Background Purpose of charges NZ proposals Transmission charging SPD Charge Charges on Rentals and Cournot setting SFE duopoly model distortion Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion Andy Philpott Tony Downward Keith Ruddell

Electric Power Optimization Centre University of Auckland www.epoc.org.nz

IPAM workshop, UCLA

January 13, 2016

1/56 Outline Background Purpose of charges • Background of transmission pricing: NZ proposals Merchant transmission. SPD Charge • Charges on Rentals Volume versus peak charges. • Cournot setting Beneficiaries-pay SPD charge method. SFE duopoly model • Perfect Competition • Equilibrium models with charges on Ricardian rents. Charges on Benefits Transmission benefits A Cournot model. Illustrative example • Supply function equilibrium. Conclusions • Conclusion -taking agents. • • Supply function equilibria with beneficiaries-pay transmission pricing. Definition of “benefits”. • Example with uniform demand shock. • Welfare analysis. • • Conclusions.

2/56 What is the value/cost of a transmission grid? Background Purpose of charges The transmission grid provides a number of different benefits: NZ proposals SPD Charge Charges on Rentals • reliability; Cournot setting SFE duopoly model • competition benefits; Perfect Competition • Charges on Benefits short-run efficiency; Transmission benefits • the ability to access electricity when needed. Illustrative example Conclusions Conclusion 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.

3/56 Merchant transmission investment? Background Purpose of charges Typically, the transmission grid is operated as a regulated NZ proposals , where investments in the grid are made to improve SPD Charge Charges on Rentals the overall social welfare of the system. Cournot setting SFE duopoly model In economic theory, locational marginal should deliver Perfect Competition Charges on Benefits congestion rentals to the grid operator to fund investment in the Transmission benefits grid. Would like these to provide ex-ante incentives for Illustrative example Conclusions market-like investments. Conclusion

Practical complications1

• the price signal is valid at the margin, whereas investment in transmission is “lumpy” and future focused; • transmission investment takes place to improve security and reliability as well as real-time power delivery.

So congestion rentals alone are insufficient to pay for what is deemed required investment in the transmission grid. Leads to a cost recovery problem. 1Joskow, P. & Tirole, J. (2005). Merchant Transmission Investment. Journal of Industrial , 53(2), 233-264. 4/56 Cost recovery Background Purpose of charges Transmission pricing seeks to recover the costs of transmission NZ proposals investment from market participants, namely: SPD Charge Charges on Rentals Cournot setting • distribution network owners (on behalf of their customers); SFE duopoly model Perfect Competition • directly connected consumers (large industrials); Charges on Benefits Transmission benefits • generators. Illustrative example Conclusions Conclusion These costs should be designed so as to promote both static and dynamic efficiency.

In particular, 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 price signals.

5/56 Transmission pricing methodologies Background Purpose of charges • MISO (postage stamp rates, 80% to load 20% to generators); NZ proposals SPD Charge • PJM (investment costs are collected from those deemed to 2 Charges on Rentals benefit from the investment). Cournot setting SFE duopoly model 3 • Argentina (affected market participants approve, and users pay). Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

2Hogan, W.W. (2011). Transmission benefits and cost allocation, May 31. JFK School of Government, Harvard University. 3Littlechild S.C. & Skerk C.J. (2008). Transmission expansion in Argentina 1: The origins of policy. Energy Economics, 30, 1367-1384. 6/56 Background Purpose of charges NZ proposals SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

New Zealand electricity grid.4

4Ministry for the Environment; http://www.mfe.govt.nz/publications/rma/national- environmental-standards-electricity-transmission-activities-introduction 7/56 Transmission pricing proposals in New Zealand Background Purpose of charges Currently the transmission pricing methodology (TPM) has three NZ proposals main charges: SPD Charge Charges on Rentals Cournot setting • connection charge ($130m); SFE duopoly model Perfect Competition • HVDC charge ($150m); Charges on Benefits Transmission benefits • interconnection charge ($630m). Illustrative example Conclusions Conclusion A market-based (or market-like) approach is being sought, where the beneficiaries of the investment pay.

8/56

Estimated revenue from each charge Figure 3: Breakdown of options by charge Background Purpose of charges NZ proposals SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

5 5.4 Figure 4 shows howRevenue each of the collected charges is underdistributed proposals. across groups of parties.

5Electricity Authority; Transmission pricing methodology review: TPM options. 16 June 2015. 9/56

Page 26

What should users pay for? Background Purpose of charges Debate over users of the grid avoidingregional coincident peak NZ proposals demand (RCPD) charges by load shifting. Inflexible participants SPD Charge Charges on Rentals advocate: Cournot setting SFE duopoly model Perfect Competition • less emphasis on peak-load charging (RCPD). Charges on Benefits Transmission benefits • more emphasis on charging by volume (deep connection and Illustrative example SPD charges). Conclusions Conclusion But volume-based charges are clearly distortionary. We are interested in understanding these distortions. We focus on the SPD charge.

SPD = “Schedule Price Dispatch” the DCOPF dispatch software. The benefits of an asset are computed using two runs of the software, with and without the asset.

10/56 SPD Charge methodology Background Purpose of charges The SPD charge is equal to a proportion α of the perceived NZ proposals benefits of a line expansion to market participants, where α is SPD Charge Charges on Rentals chosen to recover the required amount. Cournot setting SFE duopoly model For a generator, these perceived benefits are computed by SPD Perfect Competition Charges on Benefits based on the change in their infra-marginal or Ricardian rents, Transmission benefits given their supply curve offer. This benefit will be computed for Illustrative example Conclusions every trading period. Conclusion p

Si

p∗ RD

pc∗

RDc q 11/56 qc∗ q∗ Incentive to conceal perceived benefits Background Purpose of charges One of the concerns of this approach is that generators and other NZ proposals market participants may be able to conceal their perceived SPD Charge Charges on Rentals benefits by changing their offer. Cournot setting SFE duopoly model This could lead to inefficiency in the dispatch model as well as Perfect Competition Charges on Benefits shifting the burden of paying for the transmission asset onto Transmission benefits those market participants who cannot or do not behave Illustrative example Conclusions strategically. Conclusion

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 profit in the current period.

12/56 Charge on Ricardian Rents Background Purpose of charges We will initially present a model whereby a charge is simply NZ proposals applied in proportion to the Ricardian rents of a generator SPD Charge Charges on Rentals (rather than to the benefits). Cournot setting SFE duopoly model This is simpler to model, however, we will later see that it still Perfect Competition Charges on Benefits has much in common with the charge on benefits. Transmission benefits Illustrative example To illustrate some of the incentives to avoid the charge, we will Conclusions Conclusion first consider the change in behaviour of a Cournot agent with deterministic demand. p

Si

p∗ RD

pc∗

RDc q qc∗ q∗ 13/56 Cournot duopoly model Background Purpose of charges NZ proposals SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition S1(p) Charges on Benefits Transmission benefits Illustrative example K Conclusions Conclusion 1 2

S (p) D(p)= a bp 2 −

Cournot players offer supply curves Si (p) = qi

14/56 Cournot duopoly model Background Purpose of charges NZ proposals SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example RD Si Conclusions Conclusion

p∗

q∗ q

15/56 Cournot duopoly model Background Purpose of charges NZ proposals SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example RD Si Conclusions Conclusion

p∗

q∗ q

16/56 Charge on Ricardian rents Background 1 Purpose of charges A small portion α < 2 of perceived producer surplus is taxed. NZ proposals Generators respond by marking up below the dispatch quantity SPD Charge Charges on Rentals (which has no effect of the dispatch point). Cournot setting SFE duopoly model p Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

RD Si

p∗

q∗ q 17/56 Charge on Ricardian rents Background Purpose of charges Strategic producer benefits are hidden. Price taking generators NZ proposals and consumers are less able to conceal their benefits, leaving SPD Charge Charges on Rentals them with a larger share of the transmission charges. Cournot setting SFE duopoly model p Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

RD Si

p∗

q∗ q 18/56 Implications for SPD Charge transmission pricing Background Purpose of charges • In this model, producers can ‘hide’ all of their producer NZ proposals surplus and thus not have to contribute to the cost of the SPD Charge Charges on Rentals grid investment. Cournot setting SFE duopoly model Perfect Competition • However, this result relies on the demand (curve) being Charges on Benefits Transmission benefits known in advance. Illustrative example Conclusions Conclusion • What happens under more realistic assumptions about demand uncertainty?

19/56 Supply function equilibrium model Background Purpose of charges Now consider the same network, but now demand at node 2 is NZ proposals uncertain (but no longer elastic). SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition S1(p) Charges on Benefits Transmission benefits Illustrative example K Conclusions Conclusion 1 2

S2(p) D = ε

ε U[ε, ε¯] ∼ ¯

20/56 Profit maximization by suppliers Background Purpose of charges Generators try to maximize their profit functional NZ proposals SPD Charge Z Z p Charges on Rentals Π = q(p c)dψ (q, p) = (p c)q(ψ + q0ψ ) dp. Cournot setting p q SFE duopoly model S − c − Perfect Competition Charges on Benefits Transmission benefits Illustrative example • c is the ; p is the price cap, Conclusions Conclusion • ψ(q, p) is the market distribution function6 (the probability that an offer of q MW at price p is not fully dispatched).

• ψq and ψp are the partial derivatives of ψ.

First-order optimality conditions (Euler-Lagrange)

Z (q, p) = (p c) ψp qψq = 0 − − yields a system of differential equations. In symmetric duopoly this is a single o.d.e. that has solution of a linear supply curve K through (c, 0) and (p, 2 ) 6Anderson, E.J. & Philpott, A.B. (2002). Optimal offer construction in electricity markets. Mathematics of Operations Research, 27, 82-100. 21/56 Incentives to mark-up Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Si RDmax Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c RDmin

q K 2

What might happen with a charge on Ricardian rents? Suppose that α = 25% of perceived producer profits is charged to fund transmission investment. 22/56 Marking up in response to the charge – undispatched segment Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Si RDmax Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c RDmin

q K 2

A gradient discontinuity in any undispatched part of offer curve is OK.

23/56 Marking up in response to the charge – dispatched region Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Si RDmax Charges on Benefits Transmission benefits Illustrative example ? Conclusions Conclusion

c RDmin

q K 2

What about further up the curve, in the part that is sometimes dispatched?

24/56 Duopoly SFE with a charge on perceived benefits Background Purpose of charges New profit functional NZ proposals SPD Charge Z p Charges on Rentals Π = (p c)q(ψ + q0ψ ) αq(1 ψ) dp. Cournot setting p q SFE duopoly model c − − − Perfect Competition Charges on Benefits First-order optimality condition becomes Transmission benefits Illustrative example Conclusions Z (q, p) = (p c)ψp (1 α)qψq α(1 ψ) = 0. − − − − − Conclusion ψp 1 ψ Zˆ (q, p) = (p c) (1 α)q α − = 0. ⇒ − ψq − − − ψq Given offer quantity, q, and other generator’s supply function 7 S2 (p), the probability of not being fully dispatched is:

ψ (q, p) = Pr [ε < q + S2 (p)]

= (q + S2 (p)) /ε

0 Zˆ (q, p) = (p c) S (p) (1 α) q αε + α (q + S2 (p)) . − 2 − − −

7 So long as q + S2 (p) K, otherwise the probability is 1. 25/56 ≤ Duopoly SFE with a charge on perceived benefits Background ˆ Purpose of charges If we set q (p) = S2 (p) = S (p), then the condition Z(q, p) = 0 NZ proposals gives first-order linear ODE SPD Charge Charges on Rentals Cournot setting 0 (1 3α) αε SFE duopoly model S (p) = − S (p) + Perfect Competition p c p c Charges on Benefits − − Transmission benefits for the symmetric SFE. Illustrative example Conclusions General solution is Conclusion αε S (p) = A (p c)1−3α , − − 1 3α − . Since we assume that the line capacity is smaller than the highest levels of demand, A is determined by endpoint condition K S (p) = , 2 (otherwise profitable deviation is possible).8 8Holmberg, P. (2008). Unique supply function equilibrium with capacity constraints. Energy Economics, 30(1), 148-172. 26/56 Equilibrium after charge applied Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Si RDmax Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c RDmin

q K 2 In order to avoid the , the firms, in equilibrium, mark-up their offer prices for low quantities, but may also mark-down as they approach the line capacity. 27/56 Price-taking agents Background Purpose of charges Market distribution function ψ(q, p) for a price-taking agent is NZ proposals ψ(p) = Pr(P < p). Each producer seeks to maximize SPD Charge Charges on Rentals Cournot setting p Z dψ SFE duopoly model Π = (pq C(q)) αq (1 ψ(p)) dp. Perfect Competition 0 − dp − − Charges on Benefits Transmission benefits Euler-Lagrange condition is Illustrative example Conclusions Conclusion A 0 Z = (p C (q)) ψp (1 α)ψq α (1 ψ) − − − − − dψ = (p C 0(q)) α (1 ψ) = 0. − dp − −

28/56 Symmetric equilibrium from industry supply curve Background Purpose of charges Assume inelastic demand ε with density f and c.d.f. F . Assume NZ proposals n symmetric generators with total supply Q. 9 SPD Charge Charges on Rentals Cournot setting nS(p) = Q(p) = ε. SFE duopoly model Perfect Competition dChargesψ on Benefits dQ ψ(p) = Pr(P < p) = F (ε) = Pr(Q(P) < Q(p)) = F (Q(p)) . Transmission= f ( benefitsQ) . dpIllustrative example dp Conclusions Conclusion Industry cost function CI has derivative at Q = nq defined by 0 0 CI (Q) = C (q). Thus dψ Z = (p C 0(q)) α (1 ψ(p)) = 0. − dp − − dQ (p C 0(Q)) f (Q) α (1 F (Q)) = 0. − I dp − −

9related model in Frederico & Rahman (2003). Bidding in an electricity pay-as-bid auction. J. Regulatory Economics, 24(2), 175-211. 29/56 Price-taking example Background Purpose of charges Two identical firms with NZ proposals SPD Charge C(q) = q2 Charges on Rentals Cournot setting SFE duopoly model Industry cost function is Perfect Competition Charges on Benefits Transmission benefits 1 Illustrative example C (Q) = Q2. I 2 Conclusions Conclusion If demand shock is uniform on [0, 1], ordinary differential equation for industry curve Q(p) is

dQ (p Q) = α(1 Q), Q(1) = 1 − dp − Q(p) = (1 + α)p α. − So each agent offers

(1 + α) α S(p) = p 2 − 2

30/56 Incentives for price-taking firms Background Purpose of charges NZ proposals Industry Supply Curves SPD Charge 1 Charges on Rentals Cournot setting 0.9 SFE duopoly model Perfect Competition 0.8 Charges on Benefits Transmission benefits 0.7 Illustrative example

0.6 Conclusions Conclusion 0.5 Price 0.4

0.3

0.2 Marginal Cost Price−Taking Equilibrium 0.1 SFE without tax SFE with tax 0 0 0.2 0.4 0.6 0.8 1 Quantity

31/56 Charge on benefit from expanded line Background Purpose of charges The SPD Charge method does not apply a charge based on the NZ proposals entire producer surplus, only based on the difference in Ricardian SPD Charge Charges on Rentals rents compared to some counterfactual. Cournot setting SFE duopoly model Perfect Competition Charges on Benefits S1(p) Transmission benefits Illustrative example Conclusions J Conclusion 1 2

S2(p) D = ε

ε U[ε, ε¯] ∼ ¯ This counterfactual is the state of the network prior to any line upgrade.

32/56 Charge on benefit from expanded line Background Purpose of charges The SPD Charge method does not apply a charge based on the NZ proposals entire producer surplus, only based on the difference in Ricardian SPD Charge Charges on Rentals rents compared to some counterfactual. Cournot setting SFE duopoly model Perfect Competition Charges on Benefits S1(p) Transmission benefits Illustrative example Conclusions K Conclusion 1 2

S2(p) D = ε

ε U[ε, ε¯] ∼ ¯ After the line upgrade we have the following network; the size of the line has increased from J to K.

33/56 Duopoly SFE with low-capacity line (no charge) Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition S Charges on Benefits i Transmission benefits Illustrative example Conclusions RDmax Conclusion

c RDmin

q J 2

34/56 Duopoly SFE with expanded line (no charge) Background Purpose of charges p NZ proposals p SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Si RDmax Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c RDmin

q J K 2 2 Larger capacity gives a flatter curve (more competitive). The SPD-method assumes that the offer stays the same – this would

not be a valid assumption in this case. 35/56 J Tariff on benefit from expanded line (dispatch > 2 ) Background Purpose of charges Rather than paying a charge on the full producer surplus, the NZ proposals transmission charge is a proportion of the benefit accruing due to SPD Charge Charges on Rentals the increased line capacity. Cournot setting SFE duopoly model Perfect Competition p Charges on Benefits p Transmission benefits Illustrative example Conclusions Conclusion Si

RD

RDc

c

q 1 J K 2 ε 2 2 36/56 J Charge on benefit from expanded line (dispatch > 2 ) Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition S Charges on Benefits i Transmission benefits Illustrative example Conclusions RD Conclusion

RDc

c

q J K 2 2 The charge will be based on this area (which depends on the

realization of the demand shock). 37/56 J Charge on benefit from expanded line (dispatch 2 ) ≤ Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition S Charges on Benefits i Transmission benefits Illustrative example Conclusions Conclusion

RD

c

q J K 2 2 J For dispatch below 2 , the actual and counterfactual dispatch points are the same, so there is no charge. 38/56 Equilibrium offer curve (charge on benefit) Background Purpose of charges p NZ proposals p SPD Charge Charges on Rentals Cournot setting Si RDmax SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example RDmin Conclusions Conclusion c

q J K 2 2

J For quantities below 2 , the equilibrium offer curve is straight, since there is no charge payable in this region (and it does not affect the perceived benefit).

J For quantities greater than 2 , the equilibrium curve matches the curve where the charge was applied to total perceived surplus.

39/56 Illustrative example Background Purpose of charges Consider a duopoly, over a network as shown earlier. NZ proposals SPD Charge Charges on Rentals • The initial capacity of the transmission line is J = 0.2, and Cournot setting SFE duopoly model the line is expanded to K = 0.8. Perfect Competition Charges on Benefits • The marginal cost of both generators is c = 0, and there is Transmission benefits Illustrative example a price-cap in the market of 1. Conclusions Conclusion • The demand at node 2 is random, and uniformly distributed between ε = 0 andε ¯ = 1. ¯ • Firms are charged α = 25% of their benefits.

40/56 SFE depends on the proportion of benefits charged. Background Purpose of charges NZ proposals SFE with Beneficiaries−Pay Charge SPD Charge 1 Charges on Rentals Cournot setting 0.9 SFE duopoly model Perfect Competition 0.8 Charges on Benefits Transmission benefits 0.7 Illustrative example

0.6 Conclusions Conclusion 0.5 Price 0.4

0.3

0.2 Tariffed equilibrium, α = 0.25 0.1 Tariffed equilibrium, α = 0.3333 Un-tariffed equilibrium 0 0 0.2 0.4 0.6 0.8 1 Quantity

41/56 Welfare calculations Background Purpose of charges NZ proposals SPD Charge Curve α CS ΠU ΠT Tax per firm TS Charges on Rentals Cournot setting S 0.25 0.1067 0.1067 0.0833 0.0233 0.32 SFE duopoly model S 0 0.25 0.1003 0.1098 0.0887 0.0211 0.32 Perfect Competition Charges on Benefits Transmission benefits Table 1: Benefits and with a charge on line-expansion benefits. Illustrative example Conclusions Conclusion

• S is the SFE offer assuming α = 0, • S 0 is the SFE offer with α = 0.25, • CS is the consumer surplus, • TS is total surplus, • ΠU and ΠT are untaxed and taxed per-firm profits.

42/56 SFE depends on the max demand shock Background Purpose of charges NZ proposals SFE with Beneficiaries−Pay Charge SPD Charge 1 Charges on Rentals Cournot setting 0.9 SFE duopoly model Perfect Competition 0.8 Charges on Benefits Transmission benefits 0.7 Illustrative example

0.6 Conclusions Conclusion 0.5 Price 0.4

0.3

0.2

0.1 ε = 1 ε = 2 Un-tariffed equilibrium 0 0 0.2 0.4 0.6 0.8 1 Quantity

43/56 Overall markup depends on magnitude of expansion Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c

q 1 J K 2 ε 2 2

44/56 J K – some mark-up at lower end  Overall markup depends on magnitude of expansion Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c

q 1 J K 2 ε 2 2

45/56 J K – some mark-up at lower end  Overall markup depends on magnitude of expansion Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c

q J K 2 2

46/56 J K – mark-down from untaxed SFE ≈ Overall markup depends on magnitude of expansion Background Purpose of charges NZ proposals p SPD Charge p Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

c

q J K 2 2

47/56 J K – mark-down from untaxed SFE ≈ Consumer welfare comparison Background Purpose of charges NZ proposals SPD Charge 0.11 Charges on Rentals Cournot setting SFE duopoly model 0.108 Perfect Competition Charges on Benefits Transmission benefits 0.106 Illustrative example Conclusions Conclusion 0.104

Consumer Welfare 0.102

0.1

0.098 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 J

When J < 0.5 the expected consumer welfare drops as the firms try to avoid the charge; otherwise the consumers are better off.

48/56 Generator transmission charges comparison Background Purpose of charges NZ proposals SPD Charge 0.05 Charges on Rentals Cournot setting 0.045 SFE duopoly model Perfect Competition 0.04 Charges on Benefits Transmission benefits 0.035 Illustrative example

0.03 Conclusions Conclusion 0.025

0.02

Transmission Charges 0.015

0.01

0.005

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 J

When J < 0.58 the expected charge drops as the firms change their behaviour; interestingly, the firms end up paying a slightly higher charge for small increases in line size. 49/56 Producer surplus comparison (after transmission charge) Background Purpose of charges NZ proposals SPD Charge 0.19 Charges on Rentals Cournot setting SFE duopoly model 0.185 Perfect Competition Charges on Benefits Transmission benefits 0.18 Illustrative example Conclusions Conclusion 0.175 Producer Profits 0.17

0.165

0.16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 J

J When K < 0.52 the expected producer surplus increases as the firms try to reduce the charge paid. For smaller line upgrades the producers are worse off. 50/56 Comparison with perfect competition Background Purpose of charges NZ proposals SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

51/56 Variance of demand shock affects outcomes Background Purpose of charges NZ proposals 1 SPD Charge

0.9 Charges on Rentals Cournot setting 0.8 SFE duopoly model Perfect Competition 0.7 Charges on Benefits 0.6 Transmission benefits Illustrative example 0.5

Price Conclusions 0.4 Conclusion

0.3

0.2 Taxed SFE Un−taxed SFE 0.1 Taxed PTE Un−taxed PTE 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Quantity

Figure 1: Equilibrium solution for example with normally distributed ε ∼ N(0.7, 0.2).

52/56 Reducing variance of demand destroys equilibrium Background Purpose of charges NZ proposals SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

Figure 2: First-order solution for example with normally distributed ε ∼ N(0.7, 0.1). 53/56 Remarks Background Purpose of charges • If the charge is a small % of the benefits, the equilibrium is NZ proposals close to the uniform price SFE. SPD Charge Charges on Rentals Cournot setting SFE duopoly model • Incentive to mark up the lower part of curve increases with Perfect Competition probability of lost load and decreases with variance of Charges on Benefits Transmission benefits demand shock. Illustrative example Conclusions Conclusion • Competitiveness depends on size of transmission capacity expansion.

• 1 Example equilibria are valid only if α < 2 .

54/56 Conclusions Background Purpose of charges • Demand uncertainty reduces incentives to mark up offer NZ proposals curves to conceal perceived profits. SPD Charge Charges on Rentals Cournot setting • A charge based on benefits does not give an incentive to SFE duopoly model mark-up at the low end of the offer curve, since it is the Perfect Competition Charges on Benefits difference in profits from counterfactual that is taxed. Transmission benefits Illustrative example • With small-medium line expansions we found that generator Conclusions competition would increase due to the charge, and consumer Conclusion surplus and the total charge collected from generators would increase. • For large line increases, consumer welfare decreases as firms mark up the low-quantity end of their curve to minimize their transmission charge. • The SPD charge is retrospective. Related deep connection charges use flow tracing ex-post to allocate costs. Both give incentives to offer strategically in the spot market. A simpler alternative is to price the use of transmission directly within the dispatch software. Is this more or less distortionary than current proposals? 55/56 Background Purpose of charges NZ proposals SPD Charge Charges on Rentals Cournot setting SFE duopoly model Perfect Competition Thanks for your attention. Charges on Benefits Transmission benefits Illustrative example Conclusions Conclusion

Any Questions?

56/56