PORTFOLIO OPTIMIZATION MODEL FOR ELECTRICITY PURCHASE IN LIBERALIZED ENERGY MARKETS Edwin Castro CNEE Guatemala Viena, september 2009
What is the reason to develop this model? In our own electricity market (Guatemala), electricity utilities, have to satisfy their electricity demand through an open bid in the long term market, where bidders made their offer by a simple electricity and capacity price. Bidders can offer different kinds of technologies using also different kinds of fuels, renewable or non-renewable. Is this really an efficient way to purchase capacity and electricty? We think not, due to the different kinds of technologies available in our country to produce electricity we believed it is so important to purchase electricity to the minimal cost taking advantage of renewable resources with a minimal impact to the end-user tariff. This models also encourages power plants with renewable resources to compete against non renewable since the freedom they have to make an offer.
Power and electricity demand options (Buyer, input data) The electricity demand to be satisfy can be: yearly (season), monthly and hourly, with any kind of load curve behaivour. The power (capacity) demand to be satisfy can be: yearly and monthly.
Options for the power plants (sellers input data) 1. Capacity Maximal Capacity Minimal Capacity MW MW Price for the capacity US$/kW or US$/MW 2. Electricity Monthly generation Price for Electricity Generation curve MWh US$/MWh Hourly 3. Other information Contract minimal duration Period you want to start your contract Months or Years Months or years
Small hidro-power-plant example Capacity Daily generation curves Year Maximal capacity Minimal capacity Price for the capacity MW MW US$/MW-year 1 0 0 0 2 22 10 312.000,00 3 22 10 312.000,00 4 22 10 312.000,00 Electricity Month Generation MWh Price for electricity US$/MWh Jan 6,494.40 2.90 Feb 6,494.40 2.90 Mar 6,494.40 2.90 Apr 6,494.40 2.90 May 15,840.00 2.90 Jun 15,840.00 2.90 Jul 15,840.00 2.90 Aug 15,840.00 2.90 Sep 15,840.00 2.90 Oct 15,840.00 2.90 Nov 6,494.40 2.90 Dec 6,494.40 2.90
Portfolio Optimization In mathematics, the simplest case of optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set The objective function to be minimized is: Supply COST (capacity & electricity) Subjected to the condition to satisfy the capacity and electricity demand. (Hourly, monthly and yearly) This model can just be just an electricity problem or a capacity problem, or both, depending on the type of engagement and the type of market you want to satisfy.
Optimization model features The authors created a model that allows utilities (or electricity traders in the market) to obtain the best option in order to perform their electricity purchase taking into account all the above conditions. The software used for the optimization process was the Solver, developed by PSI Technologies and the optimization engine used was the XPRESS. No. Variables Constraints Horizon Results Assumptions (Risk) 1 2 Capacity to be awarded Electricity generation 5 normal 15 years or 180 months. Electricity generation (hourly, monthly, annual) Fuel prices forescast 4 bounds Awarded capacity Inflation forecast 3 Unit Commitment 2 Integer Average price for electricity 4 Share in total demand 5 Power station use 6 Minimal cost for the supply
EXAMPLE Year MW 2010 254 2011 262 2012 270 2013 278 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year GWh 1 147 143 147 147 143 147 143 147 147 133 147 143 2 152 147 152 152 147 152 147 152 152 142 152 147 3 157 152 157 157 152 157 152 157 157 142 157 152 4 161 156 161 161 156 161 156 161 161 146 161 156
RESULTS 1
RESULTS 2 Minim al Cost US$ 714,425,873 Resulting Electricity Price 98.20$/MWh Total Electricity Production 7,275,203.54 MWH YEAR Hidro 1 Hidro Hidro Hidro 2 3 4 Biom ass Coal 1 Geother mal Wind Coal 2 Natural Gas 3 Natural Gas 1 Fuel Oil Coal 3 Natural Gas 2 Fuel Oil Shorta ge 2010 0 54 22 0 0 0 20 15 0 50 0 0 93 0 0 0 254 2011 0 53 16 0 0 0 20 15 100 58 0 0 0 0 0 0 262 2012 0 56 22 0 0 0 20 15 100 57 0 0 0 0 0 0 270 2013 0 40 18 0 0 200 20 0 0 0 0 0 0 0 0 0 278 Share in total demand 0.0% 20.9 % 6.7% 0.0% 0.0% 18.2% 9.6% 5.4% 22.7% 6.9% 0.0% 0.0% 9.6% 0.0% 0.0% 0.0% 100% Power station use 0.0% 86.0 % 72.2 % 0.0% 0.0% 73.9% 100.0% 100.0 % 92.2% 34.7% 0.0% 0.0% 90.9% 0.0% 0.0% 0.0%
OTHER RESULTS, OTHER LOAD CURVES
Thank you very much! Edwin Castro CNEE Guatemala ecastro@cnee.gob.gt +502 2321-8000