Electric Power Optimization Centre
Winter Workshop 2007: Measuring and Improving Electricity Markets The Electric Power Optimization Centre at the University of Auckland held its Sixth Annual Winter Workshop on September 7, 2007 at the University of Auckland. The theme of the 2007 Workshop was Measuring and Improving Electricity Markets.
On the convergence of SDDP and related algorithms (pps)Ziming Guan and Andy Philpott (EPOC)We discuss the almost-sure convergence of a broad class of sampling algorithms
for multi-stage stochastic linear programs. Although the convergence of methods
of this type is part of the stochastic programming folklore, we provide an explicit
convergence proof based on the finiteness of the set of distinct cut coefficients.
This differs from existing published proofs in that it does not require a restrictive
assumption. Some inferences will be drawn about assumptions made in various
implementations of SDDP and their effect on convergence.
Measuring productive efficiency losses in the NZEMOwen Auger, Andy Philpott and Golbon Zakeri (EPOC)We present preliminary results of an experiment designed to study the loss of
productive efficiency in the New Zealand wholesale electricity market. The
historical dispatch over the year 2005-2006 is compared with a counterfactual
centrally-planned dispatch computed using a sampling-based stochastic
program, and implemented in a rolling horizon over this period. We assume that
demand is unchanged in each model, and focus on productive efficiency
differences as defined by the difference in fuel costs (rather than allocative
efficiency including the demand, or dynamic efficiency which includes investment
effects.) The emphasis of the talk will be an exploration of methodology rather
than numerical results, as we work towards a repetition of this experiment over a
longer time period.
Mixed integer programming models for wind farm design (pdf)Hamish Waterer, Stuart Donovan and Rosalind Archer (EPOC)There is significant potential for optimizing the design of a wind farm in New
Zealand. The complex nature of the wind resource and the larger size of the wind
farms being built increase the complexity of the decisions that need to be made,
while tight economic margins create a drive for greater efficiency. Current
industry practice utilises commercial packages that are heuristic in nature and
limited in the types of constraints that can be modelled. A mixed integer
programming model for optimizing the layout of a wind farm has been developed
that is capable of determining the optimal locations of turbines subject to
constraints on the number of turbines, turbine proximity, and turbine wake.
Results have shown that this model produces layouts that are comparable to
those from a commercial package. Moreover, this model can be extended to
include capital budget constraints, noise and line of sight restrictions, constraints
relating to wind quality such as maximum gusts, inflow angles and turbulence, as
well as modelling reticulation and different mixes of turbines.
A new dispatch model for intermittent generation (pps)Geoff Pritchard, Andy Philpott and Golbon Zakeri (EPOC)Although much attention has been paid in the NZEM to forecasting intermittent
generation, forecast errors are and will remain substantially larger than current
load forecast errors. These errors mean the pre-dispatch of generation under the
current market arrangements is likely to be less efficient than anticipated
because it must later make expensive (or at worst physically impossible)
adjustments to meet variations from the forecast. We describe a stochastic
programming model for the optimal dispatch of intermittent generation in the
NZEM. The model invovles a predispatch and real-time market, which are
dispatched simultaneously using a stochastic program, but allow for real-time
variations from forecast load using offered deviation curves. This results in two
energy spot prices for each node in each trading period. Our proposed market
mechanism will effectively discount the payments made to uncertain generation,
and impose a price premium on uncertain demand. The hope is that such prices
will provide incentives to encourage investment in intermittent generation at the
most efficient scale at the most effective locations.
Modelling competition in transmission systems (pps)Anthony Downward, Andy Philpott and Golbon Zakeri (EPOC)This talk is concerned with characterizing a set of conditions which ensure
the existence of an uncongested Cournot equilibrium over an electricity
network. Our Cournot model consists of strategic generators and
linear fringes over a pool market. When the transmission network is radial,
we derive necessary and sufficient conditions on the line capacities,
ensuring that the unconstrained Cournot equilibrium remains an equilibrium.
These conditions form a convex polyhedral set, which allows for
optimization of resources while ensuring competitive play. We extend this
work to examine the impact of other network effects (loops and losses) on
the convexity of this set.
The GEM model (pdf)Philip Bishop (Electricity Commission)The Electricity Commission has developed GEM over the past year and has
made it freely available to industry participants since May 2007. In its current
state, GEM is best described as a long range generation capacity planning
model. It is formulated as a mixed integer programming problem (MIP) and is
solved using the GAMS/CPLEX software. The main purpose of GEM is to assist
with the development of the market development scenarios that are to used as
assumptions when analyzing transmission investments, a regulatory requirement
under part F of the Rules. A stylized description of GEM will be presented
followed by a discussion of some key aspects of the model - solution strategies,
the treatment of losses, and the use of system security constraints and their
implication for the resulting build schedule. The presentation will conclude with
some comments on expected unserved energy and security margins.
Competition policy and regulation in hydro-dominated electricity markets (pps)Luiz Rangel (University of Auckland Energy Centre)This paper reviews the main competition issues that arise in electricity systems
dominated by hydro generation, arguing that technological differences between
hydro and thermal plants may allow hydropower producers to exert market
power. The paper shows that the traditional Herfindahl-Hirschman index (HHI) is
not an appropriate measure of concentration in hydrothermal electricity systems,
and describes some proposed adjustments to the index. Some market simulation
approaches to measuring market power in hydrothermal systems are reviewed.
Finally, possible interventions to mitigate market power are analysed.
Uniform-price auctions versus pay-as-bid auctions (pps)Andy Philpott (EPOC) and Eddie Anderson (UNSW)We consider the problem of optimizing a supply function bid into a discriminatory
auction in which each agent is paid their bid price on each increment of offered
capacity. The efficiency of pay-as-bid auctions in comparison with uniform-priced
auctions has been debated, as it is conjectured that in the former auction, agents
will simply bid their offer prices up to an anticipated clearing price. Using market
distribution functions, we derive optimality conditions for each agent in a pay-as-bid
auction, and compute Nash equilibria in supply functions. In most realistic cases,
there are no pure-strategy equilibria in this game. In the absence of capacities and
price-caps, there are infinitely many mixed strategy equilibria, which become
uniquely determined when generators have limited capacities and are subject to a
price cap.
Long-term network development demand forecast for Vector Networks (pps)David Spackman and Nirmal Nair (University of Auckland Power Systems Group)Long-term load forecasts determine patterns of load distribution and are useful
for planning network asset investment. This paper outlines the development of a
new long-term spatial demand forecast model for distribution networks in the
Auckland region of New Zealand. This model uses a policy guided approach to
simplify the data and simulation requirements of previous methods. The forecast
model derives the electric demand saturation limit for small geographical areas
from land use zoning policy. The model incorporates scenario analysis to modify
expected peak demand values. Results from a case study on the Auckland area
are to be presented.