Portafolio optimization model for electricity purchase in liberlized Energy markets
Edwin Castro, MSc, CNEE Guatemala, +502 23664218,
Juan Carlos Morataya, CNEE Guatemala, +502 23664218,
José Rafael Argueta, CNEE Guatemala, +502 23664218,
Overview
Due to the different kinds of technologies available today to produce electricity in liberalized energy markets it is so important to purchase electricity to the minimal cost taking advantage of renewable resources. The main target is to gain a competitive process where renewable technologies can compete against non-renewable.
In our own energy market, electricity utilities, have to satisfy their electricity demand through a bid where bidders can make their offers without any kind of constraints. Bidders can offer different kinds of technologies using also different kinds of fuels, renewable or non-renewable.
Usually the bidders make their offers for the capacity (MW), which models the investment costs, and for the electricity which models their production costs. As far as the capacity is concern the bidders can offer a maximal and a minimal capacity, the price for this capacity and the contract duration in years. The production costs (electricity) depend on power plant factors, electricity price, fuels, operation and maintenance costs and efficiencies for renewable and non renewable. The optimization model developed here is capable to model every value described, and more important these values can change over the period of the contract. Capacity can change every year and electricity production can change monthly.
Other important issue for this bidding process is to encourage new power plants with renewable resources to invest since there is no limit when the bidder could start its operation. In other words this models gives the bidders a high degree of freedom on how he wishes to make an offer.
Methods
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. This (a scalar real valued objective function) is actually a small subset of this field which comprises a large area of applied mathematics and generalizes to study of means to obtain "best available" values of some objective function given a defined domain where the elaboration is on the types of functions and the conditions and nature of the objects in the problem domain.
The objective function to be minimized is:
Where:
Ci: New capacity to be hired in MW. (Variable)
CPi: Offer for the price for Capacity in US$/kW-month for the “i” year.
Ej: Electricity Generation in MWh for the “j” month. (Variable)
EPj: Production Costs in US$/MWh for the “j” month.
With the following constraints:
Where:
EDj: Electricity demand in MWh for the “j” month.
CDi: Power demand in MW for the “i” year.
PFj: Power plant factor.
The bidder should include in the offer the capacity and its price, duration for the contract in years, the power plant factor and the electricity production costs. It is now important to outlined that the power and electricity demand is an input data for the model, the demand can be variable over the time.
The authors created a software that allows utilities to obtain the best option in order to perform their electricity purchase taking into account all the above constraints.The software used for the optimization process was the Solver, developed by PSI Thechnologies and the optimization engine used was the Standard Linear/Quadratic Programming. This software has two terminals, one of them is used to receive the offers provided by all the interested bidders. Each bidder has a determinated period of time to sent his own offer, once, all the offers has been sent and the period of time is reached, the offers are introduced into the optimization engine through the second one terminal.
Results
The results are shown in the following charts with several offers within different technologies, with a variable demand. The model also estimates the electricity generation for each month for each power plant.
Conclusions
- The model estimates the minimal cost to be paid for electricity, both for investment and for production costs.
- The electricity demand may have any kind of behaviour, it may be growing, falling or variable over the time, and the results are dependent on this behaviour.
- If a bidder includes many constraints in the offer such as a minimal years to be hired and no flexibility on the maximal and minimal power to offer, it is less likely that the bidder will be chosen by the model.
- This model allows renewable technologies to compete against non-renewable technologies since there is a big flexibility for the bidder towards making an offer.
References
- Premium Solver Premium Solver Platform , User Guide, V.5.5.
- Programming Perl, 3rd Edition Larry Wall, Tom Christiansen, John Orwant.