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PORTAFOLIO OPTIMIZATION MODEL FOR ELECTRICITY PURCHASE IN
LIBERLIZED ENERGY MARKETS
MSc. Edwin Castro, CNEE Guatemala, +502 23218000, [email protected]
MSc. Rafael Argueta, CNEE Guatemala, +502 23218000, [email protected]
Overview
Due to the different kinds of technologies available today to produce electricity in liberalized electricity 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 electricity market (Guatemala), electricity utilities, have to satisfy their electricity demand through an open bid
where bidders make their offer by a simple electricity price, usually in US$/MWh, including investment and operational costs.
Bidders can offer different kinds of technologies using also different kinds of fuels, renewable or non-renewable.
In this model 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 or months. The production costs (electricity) depends hourly
production, electricity base 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 vary every year or month and electricity production can vary monthly and
hourly, all these in order to obtain the lowest supply cost for the utilities.
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 commercial 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 or existing capacity to be hired in MW in month or year. (Variable)
CPi:
Offer for the price for Capacity in (US$/kW-month) for the “i” year or month.
Ei:
Electricity Generation in MWh for the “i” month or hour. (Variable)
EPi:
Production Costs in US$/MWh for the “i” month or hour.
With the following conditions:
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Electricity demand(MWh), monthly and hourly, has to be satisfy.
Power demand(MW), yearly or monthly, has to be satisfy.
To assign the capacity to the different power plants within the minimal and maximal value respecting the duration of
the contract.
The bidder should include in the offer the capacity and its price, duration for the contract in years or months, monthly
electricity generation, hourly electricity generation and the electricity costs. It is now important to outlined that the power and
electricity demand to be hired is an input data for the model, both power and electricity can vary over the time.
This model can just be an electricity problem or a capacity problem, or both, depending on the type of engagement and the
type of market you want to satisfy.
The authors created a model that allows utilities (or electricity traders in the market) to obtain the best option in order to
perform their electricity purchase taking into account all the above conditions. The software used for the optimization process
was the Solver, developed by PSI Thechnologies and the optimization engine used is the XPRESS.
Results
The results are shown in the following charts with several offers within different technologies, with a growing demand for a
four-year period. The model also estimates the electricity generation for each month and hour, for each power plant. The
minimal cost for this exercise is 1,367,962,640 US$ and if divided by the total production (17.248GWh) you can obtain an
average price for the supply, in this case 79.3US/MWh.
Conclusions
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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
1.
2.
Premium Solver Premium Solver Platform , User Guide, V.5.5.
Programming Perl, 3rd Edition Larry Wall, Tom Christiansen, John Orwant.