Equilibrium Models in Co-Optimised Markets

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Equilibrium Models in Co-Optimised Markets

In this chapter, the co-optimised electricity market presented in Chapter 2 has been extended using a Supply Function Equilibrium model. A two participant game has been modelled under reserve constrained generation units and transmission lines. As market participants may be active across both energy and reserve markets, it was hypothesised that reserve market power could be used to influence the energy market. To our knowledge, this work is the first to investigate reserve market power in co-optimised electricity markets.Results from this model indicate that the optimal supplier strategy is to withhold reserve and thereby limit the dispatch of risk constrained assets. This theoretical result is corroborated by market actions from the 2012 dry year, when a participant took a (contractual) dominant reserve market position in the South Island of NZ.An initial version of this work was submitted to IEEE Transactions on Power Systems. Comments were received and the work has recently been resubmitted.

Introduction and Literature Review

The smooth and competitive operation of an electricity market is important to the health of an economy. Uncompetitive markets, those dominated by a few suppliers or with market structures promoting perverse incentives, can decrease social welfare and be detrimental to productivity. Companies who exert market power can have a large effect on economic efficiency in deregulated electricity markets (Tirole, 1988, 2014).In electricity markets, the study of competition using equilibrium based models has a strong precedent. Nash equilibrium is established when no participant can unilaterally improve their outcomes (Nash, 1950). Equilibrium models are effective methods of studying market competition as they closely reflect real markets with features such as:Participants submit sealed bids to the System Operator which are cleared simultaneously Participants interact frequently with one another (Repeated Game) Participants are assumed rational Techniques to study electricity markets have arisen using a number of different models of competition. Models of competition, such as Bertrand (Bunn and Oliveira, 2003) or Cournot (Borenstein and Bushnell, 1999) at the two extremes of market power, have a large impact on the participant behaviour forecasted in different situations. More moderate levels of competition in models such as Supply Function Equilibria (SFE), which was first applied by Green (1996) and is based upon the work of Klemperer and Meyer (1989) are often more appropriate. SFE models (Hobbs et al., 2000; Baldick et al., 2000), include the price quantity bid pairs of established electricity markets. An alternative, moderate form of competition, which is recently gaining popularity is the Conjectured Supply Function (CSF) Equilibria model (Diaz et al., 2012).The principal problem of modelling electricity markets is the temporal and spatial balancing requirement. Most equilibrium models consider simple networks even though it has been shown that transmission has a major effect upon market power (Joskow and Tirole, 2000). Simplified network models are still useful for insight as the real system may be too complex to be modelled within the chosen competitive framework at the full network resolution level. Discussions regarding the depiction of the network and the effect upon equilibrium models can be found in Neuhoff et al. (2005) and Bautista et al. (2007c).Electricity markets evolved beyond energy only markets to incorporate AS upon deregulation. Historically, AS were procured through the vertically integrated utility companies who had a vested interest in market security. In some deregulated marketplaces this vertical integration has been broken and reserve markets have been introduced. Reserve markets are designed to compensate participants who provide spinning reserve and other essential services. These ancillary service markets also interact with the energy markets and thus, generation company offer structures. At the system level there are different methods of procuring reserve (N-1, fixed percentage, manual requirements, probabilistic) which link the reserve requirement to the energy market. In these systems, generators may structure their offers to avoid reserve costs.At the unit level the decision to provide ancillary services often incurs an opportunity cost as participants are partially constrained from participation in the energy market. Reserve providing generators must therefore optimise their portfolio of energy and reserve offers, not just their energy offers. Although energy offer optimisation has been considered in some depth (Anderson and Philpott, 2002a; Pritchard and Zakeri, 2003; Baillo et al., 2004; Neame et al., 2003; Anderson and Philpott, 2002b), the same level of scrutiny has not been applied to combined energy and reserve market offers.Consider the model presented in Chapter 2 with N-1 security requirements. In this model, the reserve requirement is inherently linked to the offers of market participants. If a unit is both the marginal risk setting unit and the marginal energy unit, the reserve price becomes incorporated into the energy price. Unit level considerations can also constrain the electricity market in complex ways.In this chapter we consider the effect of reserve co-optimisation under an N-1 market dispatch, based upon the model presented in Chapter 2. We present a SFE implementation across two nodes with a reserve constrained transmission line. The model is general, it may consider reserve constrained generation units and/offer reserve constrained transmission lines, across a number of nodes. In this chapter it is specifically applied to a two node market which is heavily influenced by the transmission network and market structure of the NZEM.The results of this model are discussed in terms of transmission investment and IL participation. We show that in markets with deterministically procured reserve, a dominant reserve provider has strong incentives to block the dispatch of competitor energy offers by withholding reserve. This result is applied to transmission investment and the Grid Investment Test (GIT) in Section 3.3, and to IL participation in Section 3.5.

Literature Review

This section is not intended as an exhaustive summary of the general equilibrium literature, but instead an introduction to the attempts to incorporate reserve into equilibrium models. The combined energy and reserve offers form a multi product equilibrium. As the supply of reserve can limit the ability of units to generate at high capacity levels, the equilibrium reserve offer is inherently linked to market energy offers (and vice versa). Individual units are also constrained in their combined energy and reserve offers, although we do not consider this special case here. The inverse bathtub constraints, as illustrated in Figure 3.1, constrain the feasible operating region for a unit who offers both energy and reserve.Whilst there does exist additional, general, literature on the concept of market power in reserve markets the majority of these are not applicable to this Thesis. In particular, we draw attention to the comments made in Chapter 1 where an attempt was made to indicate the usage of the term “Reserve” in this Thesis. The literature cited in the following section contains those pieces of work which align with the definition of reserve as stated in Chapter 1. Other pieces of work do exist which fall outside this definition, though sharing common names.Two research groups have undertaken the majority of the research into equilibrium models of reserve constrained electricity markets. From 2005-2007 at the University of Waterloo, Guillermo Bautista published four papers focussing upon the formulation of equilibrium models in markets with AC power formulations, an extension from the DC formulations. From 2006-2008 Hossein Haghighat, also from the University of Waterloo considered the effect of market structure on incentives and the effect of different market clearing mechanisms in a competitive framework. We note that both groups were focussed upon the techniques of establishing equilibrium as opposed to market case studies which is the approach we undertake.The inverse bathtub, a visual explanation showing the three separate feasible regions governed by separate linear programming constraints The work of Bautista, Anjos, and Vanelli concerns the application of optimisation techniques to electricity markets. The group (along with two separate co authors on a fourth paper) discuss the requirement for detailed transmission networks which incorporate active power, reactive power, and voltage (Bautista et al., 2007c). The paper discusses the challenges faced by researchers who must choose which features to approximate and which to examine accurately and was pitched as a response to an earlier piece of work by Neuhoff et al. (2005).In Bautista et al. (2006), conjectured supply functions were used to compute the opportunity cost between energy and reserve markets under oligopolistic considerations. Conjectured reserve price functions provide a measure of a generator’s ability to influence the spinning reserve price in a theoretical setting. They show that even perfectly competitive spinning reserve markets may have an effect on energy prices. Bautista et al. (2007a) used a non linear programming approach to apply game theory within a reactive power market. They proposed a detailed AC formulation of the power system and use the competitive and Cournot frameworks to model competition. Finally, in Bautista et al. (2007b), the authors proposed an SFE model that extends the active and reactive power formulations to include spinning reserves. Though the reserve market is not the focus of this paper (instead, the wider problem of determining a quantitative equilibrium in a full AC power system is), the authors identify that the presence of spinning reserve markets induces optimising generators to forgo electricity market revenue in order to maximise total profits.In Haghighat et al. (2007) the authors studied the interaction among suppliers, to develop an optimal bidding strategy for participants active in both energy and reserve markets. An SFE model is developed within a mathematical program with equilibrium constraints using two level optimisation. The authors illustrate that when capacity is fully utilised for energy and spinning reserve the prices of both products increase. However, the model utilised a “pay as bid” (not uniform pricing) approach to assess this. In Haghighat et al. (2008b) the authors appear to utilise the same model in order to understand the effect of market pricing mechanisms. The authors compare the “pay as bid” approach with the uniform pricing (UP) approach and analytically prove that the marginal clearing price is the same for both. We note that “pay as bid” approaches have been compared to « guess the final clearing price » in some discussions and it is unsure how this result applies in a practical setting. Haghighat et al. (2008a) appears to contradict their earlier result and indicates that market clearing prices in joint markets increase after a switching from uniform pricing to “pay as bid” payment mechanisms. The authors indicate that a multi generator game leads to both higher supplier profits and higher market clearing prices.One of the earliest, albeit shortest, discussions of joint energy and reserve markets is expressed in Ma and Sun (1998). The short letter covers different techniques of reserve dispatch and presents experiences from the NZEM which indicated that the presence of IL leads to decreasing market clearing prices in the reserve markets. A final model as expressed in Chitkara et al. (2009) covers the provision of reactive power. This model is not specific to the co-optimisation of reserves, but is a useful example of a market with multiple competing products. The authors illustrate that in a two person game, prices settle near the market price cap. Different price cap strategies are presented and shown, to help mitigate some of the gaming of the generation participants.

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Model Formulation

A simplified N-1 security constrained model adapted from Chapter 2 has been adapted to the SFE framework. A simplified two person game with linear marginal energy costs and constant marginal reserve costs is presented in this section. Competitive models under N-1 reserve constrained transmission are novel in the literature with prior approaches concerned largely with developing AC power formulation models under competition (Bautista et al., 2007b).The model consists of a game between two profit maximising companies who offer energy and reserve to an independent SO, to satisfy demand subject to reserve constraints. Each company is modelled as a leader with the SO as a follower. The market is nodal (Schweppe et al., 1988) for both energy and reserve, with separate energy and reserve clearing prices. Reserve is modelled as a single product although an extension to a multi product case is possible. All reserve is provisioned through separate units and thus no constraints related to the inverse bathtub constraint are apparent. The model is solved using diagonalisation, with each of the two profit maximising companies taking turns to choose their optimal market offers, under an assumed state of their opponents offers. The following nomenclature is used throughout this chapter.

1 Introduction
1.1 Motivation, Hypothesis and Structure
1.2 Electricity Markets
1.3 Co-Optimised Electricity Markets
1.4 Integrating Demand Response
1.5 The New Zealand Electricity Market
2 Theoretical Understanding of Reserve Constraints
Reserve Constraints

2.1 Introduction
2.2 Formulation
2.3 Case Studies
2.4 Empirical Assessment
3 Impact upon Decision Making
3 Equilibrium Models in Co-Optimised Markets
3.1Introduction and Literature Review
3.2 Model Formulation
3.3 Results
3.4 Grid Investment
3.5 Interruptible Load Participation .
3.6 Discussion
4 Application to IL Consumers
4 Optimising Load Curtailment for IL Consumers using kNN
4.1 Introduction
4.2 Prices in the NZEM
4.3 kNN Model Development
4.4 Results
4.5 Discussion
5 Integrating Demand Side Participation with Energy and Reserve Markets
5.1 Introduction
5.2 Theoretical Load Reduction
5.3 Development of Boomer-Consumer
5.4 Model Results
5.5 Model Extensions
5.6 Conclusions
6 Conclusions
6.1Research Motivations
6.2 Identifying Constraint Mechanisms
6.3 Application of Equilibrium Models
6.4 Classifying Reserve Constrained Periods
6.5 Optimal Combined Offers
6.6 Contributions to the Literature
On the Co-Optimisation of Reserve Markets

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