 Yes p A = 200 p B = 200 No p A = 100 p B = 100 p A = 50 p B = 50 No Zonal net positions: p A = r 1 p B = r 2 +r 3 INI Workshop

23 Deriving P directly from physics: an example Physics: r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 Are these zonal net positions feasible? p A = 0 p B = 0 Yes p A = 200 p B = 200 No p A = 100 p B = 100 No p A = 50 p B = 50 Yes Zonal net positions: p A = r 1 p B = r 2 +r 3 INI Workshop

24 Deriving P directly from physics: an example Physics: r 1 +r 2 +r 3 = r r r f 12 = 1/3r 1 1/3r 2 25 Are these zonal net positions feasible? p A = 0 p B = 0 Yes p A = 200 p B = 200 No p A = 100 p B = 100 No p A = 50 p B = 50 Yes Zonal net positions: p A = r 1 p B = r 2 +r 3 True net position feasible set P: p A +p B = p A 87.5 INI Workshop

25 Flow-Based Market Coupling with Exact Projection (FBMC-EP) space of nodal injections space of zonal net positions R := { r R N r is feasible for the real network } 4-node, 3-zone network: p A = r 1 +r 2, p B = r 3, p C = r 4 INI Workshop

26 Flow-Based Market Coupling with Exact Projection (FBMC-EP) space of nodal injections space of zonal net positions R := { r R N r is feasible for the real network } P FB EP := { p R Z r R : p z = r n z Z } n N(z) 4-node, 3-zone network: p A = r 1 +r 2, p B = r 3, p C = r 4 INI Workshop

27 Flow-Based Market Coupling with Exact Projection (FBMC-EP) P FB EP = { p R Z ( v,f,θ) [0,1] G R L R N : g G(z) g G(n) Q g v g p z = Q g v g l L(n, ) n N(z) Q n z Z, f l + l L(,n) f l = Q n n N, F l f l F l, f l = B l ( θm(l) θ n(l) ) l L } P FB EP allows for all trades that are feasible with respect to the real network and bans only trades that can be proven to be infeasible for the real network P FB A provides no guarantees: might ban feasible trades and, also, allow infeasible trades INI Workshop

28 Available-Transfer-Capacity Market Coupling (ATCMC) net positions of zones Z l 23 B n 3 flow on interconnectors between zones T t AB B n 2 l 12 l 34 t BC n 1 A l 41 C n 4 A t CA C ATCMC clears day-ahead market over the network G(Z, T) Available-transfer-capacities (ATCs): ATC t e t ATC + t How to compute ATCs? INI Workshop

29 Available-Transfer-Capacity Market Coupling (ATCMC) space of zonal net positions space of exchanges P FB EP INI Workshop

30 Available-Transfer-Capacity Market Coupling (ATCMC) space of zonal net positions space of exchanges P FB EP { E := e R T l L(t) p P : p z = t T(z, ) F l e t e t l L(t) t T(,z) F l t T, } e t z Z INI Workshop

31 Maximum-volume Available-Transfer-Capacities (ATCs) ATC limits, ATC t e t ATC + t t T, are a box in the space of exchanges Compute ATCs as a maximum volume box inside E, max ATC (ATCt +ATC t + ) t T s.t. [ ATC,ATC + ] E E ATC := [ ATC,,ATC +, ] allows for the largest subset of bilateral exchanges that can be accommodated using a box and it bans all trades that would result in infeasible zonal net positions Implemented methodology for computing ATCs provides no guarantees INI Workshop

32 Maximum-volume Available-Transfer-Capacities (ATCs) space of zonal net positions space of exchanges P E INI Workshop

33 Maximum-volume Available-Transfer-Capacities (ATCs) space of zonal net positions space of exchanges P E, E ATC = [ ATC,,ATC +, ] INI Workshop

34 Maximum-volume Available-Transfer-Capacities (ATCs) space of zonal net positions space of exchanges P { P ATC := p R Z e E ATC : p z = e t } e t z Z t T(z, ) t T(,z) E, E ATC = [ ATC,,ATC +, ] INI Workshop

35 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Policy analysis using 4-node, 3-zone network Appendix INI Workshop

36 Recap: 4 policies LMP: Minimizes cost over nodal model FBMC-A: Minimizes cost over zonal model with P = P FB A FBMC-EP: Minimizes cost over zonal model with P = P FB EP ATCMC: Minimizes cost over zonal model with P = P ATC INI Workshop

37 Inter-zonal congestion case study n 2 l 12 l 23 B n 3 l 34 Generators Q g P g g n(g) [MW] [$/MWh] 1 n n n n n 1 A l 41 C B l = 1pu l L n 4 Consumers Q n n [MW] n n F l41 = 100MW,F l = + l L\{l 41 } INI Workshop

38 Inter-zonal congestion: results Summary of clearing quantities and prices for a case of inter-zonal congestion (l 41 limited to 100MW) Policy Total Abs. error Overload ρ [$/MWh] cost [$] flow approx. [MW] l 41 [MW] LMP (8, 45, 82, 119) 0 0 FBMC-A (8, 18, 200) FBMC-EP (8, 18, 23) ATCMC (8, 18, 200) 50 Cleared quantities on all zonal markets overload line l 41 : failure to account for inter-zonal congestion Flow approximation error and overload larger in FBMC-A than in FBMC-EP Cost of ATCMC larger than cost of LMP, ATCMC clears at an infeasible point INI Workshop

39 Inter-zonal congestion: space of zonal net positions Limited flow on inter zonal line l 41 Net position zone B [MW] LMP FBMC A FBMC EP ATCMC Net position zone A [MW] Vertically shaded area: P FB A P FB EP Horizontally shaded area: P FB EP P FB A INI Workshop

40 Intra-zonal congestion case study n 2 l 12 l 23 B n 3 l 34 Generators Q g P g g n(g) [MW] [$/MWh] 1 n n n n n 1 A l 41 C B l = 1pu l L n 4 Consumers Q n n [MW] n n F l12 = 100MW,F l = + l L\{l 12 } INI Workshop

41 Intra-zonal congestion: results Summary of clearing quantities and prices for a case of intra-zonal congestion (l 12 limited to 100MW) Policy Total Abs. error Overload ρ [$/MWh] cost [$] flow approx. [MW] l 12 [MW] LMP (8, 45, 32.7, 20.3) 0 0 FBMC-A (18, 18, 200) FBMC-EP (18, 18, 18) ATCMC (8, 18, 200) 108 Cleared quantities on all zonal markets overload line l 12 : failure to account for intra-zonal congestion Flow approximation error larger in FBMC-A than in FBMC-EP INI Workshop

42 Intra-zonal congestion: space of zonal net positions Limited flow on intra zonal line l 12 Net position zone B [MW] LMP FBMC A FBMC EP ATCMC Net position zone A [MW] Vertically shaded area: P FB A P FB EP INI Workshop

43 Discussion FBMC-A, FBMC-EP, ATCMC led to clearing quantities that would overload the transmission system FBMC-A can be cleared with infeasible net positions and can prevent feasible trades from being accepted In direct conflict with EC 714/2009, Annex I, Art. 1.1 and 1.7 All zonal market designs suffer the same problem for interand intra-zonal transmission capacity allocation: losing track of nodal injections leads to inaccurate physical flow estimations Given these results, in what follows, we only use FBMC-EP for modelling flow-based market coupling INI Workshop

44 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Cutting-plane algorithms for robust day-ahead electricity markets Appendix INI Workshop

45 Nodal N-1 security criterion Nodal net injections, r n = g G(n) Q gv g Q n, should be feasible even if a single transmission element is not available n 2 l 12 n 1 A l 23 l 41 B C n 3 l 34 n 4 Generators Q g P g g n(g) [MW] [$/MWh] 1 n n n n INI Workshop

46 Nodal N-1 security criterion Nodal net injections, r n = g G(n) Q gv g Q n, should be feasible even if a single transmission element is not available n 2 n 1 A l 23 l 41 B C n 3 l 34 n 4 Generators Q g P g g n(g) [MW] [$/MWh] 1 n n n n INI Workshop

47 Nodal N-1 security criterion Nodal net injections, r n = g G(n) Q gv g Q n, should be feasible even if a single transmission element is not available n 2 n 1 n 3 l 12 l 34 A l 41 B C n 4 Generators Q g P g g n(g) [MW] [$/MWh] 1 n n n n INI Workshop

48 Nodal day-ahead market clearing problem with N-1 security min v,r g G P g Q g v g s.t. 0 v g 1 g G Q g v g Q n = r n n N [ρ n ] g G(n) r R N 1 where R N 1 = u {0,1} L R(u) and R(u) = u 1 1 { r R N (f,θ) R L R N : r n = l L(n, ) f l l L(,n) f l n N, F l f l F l, f l = B l (1 u l ) ( θ m(l) θ n(l) ) l L } INI Workshop

49 Cutting-plane algorithm for FBMC under N-1 security R N 1 is a convex polytope we can describe it as Vr W, for certain V R M N and W R N M CO(V, W) (Market Clearing Oracle): Clears day-ahead nodal market using Vr W as a description of R N 1 IO(r) (Injection Oracle): Checks if r R N 1, returning a separating hyperplane v r w if r / R N 1 1: Initialize V := 0 1, N,W := 0, inclusion := FALSE 2: while!inclusion do 3: Call MCO(V,W) r 4: Call IO(r) inclusion, (v, w) 5: V := [V v], W := [W w] 6: end while 7: Terminate: inner model of MCO(V,W) gives the optimal clearing. INI Workshop

50 Injection oracle (IO) Recall R N 1 = u {0,1} L u 1 1 R(u) Generating Benders cuts independently for every u {0,1} L, u 1 1 can be very expensive A better approach: use a distance function d between the query point r and the set R N 1 d(r,r N 1 ) := max u {0,1} L u 1 1 min r R(u) r r 1 which can be evaluated by solving a single-level MILP Cutting-plane algorithm converges finitely Algorithm inspired by original work by Street et al. (2014) on security constrained unit commitment INI Workshop

51 Zonal day-ahead market clearing problem with N-1 security Zonal net positions should be feasible even if a single transmission element is not available min v,p P g Q g v g g G s.t. 0 v g 1 g G Q g v g g G(z) p P n N(z) Q n = p z z Z [ρ z ] FBMC: P P FB EP N 1 := {p R Z there exists a feasible ( v, f, θ) for each single-element unavailability scenario} ATCMC: P projection of ATC box, computed as maximum-volume box inside E N 1 (defined in an analogous fashion to E) INI Workshop

52 Set of feasible net positions under N-1 security Define P FB EP N 1 P FB EP (u) = := u {0,1} L u 1 1 P FB EP (u), where { p R Z ( v,f,θ) [0,1] G R N R L : g G(z) i G(n) Q g v g n N(z) Q g v g Q n = Q n = p z z Z, l L(n, ) f l l L(,n) f l n N, F l f l F l, f l = B l (1 u l ) ( θ m(l) θ n(l) ) l L } is a convex polytope we can clear FBMC using an analogous cutting-plane approach to that used for LMP P FB EP N 1 Computing max-volume ATCs: similar approach, but separating hyperplanes guarantee box inclusion instead of point inclusion INI Workshop

53 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Simulation results for the Central Western European network Appendix INI Workshop

54 Two-settlement system forecast renewable energy infeed renewable energy infeed generation and transmission outages Day-ahead electricity market day-ahead commitment day-ahead net positions day-ahead cleared energy quantities Real-time electricity market day-ahead energy prices day-ahead cleared energy quantities day-ahead congestion rent reserve prices cleared reserve quantities real-time cleared energy quantities real-time energy prices real-time congestion rent real-time redispatch and congestion management cost Commitment refers to {0, 1} (on-off) decisions European rules for integer pricing, Madani and Van Vyve (2015) INI Workshop

55 Central Western European network Netherlands * Belgium Germany Netherlands France Austria Belgium Germany Austria Luxembourg France 632 buses, 945 branches (3 491 individual circuits), 346 slow thermal generators (154GW), 301 fast thermal generators (89GW) and renewable generators (149GW) 768 typical snapshots random uncertainty realizations 100 years of operation INI Workshop

56 Implementation and deployment on HPC infrastructure Implementation in Julia/JuMP, using Gurobi, Ipopt compiled with HSL and Xpress as mathematical programming solvers High-performance computing (HPC) deployment using Julia s built-in parallel computing capabilities Total simulation time: CPU-hours Cab Lawrence Livermore National Laboratory Lemaitre3 Consortium des Équipements de Calcul Intensif INI Workshop

57 CWE results: total cost performance Total costs and efficiency of different policies Policy Day-ahead Real-time Total Efficiency [Me/year] [Me/year] [Me/year] losses PF % LMP FBMC % ATCMC % PF: Perfect Foresight benchmark LMP schedules out-of-merit production to meet N-1 security, leading to inefficiencies with respect to PF Efficiency losses of zonal markets with respect to LMP amount to about 5.1% of total costs, 600Me/year FBMC and ATCMC do not present a significant difference INI Workshop

58 CWE results: costs composition Day-ahead costs Real-time costs LMP LMP FBMC FBMC ATCMC ATCMC Cost [10 9 e/year] Cost [10 9 e/year] Production slow Production fast CO2 emissions Curtailment Day-ahead costs larger for LMP, real-time costs much larger for FBMC and ATCMC than LMP Zonal policies: re-dispatching slow (cheap) generators down and re-dispatching fast (expensive) generators up in real time INI Workshop

59 Cross CWE results: production schedules and line overloading Production schedule Line overloading day-ahead schedule Line overloading day-ahead schedule comparison FBMC ATCMC L1 difference on nodal production [GW] Total line overload [GW] Total line overload [GW] LMP vs FBMC LMP vs ATCMC FBMC vs ATCMC DE/AT/LX BE/FR/NL border DE/AT/LX BE/FR/NL Cross border Large differences between day-ahead schedules of nodal and zonal policies, small differences between FBMC and ATCMC Zonal policies lead to decisions overloading inter- and intra-zonal transmission lines INI Workshop

60 CWE results: difference on commitment decisions Price change in FBMC at nodes where UC FBMC UC LMP Estimated density [-] Exclusive LMP Exclusive FBMC FBMC real-time ρ - day-ahead ρ [ /MWh] Exclusive LMP : weighted average change ρ RT n ρ DA z(n) over all nodes where LMP committed slow units and FBMC did not commit units. Exclusive FBMC series computed analogously. LMP commits capacity where it is needed. FBMC suffers from suboptimal commitment. INI Workshop

61 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Appendix Conclusions INI Workshop

62 Conclusions New framework for modelling zonal electricity markets: Projecting network constraints onto space of exports/imports Free from discretionary parameters (base case, flow approximation, etc.) ATCMC and FBMC fail at allocating inter- and intra-zonal transmission capacity CWE: ATCMC and FBMC do not present significant performance differences CWE: Nodal design outperforms ATCMC and FBMC by 600Me/year INI Workshop

63 Thank you Contact: Anthony Papavasiliou, Ignacio Aravena, Yves Smeers, INI Workshop

64 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Appendix Appendix INI Workshop

65 Future extensions Application of the developed framework to answer policy questions in European electricty markets via simulation Extensions of the proposed framework: Pricing AC power flow constraints implicitly on active power TSO-DSO coordination INI Workshop

66 Introduction Day-ahead electricity market models Cutting-plane algorithms for robust day-ahead electricity markets Simulation results for the Central Western European network Conclusions Electricity markets 101 Appendix INI Workshop

67 Transportation networks r n2 r n1 n 2 l 23 f l12 l 12 n 1 f l23 l 41 f l41 n 3 l 34 f l34 n 4 r n3 r n4 Paths are decision variables Must respect nodal balance constraints ( n N) r n = f l l L(n, ) l L(,n) Must respect capacities of branches ( l L): F l f l F l Note: n N r n = 0 f l INI Workshop

68 Transportation networks Paths are decision variables n 2 n 1 l 12 1 l 23 l 41 0 n 3 l 34 0 n Must respect nodal balance constraints ( n N) r n = f l l L(n, ) l L(,n) Must respect capacities of branches ( l L): F l f l F l f l Note: n N r n = 0 INI Workshop

69 Transportation networks Paths are decision variables n 2 n 1 l 12 0 l 23 l 41-1 n 3 l 34-1 n Must respect nodal balance constraints ( n N) r n = f l l L(n, ) l L(,n) Must respect capacities of branches ( l L): F l f l F l f l Note: n N r n = 0 INI Workshop

70 Electrical networks r n2 r n1 θ n2 n 2 l 23 f l12 l 12 n 1 θ n1 f l23 l 41 f l41 θ n3 n 3 l 34 f l34 n 4 θ n4 r n3 r n4 Flow paths are implied by injections Must respect nodal balance constraints ( n N) r n = f l l L(n, ) l L(,n) Must respect capacities of branches ( l L): F l f l F l f l Must respect power-angle constraints ( l L, branch l from m(l) to n(l)): f l = B l ( θm(l) θ n(l) ) INI Workshop

71 Electrical networks 1 n n 1 2 l l 23 l n 3 l n B l12 = B l23 = B l34 = B l41 = Flow paths are implied by injections Must respect nodal balance constraints ( n N) r n = f l l L(n, ) l L(,n) Must respect capacities of branches ( l L): F l f l F l f l Must respect power-angle constraints ( l L, branch l from m(l) to n(l)): f l = B l ( θm(l) θ n(l) ) INI Workshop

72 Nodal markets: trading power over an electrical network n 2 l 12 n 1 l 23 l 41 B n 3 l 34 n 4 Participants can trade freely when located at the same node Participants in different nodes can trade up to congestion of lines Congestion: power flow equations, thermal limits of transmission lines, among others (physics) INI Workshop

73 Zonal markets: trading power over an aggregated network n 2 l 12 n 1 A l 23 l 41 B C n 3 l 34 n 4 Participants trade freely within each bidding zone Participants in different zones can trade up to certain export/import limits Limits: aggregation of power flow equations and others INI Workshop