Water Scarcity, Market Power and Reservoir Management in a Hydro Based Electrictiy Market

Transcription

1 Water Scarcity, Market Power and Reservoir Management in a Hydro Based Electrictiy Market Evidence from New Zealand Oliver Browne 1 1 Department of Economics, The University of Chicago obrowne@uchicago.edu home.uchicago.edu/~obrowne USAEE Conference, October

2 Outline: 2 Parts: 1. Theory of hydro generator behaiour and water valuation 2. Estimate the implied value of water and risk of shortage from firm behaviour

3 Market Power in Hydro Markets Features of Hydroelectric power Generation is flexible in short and medium term. Fuel free and storable, but arrival is uncertain and seasonal. Storage capacity is limited Local environmental costs which constrain operation of existing stations and investment new plants. Necesscary for reliability in many countries. These conditions make hydro operation both dynamic and suceptibly to market power

4 Static Model: Monopolist s (Oligopolist s) Problem: max q 1,...,q T s.t T t=1 βt p t (q t Q i,t )q t qt = f t q q q Social Planner s Problem: max q 1,...,q T s.t T t=1 βt Q t q=0 p t(q)dq qt = f t q q q

5 Static Model: Implications 1. Opportunity cost of water is constant across time and equal to the shadow value of additional inflows WV t = λ for all t 2. Monopolist attempts to equalize marginal revenue across periods MR M 1 (q 1 Q i,1 ) = MR M 2 (q 2 Q i,2 ) =... MR M T (q T Q i,t ) = WV 3. Planner attempts to equalize price across periods p P 1 (Q 1 ) = p P 2 (Q 2 ) =... = p P T (Q T ) = WV 4. Market Power is exercised by shifting generation from periods with more elastic demand to less elastic. ε t ε τ qm t q M τ qp t q P τ

6 Water Scarcity and Electrictiy Prices Price ($/MWh) Date 3000 Storage (GWh) Date Figure: Correlation between prices and lake levels

7 Stochastic Dynamic Model Future inflows uncertain and have distribution f F (x, t) Constrained Lake Capacity L t+1 L Monopolist s Problem: V t (L t ) = max q i,t p(q i,t Q i,t )q i,t + βe ft+1 V t (L t+1 ) s.t 0 L t+1 min(l t q + f t+1, L) q q min( q, L) Social Planner s Problem V t (L t ) = max q i s.t Qt q=0 p( q)dq + βe ft V t (L t+1 ) 0 L t+1 min(l t q + f t, L) q q min( q, L)

8 Model Predictions: 1. Opportunity Cost of Water reflects expected marginal benefits in the future WV t Lt (q T ) d βe dq F(f ) V t+1 (min(l t q + f, L)) t 2. Monopolist use Lerner s Rule to mark-up above their opportunity cost (if interior solution) p t (q) = ε RD (q) WV t(q L t ) 3. Planner Sells at their opportunity cost p t (q) = WV t (q L t ) 4. Opportunity Cost of Water increases with current lake level and and expected future inflows WV t (q L) 0 and WV t(q L) 0 L L 5. As the storage capacity becomes arbitrarily large, the probability of capacity constraints binding goes to zero and the opportunity cost of water is constant across time and states.

9 Estimating the Opportunity Cost of Water Construct Residual Demand Curves using half hourly bid and offer data. Smoothed residual demand curve reflects ex-ante uncertainty over electricity demand / rival offers. Within each week, isolate all periods when generator capacity constriant and environmental constraints do not bind. Use elasticity of residual demand curve and Lerner s rule to infer implied Opportunity Cost of Water Average over all hours in week WV t (q L t ) = (1 + ε RD (q))p t (q)

10 Price ($/MWh) Type Bids Offers Quantity (MW) Figure: Example of bid and offer curves

11 Constructing Residual Demand Figure: Example Residual Demand Curve and Smoothing

12 How does the opportunity cost of water vary? S.D of Storage from weekly historical average Implied water cost ($/MWh) Figure: Storage Difference vs Implied Water Value

13 Price and Implied Cost variable value 200 cost p day Figure: Series of Market Price and Hydro Cost

14 Empirical Regression Model of Opportunity Cost: y i,w,y = α+β 1 l i,t +β 2 l i,t +β 3 Ef i,t+1 +β 4 E i,t+1 f i,t+1 +γ w +γ y +ɛ i,w,y Dependent variable: Opportunity Cost of Water p cost (1) (2) (3) (4) Meridian Water Stock (20.132) (19.310) (8.669) (8.354) Other Water Stock (43.431) (41.947) (18.702) (18.146) Meridian Inflows (0.070) (0.030) Other Inflows (0.142) (0.061) Meridian Forecast Inflows (0.011) (0.005) Other Forecast Inflows (0.029) (0.012) Observations Adjusted R Residual Std. Error (df = 162) F Statistic (df = 56; 162) Note: p<0.1; p<0.05; p<0.01

15 Empirically Observed Policy Function Optimal policy function infered using Lerner s rule and opportunity cost of water q i (WV t, Q i) : p t (q) = ε RD (q) WV t(q L t ) Simulate the lake levels in each period using the optimal policy function and l t=1,...,52 F l (q i (WV t), Q i, F f ) Estimate expected frequency of electricity shortage

16 Equilibriumn Lake Levels: First Week of Jan Density Equilibrium Distribution of Janurary Reservoirs Figure: Example Residual Demand Curve and Smoothing

17 Equilibriumn Lake Levels: Winter Minimum 0.06 Density Equilibrium Distribution of Winter Minimum Figure: Example Residual Demand Curve and Smoothing

18 Conclusions Dispatch decisions of hydrogenerator governed by opportunity cost of water. Variations in opportunity cost of water are governed by changes in the risk that reservoirs become full or empty. Reservoir Capacity is determined by environmental and regulatory constraints Firm s implied valuations of their water can be infered from their bidding behavoiur. This can be used to calculate the risk of water shortage. Counterfactual analysis requires more detailed structural model.

19 Questions / Comments? Oliver Browne obrowne@uchicago.edu home.uchicago.edu/~obrowne

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21 Installed Generation Capacity by firm (2008) Table: 2008 Capacity by Firm (MW) Firm Hydro Gas Coal Geothermal Wind Oil Total MERI % CTCT % MRPL % GENE % TRST % Total 66% 14% 12% 4% 3% 2% 100%

22 Lake Reservoir capacity by firm Table: Lake Storage by Firm Firm Hydro (MW) Lake Storage GWh (%) Meridian % Contact % Mighty River Power % Genesis % Trustpower %

23 CONDENSATION As the vapour rises, it cools and changes to droplets. How the Waitaki system works FACTS ABOUT ELECTRICITY GENERATION FROM MT COOK THROUGH THE WAITAKI SYSTEM. KEY * Lake Generation Canal Average Annual Generation ENERGY EXPLAINED Cumec = one cubic metre of water flowing past a given point every second. kw = 1,000 watts. e can to ource of es of great year round the upper me. The lso provide rms. We w Zealand wer Aoraki Mt Cook 3754m Lake Tekapo Max Storage: GWh Power Stations* Tekapo A Commissioned: 1951 Capacity: 25.2 MW *Annual Generation: 160GWh TEKAPO Tekapo canal Length: 25.5 km Tekapo A Construction of the Tekapo A power station started in 1938, and was due to be finished in 1943, but work stopped in 1942 as manpower and materials were concentrated PRECIPITATION Water falls to the earth in the form of rain, snow, sleet or hail. Tekapo B Commissioned: 1977 Capacity: 160 MW *Annual Generation: 833GWh Lake Pukaki Lake Ohau Max Storage: Storage: 42.62GWh GWh Pukaki canal Length: 12 km Ohau A Commissioned: 1979 Capacity: 264 MW *Annual Generation: 1140GWh TWIZEL waterproofed above the maximum lake level. Tekapo B connects with the shore by a 75-metre-long bridge. Ohau A Ohau A power station is located on the manmade Pukaki-Ohau canal and it joins the water Lake Ruataniwha Storage: 1.05GWh Ohau B canal Length: 2.4 km Ohau B Commissioned: 1984 Capacity: 212 MW *Annual Generation: 958GWh Ohau C canal Length: 8 km Ohau C Commissioned: 1985 Capacity: 212 MW *Annual Generation: 958GWH Ohau C to Benmore Canal length: 0.5 km Benmore Commissioned: 1965 Capacity: 540 MW *Annual Generation: 2215GWh Ohau C in This completed the Waitaki hydro scheme as we know it today, and the two stations add around 1916 GWh of energy a year to New Zealand s power capacity. Benmore Benmore power station has New Zealand s Lake Benmore Lake Aviemore Storage: 24.45GWh Storage: 4.04GWh OTEMATATA FACT One cubic metre of water passing through the eight power stations of the Waitaki system generates 2,500 kwh about 30% of an average household s annual power needs. Aviemore Commissioned: 1968 Capacity: 220 MW *Annual Generation: 942GWh Figure: Waitaki System (Source: Meridian Energy) Lake Waitaki Storage: 0.54GWh Waitaki Commissioned: 1935 Capacity: 105 MW *Annual Generation: 496GWh KUROW MW = GWh = 1,000 kw. 1,000 MW passing through a given point over an hour. EVAPORATION Water evaporates from the surface of the ocean. DUNTROON Pacific Ocean in the South Island. A diversion tunnel was built to take the outflow from the lake while the dam was being constructed. Its construction saw the country s first large-scale use of low-heat cement, which allows a record rate of concrete to be poured without using cooling coils. Aviemore

24 Average Storage 2000 Energy Storage (GWh) Week of Year Figure: Average Storage

25 Inflows Inflow (GWh) Crisis Crisis Year Normal Year Week Figure: Inflows between