TPP126: Setting Electricity Rates
ESD 126: Setting Electricity Rates Problem Set
handed out: March 18
due: April 1
Read through the entire problem set first - some questions build on earlier ones. Clearly state any assumptions you make to answer the questions.
Problem 1: Setting Rates with Price Regulation
a)An electric power utility, operating under price regulation has total assets worth 86 B$ (billion dollars). The debt to equity ratio is 50:50, with an 8% return on debt and a 12% return on equity. Other utility information, relevant for each year is:
Fuel Cost$1,461,330,000
O&M Costs$104,010,000
Total energy generated78,500 GWh
i)Calculate the weighted cost of capital for this utility.
ii)Calculate the electricity rate(s) under rate of return (cost based) regulation for five years into the future. Assume 2% demand growth per year. Assume a straight line depreciation of the assets over 30 years.
iii)In year 6 the utility adds a plant worth $500,000 to its total remaining assets (this plant has a 30 year life from the time of installation). Assume the same capitalization ratio (50:50 debt:equity), and calculate the electricity rates for this utility for the next five years (again assuming a 2% demand growth per year).
b)Briefly compare and contrast incentive based regulation to rate of return regulation. What are the benefits and drawbacks of each? Explain why the differences of these two approaches (in terms of economic incentives to utilities) become less pronounced over time.
Problem 2: Time of Use Rates (TOU)
General information for parts (a) and (b) is provided in the load duration curve below.
Figure 1: Load Duration Curve
The table below shows one possible method of defining time of use blocks for this utility, using information from the load duration curve and the plant generating data (not shown).
Table 1: Possible Time-Of-Use Block Definition
Demand Level / # Hours Operating / Approximate Energy Generated / Expenses(Fuel + O&M)
base plants / 8760 / 51,000 GWh / $ 687,100,000
intermediate / 7940 / 26,000 GWh / $ 760,065,000
peaking / 800 / 1,500 GWh / $ 118,167,000
a)The power company for part (a) is price regulated and must meet its revenue requirements as defined by the regulatory structure. As in problem (1), let total utility assets equal 86 B$, with a 30 year life time. Design and report a time of use rate structure for this utility, using the three generation blocks defined in the table above as the time-of-use blocks. Be certain that the revenue collected from the rates covers the utility’s revenue requirements (ignore any dynamic effects of demand growth, or of demand shifting or decreasing due to price elasticity).
b)Now assume that the power company for this problem is located where there is a well established and fully competitive market for electric energy. Use the theory of LRMC pricing as presented on pp. 17-19 in the Munasinghe reading to define a TOU rate structure which will facilitate (financially) future capital expansion of a plant which costs $500,000 and begins to generate five years from now. Specify the time horizon over which rates will change. *Note that for this problem you must assume a specific capacity factor for the plant. Also note that a competitive market is forward looking with respect to capital recovery, rather than backward looking as with rate of return, or cost based regulation.
c)Parts (a) and (b) are both allocation problems, in that you must decide on a policy for allocating capacity costs across the user base. For part (c) explain your decision for how to allocate the cost of capacity across the users or customers in the different time periods (blocks). Explain these decisions for both parts (a) and (b).
d)As in part (b) assume that the power company is in a competitive environment for generation. Use the theory of LRMC pricing as presented in Appendix C of the Munasinghe reading. Select two different generating technologies which will be in different sections of the loading order (i.e. base load, intermediate or peaking). One of these plants must be a renewable energy technology, and the other a conventional plant - fossil fuel or nuclear powered.
i)List the plants you have selected and state the capacities and capacity factors you assume for each. Assume and report a load growth consistent with the plant capacities you select (this should be between 2% and 5%).
ii)Using published capacity and O&M costs for your plants calculate the annualized capacity costs for each and hourly operating costs (the excerpts from the TAG, pp. 2-1 to 2-6 explain a simple method for these calculations). To perform these calculations you will need approximate plant costs, which can be found in the books on my desk or in the TAG or in the library - you do not need to find current year values - estimates are fine. Assume a discount rate of 10%.
iii)Using this information, design a TOU rate structure for the power company. Report the rate structure for the time horizon necessary to show the impacts of investing in your selected plants.
iv)Briefly explain your allocation decisions for deciding which groups of consumers should pay for the cost of capacity expansion.
e)Now use new discount rates for the renewable energy technology and the conventional plant, as described below:
i)5% for the renewable plant and 12% for the conventional plant, then
ii)12% for the renewable and 5% for the conventional
Repeat the calculations in part (d) sections (d-ii) and (d-iii) for both sets of discount rates specified above. How does discount rate affect the impact of these technologies on the rate structure and the relative attractiveness of the technologies.
Problem 3: Real Time Pricing
For this problem you will calculate a very simplified real time price or spot price rate schedule for a 5 bus power system. The method is based on the economic dispatch formula as in the Bergen readings.
The 5 bus power system is shown below. This system has 3 generators and 2 load centers.
The following cost curves describe the generators’ operating costs.
Subject to the constraints on generator output of:
i)The histogram below shows the daily load shapes for each load center. Assume each 24 hour period (i.e., each day) has the same load shape. Calculate the aggregate system load by summing these two curves.
ii)Using the generator cost equations given above calculate system lambda for each system load value. (System lambda is defined in the Bergen reading. It is typically calculated using (Lagrangian) constrained optimization - see the Bergen reading for this formulation. *Note - Excel and other spreadsheets will solve constrained optimization problems for you. In Excel, select ‘Solver’ under the ‘Tools’ menu, and it will provide a dialog box to guide you in specifying the objective function and constraints.)
iii)If the total annual revenue requirements of this power company are $60,000,000, determine the generation revenue reconciliation term (as a c/kWh adder to the system lambda calculated above) so that the utility will meet its revenue requirements. As in problem (2) this is an allocation question. Select and explain a simple rule for allocating these costs. Make any necessary assumptions.
iv)Report the daily spot price schedule you have designed, specifying the components of the spot price at each system load level (system lambda and revenue reconciliation). Report also the total revenue the company will collect for one year with your rate structure, and explain any significant deviations from the required revenue, if any.
ESD 126, Spring 2002page 1