Discuss about the Nash Equiibrium Electricity Market.
Electricity markets in Sweden and Europe have gone through many and major changes, implicating planning for transmission expansion. Eventually, as the first step, electricity markets had been deregulated after restructuring and the expansion decisions of transmission and generation are now not implemented and done by the same entity. With the aim of single market, volume of international and interregional electricity trade has been increasing, secondly. And great amounts of generation of intermittent renewable electricity that is connected to the grid, usually, farer physically, from the location of demand. All these three factors have added much uncertainty as well as complexity and demands the development of new models from the theories, for the planning of transmission expansion, of several Gencos.
An omniscient system operator is able to utilize a set of generation assets, as ewll as the consumption assets. The operator could obtain efficient dispatch of the generation resources and consumption resources, eventually, can obtain short-run outcome that is efficient economically, irrespective of how the industry of the electricity is organized. However, achieving long-term is not easy, as it demands getting the incentives right that includes incentives for investment, cooperation, efficiency, coordination and innovation. Any competitive electricity market demands efficient integration of consumption conditions and individual production with the network’s physical limitations. Result is that all the competitive electricity markets are to be organized around smart market that is centrally coordinated.
In the deregulated power system, independent entities take many decisions, like decisions of on and off, of power plants and Genco expansion planning. When these entities mis-coordinate and move simultaneously, the undesirable result in Nash equilibrium. Eventually, no player would be able to play better, if the player changes the action unilaterally. Nash equilibrium can be calculated, for smaller scale networks, but not an easy task for larger scale network, since exponential growth of the possible outcomes become numerous, by the total strategies.
The operation of small market starts with sending a key supply along with demand information by each market participant, to a market operator or system operator. The dispatch outcome would then be calculated by the system operator, and then be maximize the complete output, delivered from this process. Finally, the system operator communicates back to each of the key information of the market participant, like the output level, they have to consume or produce, to take the decision to start or not and how much or consume or produce. Here the key point is that the actions of one participant can affect the results or outcomes of other participants and it is modeled as an economic game. Nash equilibrium of this game is the key to deal and resolve the issue. Nash equilibrium is a set of action, influenced by the decisions of the participants. In the mechanism of the economic market, where reporting of information is done by each of the market participant, to the system operator, Nash equilibrium would possess a property that no player would get any incentive to change the reported information to the system operator, given by any other player.
The mechanism of the market can be assumed to be support optimal dispatch, in only cases, such as,
The problem associated with the project is the modeling of Nash Equilibrium for Generation expansion planning of several Gencos, present in Sweden, as a two or bi-level problem, strategic generation investment at higher level and capacity bidding strategy at lower level.
The major aim and objective of the project is to develop a methodology to assess the current general transmission and development of a model for general transmission planning in a complex and competitive electricity market of Sweden.
Ethics of electricity marketing is an area of applied ethics which deals with the principles of moral which is behind the operation and regulation of marketing. In the electricity industry, the ethics are very important because the house would likely be the largest single investment for consumers. These ethics defines the internal control, reaffirms the values and principles that the electric power supply industry’s companies must follow in doing their business activities. The rules which are well constructed, consistent and clear are also required. The strongest commitment to the ethical standards will not result in the market without the good rules. It is useful for the consumers to provide the maximum benefits. Each electric power supply company will take these reaffirms, like its excellence, its commitment, unwavering ethical conduct and professionalism. The essence of the ethical conduct is to conduct the business activity, with integrity. Here, conducting the business activities are principled in an upright manner, which is called as Integrity.
The electrical power suppliers have the following ethical standards as follows (Casazza, 2003):
Electricity Market
Electricity is basically considered as a commodity, in economic terms, treating it as a product, used on day to day basis. So, it is also considered as a commodity that can be sold, bought and traded, electronically. This trading is usually done as financial swaps. The price of electricity at that moment is set as a regular supply and demand principle. When this is the shorter term trade, longer term trade is also done through contracting, through power purchase agreements.
Nature
Electricity cannot be stored, to supply on the basis of varied demand. Hence, it should be supplied instantly and according to demand. Therefore, electricity demands physical requirements of units for coordination of dispatch of generation, transmission system operator to meet the demand expected, across the huge and long transmission grid. When the mismatch occurs in between the supply and demand, the speed of the generator fluctuates, slows down or speeds up, resulting in the fluctuation or increase or decrease of frequency. Consequently, the system operator has to remove or add either load or generation, in case the frequency falls over a predetermined range. Eventually, the electricity lost proportion in transmission and the congestion level over any specific network branch, will influence the generation units economic dispatch.
The principle challenges in the electricity marketing are the definition and management of the usage of transmission.
Figure: Transmission Capacity (Hogan, W., 2008, Electricity Market Design: Coordination, Pricing and Incentives, Austin)
Contract Path
It is the path, which designated to form a single electrical path that is continuous, on agreement in between the parties. Actual power flow flows hardly follow this control path, because of the physics laws. Contracting or flow based pricing would account for the flow of actual power over the transmission system. In this context, ‘unscheduled flows, occurring under regime of contract path would be taken into account.
Importance
Interactions of electric transmission network are important and large. The capacity of network interface transfer depends over the load conditions that are assumed. Capacity of transfer would not be guaranteed or defined over any of the reasonable horizon. So, capacity of the power transfer varies, on the basis of load.
Figure: Power transfer capacity varying with load
Capacity, basically, represents resources commitment to deliver, when the need arises, especially, during the emergency of grid. For example, parking space of a shopping mall, this is filled usually, during the peak business time. These spaces are used year round, but needed only during busy period. The same capacity, when it is related to the electricity, it is defined as an adequate resource over the grid, towards fulfilling the demand for electricity. Therefore, the electricity supplier or utility supplier has to meet the demands of the customer, as well as manage the reserves. Suppliers would be able to meet such requirements, from their own generation capacity and with their purchase capacity, from other contracts, as a response to the demand response.
Elements
Capacity markets have essentially three elements.
Working
Capacity bidding is done into the auction, at its operation total cost. As the depreciation of power plants in under course, the capacity bid would be very low sometimes, if the plant continues to be for a longer period of time. Therefore, capital investments would be paid off in the plant and the total operation cost would be fuel and salaries of employees. Initially, total cost of the new plants would he higher, as capital costs are present, including the operational costs.
Fundamentally, Nash Equilibrium is a game theory, in a non-cooperative game that involves more than one player and each of the player plays with the assumption to know the strategies of equilibrium, of the fellow players and no player can gain anything, through attempting to change only the strategy of him or her only. In case a player chooses a strategy and it benefits no player, through strategy changes, when the strategies of other players are unchanged, Nash Equilibrium will be constituted, by the current strategy choices set and the payoffs correspondingly.
So, the definition of Nash Equilibrium as a vector, would be done, among the players, who are non-cooperative, if and only if,
Where, v*1, v*2, …. v*z, ……. v*card(z), are the vectors
Network
Figure: Sample Transmission Network Graph
The primary application of the Nash Equilibrium is to determine the flow of traffic to the expectations, in a specified network. Let us assume that there is one channel to flow the electricity from the transmission grid from P to S.
Then the expected traffic distribution in the network can be calculated as the following.
Let us assume that the situation is modeled as a game, in which the electricity flow has total 3 choices of strategies to flow from P to S,
So, the calculation of payoff correcpsonding to each strategy varies, based on on the other electricity paths’ choice.
Since Nash Equilibrium is a mixed strategy game, the concept of stability in the electricity marketing can be applied. So, when a small change is occurred in probabilities for a single player, it would lead to certain situation, in which it holds conditions,
The result will be a three-fold, based on mix of the above two conditions.
Generation investment is a key issue and concern and at the same time opportunity for optimal general investment. It stands as a key to choose the right type, amount of time, all at the right time. Having assumed that there are different types of generation available in each of the location in Singapore, in this context, the problem of optimal generation investment lies as a question to choose the optimal capacity for different generation types, in different locations.
The challenge in the generation investment is also in taking the decision, for longer term. The generator capacity is assumed to get fixed during the short-run. So, a model is needed towards marking distinction, in between long run and short run.
The sponsor or owner of the project tends to take the decentralized generation investment decisions, based on certain factors and assumptions as the following.
These factors are well taken into consideration, when there are considerably, a great number of generation entrepreneurs, investing independently. It also helps to set control over the effect over the market price. Eventually, the scale of generation of electricity can be set according to the demand and consumption by the consumer, while the market price is well in control. The overall generation investment profitability depends on the price-duration curve area that lies over the variable cost, as shown in the below figure.
Figure: Profitability curve for generation investment
The same factors mentioned above are considered for both the optimal mix of generation and optimal level of capacity of the generation. Eventually, decentralized investment decisions can result in generation investment optimal levels and generation investment optimal mix.
So, decentralization of the generation investment can be concluded that the capacity’s equilibrium level is optimal, when chosen for each generator type, in a free-entry-and-exit equilibrium, when there is great level of competition, in between the generators and under certain assumptions. This result suggests that an efficient and great levels of generation investment is yielded by the decentralized competitive markets, under certain and fairly restrictive conditions.
However, generation investment is complex, tedious process, since it needs considerations in multiple dimensions. Generation investment is very lumpy. Decision of building a huge generator would eventually have the impact over the prices. The substantial sunk costs involved in the generation investment are another challenge to consider and overcome. The previous conditions may not hold always with likely episodes of under capacity, over-capacity and high prices periodic bouts.
However, till date experience from the liberalized markets, do not signal that electricity markets would fail systematically, in practice, towards delivery of the needed investment. (Ellis and Heneghan, 2015).
When there are no network constraints, resources of generation and consumption can be used efficienctly. Though principle shows that such efficient outcome can possibly achived in a electricity company that is vertically integrated, however, the statistics and experience indicate that the effective incentives establishment, in the entities that are large vertically integrated, especially, when these businesses are owned by the government. Reforms have been made with the primary objective, in the late twentieth century to introduce the competition, into the electricity industry segments, wherever feasible.
Efficient generation and consumption resources use can be achived through a mechanism called competitive market. Such market mechanism enables decentralization of decisions of production and consumption to the participants of competing market, strengthening significantly, incentives for efficiency of production, customer responsiveness and innovation.
When there are network constraints, certain issues are anticipated and then centralized market mechanism would be anticipated with a system operator. Supply and demand information is communicated by the market participants, to the market operators. The job of market operator is optimal dispatch computation and then share and communicates the information of price and dispatch, back to the participants in the market. Here participants act as price takers and they submit the true information about the supply and demand, resulting in efficient market process.
Two-stage market is operated by many countries, making the settlements to occur at both real-time price and day-ahead price. When the day-ahed price is operated, it is quite similar to the market of short-term forward. Though better price forecasts can be resulted from the centralized day-ahead market, it is only theoretical.
Game theory and electricity market applications show that strategic bidding technique is used by the generators that leads to long term goals achievement, though it is time consuming. In this context, the idea of Nash is considered and implemented by the generators. Market can be successful, when the three ways related to the strategic bidding. (Wang and Lo, 2016), (Osborne, 2002)
The bidding behavior would then be analyzed by the market, of the firms of marketing. Therefore, bidding behavior defines the marketing power. So, when the electricity power marketing is considered in real time, it is not possible to achieve the long term strategies, because of Lack of knowledge of Nash technology or wrong information shared.
When a game consists of Nash equilibrium that is unique and when the game is played among multiple players, under specified conditions, then the set of Nash Equilibrium would be adopted. There is another set of Nash Equilibrium to adopt, when there are conditions not met and differently for the conditions that are met.
The resulting Nash equilibrium from competitive and complex Gencos, has to be solved through modeling of Nash equilibrium for generation expansion planning of several Gencos, in two levels, strategic generation investment performed at higher level and capacity bidding strategy performed at lower level.
Generating units have variable costs. Generating units is assumed to invest, to the best capacity, having variable investment cost, when generation investment is considered. Social cost is an important factor that determines the level of Nash Equilibrium, either best or worst.
Let us consider that the generating companies have set of units and each unit has a set of portfolios. Generating units have both strategic and non-strategic units. Strategic units may get withheld, partial output for gaining more profit. Non-strategic units offer full output at marginal cost to the market. Generating companies that have at least one strategic generating unit, is considered for modeling of Nash equilibrium, in this context. The strategic generating unit has certain volume of capacity, offering to the market.
Transmission in Swedish or in any modern markets would not be optimized, when isolated, since transmission is considered to be substitute as well as complement for generation. The problem of coordination is the key point of discussion in the project (Sebastiá, T. and Contreras, 2004).
The problem is a two-level optimization problem. When considered at the lowest level, the decisions of strategic investment for generators are modeled as game with simultaneous move. This game can have solution with multiple Nash equilibrium. In this context, Nash equilibrium is perceived as in game theory, for describing an equilibrium, in which the strategy of each player would be optimal, given, the other players’ strategy. The transmission planner behavior can be modeled by the upper models and the entire model is considered to be the game of leader follower. Here, the transmission planner act as leaders initiating the first step and certain upgrade commitment as well as expansion options. Generators that are competing and independent react to the specified options.
The simultaneous-move game can have the solution, as the solution would be the input to the game of leader-follower. Eventually, the decision of committing would be taken by the generator, to a certain option and it is done according to the simultaneous-move game outcome. The fact of multiple equilibrium is solved through finding the worst Nash equilibrium, which is considered as the electricity market equilibrium, for the transmission investment purpose, having highest cost, incurring to the society.
There are market simulators that can replicate the actual electricity market behavior. These tools can be used by the regulators, in order to detect the market power, after monitoring. They help refining the bids, by the sellers and buyers. Market power is fluctuated by several factors, such as bidding behavior, numerous market players and the imposed restriction. So, the design of the simulator must be good enough and should contain the existing rules of the existing market.
Modeling electricity market that is pool-based would be a complex task, because of the transmission network modeling, non-differentiable and non-convex bid functions nature, need for integer variables and varied time spans, to name a few (Marwali & Shahidehpour, 1999). The current and existing market models offer qualitative and valuable insight, however, lack in all or some of the potential features (Day, et al., 2002.0.
With the new methodology and modeling, Nash equilibrium can be applied to electricity market Cournot models, having constraints of network, however, may lack nonlinear losses. This model is a full ac model, in which Nash bargaining game is developed for transmission analysis, in which analysis of two-area system power exchanges is done.
Another game theory method that can be applied for obtaining equilibrium, like Stackelberg leader-follower model or supply function equilibrium model
Generating Companies Model
Genco behaves as either price-take or price-maker, based on its generating mix and relative size. The price maker profit is expressed by the objective function. Then the total revenue would then linearly expressed, through binary variables and positive real variables. Every unit has working scope within the operating region that is feasible, over the horizon of whole planning, and the same is enforced by set of constraints. Constraints as a set expresses price-maker quota hourly, as the unit’s power production sum.
Power balance is defined at every node, as the difference between the power that reaches a specific node and the power that leaves the same node, should be zero. It considers the power injected from the participants other than Genco in the node and from the Genco. The quota or capacity of a price-maker is considered as total power, for serving the demand in an hour.
Eventually, for all the Gencos, the bidding strategy for any specific hour is,
1.Only power blocks, having values of optimal self-scheduling, differing from zero would be provided at corresponding costs of margi
2.The rest of the blocks would then be offered at infinity price.
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