Peak load pricing in the electric utility industry John T. Wenders

1. Peak load pricing in the electric utility industry John T. Wenders Date: March 28,2013 Presented by Tej Gautam

2. Objective The objective of this paper is to argue caution in the application of peak load Pricing theory to the electric utility industry. Study includes: Long –run capacity adjustment Marginal cost pricing with homogeneous capacity Marginal cost pricing with mixed capacity Peak load pricing and the regulated firm

3. Introduction • Traditional theory of peak-load pricing argues- peak period users should bear marginal • operating cost and all of the marginal capital cost; • Off-peak users should be charged only marginal operating cost, • Economist extended Peak-load pricing to include the effect of a regulatory constrained; • Regulated utility will set off-peak prices at the same level as an unconstrained monopolist • and set peak prices below the unconstrained monopolist; • Implication is: regulated firm will expand productive capacity beyond the level that would • be set by the unconstrained monopolist, possibly even beyond the level that would • maximize social welfare(A-J-W theory of over capitalization); • This paper shows that off-peak marginal cost prices always should include some marginal • capacity costs and that the profit maximizing regulated electric utility may set • price above marginal cost at the peak and below marginal cost during the off-peak • in order to encourage the expansion of capital-intensive base load generating capacity.

4. Long-run capacity adjustment • Electricity production should adopt different technologies or capacity mixes that will • meet the demand at minimum cost. • Assume thee are three technologies: base, intermediate & peak load which are • represented by subscripts 3, 2 & 1 respectively. • Bi &bi represents annual marginal and average capital cost and marginal energy cost . • It is assumed that B3> B2 > B1, b1 > b2 > b3 & b, + B1 > b2 + B2> b3 + B3. • Fraction of each period is defined as w1 = t1/t*, w2 = (t2 - t1)/t*, W3 = (t* - t2)/t*. Annual load duration curve

5. LR capacity contd. • Suppose the utility has KW3 units of base load capacity and increasing capacity by 1 kw. • As an alternative, cost of 1 additional unit of intermediate capacity, thus MC3 must be • Weighted against MC2. Relevant MC are: MC3 = B3 + (t2/t*)b3 MC2 = B2 + (t2/t*)b2 • Base load should be added until MC3= MC2, . i.e. t2/t* = WI + W2= (B3 - B2)/(b2-b3) • Add intermd. capacity s.t. MC2= MC1 & t1/t*=w1=(B2- B1)/(b1-b2) & • w3=1-(B3-B2)/(b2-b3) • It indicates that w1,w2 & w3 depend only on relative capital and energy costs of three • alt. capacities and do not depend on shape of the load duration curve.

6. Marginal cost pricing with homogeneous capacity • It defines optimal prices to be charged. • Usual peak load pricing assumes homogeneous capacity • Q1, Q2 & Q3 be the annual demand for z1,z2 & z3 period of the year where,Q1 > Q2 > Q3. • Assumed these periods are separable and independent with same annual capacity cost B • Welfare optimum will be reached by maximizing the sum of the CS and PS (Demand curve less cost, P is annualized prices) • Objective function is • Maximization yield the following optimal prices P1 = b1 + B/z1 , P2 = b2 & P3= b3 • It indicates that only peak users bear marginal capital coat and off-peak users marginal • energy cost of usage i.e. peak usage presses against capacity- similar to previous study.

7. Marginal cost pricing with mixed capacity z1 = t'1/t*, z1 + Z2 = t'2 /t*, z1 < w1 and z1 + Z2 < W1 + W2 Total energy cost is given by Total capital cost is Total welfare is Maximizing w w.r.t. output yields: Comparing with price from MC pricing of homogeneous, these prices are for off-peak period.

8. MC pricing mixed contd. Following generalization can be drawn from these pricing: Off-peak price will have no marginal capital cost component only when the supply and pricing periods are such that: (a) only one kind of generating capacity should be built, e.g., when z1 > W2, (b) the supply and pricing periods exactly coincide, when z1 = w1, or z1 + Z2 = W1 + V2, or (c) an off-peak pricing period is wholly contained within one of the supply periods (e.g., when z1 > rv1 and z1 + Z2 < WI + W2). Off-peak prices will contain a marginal capital cost component. The size of the off-peak price varies inversely with the size of the next highest pricing period(s)-the partial derivatives of P2 with respect to z1 and P3 with respect to (z, + Z2) are both negative. This is due to the fact that the energy saving off-set to marginal capital costs varies directly with z1 (for pricing period two) and z1 + Z2 (for pricing period three)

9. Peak load pricing and the regulated firm Maximize profit subject to regulatory constraint governing its rate of return on total capital maximize Subject to where assumes Further assumed that the firm is able to operate off the production frontier and carry excess generating capacity of each kind (Xi)

10. Summary of peak and off-peak prices for welfare maximum, unconstrained and regulated monopoly Mci= annualized MC Ei=elasticity of demand • BW findings for independent demands: off-peak prices are same as unconstrained monopolist • but here below unconstraint monopolist • off-peak prices will be reduced below the welfare maximizing prices when • With the values for capital and energy costs presented in first table , these critical values for the elasticity of demand are 0.74 and 0.21 respectively.

11. It indicates that off-peak prices which are below the welfare maximizing prices are not improbable. This conclusion is modified somewhat when interdependent demands are allowed (2nd table, row four), and where strong substitution relationships among the three pricing periods serve to raise the regulated monopoly's off- peak prices. • BW emphasize - the regulatory constraint results in a lowering of peak price below the unconstrained monopoly level and that peak price might even be lowered below the welfare maximizing level. But off-peak prices will be lower in this model- and quite possibly below the welfare maximizing level-the necessity for the lowering of peak prices is reduced. • It can be shown that, with independent demands, the peak price will be kept above the welfare maximizing level when • BW emphasized the possibility of a reversal between peak and off-peak prices. Since our model has shown that off-peak prices will be lower, and peak prices higher, than those obtained with BW's model, the possibility of peak/off-peak price reversals is similarly reduced.

12. conclusion The traditional theories of peak load pricing and the regulated firm both assume homogeneous production capacity. The above analysis has demonstrated that when it is optimal to employ capacities with different capital and energy costs, the conclusions of both these theories are modified considerably, and these modifications are particularly relevant to the application of these theories to the electric power industry.

13. Question?