INTRODUCTION
History of electricity markets
The development of the vertically integrated utilities in the market was mainly inspired by the economies of scale in the generation sector, as well as the complexity of coordinating generation with transmission, which was considered inseparable at the time. Jarrell's empirical results, based on the year in which various states underwent state regulation, turned out to contradict the tenets of public interest theory. This feature of the market allowed companies to raise prices above competitive levels.
However, in the struggle to restructure the market, the movement to restore the elements of competition, especially in the wholesale market, was inevitable.23. Over the past decade, the urgent need for a more efficient and reliable electricity market has been driven by environmental concerns, as well as the dire experiences of the California energy crisis and massive power outages in the Northeast. These challenges have led to the introduction of smart grids as the future of electricity markets.
Smart Grids
In the face of the energy crisis, California and federal government authorities have taken several measures to mitigate the effects of the energy crisis.22 Lessons from the California energy crisis have hindered the restructuring of the electricity market in other states. This quality of smart grids increases generation capacity and, if properly regulated, can result in lower electricity prices for local end-users. Additionally, given the high penetration of Plug-in Electric Vehicles (PEVs) expected in the US, these small suppliers can also act as utility grid storage devices when needed.
In addition to a smart management system, a smart grid includes many features that ensure network efficiency, among which smart infrastructure and smart protection systems stand out. The benefits of a smart grid at the societal level, provided by a reliable grid with a reduced probability of power outages and lower prices, are facilitated by the active participation of end users in the supply chain. In this respect, game theory is expected to provide a key analytical tool in market planning and optimization.
Game Theory
Non-Cooperative game theory in design
In a non-cooperative game, each player has control over a set of variables and seeks to optimize his individual objective function, regardless of its impact on other players. If the players get an equilibrium solution, it is called a Nash equilibrium, which is the most common concept of a non-cooperative game. Finding a Nash equilibrium is a challenging task, especially when the number of players is more than two.
One of the methods that have been proposed to find the Nash equilibrium is the Nikaido-Isoda function.43 Rational reaction set with DOE-RSM44 (design of experiment - response surface method), proposed by Lewis and Mistree, has been widely used by authors to investigate the Nash solution for non-cooperative games. For convenience, this study uses the DOE-RSM method to find the solution to the market model. While closed-form expressions for Nash equilibrium can be obtained in some design problems, numerical techniques are generally required to find the solution.39.
Cooperative game theory in design
A game approach to a retail electricity market
MATERIALS AND METHODS
Market Framework
The disturbing experience of California's 2000 large black-outs, which were the result of market manipulation by suppliers, hindered deregulation in California's electricity market.21 Liberalization of the traditionally regulated electricity markets gave rise to the growth of Independent System Operators (ISO ), which is mainly responsible for scheduling, dispatch of power, reliability and additional services.59 In the proposed Energy Internet market are small suppliers, which are composed of generation and storage units, such as wind turbines, solar power systems, diesel generators and Distributed Energy Storage devices. (DESDs), can communicate and exchange information with other market participants through an Internet-like structure. In this market structure, electricity suppliers become independent from the conventional electricity suppliers.60 This model enables the large integration of renewable resources, which is an essential factor in moving towards a more sustainable design for the future of the electricity market. Since the decisions of all agents in the market will affect their competitors' choice, it is necessary to use a tool that takes into account the strategic interactions between all these players.
Game theory offers a suitable approach to model the interactions between these players.34 The active participation of small distributed producers in the market results in a very complex and dynamic market structure. The degree of complexity and competition in the market play a determining role in selecting a gaming approach that best suits the market structure. In this market structure, the electricity grid no longer has a monopoly on the entire market.
The focus is on the interactions between a large number of suppliers and customers, but the important role of the utility network is evident when a small supplier makes a strategic decision to purchase electricity from the network instead of switching on a diesel generator with high financial and environmental costs. While consumers in many market structures have negligible influence on the market framework, this model allows them to control and manage load demand in response to price fluctuations, leading to cost minimization. Finally, the non-cooperative game between consumers and suppliers is considered in the search for the Nash equilibrium.
The Cournot model is an economic model in which firms compete on the amount of output they will produce. The strategy of any company is static in nature and consists of the amount of output for a homogeneous good. The market price is influenced by the total supply and is fixed for all units.
The electricity cost function is based on the well-known Cournot model, which is widely used to approximate competition on the electricity market.61 In particular, the electricity price is considered to be a function of the total electricity production of all suppliers.
Problem Formulation
Objective functions
The objective function of the ith supplier is defined as the summation of the differences between revenue and cost over 24 hours in an hourly interval. The electricity price is a function of total demand and is characterized in this market by an inverse demand function for each hour, with a negative slope. This price is the intersection of the supply and demand curves and is called the market equilibrium.
The supply curve shows the relationship between the price of electricity and the quantity they can supply. Therefore, as the price increases, the quantity of goods supplied will also increase. Exact values for these coefficients are available for DGs with high power ratings.64 In this research, diesel generators are included in emergency backup generation only.
For electricity consumers, the targeted function is to minimize costs by managing their own load. In this type of energy cell, each player has the ability to manage and control his hourly load demand, subject to a local constraint. As mentioned before, the main role of the supply network in this model is to ensure the critical load.
The limited flexibility of the utility network in this market structure makes it unable to exercise market power. An entity that is unable to exercise market power is known as a price taker66 and in this work, small suppliers are considered price takers, as they have no influence on the final price of electricity. Here, the utility network does not act as an active player; does not have a monopoly on the electricity market.
This characteristic can be considered as the result of purchasing the additional power generation from suppliers.
Constraints
Pwi,min and Pwi,max are respectively the minimum and maximum power output of the wind turbine. Pdgi,min and Pdgi,max are respectively the minimum and maximum power outputs of the diesel generator. In this model we assume that the capacity of the diesel generators for the first and second suppliers is 20 and 30 kw.
Pdesdi,min and Pdesdi,max are respectively the minimum and maximum power output of the storage unit. Due to small and medium capacity of the suppliers in this paper, the amount of power loss is considered negligible. The structure of the market defines the extent to which market participants can influence market prices through their own behavior.
By applying DOE to the game among suppliers, the rational response set of each player can be approximated as a function of the total load demand. Each player solves his own problem for each level of the other players' cargo question. Finding the intersection of the hourly linear equations gives us the Nash equilibrium among consumers.
The second factor that has a significant impact on power generation at different hours is the electricity price at that hour, which is a function of electricity demand on the part of the consumer. The inverse proportionality of the electricity price to the total electricity demand causes consumers to increase their demand for electricity to reduce the electricity price. Therefore, adopting a pricing strategy that accurately reflects the complexity of the electricity market is crucial.
Once the economics of a smart grid with large penetration of small suppliers are resolved, the procedures in this paper can be used to optimize the behavior of market participants. In other words, both consumers and suppliers have no influence on the final price of electricity and can only optimize their objective function according to the imposed prices. Jiang, “A Supply Function Model for Representing Producers' Strategic Bidding in Constrained Electricity Markets,” Int.
RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
FUTURE WORK
MATLAB code
MATLAB code for suppliers
MATLAB code for consumers
