Electricity Market Equilibrium Models 

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Electricity market liberalization

Electricity sectors have been designed as centralized electricity systems. Usually government plays an important role in generation, transmission and distribution of electricity in these centrally planned systems. In these systems, for each time period in a day (e.g. every half hour) a central planner (usually a department or government-owned company) determines demand and generation quantities by solving an optimization problem. The optimization problem minimizes total cost of generation (or maximizes social welfare). This cost is charged to consumers. Over the past decades, in many jurisdictions, electricity sector has undergone a liberalization process. In a deregulated electricity market, government or the monopoly regulator is replaced by several independent entities including a system operator, producer companies, and load serving entities. Liberalization has some characterizing properties including reduction of the state interference in control and management, increase of competition due to deregulation, and increase in the demand side participation in the market.
There are several reasons for the liberalization of the electricity markets. Centralized electricity systems usually cause overcapacity in electricity generation that makes the system work inefficiently [54]. On the other hand, a general trend to liberalize state-owned industries was an important reason for this change. Technological improvements have also allowed for this sort of reform, as some of the required mechanisms for liberalization of electricity markets are quite complex. These factors caused electricity sectors around the world to shift toward a market approach from late 1980s.
The fact that all the risks and costs are on the consumer, and not the decision-makers is touted as the main reason that such systems lead to inefficiency[39]. It is difficult to enable consumers to participate in vertically-integrated electricity sectors. In contrast, in an electricity market, the free choice of supplier, for example, can lead to greater value for the consumers and can encourage innovation amongst the supplyside agents. National or regional integration is another driving factor in improving efficiency in electricity markets. It increases the incentives for improvement and innovation as it increases competition, because there is no guarantee anymore for covering the costs in a deregulated electricity market.
There are different indicators for success of electricity markets discussed in different papers and books such as [54]. Electricity prices paid by the consumers is one of these indicators. Figure 2.1 is taken from [54], and shows that electricity prices have a (somewhat) decreasing trend in different countries after liberalization. For more information about the experiences and challenges of this process (e.g. the difficulties in transition to liberalized markets) see [50].

Electricity markets

Unlike more traditional goods that are bought and sold, electricity can not be easily stored and should be consumed as produced. This property is one of the reasons why electricity markets are difficult to form without any regulation or governance. In electricity markets, an organization is required to ensure that supply and demand are balanced in any given time (real-time balancing). Trade of electricity is too fast to allow for a market to form automatically. The complex nature of electricity networks is another important difficulty in trade of electricity. There are different laws of physics (e.g. Kirchhof’s laws) that prevent the automatic formation of an electricity market. There is a need to design a mechanism to allow for market participants (i.e. producers and consumers) to interact and trade electricity, given the physical laws, while at the same time balancing production and consumption of electricity. These regulations are supposed to provide the participants with a
framework in which they can trade easily, fast, and safely.
Trading electricity is often not as simple as trading energy, in some places, capacity markets exist. By energy market, we mean the market in which energy is traded in a short time. Capacity market is a market for investment in generation or transmission of energy. In this thesis, the focus is on mechanism design for energy markets, as New Zealand only operates an energy market.
Energy markets can also consist of different stages that take place at different times. Each stage is a market itself. Normally there is one market for trading electricity between producers and retailers named the wholesale electricity market. There is also a retail market to trade electricity between retailers and consumers. The focus of this thesis is on the wholesale market, where producers and retailers interact to determine production quantities and prices. Henceforth, when we say electricity
market we mean wholesale electricity market.

Independent system operator (ISO)

After market restructuring, different components of the electricity sector including production, transmission and distribution are not vertically integrated anymore. These components should operate independently. The responsibility of economic dispatch and system security then becomes that of an independent system operator (ISO).
The ISO must be independent from all market participants i.e. producers, consumers, transmitters, and distributors. As an independent entity, ISO is able to determine generation quantities and market prices. It should determine these values in such a way so as to make sure that the optimal dispatch is matched with total demand. The optimal dispatch should also be physically possible (i.e. it must be a feasible solution). For example, the optimal dispatch should meet certain constraints
such as Kirchhof’s laws. Other responsibilities of an ISO include determining tariffs on the transmission network and managing congestion of transmission lines [83].

1 Introduction 
2 Introduction to World Electricity Market Mechanisms 
2.1 Electricity market liberalization
2.2 Electricity markets
2.3 Wholesale electricity market structure around the world
3 Electricity Market Equilibrium Models 
3.1 Definition of a game
3.2 Nash equilibrium
3.3 Cournot model .
3.4 Bertrand model .
3.5 Supply function equilibrium
3.6 Perfect competition
3.7 Optimization techniques and KKT conditions
3.8 History of equilibrium models and other mathematical tools in electricity
markets
4 Modelling Counter-intuitive Effects on Cost and Air Pollution from
Intermittent Generation 
4.1 Introduction
4.2 Market environment .
4.3 Market before the introduction of wind
4.4 Market after introducing wind
4.5 Comparison and results
4.6 Results of a stochastic settlement mechanism
4.7 Conclusion
5 Single and Multi-settlement Approaches to Market Clearing Mechanisms
under Uncertainty 
6 The Global Optimization Method Used to Solve Firms Optimization
Problems 
7 The Effects of the Stochastic Market Clearing on the Cost of Wind
Integration: a Case of New Zealand

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Mechanism Design for Electricity Markets under Uncertainty