Transmission charging and market distortion

Transcription

1 Transmission charging and market distortion Andy Philott Tony Downward Keith Ruddell s Electric Power Otimization Centre University of Auckland IPAM worksho, UCLA January 13, /56

2 Outline of transmission ricing: Merchant transmission. Volume versus eak charges. Beneficiaries-ay SPD charge method. Equilibrium models with charges on Ricardian rents. A Cournot model. Suly function equilibrium. Price-taking agents. s Suly function equilibria with beneficiaries-ay transmission ricing. Definition of benefits. Examle with uniform demand shock. Welfare analysis. s. 2/56

3 What is the value/cost of a transmission grid? The transmission grid rovides a number of different benefits: reliability; cometition benefits; short-run efficiency; the ability to access electricity when needed. The cost of a transmission line is mainly in its construction, and there are large economies of scale. The cost of using the line is near $0 / MWh. s 3/56

4 Merchant transmission investment? Tyically, the transmission grid is oerated as a regulated monooly, where investments in the grid are made to imrove the overall social welfare of the system. In economic theory, locational marginal rices should deliver congestion rentals to the grid oerator to fund investment in the grid. Would like these to rovide ex-ante incentives for market-like investments. s Practical comlications 1 the rice signal is valid at the margin, whereas investment in transmission is lumy and future focused; transmission investment takes lace to imrove security and reliability as well as real-time ower delivery. So congestion rentals alone are insufficient to ay for what is deemed required investment in the transmission grid. Leads to a cost recovery roblem. 1 Joskow, P. & Tirole, J. (2005). Merchant Transmission Investment. Journal of Industrial Economics, 53(2), /56

5 Cost recovery Transmission ricing seeks to recover the costs of transmission investment from market articiants, namely: distribution network owners (on behalf of their customers); directly connected consumers (large industrials); generators. These costs should be designed so as to romote both static and dynamic efficiency. s In articular, if a line has been built it is desirable that: the line be used to reduce short-run (fuel) costs; the charging mechanism does not distort efficient locational rice signals. 5/56

6 Transmission ricing methodologies MISO (ostage stam rates, 80% to load 20% to generators); PJM (investment costs are collected from those deemed to benefit from the investment). 2 Argentina (affected market articiants arove, and users ay). 3 s 2 Hogan, W.W. (2011). and cost allocation, May 31. JFK School of Government, Harvard University. 3 Littlechild S.C. & Skerk C.J. (2008). Transmission exansion in Argentina 1: The origins of olicy. Energy Economics, 30, /56

7 s New Zealand electricity grid. 4 4 Ministry for the Environment; htt:// 7/56

8 Transmission ricing roosals in New Zealand Currently the transmission ricing methodology (TPM) has three main charges: connection charge ($130m); HVDC charge ($150m); interconnection charge ($630m). A market-based (or market-like) aroach is being sought, where the beneficiaries of the investment ay. s 8/56

9 Estimated revenue from each charge Figure 3: Breakdown of otions by charge s Figure 4 shows how Revenue each of the collected charges is under distributed roosals. across grous 5 of arties. 5 Electricity Authority; Transmission ricing methodology review: TPM otions. 16 June /56

10 What should users ay for? Debate over users of the grid avoiding regional coincident eak demand (RCPD) charges by load shifting. Inflexible articiants advocate: less emhasis on eak-load charging (RCPD). more emhasis on charging by volume (dee connection and SPD charges). s But volume-based charges are clearly distortionary. We are interested in understanding these distortions. We focus on the SPD charge. SPD = Schedule Price Disatch the DCOPF disatch software. The benefits of an asset are comuted using two runs of the software, with and without the asset. 10/56

11 methodology The SPD charge is equal to a roortion α of the erceived benefits of a line exansion to market articiants, where α is chosen to recover the required amount. For a generator, these erceived benefits are comuted by SPD based on the change in their infra-marginal or Ricardian rents, given their suly curve offer. This benefit will be comuted for every trading eriod. s S i RD c q RD c q q 11/56

12 Incentive to conceal erceived benefits One of the concerns of this aroach is that generators and other market articiants may be able to conceal their erceived benefits by changing their offer. This could lead to inefficiency in the disatch model as well as shifting the burden of aying for the transmission asset onto those market articiants who cannot or do not behave strategically. s We will show that: with known demand, generators can avoid charges altogether; with uncertain demand, a firm must balance its incentive to minimize the transmission charge against the incentive to maximize its rofit in the current eriod. 12/56

13 Charge on Ricardian Rents We will initially resent a model whereby a charge is simly alied in roortion to the Ricardian rents of a generator (rather than to the benefits). This is simler to model, however, we will later see that it still has much in common with the charge on benefits. To illustrate some of the incentives to avoid the charge, we will first consider the change in behaviour of a Cournot agent with deterministic demand. s S i RD c q c RD c q q 13/56

14 Cournot duooly model S 1 () K 1 2 s S 2 () D() = a b Cournot layers offer suly curves S i () = q i 14/56

15 Cournot duooly model RD Si s q q 15/56

16 Cournot duooly model RD Si s q q 16/56

17 Charge on Ricardian rents A small ortion α < 1 2 of erceived roducer surlus is taxed. Generators resond by marking u below the disatch quantity (which has no effect of the disatch oint). RD Si s q q 17/56

18 Charge on Ricardian rents Strategic roducer benefits are hidden. Price taking generators and consumers are less able to conceal their benefits, leaving them with a larger share of the transmission charges. RD Si s q q 18/56

19 Imlications for transmission ricing In this model, roducers can hide all of their roducer surlus and thus not have to contribute to the cost of the grid investment. However, this result relies on the demand (curve) being known in advance. What haens under more realistic assumtions about demand uncertainty? s 19/56

20 Suly function equilibrium model Now consider the same network, but now demand at node 2 is uncertain (but no longer elastic). S 1 () K 1 2 s S 2 () D = ε ε U[ ε, ε] 20/56

21 Profit maximization by suliers Generators try to maximize their rofit functional Π = S q( c)dψ (q, ) = c is the marginal cost; is the rice ca, c ( c)q(ψ + q ψ q ) d. ψ(q, ) is the market distribution function 6 (the robability that an offer of q MW at rice is not fully disatched). ψ q and ψ are the artial derivatives of ψ. s First-order otimality conditions (Euler-Lagrange) Z (q, ) = ( c) ψ qψ q = 0 yields a system of differential equations. In symmetric duooly this is a single o.d.e. that has solution of a linear suly curve through (c, 0) and (, K 2 ) 6 Anderson, E.J. & Philott, A.B. (2002). Otimal offer construction in electricity markets. Mathematics of Oerations Research, 27, /56

22 Incentives to mark-u S i RD max s c RD min K 2 q What might haen with a charge on Ricardian rents? Suose that α = 25% of erceived roducer rofits is charged to fund transmission investment. 22/56

23 Marking u in resonse to the charge undisatched segment S i RD max s c RD min A gradient discontinuity in any undisatched art of offer curve is OK. K 2 q 23/56

24 Marking u in resonse to the charge disatched region? S i RD max s c RD min What about further u the curve, in the art that is sometimes disatched? K 2 q 24/56

25 Duooly SFE with a charge on erceived benefits New rofit functional Π = c ( c)q(ψ + q ψ q ) αq(1 ψ) d. First-order otimality condition becomes Z (q, ) = ( c)ψ (1 α)qψ q α(1 ψ) = 0. Ẑ (q, ) = ( c)ψ (1 α)q α 1 ψ = 0. ψ q ψ q s Given offer quantity, q, and other generator s suly function S 2 (), the robability of not being fully disatched is: 7 ψ (q, ) = Pr [ε < q + S 2 ()] = (q + S 2 ()) /ε Ẑ (q, ) = ( c) S 2 () (1 α) q αε + α (q + S 2 ()). 7 So long as q + S 2 () K, otherwise the robability is 1. 25/56

26 Duooly SFE with a charge on erceived benefits If we set q () = S 2 () = S (), then the condition Ẑ(q, ) = 0 gives first-order linear ODE S () = for the symmetric SFE. General solution is. (1 3α) αε S () + c c S () = A ( c) 1 3α αε 1 3α, s Since we assume that the line caacity is smaller than the highest levels of demand, A is determined by endoint condition S () = K 2, (otherwise rofitable deviation is ossible). 8 8 Holmberg, P. (2008). Unique suly function equilibrium with caacity constraints. Energy Economics, 30(1), /56

27 Equilibrium after charge alied S i RD max s c RD min In order to avoid the tax, the firms, in equilibrium, mark-u their offer rices for low quantities, but may also mark-down as they aroach the line caacity. K 2 q 27/56

28 Price-taking agents Market distribution function ψ(q, ) for a rice-taking agent is ψ() = Pr(P < ). Each roducer seeks to maximize Π = 0 (q C(q)) dψ d Euler-Lagrange condition is αq (1 ψ()) d. Z A = ( C (q)) ψ (1 α)ψ q α (1 ψ) = ( C (q)) dψ α (1 ψ) = 0. d s 28/56

29 Symmetric equilibrium from industry suly curve Assume inelastic demand ε with density f and c.d.f. F. Assume n symmetric generators with total suly Q. 9 ns() = Q() = ε. ψ() = Pr(P < ) = F (ε) = Pr(Q(P) < Q()) = F (Q()). Industry cost function C I has derivative at Q = nq defined by C I (Q) = C (q). Thus Z = ( C (q)) dψ d α (1 ψ()) = 0. dψdq Illustrative = f examle (Q) d d s ( C I (Q)) f (Q) dq α (1 F (Q)) = 0. d 9 related model in Frederico & Rahman (2003). Bidding in an electricity ay-as-bid auction. J. Regulatory Economics, 24(2), /56

30 Price-taking examle Two identical firms with Industry cost function is C(q) = q 2 C I (Q) = 1 2 Q2. If demand shock is uniform on [0, 1], ordinary differential equation for industry curve Q() is s ( Q) dq d So each agent offers = α(1 Q), Q(1) = 1 Q() = (1 + α) α. S() = (1 + α) α /56

31 Incentives for rice-taking firms Price Industry Suly Curves s Marginal Cost Price Taking Equilibrium 0.1 SFE without tax SFE with tax Quantity 31/56

32 Charge on benefit from exanded line The method does not aly a charge based on the entire roducer surlus, only based on the difference in Ricardian rents comared to some counterfactual. S 1 () J 1 2 s S 2 () D = ε ε U[ ε, ε] This counterfactual is the state of the network rior to any line ugrade. 32/56

33 Charge on benefit from exanded line The method does not aly a charge based on the entire roducer surlus, only based on the difference in Ricardian rents comared to some counterfactual. S 1 () K 1 2 s S 2 () D = ε ε U[ ε, ε] After the line ugrade we have the following network; the size of the line has increased from J to K. 33/56

34 Duooly SFE with low-caacity line (no charge) S i RD max s c RD min J 2 q 34/56

35 Duooly SFE with exanded line (no charge) S i RD max s c RD min J K 2 2 Larger caacity gives a flatter curve (more cometitive). The SPD-method assumes that the offer stays the same this would not be a valid assumtion in this case. q 35/56

36 Tariff on benefit from exanded line (disatch > J 2 ) Rather than aying a charge on the full roducer surlus, the transmission charge is a roortion of the benefit accruing due to the increased line caacity. S i s RD RD c c 1 2 ε J 2 K 2 q 36/56

37 Charge on benefit from exanded line (disatch > J 2 ) S i RD s RD c c The charge will be based on this area (which deends on the realization of the demand shock). J 2 K 2 q 37/56

38 Charge on benefit from exanded line (disatch J 2 ) S i s RD c For disatch below J 2, the actual and counterfactual disatch oints are the same, so there is no charge. J 2 K 2 q 38/56

39 Equilibrium offer curve (charge on benefit) c S i RD max RD min s J 2 K 2 q For quantities below J 2, the equilibrium offer curve is straight, since there is no charge ayable in this region (and it does not affect the erceived benefit). For quantities greater than J 2, the equilibrium curve matches the curve where the charge was alied to total erceived surlus. 39/56

40 Consider a duooly, over a network as shown earlier. The initial caacity of the transmission line is J = 0.2, and the line is exanded to K = 0.8. The marginal cost of both generators is c = 0, and there is a rice-ca in the market of 1. The demand at node 2 is random, and uniformly distributed between ε = 0 and ε = 1. s Firms are charged α = 25% of their benefits. 40/56

41 SFE deends on the roortion of benefits charged. Price SFE with Beneficiaries Pay Charge s Tariffed equilibrium, α = Tariffed equilibrium, α = Un-tariffed equilibrium Quantity 41/56

42 Welfare calculations Curve α CS Π U Π T Tax er firm TS S S Table 1: Benefits and taxes with a charge on line-exansion benefits. s S is the SFE offer assuming α = 0, S is the SFE offer with α = 0.25, CS is the consumer surlus, TS is total surlus, Π U and Π T are untaxed and taxed er-firm rofits. 42/56

43 SFE deends on the max demand shock Price SFE with Beneficiaries Pay Charge s =1 ε =2 Un-tariffed equilibrium Quantity 43/56

44 Overall marku deends on magnitude of exansion s c 1 2 ε J 2 K 2 q 44/56

45 Overall marku deends on magnitude of exansion s c 1 2 ε J 2 K 2 q 45/56

46 Overall marku deends on magnitude of exansion s c J 2 K 2 q 46/56

47 Overall marku deends on magnitude of exansion s c J 2 K 2 q 47/56

48 Consumer welfare comarison Consumer Welfare s J When J < 0.5 the exected consumer welfare dros as the firms try to avoid the charge; otherwise the consumers are better off. 48/56

49 Generator transmission charges comarison Transmission Charges s J When J < 0.58 the exected charge dros as the firms change their behaviour; interestingly, the firms end u aying a slightly higher charge for small increases in line size. 49/56

50 Producer surlus comarison (after transmission charge) Producer Profits s J When J K < 0.52 the exected roducer surlus increases as the firms try to reduce the charge aid. For smaller line ugrades the roducers are worse off. 50/56

51 Comarison with erfect cometition s 51/56

52 Variance of demand shock affects outcomes Price s Taxed SFE Un taxed SFE 0.1 Taxed PTE Un taxed PTE Quantity Figure 1: Equilibrium solution for examle with normally distributed ε N(0.7, 0.2). 52/56

53 Reducing variance of demand destroys equilibrium s Figure 2: First-order solution for examle with normally distributed ε N(0.7, 0.1). 53/56

54 Remarks If the charge is a small % of the benefits, the equilibrium is close to the uniform rice SFE. Incentive to mark u the lower art of curve increases with robability of lost load and decreases with variance of demand shock. Cometitiveness deends on size of transmission caacity exansion. s Examle equilibria are valid only if α < /56

55 s Demand uncertainty reduces incentives to mark u offer curves to conceal erceived rofits. A charge based on benefits does not give an incentive to mark-u at the low end of the offer curve, since it is the difference in rofits from counterfactual that is taxed. With small-medium line exansions we found that generator cometition would increase due to the charge, and consumer surlus and the total charge collected from generators would increase. s For large line increases, consumer welfare decreases as firms mark u the low-quantity end of their curve to minimize their transmission charge. The SPD charge is retrosective. Related dee connection charges use flow tracing ex-ost to allocate costs. Both give incentives to offer strategically in the sot market. A simler alternative is to rice the use of transmission directly within the disatch software. Is this more or less distortionary than current roosals? 55/56

56 Thanks for your attention. s Any Questions? 56/56