Electricity markets, perfect competition and energy shortage risks

Transcription

1 lectric ower ptimization entre lectricity markets, perfect competition and energy shortage risks Andy hilpott lectric ower ptimization entre University of Auckland joint work with Ziming Guan, Roger Wets, Michael Ferris

2 lectric ower ptimization entre What this talk is about A description of the New Zealand electricity system and the wholesale electricity market. A description of the problem of understanding and measuring how effective this market structure is. Measuring efficiency: productive (avoid waste of fuel) allocative (avoid waste of purchasers money) dynamic (avoid wrong investments) We focus on productive efficiency: short-term efficiency long-term efficiency the effects of risk aversion

3 lectric ower ptimization entre The New Zealand wholesale electricity market Before 1996, the New Zealand wholesale electricity system was operated as a state monopoly. Since ctober 1996 this has been run as an electricity pool market. Generation ownership last changed in 1999 when NZ was broken up. The system is dominated by generation from hydro-electric reservoirs (60-70% of energy is from hydro)

4 lectric ower ptimization entre The New Zealand wholesale electricity market Source:

5 lectric ower ptimization entre New Zealand has energy shortages Source:

6 lectric ower ptimization entre The New Zealand electricity pool Waitaki system Generators specify supply Waikato River curves defining prices at which they will generate. urves fixed for each half hour Linear programming model runs every five minutes to determine electricity generated electricity flows in network spot price (shadow price) of electricity at 244 out of 470 network nodes

7 Department of ngineering Science lectricity markets and perfect competition

8 lectric ower ptimization entre The economic dispatch problem p m (x) q p i

9 Department of ngineering Science lectricity markets and perfect competition

10 Department of ngineering Science lectricity markets and perfect competition

11 lectric ower ptimization entre lectricity markets and perfect competition "rivate market disciplines are important in competitive industries. And the energy market is becoming increasingly competitive. And the government, in our experience, is not an adaptable, risk-adjusted 100 per cent owner of assets in competitive markets. Bill nglish, NZ Minister of Finance, nergy News, Nov. 9. Q: How competitive is the market? Q: How can you tell?

12 lectric ower ptimization entre It wasn t competitive two years ago There is something fundamentally wrong in the way in which we re marketing electricity in New Zealand, Mr Brownlee said. ower generators overcharged customers $4.3 billion over six years by using market dominance, according to a ommerce ommission report. (New Zealand Herald May 21, 2009, downloaded from site:

13 lectric ower ptimization entre The view from economics Source: Report, p 177

14 lectric ower ptimization entre Dry winters and prices

15 lectric ower ptimization entre Benchmark against counterfactual Market power rents add up to $4.3 B

16 lectric ower ptimization entre The hindsight benchmark Fix hydro generation (at historical dispatch level). Simulate market operation over a year with thermal plant offered at short-run marginal (fuel) cost. The Appendix of Borenstein, Bushnell, Wolak (2002)* rigorously demonstrates that the simplifying assumption that hydro-electric suppliers do not re-allocate water will yield a higher system-load weighted average competitive price than would be the case if this benchmark price was computed from the solution to the optimal hydroelectric generation scheduling problem described above [ommerce ommission Report, page 190]. (* Borenstein, Bushnell, Wolak, American conomic Review, 92, 2002)

17 lectric ower ptimization entre What is wrong with this? wet The hindsight benchmark In the year under investigation, suppose all generators optimistically predicted high winter inflows and used all their water in summer. Suppose they were right, and no thermal fuel was needed at all. Benchmark prices are zero. summer dry winter A realistic benchmark The optimal generation plan burns thermal fuel in stage 1 just in case there is a drought in winter. The competitive price is high (marginal thermal fuel cost) in the first stage, high in the second if dry and zero in the second if wet.

18 lectric ower ptimization entre Research question What does a perfectly competitive market look like when it is dominated by a possibly insecure supply of hydro electricity?

19 lectric ower ptimization entre A welfare result Suppose that the state of the world in all future times is known, except for reservoir inflows that are known to follow a stochastic process that is common knowledge to all generators. Suppose that, given electricity prices, these generators maximize their individual expected profits as price takers. There exists a stochastic process of market prices that gives a price-taking equilibrium. These prices result in generation that maximizes the total expected welfare of consumers and generators. So the resulting actions by the generators maximizing profits with these prices is system optimal. It minimizes total expected generation cost just as if the plan had been constructed optimally by a central planner.

20 lectric ower ptimization entre An annual benchmark Solve a year-long hydro-thermal problem to compute a centrally-planned generation policy, and simulate this policy. We use DASA, s implementation of SDD. We account for shortages using lost load penalties. In our model, we re-solve DASA every 13 weeks and simulate the policy between solves using a detailed model of the system. We now call this central. includes transmission system with constraints and losses river chains are modeled in detail historical station/line outages included in each week unit commitment and reserve are not modeled

21 lectric ower ptimization entre Long-term optimization model demand demand WK MAN N H S HAW demand

22 lectric ower ptimization entre We simulate policy in this 18-node model WK MAN HAW

23 lectric ower ptimization entre Historical vs centrally planned storage

24 lectric ower ptimization entre Additional annual fuel cost in market Total fuel cost = (NZ)$400-$500 million per annum (est) Total wholesale electricity sales = (NZ)$3 billion per annum (est)

25 lectric ower ptimization entre South Island prices over 2005

26 lectric ower ptimization entre South Island prices over 2008

27 lectric ower ptimization entre Historical vs centrally planned storage

28 lectric ower ptimization entre Value at risk VaR 1-a [Z] frequency a=5% VaR 0.95 = 150 cost

29 lectric ower ptimization entre onditional value at risk (VaR 1-a [Z]) frequency VaR 0.95 = 162 cost

30 The University of Auckland Department of ngineering Science lectric ower ptimization entre Measuring risk The system in each stage minimizes its fuel cost in the current week plus a measure of the future risk.(shapiro, 2011; hilpott & de Matos, 2011) For two stages (next week s cost is Z) this measure is: r(z) = (1-l)[Z] + lvar 1-a [Z] for some l between 0 and 1

31 lectric ower ptimization entre Recursive risk measure For a model with many stages, next week s objective is the risk r(z) of the future cost Z, so we minimize fuel cost plus (1-l)[r(Z)] + lvar 1-a [r(z)] for some l between 0 and 1. Here r(z) is a certainty equivalent: the amount of money we would pay today to avoid the random costs Z of meeting demand in the future.(it is not an expected future cost)

32 lectric ower ptimization entre DASA with risk hilpott & de Matos, 2011 For a model with many stages, next week s objective is the risk r(z) of the future cost Z, so we minimize fuel cost plus (1-l)[r(Z)] + lvar 1-a [r(z)] for some l between 0 and 1. If r(z) is a coherent risk measure (convex and monotone) then we can show that the fuel cost in any next stage scenario + the risk r(z) of the future cost Z is a convex function of the reservoir storage. Future can then be approximated by cutting planes.

33 lectric ower ptimization entre roperties of r(z) r(z) is a coherent risk measure (convex and monotone) so we can show that fuel cost in any next stage scenario + the risk r(z) of the future cost Z is a convex function of the reservoir storage. Future can then be approximated by cutting planes. If a=10% and we have 10 scenarios then r(z) is the expectation of Z with worst scenario weighted by 0.1(1+9l) and the rest weighted equally.

34 lectric ower ptimization entre Simulated national storage 2006

35 lectric ower ptimization entre Historical vs centrally planned storage

36 lectric ower ptimization entre Some observations The historical market storage trajectory appears to be more risk averse than the risk-neutral central plan. When agents are risk neutral, competitive markets correspond to a central plan. so either agents are not being risk neutral, or the market is not competitive. Question: Is the observed storage trajectory what we would expect from risk-averse agents acting in perfect competition?

37 lectric ower ptimization entre Ralph-Smeers quilibrium Model What is the competitive equilibrium under risk? Assume we have N agents, each with a coherent risk measure r i and random profit Z i. If there is a complete market for risk then agents can sell and buy risky outcomes. The equilibrium solves V(Z 1,..) = min {S i r i (Z i -W i ): S i W i =0} quivalent to using a system risk measure r s (S i Z i ) an compute equilibrium with risk-averse optimization.

38 lectric ower ptimization entre Incomplete markets? What is the competitive equilibrium under risk? We need to solve a competitive equilibrium model using a numerical method.

39 lectric ower ptimization entre erfect competition in incomplete markets with risk (Joint research with Roger Wets and Michael Ferris) A two-stage model 15 HYDR THRMAL DMAND Demand is 13, thermal cost is 1, initial storage=15 Hydro inflow is 4 in period 1, and then 1,2,3,4,5,6,7,8,9,10. Generation plants have quadratic production functions. Residual storage has quadratic value function.

40 lectric ower ptimization entre A competitive equilibrium model

41 lectric ower ptimization entre GAMS M xtended Mathematical rogramming equations tpobjdef(t), hpobjdef(h), tpcvar(s,t), hpcvar(s,h); variables tpobj(t), hpobj(h), vtp(t), vhp(h); positive variables pi1, pi2(s), ytp(s,t), yhp(s,h); tpobjdef(t).. tpobj(t) =e= -pi1*ut1(t) + st(ut1(t)) + (1-lambdaT(t))*sum(s,prob(s)*(pi2(s)*( -ut2(s,t)) + st(ut2(s,t)))) + lambdat(t)*var(1-alpha,vtp(t),sum(s,prob(s)*ytp(s,t))); tpcvar(s,t).. ytp(s,t) - (pi2(s)*(-ut2(s,t)) + st(ut2(s,t))) + vtp(t) =g= 0; hpobjdef(h).. hpobj(h) =e= -pi1*util(uh1(h)) +(1-lambdaH(h))* sum(s,prob(s)*(pi2(s)*( -Util(uh2(s,h))) - TermV(x2(s,h))) ) + lambdah(h)*var(1-alpha,vhp(h),sum(s,prob(s)*yhp(s,h))) hpcvar(s,h).. yhp(s,h) - ( pi2(s)*( -Util(uh2(s,h))) - TermV(x2(s,h)) )+ vhp(h) =g= 0;

42 lectric ower ptimization entre GAMS M xtended Mathematical rogramming dynamics1(h).. x1(h) =e= x0(h)-uh1(h)-sh1(h)+inflow('1',h,'1'); dynamics2(s,h).. x2(s,h) =e= x1(h) -uh2(s,h)-sh2(s,h)+inflow(s,h,'2'); meetdemand1.. sum(h, Util(uh1(h))) + sum(t, ut1(t)) =g= demand('1','1'); meetdemand2(s).. sum(h,util(uh2(s,h))) + sum(t, ut2(s,t)) =g= demand(s,'2'); model hydroemp /tpobjdef,hpobjdef,tpcvar,hpcvar,dynamics1,dynamics2, meetdemand1,meetdemand2 /;

43 lectric ower ptimization entre GAMS M xtended Mathematical rogramming file info / '%emp.info%' /; put info; put / 'equilibrium'; loop(h, put / 'min ' hpobj.tn(h); put / x1.tn(h) ' ' uh1.tn(h) ' ' sh1.tn(h) ' ' vhp.tn(h); loop(s, put / x2.tn(s,h) ' ' uh2.tn(s,h) ' ' sh2.tn(s,h) ' ' yhp.tn(s,h)); put / hpobjdef.tn(h) ' ' dynamics1.tn(h); loop(s, put / dynamics2.tn(s,h) ' ' hpcvar.tn(s,h));); loop(t, put / 'min ' tpobj.tn(t); put / ut1.tn(t) ' ' vtp.tn(t); loop(s, put / ut2.tn(s,t) ' ' ytp.tn(s,t)); put / tpobjdef.tn(t); loop(s, put / tpcvar.tn(s,t));); put / 'vifunc'; put /' ' meetdemand1.tn ' ' pi1.tn; put / 'vifunc'; loop(s, put / ' ' meetdemand2.tn(s) ' ' pi2.tn(s) ); putclose info /; solve hydroemp using emp;

44 lectric ower ptimization entre entral planning solutions Risk neutral planner Risk averse planner with 0.8[Z]+0.2VaR 0.9 (Z)

45 lectric ower ptimization entre ompetitive market solutions (computed with GAMS/M) Risk neutral agents Risk averse agents with 0.8[-Z]+0.2VaR 0.9 [-Z]

46 lectric ower ptimization entre Low storage example A two-stage model 5 HYDR THRMAL DMAND Demand is 13, thermal cost is 1, initial storage=5 Hydro inflow is 4 in period 1, and then 1,2,3,4,5,6,7,8,9,10. Generation plants have quadratic production functions. Residual storage has quadratic value function.

47 lectric ower ptimization entre Risk neutral solutions: low storage entral planner Risk neutral equilibrium

48 lectric ower ptimization entre Risk averse solutions: low storage entral planner Risk averse agents with 0.8[-Z]+0.2VaR 0.9 [-Z]

49 lectric ower ptimization entre onclusion When agents are risk neutral, competitive markets correspond to a central plan. When agents are risk averse, competitive markets do not always correspond to a central plan. In general we need aligned risks, or completion of the risk market. This is true even if there is only one risk-averse agent. A new benchmark is needed for the multi-stage hydrothermal setting: risk-averse competitive equilibrium with incomplete markets for risk.

50 lectric ower ptimization entre FIN