Retail Electricity Markets with Risk Aversion and Asset Swaps

1. Retail Electricity Markets with Risk Aversion and Asset Swaps A. Downward, D. Young, G. Zakeri University of Auckland. EPOC Workshop: Optimization under Uncertainty

2. Overview Motivation Risk Aversion Background Risk Aversion Example Retail Market Model • Differentiated Products Model • Single-node Example Two-Node Model Inspired by New Zealand Conclusions EPOC Workshop: Optimization under Uncertainty

3. Motivation Wolak Report In early 2009, Frank Wolak’s report to the Commerce Commission was released. It highlighted some shortcomings of the NZEM, including: • limited competition for thermals in dry years, • only one firm with generation in both islands. It suggested that asset swapping may improve market outcomes. EPOC Workshop: Optimization under Uncertainty

4. Motivation Distribution of Generation Mighty River Genesis Contact Meridian EPOC Workshop: Optimization under Uncertainty 4/38

5. Motivation Ministerial Review The Electricity Technical Advisory Group produced a discussion paper that presented three asset swap proposals. In December 2009, the government stated its intent to transfer: Tekapo A & B to Genesis, and Whirinaki to Meridian. Virtual swaps were also proposed, where contracts for energy in either island are compulsorily traded. EPOC Workshop: Optimization under Uncertainty

6. Retail Market Overview In this work, we investigate how risk-aversion affects entry and pricing of retailers in electricity markets. Consumers enter into contracts with retailers, reducing the risk that they would otherwise face buying from the spot market. Retailers compete with each other for the same consumers through mainly price competition. Retailers must pass on the risk of purchasing from the spot market to consumers. EPOC Workshop: Optimization under Uncertainty

7. Retail Market Market Risks There is significant risk involved in participating an electricity retail market. Retailers purchase electricity at the spot price and sell to consumers at predetermined fixed prices. In New Zealand, vertical integration is common; this acts as an internal hedge against spot price fluctuations. However, even with generation, transmission price risk may still be of concern. EPOC Workshop: Optimization under Uncertainty

8. Retail Market Transmission Price Risk For example, consider the following situation. The profit for the firm is: Profit = 100p1 – 50p1 – 50p2 + Retail Payments 100 MW generation 50 MW retail contracts 50 MW retail contracts EPOC Workshop: Optimization under Uncertainty 8/38

9. Retail Market Model Overview The full model consists of three stages: Entry – here firms make 0/1 decisions regarding whether they have a retail base at each node. Retail competition – each firm sets a retail price at each node. Wholesale market – the uncertainty is resolved and wholesale prices and profits are computed. EPOC Workshop: Optimization under Uncertainty 9/38

10. Risk Aversion Definition Often in stochastic optimization problems we wish to maximize expected profits, given various scenarios that may eventuate. This may be a fair thing to do if the problem is repeated daily – within a week any positive outcomes will likely balance out the negative outcomes. However, if the problem being solved involves a one-off decision or covers an extended time horizon with limited recourse decisions, it may be important that the firm protects itself from the worst-case outcomes. In such a situation the firms may wish to behave in a risk-averse manner. EPOC Workshop: Optimization under Uncertainty

11. Risk Aversion Definition For example, consider a firm with a binary decision of whether to purchase an asset costing $50,000. Depending on whether the firm chooses to purchase the asset, the density functions for its returns may look like: EPOC Workshop: Optimization under Uncertainty

12. Risk Aversion Definition EPOC Workshop: Optimization under Uncertainty

13. Risk Aversion Risk-adjusted Profit ρ(Profit) = (1 – θ) E[Profit] – θ CVaR5%[Profit] EPOC Workshop: Optimization under Uncertainty

14. Risk Aversion Risk Averse Newsboy Example Suppose that a newsboy needs to decide how many papers to buy in the morning at $0.30 each. Unfortunately, his demand is uncertain and has the following three equally likely outcomes: Low demand: dL = 80 papers (pL=1/3) Medium demand: dM = 100 papers (pM=1/3) High demand: dH = 120 papers (pH=1/3) Choi and Ruszczyński EPOC Workshop: Optimization under Uncertainty

15. Risk Aversion Risk Averse Newsboy Example If the newsboy were risk-neutral then his optimization problem would look like: EPOC Workshop: Optimization under Uncertainty

16. Risk Aversion Risk Averse Newsboy Example The optimal solution to this problem is to purchase 120 papers. The number sold in each of the scenarios are: yL=80, yM=100, yH=120. EPOC Workshop: Optimization under Uncertainty

17. Risk Aversion Shapiro et al. (2009) discuss the relationship of weighted mean deviation from quantile to conditional value at risk, in mean-risk optimization problems. With some algebra, this can be reduced to a weighted sum, maximizing expected profits and minimizing conditional value at risk. Weighted Mean Deviation from Quantile EPOC Workshop: Optimization under Uncertainty

18. Risk Aversion This formulation of CVaR can be solved using convex optimization. Using a substitution of the form: We can formulate an optimization problem for a risk averse agent: Mean-risk Measures EPOC Workshop: Optimization under Uncertainty

19. Risk Aversion Risk Averse Newsboy Example Back to the newsboy: if the newsboy were interested in taking into account risk, rather than maximizing expected revenue, then we solve the following problem: EPOC Workshop: Optimization under Uncertainty

20. Risk Aversion Risk Averse Newsboy Example EPOC Workshop: Optimization under Uncertainty

21. Retail Market Market Share Each firm competing in the retail market at a given node chooses a price at which it will offer power to consumers. Using a differentiated products model (similar to that found in Vives (2001)), we compute the market share for each of the firms. This model assumes that total demand is inelastic, and consumers merely switch between retailers. The market share of retailer f is: Where p is a vector of retail prices (one for each firm), and b is the cross-elasticity. EPOC Workshop: Optimization under Uncertainty

22. Retail Market Wholesale Market We allow retailers to also own generation (vertical integration). We assume that the generation is bid into the market at cost. This is said to be a competitive equilibrium. At the time that retail contracts are determined, the future wholesale prices are unknown, due to uncertainties around hydro inflows and outages. EPOC Workshop: Optimization under Uncertainty

23. Retail Market Retail Market Competition All firms optimize the following profit maximisation problem simultaneously. EPOC Workshop: Optimization under Uncertainty

24. Single Node Example Setup First we consider a situation with two gentailers at a single node. Firm A owns a thermal plant whereas B owns a hydro, each with capacity of 100MW. The firms compete for customers in the retail market. The total demand is 150MW. Water value: h ~ U[0,100]. EPOC Workshop: Optimization under Uncertainty

25. Single Node Example Wholesale Prices and Profit As a function of the water value, h, the wholesale prices and profits can be computed: EPOC Workshop: Optimization under Uncertainty

26. Single Node Example Risk-neutral Equilibrium If firms are risk-neutral, it can be shown that the profit from the wholesale market has no bearing on the retail pricing. We can compute the equilibrium retail prices for both firms to be $137.50 in this case. In this situation, both firms share the retail demand equally. EPOC Workshop: Optimization under Uncertainty

27. Single Node Example Best-response Now let us examine the optimal retail prices for the firms as they increase their risk-aversion. The hydro plant makes more profit when water values are low, whereas the thermal plant makes more profit when the water values are high. EPOC Workshop: Optimization under Uncertainty

28. Single Node Example Best-response These plots show the distributions of profits for the firms, under risk-neutral and risk-averse pricing strategies. EPOC Workshop: Optimization under Uncertainty

29. Two Node Example Background In this model we have 2 nodes and 3 firms: • firm A owns 2 thermal plants in the North, • firm B owns 2 hydro plants in the South, • firm C owns 1 thermal in the North and 1 hydro in the South. The North and South have separate retail markets. Firm B is not in the North, whereas firm A is not in the South. There is a fixed cost of entry C associated with entering a market. EPOC Workshop: Optimization under Uncertainty

30. Two Node Example Asset Swap Before Swap After Swap Virtual Swap Firm A Firm A Firm A T T T T T T T T T Firm C Firm C Firm C H H H H H H H H H Firm B Firm B Firm B EPOC Workshop: Optimization under Uncertainty

31. Two Node Example Wholesale Market In the wholesale market, we have two plant-types: hydro and thermal. The thermal cost function is: The hydro cost function is: where h (the measure of water scarcity) is normally distributed. The nominal capacity of the line is 250MW, although there is a 5% chance of an outage in any period. Demand in the North is 2000MW, and in the South in 1000MW. EPOC Workshop: Optimization under Uncertainty

32. Two Node Example Wholesale Nodal Price Differences EPOC Workshop: Optimization under Uncertainty

33. Two Node Example Wholesale Profits for the Firms EPOC Workshop: Optimization under Uncertainty

34. Two Node Example Risk Averse Behaviour In order for each firm to determine its best pricing strategy it must now solve a similar optimization to what we encountered in the single-node example, adjusted for multiple nodes (and hence multiple retail markets). It is interesting to note that when an agent is risk averse, its pricing decision at one node may affect the optimal price at another. EPOC Workshop: Optimization under Uncertainty

35. Two Node Example Risk Averse Behaviour If the asset swap does not incentivise an additional firm to enter into each retail market, then we find the following change in prices. EPOC Workshop: Optimization under Uncertainty 35/38

36. Two Node Example New Retailer in Each Market On the other hand, if firm A enters the retail market in the South and firm B enters in the North, we find the following prices. EPOC Workshop: Optimization under Uncertainty 36/38

37. Two Node Example Cost of Entry EPOC Workshop: Optimization under Uncertainty 37/38

38. Two Node Example Conclusions Risk aversion for firms can affect whether or not they enter a market. If they do enter, whether there exists a risk premium or discount for the consumers depends on the particular circumstances. From our model, we find that physical asset swap will only have a beneficial effect on consumer prices if additional retailers enter each market. The ‘virtual asset’ improves retail competition since the hydro risk is eliminated for the firm not owning hydro. EPOC Workshop: Optimization under Uncertainty 38/38