# Mathematics and energy policy. Markets or central control power

7 March 2014
10:00
John Rhys (The Oxford Institute for Energy Studies)
Abstract
This talk is intended to explain the link between some relatively straightforward mathematical concepts, in terms of linear programming and optimisation over a convex set of feasible solutions, and questions for the organisation of the power sector and hence for energy policy. Both markets and centralised control systems should in theory optimise the use of the current stock of generation assets and ensure electricity is generated at least cost, by ranking plant in ascending order of short run marginal cost (SRMC), sometimes known as merit order operation. Wholesale markets, in principle at least, replicate exactly what would happen in a perfect but centrally calculated optimal dispatch of plant. This happens because the SRMC of each individual plant is “discovered” through the market and results in a price equal to “system marginal cost” (SMC), which is just high enough to incentivise the most costly plant required to meet the actual load. More generally, defining the conditions for this to work - “decentralised prices replicate perfect central planning” - is of great interest to economists. Quite apart from any ideological implications, it also helps to define possible sources of market failure. There is an extensive literature on this, but we can explain why it has appeared to work so well, and so obviously, for merit order operation, and then consider whether the conditions underpinning its success will continue to apply in the future. The big simplifying assumptions, regarded as an adequate approximation to reality, behind most current power markets are the following: • Each optimisation period can be considered independent of all past and future periods. • The only relevant costs are well defined short term operating costs, essentially fuel. • (Fossil) plant is (infinitely) flexible, and costs vary continuously and linearly with output. • Non-fossil plant has hitherto been intra-marginal, and hence has little impact The merit order is essentially very simple linear programming, with the dual value of the main constraint equating to the “correct” market price. Unfortunately the simplifying assumptions cease to apply as we move towards types of plant (and consumer demand) with much more complex constraints and cost structures. These include major inflexibilities, stochastic elements, and storage, and many non-linearities. Possible consequences include: • Single period optimisation, as a concept underlying the market or central control, will need to be abandoned. Multi period optimisation will be required. • Algorithms much more complicated than simple merit order will be needed, embracing non-linearities and complex constraints. • Mathematically there is no longer a “dual” price, and the conditions for decentralisation are broken. There is no obvious means of calculating what the price “ought” to be, or even knowing that a meaningful price exists. The remaining questions are clear. The theory suggests that current market structures may be broken, but how do we assess or show when and how much this might matter?
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