Measuring Performance of Long-Term Power Generating Portfolios - Green Energy and Efficiency: An Economic Perspective - page 390

while others are decommissioned. Each year is broken down into 60 time steps
(5 per month); i.e. the relevant period for the optimization problem is 1/60 year. 1
The optimization model is nested in Monte Carlo simulation. Needless to say, if
simulations are to be realistic then we must work with numerical estimates of the
underlying parameters from of

cial statistics, market data, and the like. A single run
determines the operation state of generation infrastructures over 60 20 = 1,200

consecutive time steps. The same holds for the value of stochastic load, wind- and
hydro-based generation, fossil fuel prices, and carbon price. Under each setting, the
optimization problem is solved: depending on the circumstances in place, genera-
tion is optimally dispatched subject to the network topology. Therefore, one sim-
ulation run involves 1,200 optimizations. We repeat the sampling procedure
750 times (so we solve 900,000 optimization problems). We thus come up with 750
time pro

×

les of each variable of interest. Out of these simulations, we can determine
several metrics (not only averages) and derive the cumulative distribution function
of effects over major variables.
Therefore our model can assess the performance of a pre-speci ed generation

eet in terms of the resulting expected price and the standard deviation around that
expectation. These two pieces of information fall naturally within the MV approach
to portfolio theory. At this point, it is possible to assess the performance of the
whole system (under different generation mixes) according to several other metrics,
e.g. operation costs, unserved load, carbon emissions, etc. Comparing their relative
performance sheds light on their respective advantages and weaknesses.
Of course, uncertainty about the future affects the rate at which future cash

ows
must be discounted to the present. Some related papers develop their analyses under
two (or more) discount rates, e.g. Roques et al. [ 32 ]. Another usual practice is to
assume a particular utility function that characterizes the tradeoff between risk and
return [ 22 ]. One of the inputs to this function is the coef

cient of risk aversion.
Analyses are then developed under two, three or more levels of risk aversion
[ 16 , 33 , 38 ]. In our approach, futures markets play a major role. In addition to their
informational role, the use of futures prices allows discount at the risk-free interest
rate. This fact sidesteps the discussion about the appropriate discount rate.
To demonstrate how the model works we undertake a heuristic application. In
particular, we consider the UK Future Energy Scenarios up to 2032. We consider
both base- and peak-load technologies, and also installed capacities of power
technologies as scheduled by the UK Department of Energy and Climate Change
(DECC) over the planning horizon (2013

2032). The UK is covered by the EU
Emissions Trading Scheme (ETS), so their electricity generators operate under

-

1 This is in contrast to related papers that usually perform economic dispatch on an hourly (or
shorter) basis with a time horizon extending over one (or a few) year(s). For example, Delarue
et al. [ 12 ] take hourly load patterns into account (over 7 weeks) and corresponding dispatch issues
as ramping constraints. There would be no major problem in using our model for a yearly period
on an hourly basis (8,760 steps) apart from the increase in the time required for computation.
Unfortunately, our long-term simulation comes at the cost of framing the optimization problem on
a longer time span (for example, a week instead of an hour).