Company Optimisation in EMarket
Introduction
This technical bulletin is intended to provide users and interested parties with a detailed explanation of how EMarket’s company optimisation feature works.
This paper includes a brief overview of other features in EMarket and a note on enhancements planned in the short to medium term.
Other Documents
This bulletin is one of a series of technical bulletins relating to Energy Link’s EMarket model. Taken together, the bulletins replace the old EMarket User Guide. The full series of bulletins covers an overview of the EMarket model, the details of the four major New Zealand hydro systems modelled in EMarket, water values and hydro offers, power flows, dispatch and nodal pricing, short term river chain optimisation and company optimisation.
Company Optimisation
EMarket is designed to produce stable offering schemes for generation that are, in principle, based on static short or long run marginal costs for each generator. However, when a company owning a generation, retail and hedge portfolio is considered then the optimal offering behaviour for that company as a whole will affect the value of each generation offer. EMarket can now adjust offers to simulate this behaviour, which is called Company Optimisation (CO).
Market Sensitivity
Market sensitivity is loosely defined as the change in price that can be affected by removing or adding generation to the available supply. On an incremental basis, given a supply curve P(s), where P(s) is the price at which a supply of generation s is available, then market sensitivity can be defined as
or the negative derivative of the supply curve.
In practice the supply curve is a lumpy, non-differentiable curve and is not all that useful. In the following analysis we look for more general and approximate relationships between supply and price.
The Supply Curve
Figure 1 is taken from supply curve data over the period of a week from the New Zealand market. For a given price market sensitivity is estimated by first finding the generation available at that price and then finding the price at which 100 MW less generation is available. This shows the average market sensitivity for a range of prices. The average standard deviation is shown by the dotted lines.
This particular week's data indicates that it is possible to estimate market sensitivity (MS) as a linear function of price:
MS = - dP(s) / ds ≈α p
In this case α = 0.005.
The analytical solution to 
is P = e-ãs so an exponential fit to the supply curve is indicated.
Company Optimisation Calculators
In the following analysis, location factors are ignored. The problem of optimisation taking location factors into account is considerably more complicated and most of the benefits can be achieved without taking them into consideration, at least for longer term modelling (Optimisation on a short term basis, eg period-by period, is recommended using our EMarketOffer model with its optional Offer Optimiser). The effect of reserve offers is also ignored.
Gross Profit
The gross profit including generation costs for a company in one period (reserve revenue aside) is given by:
π = PEg - μg - PEL + PSL + (PR - PE)*Q
where π is gross profit, g is total generation, PE is the energy price, μ is the costs for generation, L is the retail load and PS is the retail price, Q and PR are the hedge quantity and reference price respectively.
Optimum Gross Profit
With respect to generation, and treating PE as a function of g to account for market sensitivity, the optimum gross profit is given by:
∂π/∂g = 0 =>
dPE / dg * (g - (L + Q)) + PE - μ = 0
Optimum Price/Generation Relationships
Using the Optimum Gross Profit equation, where s0 is the supply without any generation from the company in question.
PE = Exp(α(s0 + g))
dPE/dg = α Exp(s0 + g) = -αPE
which becomes
-αPE * (g - (L + Q)) + PE - μ = 0 or
PE = μ / (1 + α((L + Q) - g))