基于博弈论的尼日利亚电力市场改革分析

The Analysis Of Nigeria Electricity Market RestructuringUsing Game TheoryO. I. Nwankwo+, SMIEE, A.U. Chuku*, S.O. E. Ogbogu*, MIEEE and E.N.C. Okafor*, MIEEE+ Federal Polytechnic Nekede, Nigeria* Federal University Of Technology, Owerri, Nigeriaonyinwakwo2003@Abstract- Investments in electricity markets contain high uncertainties about the future. It can also be seen as a game, as only a number of large players act in the market.A dynamic stochastic oligopolistic model to describe the production and investment in such a situation is developed and applied to the Nigerian electricity market. The demand growth rate is modeled as a stochastic variable with a time horizon of ten years. The strategies of firms consist of investment and production levels for base and peak load periods. The firms employ hydro, gas and steam capacities. Using the Sample-Path Adopted Open Loop Information Structure, the model contributes to the understanding of the dynamics of production, investment, and market power in medium time horizon.I.INTRODUCTIONGame Theory is generally used in practice to analyse the problems of conflict among interacting decision makers. In electricity markets, game theory is widely used to analyze the competition among power suppliers, [1], [2] & [3]. Gaming refers to certain scenarios whereby market suppliers take advantage of certain rules and system conditions and intend to deviate from normal bidding, scheduling, and operational patterns in order to increase their profit.The Nash equilibrium method is the universally adopted concept for the solution of games. At Nash equilibrium, a player’s payoff will decrease if the player changes its strategy unilaterally while the other players retain their strategies. That is to say, at Nash equilibrium, each player’s bidding is optimal for the given strategies of other players. The cooperative game theory was used to analyze possible collusions and coalitions among suppliers [1], [3]. The non-cooperative game theory is employed to study the competition among suppliers [4]. Since the beginning of the 1990’s the electric power industry has been going through a fundamental transformation in countries around the world. The industry that was traditionally seen as a natural monopoly is moving from central coordination towards decentralization and competition. The United Kingdom was the first country to set up a competitive power system in 1990 and since then, many others have followed. The Nordic countries have been in the forefront. Finland, Norway and Sweden have a common power exchange and constitute the first multinational electricity market in the world [5], [6], [7], [8] and [9]. The purpose of these market restructurings is to increase economic efficiency. There are both short and long-term objectives for restructuring [10]. In the short-term, the objective is to ensure that energy and transmission prices give correct signals so that the existing production, capacity and transmission network are used efficiently. The long-term objective is to induce efficient capacity investments and promote technical innovation.This paper concentrates on the long-term objective with the assumption that power generation in Nigeria is fully deregulated. This means that the electricity producers are free to determine their investments and outputs in order to maximize their profits. The industry outcome is modeled as equilibrium of such players.II. A DYNAMIC-STOCHASTIC MODEL OFELECTRICITY MARKETIn the short term, firms have to decide their production patterns in order to maximize the profitwith given capacities. On the other hand, firms mustdecide how much to invest in new production capacities in order to maximize profits in the longrun. These investment decisions have to be made under high uncertainties concerning the feature.Also, the firms acknowledge that optimal investmentlevel is conditional on the investments of the otherfirms. The most crucial features of the model are thestrategic behavior of the players (i.e the strategic variables defining the market equilibrium), the information structure adopted and finally incorporating the uncertainty in the model.Event trees are often used to model stochastic events. Fig 1 shows a typical node where two growth levels can occur with their own probabilities. The growth levels are devoted S T and can be high (H) or low (L). The demand parameter A j is affected by the realizationof a particular growth level.978-1-4673-0759-8/11/$26.00©2011 IEEEA j t,B CFig 1. Event trees scenario BC = base case, L = low,H = high.When the model has many periods, these nodes form an event tree. A certain path through the tree correspondsto a scenario of events. The strategies of the players at each node take into account all possible future nodes and the probabilities which they will be faced with.III.THE INFORMATION STRUCTURE: S-ADAPTEDDiscrete time periods are used to model the dynamics of the market. This was unavoidable in this case, since we wanted to solve the model numerically. Continuous time formulation for the type of model we considered would make this infeasible. Discrete periods are also more natural to the study of investment decisions.When a game model has many time periods, the information structure used is important to assess the soundness of the strategies obtained for the players. Usually, three different cases are distinguished in the literature, namely: open-loop, feedback, and closed-loop information structures [11]. In the open-loop structure the strategies are only functions of time and initial state. In the feedback structure the players use Markovian strategies, which are functions of the current state of the system. In the closed-loop structure the strategies are based on all available past information on the state of the system and actions of the players. The closed-loop information structure is desirable in the sense that the actions defined by the strategies are completely adapted to other players decisions during the time horizon.The problem with closed-loop and feedback information structures is that they make the solving of the model generally difficult to solve. In the model formulation we considered in this paper, the solution of the closed-loop is problematic. This is mostly due to the fact that while the state of the system is defined by the investment decisions of the players, the profits given the state of the system are defined only implicitly through Nash equilibrium conditions concerning the short-termoutput variables. Also, the large number of periods and players prevent an easy use of backward induction. In addition, uncertainty was included in the model, which further complicated the problem.The uncertainty was included in the model as a stochastic external variable, which was realized at the beginning of each period (the demand growth). The firms naturally have to make their investment decisions for the next period before the value of this variable is known.An information structure called S-adapted, introduced in[12], suited well to the situation under consideration.This is like open-loop structure, except that the strategies of the players are adapted to the sample path of the stochastic variable (therefore the name S-adapted).In [12], it was shown that the Nash solution corresponding to this information structure can be calculated using stochastic equilibrium programming techniques that are the possible realization of the stochastic variable form of a tree-type of structure.Instead of using the optimization criterion as in stochastic programming, the Nash-Cournot equilibrium computation is performed over the whole sample space so that the players maximize their expected profits.The Nash equilibrium corresponding to S-adapted information structure bears the main properties of the normal open-loop solution. The equilibrium corresponds to the situation where the players have to commit themselves to certain action patterns at the beginning of the game, although in S-adapted case they are adapted to the stochastic variable. It is somewhat problematic to apply the open-loop concept to a situation where the players can adapt their actions to the actions of the others during the game. Namely, even if an open-loop equilibrium strategy of a particular player is optimally given the corresponding open-loop strategies of the other players, it is not credible that the others would stay in their strategies. The problem is that the strategies of the players are optimal given that others’ actions are fixed. If this assumption is relaxed, the equilibra would in general be different [13].Despite the critique given above, one may believe that the S-adapted open-loop solution is still valuable in analyzing the dynamic market under uncertainty. It is, at least in some degree, relevant in the electricity field, where it can be argued that the firms commit themselves to certain investment plans for some time. Moreover, it is more likely that the firms adapt their investment decisions to the external shocks than to the investment decisions of the other firms. In that sense also, the solution concept we used can be a useful representation of the producers’ actions. With no other models available to analyze investmentdynamics under uncertainty in an oligopoly context, this characterization gives a contribution to the analysis.IV. SET OF DATATable 1: Breakdown of Peak & Off Peak Generation(Source PHCN, 2011).S/NLOCATION TYPE OF TURBINE PEAKGEN (MW)OFF-PEAK GEN.(MW)1 KAINJI HYDRO 328 3112 JEBBA HYDRO 345 3403 SHIRORO HYDRO 290 504 EGBIN STEAM 963 8995 TRANS AMADI GAS 25.5 22.86 AES GAS 175.2 162.07 SAPELESTEAM - -8 IBOM POWER GAS 77.3 -9 OKAPIGAS 468 40610 AFAM 1 – 5 GAS - -11 AFAM VI GAS 387 -12 DELTA GAS 90 90 13 GEREGU GAS 280 240 14 OMOKU GAS 27.1 21.715 OMOTOSHO GAS 55.5 55.8 16 OLORUNSOG O PHASE I GAS - - 17 OLORUNSOG O PHASE IIGAS - -TOTAL 3511.6 2598.3Table 2: Capacity (MW) and Investment Cost perMW per station (Type Of Turbine)STATION TYPE OF TURBIN ECAPACITY (MW)INVESTMEN T COST USD,(M)INVESTME NT COST PER MW USD (M)KAINJI HYDRO 328 89.4 0.2726 JEBBA HYDRO 345 92.77 0.2689 SHIRORO HYDRO 290 86.53 0.2984EGBIN STEAM 963 125.10 0.1299 TRANS AMADIGAS 25.5 6.88 0.2700 AES GAS 175.2 26.13 0.150 IBOM RIVERGAS 77.3 15.72 0.2034 OKPAI GAS 468 54.98 0.1175 AFAM GAS 387 56.68 0.1465 GEREGU GAS 280 28.80 0.1029 OMOKU GAS 27.1 6.95 0.2565 OMOTOS HOGAS 55.5 11.77 0.2121 OLORUNSO GOGAS - - -TOTAL 3511.6 601.72Table 3: Total Capacity and (MW) Investment Costsper Type of Technology.Type of Technology No of station s Total Capacity (MW) Total Investment Cost USD (M) AverageInvestment Cost USD (M) HYDRO 3963 268.7 89.57STEAM 1 963 125.10 125.10GAS 9 1585.6 207.91 23.11 TOTAL 13 3511.6 601.71Table 4: Total and Average Investment Cost per MWper type of Technology. Type ofNo of Station Total Investment Cost/MW USD(M) Average investment Cost/MWUSD(M) HYDRO3 0.83990.2799 STEAM 1 0.12990.1299 GAS 9 1.46740.2095V.The Formal Definition of the ModelThe Nigerian electric industry will be represented by many strategic players and a competitive scenario inproduction. At each period, players will choose their investment and quantities to be produced by each production unit and decide to which of the two market-segments they sell their electricity. Time horizon isfinite (10 years). It is divided into five two-year periods. This setting is explained by the following reasons.First, the production strategies need a certaincommitment from players, as they cannot constantly and so easily change their production planning. The time period of two years is approximately the time implementation of new thermal production units. Second, the horizon considered is long enough to let investment take place in new thermal capacity. Putdifferently, a short time horizon may not involve positive investment due to the fact that actual capacities are sufficient to fulfill the demand. In this framework, each player seeks to maximize his discounted stream ofprofits. For simplicity, it is assumed that all players adopted the same market discount rate.As stated above, each player maximizes his expected profit πi. The argument is omitted when no confusion is possible.Subject to the following constraints:The objective function equation 3.7 is simply the discounted sum over all five periods of expected revenues minus total production and investment costs, plus the salvage value. Transmission price was not considered for two reasons. The first is that transmission price is negligible compared to production cost. The second is that in Nigeria transmission network will not be a limitation for trading nor could it become a strategic advantage for one generator. This is so because the policy of the transmission grid is to maintain over capacity on all lines and to take upon itself any congestion problem (by buying out of merit power to compensate for limits imposed by bottlenecks). In such a context, ignoring transmission pricing and constraints is almost not a simplification.VI. CONCLUSIONThis is an ongoing work. The program for the evaluation of above equations is in the developmental stage.The Nigerian electric industry will be represented by many strategic players and a competitive scenario in production. At each period, players will choose their investment and quantities to be produced by each production unit and decide to which of the two market-segments they sell their electricity. Time horizon is finite (10 years). It is divided into five two-year periods.When completed this work enable consumers to avail themselves of energy from the cheapest and most reliable source. Also, this will stimulate investment in the sector.APPENDIXNOTATIONSThe notations are as follows: [money is expressed in Nigerian Naira]1USD = 151 Nairai = 1, …, m player (generator)l = 1,2 production unit of generator i (l = 1 ishydro; l = 2 is thermal)j = 1,2 load period (j = 1 is base load; j = 2,peak load)hj number year for load period j(h1 = 7008, h2 = 1752) (assumed)τ = 1, …,5 periodsτdemand growth at τ (random variable) = (S1, …, Sτ) history of growth level developmentfrom 1 to τCaCapacity addition of player i in type I atperiod τ and(MW)production of i in unit l for load period j atperiod j at period τ and (MWh)ti Ip。