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This paper presents a three-level oligopoly power producer’s capacity investment game model, whose first level considers optimal regulation policy, and second-level models producer’s capacity investment strategy based on the analysis of power producer’s equilibrium biding strategy with capacity and price cap constraints at third level. We solve the model with backward induction and simulate the symmetric case. Precisely, we examine the effect of the number of oligopoly power producers, price cap, and contracts for differences (CFDs) on the unit load and power sale price and explore the optimal investment policy based on the maximization of discounted social welfare. For the proportion of power in CFDs being very big and power supply being relatively nervous in Chinese power market, we discuss the effect of power capacity investment subsidies and CFDs power price on power supply and demand, whose results indicate that reducing the proportion of CFDs’ power in the power producer’s access grid power is an effective way to alleviate the tension in power supply and demand, and the current renewable energy policy can neither necessarily ease the tension condition of power supply nor can it necessarily promote the construction of renewable power generation units.

Before market-oriented reforms of the Chinese electric power industry, two types of power pricing policy, repaying capital with interests pricing and operation period pricing, were implemented in turn. Therefore, there was no risk of power capacity investment for investor, and the investment strategy was ignored. But in a mature power market, power capacity investment is a market behavior regulated by government, and power producer faces lots of uncertain factors such as market demand and relevant policy; how to avoid the risk is important for investors [

Murphy and Smeers [

Grenadier [

The available literature of option game has shown that there is no general method to solve the model when three or more than three compete investment, and analytical solution is almost impossible (Bouis et al.) [

Dangl (1999) [

This paper is structured as follows. Section

Generally, power demand function is difficult to be truly described because power demand is influenced by many factors, but the empirical analysis of Pindyck [

We assume that the cost function of power producers is a quadratic function of power quantity; there is

Supposings that the range ability of power producer

In China, power sale price includes average access grid price, transmission cost, and reasonable profit ignoring taxes. And access grid power can be divided into two kinds including competitive power and uncompetitive power. In this paper, competitive power is assumed to be determined by (

In the lower carbon economic environment, Chinese regulator forcibly sets a certain proportion of renewable energy in power producer’s access grid power, and we set this proportion as

Solving (

Iterating (

Substituting this equation into (

Obviously, oligopoly power producer’s power quantity should satisfy

In market equilibrium, we can get an equation as follows from (

If given price cap

Apparently, power producer’s equilibrium power quantity function and competitive equilibrium price function are piecewise function with

With classical real option theory, power producer

The result of this differential equation is

Obviously, substituting (

Substitute (

Applying (

To solve the above equation, there is

Combining (

For regulation institute, the purpose of regulating power capacity investment includes two aspects, one is to assure power system’s safe operation and adequate power supply and the other one is to accomplish economic operation of power unit; that is, the vacancy rate of capacity is at a low level and the power price can be accepted by consumers. With (

From economic theory, the total society welfare is the sum of consumer surplus and the profit from all the power producers, while grid companies should be nonprofitable in mature power market, so we did not consider grid companies’ profit; then there is

Therefore, the aim of regulation institute can be simply described by

Obviously, (

In symmetrical oligopolistic power capacity investment market, all the power producers’ cost parameters are the same, so we substitute (

When

When

When

Substituting (

It is quite clear that the analytic solution of investment threshold

If given

Investment value curve when

We can see several phenomena from Figure

The effect of oligopoly power producer’s price cap

Investment threshold and optimal capacity. Parameters:

Power producer’s investment threshold and capacity curve are shown in Figure

Investment threshold and optimal capacity. Parameters:

Simplifying (

Substituting parameters in Figures

Discounted society welfare curve.

We can clearly see that the total society welfare is increasing with increasing price cap and increasing number of power producers but decreasing with increasing rate of CFDs. So regulation organizations should choose higher price cap, larger number of power producer, and lower rate of CFDs to maximize the total society welfare under the constraint of unit load and sale power price.

Figure

Power unit load and sale power price corresponding to Figure

From Figure

Power unit load and sale power price corresponding to Figure

The above analysis results show that if given the ceiling and floor of unit load and weighting access grid power price exogenously, we can get the optimal price cap, the number of power producers, the contract power’s rate, and price by (

Chinese power industry has been in market reforming for 30 years, while the original administrative monopoly has been broken. Some part of power industry has been brought in market mechanism, especially the experiment exercised in northeast power market of China from 2004 to 2005, although it did not realize the expected aim, it basically built the fundamental framework of Chinese competitive power market. At present, the real condition of Chinese power market is that generally power supply is nervous, and most of power is traded at the price set by government regulation institutes, but little is traded through market regulation and do not form a market clearing mechanism. The problem about power capacity in China is complicated; simply, we will discuss two aspects: one is the reason of nervous power supply and relevant suggestion, and the other one is the impact of renewable energy policy on power capacity investment.

The above oligopoly power producer’s investment model and analysis framework can be used to examine Chinese oligopoly power producer’s investment strategy and market behavior. We can regard the access grid power price set by government regulators as CFDs and its price as CFDs’ power price

The results of above model analysis are consistent with present power supply condition in China. For efficient power supply being directly related to national economic development and people’s daily lives, government regulators generally propose inspiring policy to encourage power producer to increase capacity investment to mitigate nervous power supply. Based on the above power capacity investment model, there are simple and direct inspiring policies that give power producer subsidy of capacity investment or increasing the price of CFDs, and Figure

Power producer’s investment strategy and its market behavior. Parameters:

It is easy to see in the figure that increasing CFDs’ power price or reducing the rate of CFDs can delay investment timing of power producers to a certain extent, but once they invest they will increase capacity investment and reduce unit load to a certain degree, while further analysis indicates that decreasing unit load caused by increasing CFDs’ power price is for the reason that increasing sale price restrains power demand. And reducing the rate of CFDs can increase unit capacity through power market competition, reduce unit load and sale price and increase total society welfare, so this is more effective in alleviating nervous power supply than increasing CFDs’ power price. What is more, if regulation institutes subsidize capacity investment directly, it can reduce investment threshold and bring more capacity investment, but it may reduce unit load only when subsidy reaches a certain degree; that is, small subsidy cannot improve power supply condition, and the effect of this direct subsidy on sale price is not obvious and depends on other factors. From the above, if reducing the rate of CFDs such as 0.85

Furthermore, we would like to consider the effect of regulators’ subsidy to power capacity investment on power producer’s actual investment. As shown in Figure

The effect of policy subsidy on net investment of producer.

Therefore, reducing rate of CFDs is a simpler and more efficient way to alleviate nervous power supply in China comparing to increase CFDs price and subsidy capacity investment directly; that is, reducing rate of CFDs can increase competitive to encourage power producers to increase unit capacity, reduce unit load to supply power adequately, and reduce sale price to enhance society welfare and make better use of limit power resources.

Nowadays, Chinese renewable energy policies in power generation mainly are investing and tax policies supporting wind power generation and photovoltaic power, and compelling policy for nonrenewable energy power companies such as coal-fired plant to set a certain proportion of renewable energy power in access grid power. In the short term, nonrenewable energy power companies can only buy renewable energy “index” from renewable energy power companies to satisfy the rule, which is expressed by

Figure

The effect of renewable energy policies on investment strategy. Parameters:

Power industry is a basic industry, and adequate power supply is significant for national economic development and people’s everyday lives. In power market environment, power producers face great risk in investing power capacity, so regulation institute needs to consider this and establish optimal investment policy to promote efficient power supply. To discuss oligopoly power producer’s investment strategy and relevant investment policy, this paper presents a three-layer investment game model, which begins with relevant policy setup by regulation institutions, then considers oligopoly power producer’s investment strategy, and analyzes power producer’s biding strategy with capacity and price cap constraint. Based on the backward induction thought in dynamic game theory, we solve and simulate the model in symmetric case and examine the effect of oligopoly power producer’s number, price cap, the proportion of contracts for differences (CFDs) and CFDs’ power price on the unit load, and power sale price, and we try to find the optimal investment policy based on the maximization of discounted social welfare.

For the proportion of power in CFDs in Chinese power market being very big and power supply being relatively nervous, we discuss the effect of power capacity investment subsidies and CFDs power price on power supply and demand. The results indicate that reducing the proportion of CFDs’ power in the power producer’s access grid power is an effective way to alleviate the tension in power supply and demand, and the current renewable energy policy can neither necessarily ease the tension condition of power supply nor can it necessarily promote the construction of renewable power generation units.

Combined with actual condition of power capacity investment, the above model expands Dangl (2009) [

This work was supported by National Nature Science Foundation of China under 71271033 and 70971012, Education Department Talent Support of New Century under NCET-11-0978, and Scientific Research Fund of Hunan Provincial Education Department under Grant 13K057.