A Few More Thoughts on Appropriate Risk Management Techniques for the Energy Markets
Before starting the discussion on the advantages or disadvantages of various modelling approaches in the Australian electricity market, let’s make a philosophical intermission. What should be the purpose of mathematical modelling? There is another, rather unrelated question to ask: why is there no Nobel Prize in Mathematics when even lifetime enemies may win a Noble Peace Prize?
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality”
Albert Einstein
There is an “urban myth” about a romance between Alfred Nobel’s wife and a famous Swedish mathematician named Mittag-Leffler with Nobel reputed to proclaim: “This tribe of bastards will not get a single penny out of me!” The truth of the matter is that Alfred Nobel was never married.
The Nobel Prize is awarded for the discovery or achievement that has “done mankind the greatest good.” When mathematics is not applied to explain the result of physical, biological or economic experiments, then it is all just a game played between “beautiful minds”.
The aim of this digression is to point out the importance of studying the physical world before attempting to model it. Returning to our original question, the purpose of mathematical modelling is to help explain the physical world. Thus before any electricity market models are discussed, let’s first analyse and understand the underlying Electrical Grid.
The Grid is a giant Automatic Control System (ACS) where multiple switches, fuses and peaking generators constantly support the supply-demand balance. They also ensure the frequency of 50Hz (±0.2%)[1] in the network (otherwise your electric shaver might spin a bit fast for you!). This ACS is governed by the so-called ‘Optimisation of Power Flow’ (OPF) algorithm. The inputs to this algorithm are designated voltages and currents in every line of a circuit as well as the load in every system node (or bus), which is a connection point for a large consumer or a generator. By minimizing the rather unfortunately named ‘Social Welfare Function’, the OPF algorithm outputs the price in every node and the dispatch schedule for every generator in a network[2].
Just to give you a fleur of the overall complexity, we present a sample of the 30-bus grid[3] (Fig.1). A similar circuit diagram, but with hundreds of nodes, flashes like a Christmas tree on the wall of NEMMCO’s Control Centre at Carlingford, NSW.
Fig1. 30- Bus system. Bars represent nodes, blue circles represent generators, the arrows represent scheduled loads.
The peculiar fact is that even though such an eye catching display is continuously blinking before NEMMCO’s collective eyes, the OPF is not used there as the price determination mechanism. In contrast to our Trans-Tasman neighbors who price electricity in every single node of their 244-node grid[4], NEMMCO has introduced a simplified five-region model with only five Regional Reference Prices (RRP) to be determined (Fig 2). In order to mimic the OPF, myriad of loss factors and special approximations were introduced into NEMMCO’s Linear Programming Engine (called either NEMDE or SPD depending on the NEMMCO document’s author).
Fig. 2 National Electricity Market physical model
As a result, NEMDE operates as the so-called ‘Greedy Algorithm’[5], which works as follows.
In order to satisfy demand, subject to system constraints, it fully ‘consumes’ every bid submitted to the pool (sorting them by creating bid-price couple and then ordering these couples by arranging price bands in ascending order). It accumulates these bids until the demand is met, so that the last (partly dispatched) bid of the marginal generator will define the RRP. This procedure is performed every five minutes and averaging the bids over six five-minute intervals yields the half-hourly market price.
Graphically, the price formation could be visualised by a crossover of the vertical ‘demand’ line with a regional five-minute bid stack, which is comprised from bids that are stacked in order of increase of respective prices. (Fig. 3)
Fig. 3. Bid stack evolution across one day. Yellow line represents one generator (ACIL Tasman in isolation). Vertical line represents regional demand as at 6:00.
In times of moderate demand the flatter part of the bid stack is being dispatched and a small incremental change in demand will cause a correspondingly small change in price. When the demand is higher, the action happens on a steep part (or, what is even worse, inflection points) of the bid stack. In this case even a minuscule change in demand will trigger a jump in price. This part of the bid stack is particularly vulnerable for gaming by generators (still bidding “in good faith”[7]).
So, once again we are left with the question: what is the most adequate (i.e., reflecting the properties of the underlying Grid) and practical framework for Risk Management? I will tackle this in a future article.
To be continued…
[1] Guide To Ancillary Services in the National Electricity Market, available from www.nemmco.com.au
[2] Evaluation of Power Systems Congestions Using Nodal Price Analysis, G. C. Stamtsis, J. Christiansen, I. Erlich, available from http://www.uni-duisburg.de/FB9/EAN/downloads/papers/article_for_meps02.pdf
[3] Taken from THE USES AND MISUSES OF OPF IN CONGESTION MANAGEMENT, presentation by George Gross University of Illinois at Urbana-Champaign Seminar “Electric Utilities Restructuring” Institut d’Electricité Montefiore Université de Liège December 8, 1999 © Copyright George Gross, 1999
[4] http://en.wikipedia.org/wiki/New_Zealand_Electricity_Market
[5] http://en.wikipedia.org/wiki/Greedy_algorithm
[6] From Ho King Calvin Kwok, PhD Thesis Proposal, UNSW, April 2004
[7] Clause 3.8.6 (f): “…prices specified for each price band being offered must increase monotonically with an increase in available MWs”
