JP2004252967A - Power transaction risk management system and power transaction risk management method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a power transaction risk management system which measures the market risk accompanied with power transactions and maximizes earnings while keeping the risk smaller than an allowable value. <P>SOLUTION: The power transaction management system is provided with; a means 102 which evaluates and inputs a predicted value 100B of power demand, a power price 100C in a spot market, and the cost function, fuel price, fixed expenses, etc. 100A of a generator for use; a means 104 which models a future random variation of the power price from the past variation of the power price; a means 105 which calculates earnings or the like resulting from power dealings; a means 106 which evaluates the risk resulting from the random variation of the power price; a means 109 which constructs a proper power portfolio; a means 111 which re-evaluates the value of the portfolio everyday; a means 108 which rearranges the portfolio in order to reduce the risk; and a means 114 which determines the price of a derivative for a risk hedge. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

  The present invention relates to a power trading risk management system that manages risks in power trading.

  Since March 2000, retail trade has been liberalized for large customers (20,000 V, 2000 kW or more). This partial liberalization is supposed to be reviewed at the prospect of three years, is expected to liberalization is greatly expanded from around 2004. When power trading is liberalized in this way, power prices fluctuate in market conditions, and there is a possibility (risk) that profits and costs fluctuate in generators, power traders, and consumers. This is similar to the situation where stock prices fluctuate in the current stock market. In response, the financial and securities industries have developed methods for hedging (reducing or eliminating) price fluctuation risks using financial engineering. This financial engineering technique is also considered effective for hedging the risk of electricity prices.

  Financial engineering makes the assumption that future prices will fluctuate quite randomly. That is, it is assumed that the future price cannot be predicted at all except for the drift term corresponding to the interest rate. However, in the case of electric power prices, the degree of influence on supply and demand is greater than that of stocks and the like. In addition, since demand generally decreases at midnight or on weekends, fluctuations in the electricity price are observed on a daily or weekly cycle. In addition, demand fluctuates greatly depending on the weather, and consequently prices tend to fluctuate according to the weather. For this reason, seasonal variations with a cycle of one year are also observed. Since such fluctuations are predicted to some extent, the assumption that the future price cannot be predicted at all, as in the case of stocks, does not always hold. In addition, when the supply-demand relationship becomes tight, the price may rise sharply and show a spike-like price fluctuation. This relationship between demand and price is a concept not found in conventional financial engineering. In addition, electric power products are characterized in that they are difficult or expensive to store, and that a power transmission system must be used to deliver the products. For this reason, the relationship between supply and demand is defined by the electrical law. For the above reasons, fluctuations in electricity prices appear to be slightly different from fluctuations in stocks.

To manage the risks in electricity trading, it is necessary to numerically evaluate the amount of risk, but to do so, it is necessary to model future fluctuations in electricity prices. In such a case, financial engineering often uses a geometric Brownian motion model. Here, the prior art will be described using an example of stocks. In financial engineering, a small change in stock price dS

Describe as follows. Here, S is a stock price, μ is a drift rate (trend term), t is time, σ is volatility, and z is a variable that follows the Wiener process.

Volatility is the uncertainty of future price fluctuations, and is used in financial engineering to indicate the magnitude of market price fluctuation risk. This is equivalent to the annualized standard deviation, and is defined by the following formula.

Here, S _i is the stock price (power price in the case of electric power) at time i, and u _i is the continuous compound interest (or profit rate) from time i-1 to time i. If the price is the value of every other day, u _i is the daily rate of return. Further, if the unit of τ is year, σ is the volatility of the annual rate and is an index for the magnitude of price fluctuation.

On the other hand, the Wiener process is one of the Markov stochastic processes, and is used to represent the motion of fine particles called Brownian motion in the physics world.

There is a relationship. Here, ε is a random sampling from a standard normal distribution (mean 0, standard deviation 1). However, dz is independent for different minute times dt.

  The Wiener process (Brownian motion) including a drift term and having a coefficient of dz other than 1 as in Equation 1 is called a generalized Wiener process (Ito process). Equation 1 means that the logarithm of the stock price makes Brownian motion, and such a stochastic process is called geometric Brownian motion. That is, Equation 1 approximates the change in the logarithm of the stock price as the sum of a trend term and a normally distributed random change term. This reflects investors' interest in return, not absolute value. When assessing the risk of a stock asset, usually, a price fluctuation is modeled using this geometric Brownian motion model, and the risk is evaluated (measured) according to the obtained price distribution.

  On the other hand, in the case of electric power prices, there is a problem that the price distribution cannot be accurately reproduced by the geometric Brownian motion. In the following, the problems of the prior art will be described by taking, as examples of power prices, market data of the California Power Exchange (CalPXia Power Exchange) and the Leipzig Power Exchange (LPX) in Germany. . In addition, these electric power price data used what was published on the Internet (www.ucei.berkeley.edu/ucei).

  FIG. 1A and FIG. 1B show the power prices of the day before market of the California Electric Power Exchange (CalPX) in 1999 and 2000 as a daily average value. FIG. 1C shows the daily electricity prices of the Leipzig Electricity Exchange (LPX) in 2001. FIG. 1D shows the transition of the closing price of the company A stock price in 2001 shown for reference.

  The first thing we can see from these is that price or daily rate of return fluctuations are much greater than for stocks. The volatility is 55% for Company A, 343% for CalPX in 1999, 456% in 2000, and 588% for LPX in 2001. Therefore, in each case, it can be seen that the volatility of the electricity price is about one digit greater than that of the stock.

  Since the prices of many financial derivatives are sensitive to volatility values, there has been a problem that it is difficult to hedge risks in electric power transactions using conventional financial engineering techniques. For example, it has been pointed out that the option price becomes too large (Yoshi Murakami, et al., Japan Society for Financial and Securities Metrology, Proceedings of the 2002 Summer Conference, 2002).

  Second, there is a phenomenon that the distribution of the rate of return deviates greatly from the normal distribution. FIG. 2A and FIG. 2B show distributions of the daily average rate of return of the electricity price of CalPX and the daily rate of return of the shares of Company A. Although the dotted line in the figure indicates the normal distribution, it can be seen that the tail portion is larger than the normal distribution in the probability distribution of the profit rate of CalPX in FIG. 2A. This phenomenon is called fat tail and is often observed in energy-related products. This is also observed in stocks, but this trend tends to be more pronounced in electricity prices.

Deviation from the normal distribution is expressed by statistic called skewness a ₃ and kurtosis a _4. These are defined by the following equations.

Here, x bar is an average of the data x _i, N is the number of data, the sigma _x is the standard deviation of the data. The kurtosis is 3 in the case of the normal distribution, and increases as the distribution becomes sharper. The skewness is 0 when symmetric.

In the case of the CalPX power price, the skewness a ₃ = 0.26 and the kurtosis a ₄ = 6.2. In other words, it can be seen that the distribution is almost symmetrical but sharper than the normal distribution. In the case of the stock price of Company A in FIG. 2B, the skewness a ₃ = 0.2 and the kurtosis a ₄ = 3.3, which indicate that the distribution is almost close to a normal distribution. Conventional financial engineering models usually assume a normal distribution as the distribution of the rate of return. For this reason, there has been a problem that the conventional financial engineering technique cannot be used for electricity trading as it is.

One of the methods for numerically evaluating the market price fluctuation risk is an amount called Value at Risk (VaR). FIG. 3 is a diagram showing a loss amount when the value of the power asset falls to _XL1 or less at a certain probability, assuming that the value of the power asset fluctuates according to the normal distribution of the average μ and the standard deviation σ. This loss amount is a risk amount generally called VaR. Here, the power asset is the product of the power price and the power amount, and can be similarly defined in the case of multiple assets. Also, assets of different types can be defined by converting them into monetary amounts. In the case of multiple assets, if the assets have a correlation, the standard deviation of the distribution of all the assets is calculated using the correlation coefficient. 3, for example, assets 1% chance When drops X _L1, a normal distribution corresponding to the mu-X _L1 is 2.33 × sigma. As the standard deviation σ, the standard deviation of the probability distribution in the future of the period under consideration (for example, one month) is used. Since this value is proportional to the square root of time when assuming geometric Brownian motion,

Is calculated. In the case of FIG. 3, it is expressed as “VaR for one month is (μ−XL ₁ ) circle with 99% reliability”. The magnitude of the risk is evaluated based on the magnitude of this value.

Similar definitions are possible when the distribution is not a normal distribution. FIG. 4 shows an example in which the value of an asset changes according to a probability distribution having a fat tail. In this case, when the cumulative probability (area ratio of X _L2 following parts of the probability distribution function) is to X _L2 seeking a point corresponding to 1%, because it is X _L2 <X _L1, the same 99% confidence level On the other hand, the loss amount, that is, VaR becomes large. That is, in a distribution having a fat tail, when a VaR is evaluated assuming a normal distribution, the distribution is underestimated. For this reason, it is important for risk assessment to determine the probability distribution of future prices as accurately as possible. However, there is a problem that it is difficult to evaluate this probability distribution by the conventional method.

  Further, in practice, errors in the amount of loss also become a problem. 5A and 5B show the difference between the actual profit and the evaluation based on VaR. This is called a backtest. In this case, the daily profit and loss (difference between the current day price and the previous day price) calculated for the CalPX power price in 1999 and the value of VaR calculated assuming a normal distribution are displayed. FIG. 5B is an enlarged view of a part of FIG. 5A. In the figure, the value shown by the bar graph is the daily profit and loss per MWh. The value shown by the dotted line in the figure is VaR after 1 day per 1 MWh based on 95% reliability. The volatility was calculated based on data for the past two weeks (14 days) from the time of evaluation.

  From these figures, the frequency of occurrence of loss exceeding the value of VaR is about 1/20 (5%). However, it can be seen that the amount in the event of a loss can be quite large. Therefore, in the conventional method, the frequency of occurrence of loss can be correctly evaluated, but the amount of loss is underestimated.

  In addition to the above problems, in the case of electricity prices, it is necessary to consider the relationship between demand and the weather, and there is also a problem that risk management is much more complicated than for stocks.

  Further liberalization of electricity trading will dramatically change the business strategies of power producers. That is, before liberalization, the main uncertainties were fluctuations in power demand and unscheduled generator shutdowns. (Fuel prices were basically passed on to selling prices). Therefore, the purpose of risk management was to predict demand and minimize power generation costs. On the other hand, after liberalization, risk factors due to fluctuations in electricity prices are the main factors. However, this risk is basically an advantage for power producers if properly managed as described below. That is, liberalization allows a power producer to select "no power generation". This does not mean abandoning the supply obligation, but rather the option of stopping the generator and procuring it from the market and selling it. In this case, it is important how much power is generated and how much is procured. Hereinafter, a simple example will be described.

Before liberalization, assuming that the power generation cost per unit power is C, the fixed power price per unit power is P, and the demand is L, the profit per unit power of the power producer is

Becomes

On the other hand, income from power generation after liberalization, it is assumed to be sufficiently fluid spot market is present in order to discuss the ideal case, ignoring the technical constraints of the generator, at the maximum power Q _MAX below Assuming that power can be freely generated, the power generation cost per unit power is C, the fixed power price per unit power is P, the demand is L (L ≦ Q _MAX ), the power generation is Q (Q ≦ Q _MAX ), Assuming that the procured amount from the market is B (the amount sold to the market if negative) and the spot price per unit of power is S, the following is obtained.
[Equation 7]
If S ≦ C,
Power generation Q = 0
Procurement amount B = L
Profit G = L (PS) ≧ G ₀
[Equation 8]
If S> C,
Power generation Q = Q _MAX
Procurement amount B =-(Q _MAX -L)
Profit G = L (P-C) + (Q MAX -L) (S-C)> G 0
It is. In other words, if the spot price is lower than the power generation cost, power generation can be stopped and the entire amount can be procured from the market. can get. In each case, it can be seen that profits increase from before liberalization. In practice, it is necessary to find B that maximizes profit while satisfying technical constraints. If there is a cost C 'even without power generation, the condition of procurement from the market is S≤CC'.

Furthermore, in the future, if emissions trading of CO ₂ gas, etc. is conducted, the thermal power plant must have the emission right, so if the power generation is stopped and the power is procured from the market, the emission right will be The sale could be even more profitable.

  It is clear that there is an optimal combination of these even when considering a single power plant and spot market as described above. When a large number of generators are used, the power generation cost of each generator is different, so that the method of determining the optimum combination is further complicated.

  Even current power generation companies have many power plants with different power generation costs, so they determine the optimal combination of power plants for demand determined by external factors. However, when electricity trading is liberalized, the electric power price fluctuates with time and the price differs for each demand, so the means of optimally combining power plants and demands naturally changes. For this purpose, the concept of portfolio used in the financial securities field can be applied. This is an approach that optimally combines assets with different risks (temporal fluctuations in price) and different returns. For example, risk can be reduced by combining different types of assets. In the simple portfolio optimization problem, the holding period is not considered so much, but in the case of power assets, there is a concept of a period for transmitting power and a period for receiving power. Therefore, a method of optimizing a portfolio in consideration of time is required.

  Even today, there are many types of electricity prices depending on the terms of the contract. When power trading is liberalized, power companies will have many types of power assets with different prices and holding periods in order to increase the degree of freedom in setting prices. If power generation costs were assumed to be constant, these would be assets with different rates of return and maturities. Derivatives such as futures and options are expected to appear in the future. The means to properly manage these has not yet been established overseas in advanced liberalized countries.

  One of the portfolio management methods considering the holding period is ALM (Asset and Liability Management: comprehensive management of assets and liabilities). In a financial institution, if there is a mismatch between short-term funds and long-term funds in investment and procurement, profitability will deteriorate due to interest rate differences and other factors. To prevent this, a number of techniques have been developed for comprehensive control of assets and liabilities.

  The history of ALM began as early as the early 1980s, and at first, a maturity ladder analysis (understanding the effects of falling interest rates by interest rate stratum), a gap analysis of maturity, and a sensitivity analysis were carried out. The importance of risk management has been recognized, and it has been developed into duration analysis, VaR (Value at Risk), EaR (Earnings at Risk), and the like. Recently, it has been applied to credit risk management. In ordinary ALM, interest rate changes are mainly considered, but this method can also be applied to risk management in power trading. However, the ALM method as described above has not been used for power asset management except for a part of VaR or the like.

  Therefore, we consider power procured from power plants and markets to be a financial asset with a fixed maturity and dividend period, and consider the demand for power in various contract forms by considering the amount of contract power, contract period, contract conditions, etc. Consider the method of treating financial liabilities as having a fixed dividend period and managing them as a portfolio that considers the maturity and dividend period.

In the case where power generation facilities that supply power are managed according to the magnitude of the risk and a portfolio is formed with the power demand, the optimal combination method of the generators (economic allocation) also differs. Conventionally, in order to determine the generator to be started, a combination that minimizes the power generation cost has been selected. (Ignore startup and shutdown costs for simplicity). This is equivalent to determining a generator output combination that minimizes fuel cost for a given demand. For example, the generator has two power generation amount required is P _0, optimal generated power is P ₁ and P _2. If the power generation cost of each generator is represented by f ₁ (P ₁ ) and f ₂ (P ₂ ), the problem is as follows.

Under the conditions of

The problem is to determine P ₁ and P ₂ that minimize.

The optimal solution to this problem is found using Lagrange's undetermined multiplier method,

Against

Can be solved simultaneously. So, ultimately,

Is obtained. This λ is called the incremental fuel cost. That is, it is only necessary to perform the operation such that the incremental fuel costs become equal even when there are a large number of generators.

For example, if _{f 1 (P 1) = a} 1 P 1 2, f 2 (P 2) = a 2 P 2 2, solutions of Equation 13 Equation is as follows.

Becomes

  However, the ultimate goal for generators is not to minimize generation costs, but to maximize profits. As in the conventional case, when the power price is constant, minimizing the power generation cost is equivalent to maximizing the profit. The situation changes when the price of electricity fluctuates due to the liberalization of electricity. A similar technique can be used when only individual generators are considered even when the power price fluctuates. Although the two do not match in consideration of realistic starting and stopping costs, the starting and stopping costs are generally relatively small.

  However, when the price is different for each demand, the simplification cannot be performed as described above. Further, for example, when it is considered that a low-risk generator should be in charge of a low-risk demand, the two do not match because the fluctuations in the target power prices are different. Alternatively, even when a generator is selected according to the period and amount of demand to make a power generation plan, the two do not match. Therefore, the conventional economic operation method based on the incremental fuel cost has a problem that the result is not optimal under the liberalization of electric power.

As described above, if electricity trading is liberalized, a variety of contracted power products will appear more than now, and the power price will differ for each demand, and the price will change over time. There was a problem that the assets of power supply and power demand had to be comprehensively managed. In addition, the time factor of the power transmission period and the power reception period is important for power assets, and there has been a problem that it is difficult to optimize a portfolio by a normal method. Furthermore, the price distribution of these assets has a large deviation from the normal distribution, so that the conventional model has a problem that the error increases. In addition, when a power producer conducts power trading in a free power market, there is a problem that profit cannot be maximized if only power generation costs are considered. Furthermore, it is difficult to maximize profits while keeping the risk below an allowable value, and there is a problem that the power plant alone cannot optimize risk management.
JP 2001-67409 A JP 2002-157425 A Y. Uenohara et. al. , Proc. 5th JAFEE Int. Nat. Conf. Pp. 18, 1999

  The present invention has been made in view of such a technical problem, and a power company having a large number of power plants has a methodology for responding to a large number of power demands through procurement from a spot market and trading of related financial products. The purpose of the present invention is to provide a risk management technique for electric power trading, which treats these as a portfolio and enables the risk management.

  Another object of the present invention is to provide a power trading risk management technique that can manage power trading risks by treating spot market power as a portfolio.

  The power trading risk management system of the present invention regards power procured from a power plant or a market as a financial asset with a fixed maturity and a dividend period, and converts power demand in various contract forms into a contract power amount, a contract period, and a contract condition. It is characterized by financial liabilities with maturity and dividend periods based on the above, etc., which are comprehensively managed as a power portfolio that takes into account maturity and dividend periods.

  The power transaction risk management system according to the first aspect of the present invention is a power demand plan creating means for creating a power demand plan using individual power demand by using data of a related contract condition such as a contract power amount, a contract period, and a contract type. Based on the power demand plan, a total power generation / procurement curve creation means for preparing a target total power generation / procurement curve, and an electric power portfolio combining in-house generated power and procured power corresponding to the total power generation / procurement curve Power portfolio creation means, risk amount evaluation means for evaluating the risk amount of the power portfolio, profit calculation means for calculating the power sales revenue based on the power portfolio, and rearrangement of the power portfolio to reduce the risk amount in the power sales revenue for a certain period Determine a power portfolio that maximizes that power sales revenue while keeping it below an acceptable value It is obtained by a gain maximization portfolio determining means.

  According to a second aspect of the present invention, in the power transaction risk management system according to the first aspect, there is provided a generator combination determining unit that determines a combination of generators that operate so as to maximize profits generated by the company. Things.

  According to a third aspect of the present invention, there is provided the power transaction risk management system according to the first aspect of the present invention, wherein a future power price is calculated from power demand, price data, a power demand / price relational expression, and future demand fluctuation prediction data for a certain period in the past. Power price fluctuation estimating means for estimating fluctuations, the power portfolio creating means combines the power portfolio with carbon emission credit prices, and the profit maximizing portfolio determining means comprises the power portfolio combining the carbon dioxide emission credit prices. Is characterized by determining a power portfolio that maximizes the power sales revenue while keeping the risk in the power sales revenue for a certain period of time at or below an allowable value.

  According to a fourth aspect of the present invention, there is provided the power transaction risk management system according to the first aspect, wherein a future power price is calculated from power demand, price data, a power demand / price relational expression, and future demand fluctuation prediction data in a certain period in the past. Power price fluctuation estimating means for estimating fluctuations, the power portfolio creating means combines the power portfolio with financial products related to the weather in the corresponding region, and the profit maximizing portfolio determining means selects the financial products related to the weather. With respect to the combined power portfolio, the power portfolio that maximizes the power sales profit while maintaining the risk amount in the power sales profit for a certain period at or below an allowable value is determined.

  According to a fifth aspect of the present invention, in the power transaction risk management system of the first aspect, the risk evaluation means uses a different power demand / price relational expression for each country, region, and time in which the system is operated, to determine a position of the power portfolio. It is characterized by calculating management or risk indicators.

  According to a sixth aspect of the present invention, in the power transaction risk management system according to the fifth aspect, the risk evaluation means includes: a risk index such as volatility, risk sensitivity (exposure), delta, etc., in position management of a power portfolio or calculation of a risk index. It is characterized by using the skewness and kurtosis of the rate of return distribution, the percentage point of the rate of return and price distribution, or value-at-risk or learning-at-risk.

  According to a seventh aspect of the present invention, in the power transaction risk management system according to any one of the first to sixth aspects, the risk evaluation means uses a probability distribution other than a normal distribution as a rate of return on the power transaction in the risk evaluation of the power portfolio. Things.

  According to an eighth aspect of the present invention, in the power transaction risk management system of the first to sixth aspects, the risk evaluation means uses a financial Boltzmann model as a probability distribution that is not a normal distribution as a distribution of a rate of return by the power transaction in the risk evaluation of the power portfolio. It is characterized by using the obtained probability distribution.

  The power transaction risk management system according to the ninth aspect of the present invention simulates the fluctuation of the profit of each power plant based on the profit data of the power plant and the fluctuation data of the fuel price, and generates the power generation risk parameter from the fluctuation of the fuel price. Power generation risk parameter evaluation means to evaluate, external procurement risk parameter evaluation means to evaluate external procurement risk parameters of power procured from the power market, and demand power to evaluate the risk parameters of individual customers' power contracts Risk parameter evaluation means and power portfolio creation to create a power portfolio including the ratio of the amount of power generated by the power plant to the amount of power procured from the power market, power generation risk parameters, external procurement risk parameters, and power contract risk parameters Means for evaluating the amount of risk in the power portfolio; Power portfolio rearrangement means to adjust the ratio of the amount of power generated by the power plant to the amount of power procured from the power market so as to maximize profits while keeping the amount of power below the allowable value and to rearrange the power portfolio, and to allow the amount of risk And an optimal power generation plan creating means for outputting a power generation plan that optimally combines the ratio between the power generation amount of the power plant and the amount of power procured from the power market to maximize profit while keeping the value below the value.

  According to a tenth aspect of the present invention, in the power transaction risk management system of the ninth aspect, there is provided a means for determining a combination of generators to be operated so as to maximize profits generated by the company.

  According to an eleventh aspect of the present invention, in the power transaction risk management system of the ninth aspect, the risk amount evaluating means evaluates a risk amount of the power portfolio, such as a maturity ladder analysis, a period gap analysis, a duration gap analysis, and the like. Is characterized by using the ALM method described above.

  A power transaction risk management method according to a twelfth aspect of the present invention provides a power transaction risk management method, comprising the steps of: creating an electric power demand plan for each electric power demand using related contract conditions such as a contract power amount, a contract period, and a contract type; Creating a target total power generation and procurement curve, creating a power portfolio that combines in-house generated power and procured power that matches the total power generation and procurement curve, and evaluating the risk amount of the power portfolio Calculating a power sales revenue based on the power portfolio; and rearranging the power portfolio, and determining a power portfolio that maximizes the power sales revenue while maintaining a risk amount in the power sales revenue for a certain period of time equal to or less than an allowable value. And

  The electric power trading risk management method according to the invention of claim 13 simulates the fluctuation of the profit of each power plant based on the profit data of the power plant and the fluctuation data of the fuel price, and evaluates the power generation risk parameter from the fluctuation of the fuel price. Assessing external procurement risk parameters for electricity procured from the electricity market, assessing the risk parameters of individual customer electricity contracts, generating electricity from power plants and procuring electricity from the electricity market. Creating a power portfolio that includes the percentage of electricity, power generation risk parameters, external procurement risk parameters, and power contract risk parameters; evaluating the amount of risk in the power portfolio; In order to maximize profits while maintaining the same, adjust the ratio of the power generated by the power plant to the amount of power procured from the power market, Power portfolio and the optimal ratio between the amount of power generated by the power plant and the amount of power procured from the power market that maximizes profit while keeping the amount of risk below the allowable value, and output this as a power generation plan And steps.

  According to the present invention, a power producer having a large number of power plants provides a methodology for responding to a large number of power demands through procurement from a spot market and trading of related financial products, and treats them as a portfolio. It is possible to provide a risk management technique for power trading that enables management.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 6 shows a functional configuration of the power transaction management system according to the first embodiment of this invention. In the power transaction management system, the demand data input unit 1001 inputs target demand data (individual demand as a function of time and its risk index). The demand curve creating unit 1002 creates a demand curve 1010 for a certain period from the demand-related data input by the demand data input unit 1001. The total power generation / procurement curve creation unit 1003 approximately generates the total power generation / procurement curve 1020. The demand curve 1010 created by the demand curve creation unit 1002 is equal to the total power generation / procurement curve 1020 approximately created by the total power generation / procurement curve creation unit 1003.

  The power procurement plan creation unit 1004 matches the amount of power generation (or procurement) and the amount of time with the amount of demand and time as much as possible, and sets the operation plan of the generator and the power from the market or other power companies so as to minimize the risk. A power generation and procurement plan curve 1030 is prepared and output as target data 1005 for power generation and procurement. FIG. 7 shows the result in comparison with the conventional method.

  7A to 7C show the principle of creating an optimal power generation plan by the power trading risk management system according to the first embodiment. Power contracts generally specify a maximum amount of power and a delivery period. Therefore, discussion cannot be made only at a cross section at a certain time, and it is necessary to consider the time axis. FIG. 7A conceptually illustrates this. In this case, there are five customers, and the total is a demand curve 1010. The horizontal axis is time. This horizontal axis may be considered as a daily change or a yearly change. Consumers, on the other hand, procure power by generating power from their own generators or purchasing from the market, and balance the two. The actual contract terms are not simple and the power used is not constant over time, but here the individual demands are represented by rectangles for simplicity. On the other hand, the procurement side conventionally moves from the generator with the lowest power generation cost in the order of the total power generation / procurement curve 1040 in FIG. The idea was to move the cheaper generator to the next one. In some cases, the base power source is selected because it is difficult to start and stop or output fluctuations, and it is not simply moving from a cheap power source, but if the price does not fluctuate over time (there is no risk), Generally, the above-described concept holds. There is no reason to use a higher power supply as the base power supply.

On the other hand, if the electricity price fluctuates with time due to the liberalization of the electricity trade, it will not be possible to simply determine the generator to be operated only by the power generation cost. That is, it is necessary to consider the risk factors. Since generators have different rates of return and different price fluctuation risks, a so-called portfolio approach is needed. The rate of return Y of the portfolio is the weighted average of the rate of return y _i of each asset. That is, the weights of each asset as equation (15) When w _i.

At this time, the variance σ _Y ² of _Y is expressed by Expression 16.

Here, σ _ij is the covariance of assets i and j. There are current i-1 assets, and how the risk (variance) of the new portfolio changes when one new asset i is added is the most important part of portfolio theory. How the risk of the entire portfolio changes by adding the i-th asset to the portfolio can be found by partially differentiating Equation 16 with w _i . That is,

Becomes This corresponds to the covariance of the ith asset and the entire portfolio. In other words, it can be seen that the risk of the new portfolio is affected not by the variance of the i-th asset but by the covariance with other assets. Whether a power producer should capture new demand will need to be determined in relation to other demands.

  The above-mentioned value-at-risk (VaR) is also used when evaluating the risk of the portfolio. For example, assume that the VaR of the current portfolio is 100 million yen. Here, it is assumed that it is necessary to make a new power contract which is expected to generate a profit of 20 million yen. Assume that the VaR of this transaction is, for example, 30 million yen. In this case, the ratio of risk to return is 3: 2, which is not an efficient transaction. However, if the total VaR increases by 10 million yen to 110 million yen when incorporated as a portfolio, the ratio between risk and return is 1: 2, and the transaction is efficient. Therefore, it is not possible to judge the pros and cons of the transaction only from the profits of the individual power transactions.

  This also applies to the relationship between supply and demand. Electricity contracts are also a kind of property, so they are divided into assets (positive property) and liabilities (negative property). If this is applied by analogy with the financial securities field, assets are generated power or power procured from the market, and liabilities are power supplied to consumers.

Normally,
[Equation 18]
Asset = liability + equity, but here capital is assumed to be zero. In power trading, if the balance between supply and demand is disrupted, a power outage will occur, so to say, assets and liabilities are balanced without sufficient capital. For this management, the ALM (Asset and Liability Management) concept of a financial institution is effective. In this case, it can be considered that the fluctuation of the electricity price corresponds to the fluctuation of the interest rate in the conventional technology. Some assets and liabilities have large uncertainties and large risks, while others have small uncertainties and small risks. Therefore, by appropriately combining short-term contracts and long-term contracts, high-risk contracts and small-risk contracts, appropriately maintain the portfolio against fluctuations in electricity prices (maximize the expected rate of return according to risk tolerance). Can be. The power generation / procurement planning curve 1030 in FIG. 7C conceptually illustrates this state. In this case, the optimal procurement is performed in response to each demand, instead of accumulating in order from inexpensive generators as in the total power generation / procurement curve 1040 in FIG. 7B. In this figure, demand and procurement are represented by the same rectangular block, but in practice, they need to be adjusted individually from the perspective of risk and profit. In other words, instead of simply starting from a cheap generator, it is necessary to procure the most suitable for the demand.

  As a specific technique for this, techniques such as (1) maturity ladder analysis, (2) period gap analysis, and (3) duration gap analysis can be used. (1) Maturity ladder analysis is a method of totalizing and analyzing when assets and liabilities currently held expire. This method is suitable for creating a database of assets. The period gap analysis of (2) is a method in which data of the maturity ladder analysis is tabulated for each month, for example, and the maturity gap in each period is grasped. This is a method of calculating the sensitivity of profits when interest rates fluctuate using this.

  In some cases, it is necessary to evaluate interest rate risk in electricity, but here we will explain the method of sensitivity analysis for price risk. For example, assume that power procurement and power demand are as shown in FIG. In this case, how the profit changes when the power price rises, for example, by 100 yen is easily calculated from FIG. In this case, the risk to price fluctuations has been canceled because demand and supply are composed of the same amount and duration. If the demand and supply volumes are different, the price volatility risk will not be cancelled. A means for easily expressing such a situation is duration.

In the financial field, in general, the price volatility of coupon bonds increases as the coupon (cash flow) remains the same as the remaining period becomes longer. Therefore, the remaining life of a loan is a measure of price volatility. Therefore, the duration weighted by the present value of the cash flow is the duration. This is defined by equation (19).

Here, r is the interest rate (final yield of the coupon bond), and P is the price of the coupon bond at which c _i is paid at t _i .

  In power prices as well, the risk of price fluctuations is, roughly speaking, the greater the contract period and the higher the price. Therefore, the price sensitivity can be checked by defining the amount corresponding to the duration.

When the power generated by the generator is considered as an asset, the superiority of the asset can be evaluated using the rate of return. The return on risk assets, such as stocks and securities, is the sum of income and capital gains. In the case of electric power, there is no income gain, so only the capital gain due to a change in electric power price needs to be considered. If the future price is unknown, the rate of return can be viewed as a stochastic variable, and the profit or loss of the power asset can be expressed as a probability distribution function. In practice, the distribution of the rate of return is estimated from historical data assuming that the observations are independent and follow the same distribution. If one period from time j-1 to time j is referred to as period j, the rate of return in period j is represented by equation (20).

Here, Sj is the power price at the time point j. Here we do not consider fuel price fluctuations. When calculating the continuous compound interest rate of return in the j-th period, it is calculated by Expression 21.

  If one period is one day, the latter of Expression 21 is a logarithmic daily rate of return.

As described above, duration is the remaining life of a portfolio weighted by the present value of cash flows. In the case of a power asset (liability), since it is considered that there is a continuous cash flow c (t), the duration d can be defined as in Expression 22.

Here, r is the interest rate, c _i (t) is the cash flow at time t of the i-th element of the currently contracted portfolio, and τ _i is the contract period. Thus, in this case, the duration changes momentarily as a function of time. Since the cash flow varies depending on the contract content and market price fluctuations, the duration of the portfolio is calculated by Monte Carlo simulation. In some cases, it is necessary to determine the probability distribution of the duration.

  It is generally known that the market risk of a portfolio can be immunized by matching the duration of the portfolio with the investment period (L. Fisher and R. Weil, Journal of Businesses, (1971) pp. 408-431). This is a case of a parallel shift of interest rate risk, but is approximately established even for fluctuations in the electricity price in a short-term risk evaluation or the like. When long-term risks and price fluctuations are severe, it is necessary to determine the optimal portfolio combination by performing Monte Carlo simulation.

  If futures are available, the duration of the portfolio can be changed without changing the physical position. Investing in long-duration assets increases portfolio risk. In this case, the duration can be shortened by selling futures.

  In the financial field, the portfolio is regularly reshuffled using the exchange of short-term interest rates and long-term interest rates by swap transactions. These technologies can also be applied to the risk management of the power portfolio.

  FIG. 9 shows a detailed functional configuration of a power procurement plan creating unit 1004 in the power transaction risk management system according to the first embodiment as a second embodiment of the present invention. 10A and 10B show flowcharts of the power procurement plan creation processing. Here, a power company creates a power procurement plan by combining the power generated by its own generator and the power procured from the spot market. It manages and performs the process of maximizing the profit while keeping the risk in the power sales profit for a certain period of time below the allowable value.

  The market database 100 stores economic-related data required by this system, such as spot power prices, power generation prices, contract periods, and interest rates.

  Since the power generation cost is a function of the power generation amount, the power generation cost calculation unit 101 determines the power generation cost from the power plant cost function 100A, the demand data 100B, and the fuel price data 100D (step S101). For this, a conventional method can be used, but a method described later can also be used.

  The total demand curve calculation unit 101A creates a total demand curve from the demand data 100B (step S101A).

  The portfolio creating unit 102 creates a power portfolio serving as a starting point (step S102). In this method, it is possible to use a device in which the total demand is covered by the in-house power generation and which is set in advance and which generator is to be used and in what proportion for the demand. Alternatively, it is also possible to set such that the in-house power generation and the external power supply are set at 2: 1.

  The power generation plan formulation unit 103 creates (establishes) a power procurement plan (power generation plan) related to power demand and supply while comparing the obtained power generation cost with the power price 100C in the spot market (step S103). The procurement plan created here is quantitatively balanced with demand. However, the risks are not always optimized. Therefore, using the volatility (historical volatility) calculated using the past data of the demand amount and the spot market price provided by the database 104, the risk of the portfolio (for example, VaR) is calculated by using the profit distribution evaluation unit 105. Is evaluated (steps S105 and S106).

  The risk allowable value determination unit 107 performs risk allowable value determination using the evaluation data of the risk amount (step S107). If the value is equal to or larger than the allowable value (for example, it is assumed to be the capital), the process returns to the portfolio rearranging unit 108 to rearrange the current portfolio and reduce the risk (step S108). If the risk does not fall below the tolerance for any combination, consider reducing supplies. In the following description, it is assumed that the allowable value is the above-mentioned capital.

  If the risk of the portfolio is equal to or less than the allowable value, the profit maximization judging unit 107-1 judges the maximization of the profit. Creation of a portfolio for investment is also considered (step S107-1).

  This maximizes revenue while keeping risk below tolerance. Then, the power generation / procurement execution unit 109 causes the power supplier to execute power procurement based on the generated power generation / procurement plan (step S109).

  The risk index 110A, the position 110B, and the current ALM data 110C of the portfolio obtained here are re-evaluated daily by the position reviewing unit 111 (step S111), and the results are stored in the database 112 (step S112) and output. The unit 113 outputs a risk-related index (step S113). Here, the “position” indicates a balance between supply and demand. The position reviewing unit 111 further rearranges the portfolio by, for example, buying and selling the market if necessary, and in some cases, performs risk hedging of the portfolio using the risk hedging executing unit 114 (Step S114). The means used by the risk hedging unit 114 include options, swaps, futures, and the like.

  Next, as a third embodiment of the present invention, another functional configuration of the power procurement plan creation unit 1004 in the power transaction risk management system of the first embodiment will be described with reference to FIG. Here, in addition to the input data 110A to 110C, the emission credit market data 121 and the weather derivative price data 122 are additionally used in the second embodiment shown in FIG. Note that, in the third embodiment shown in FIG. 11, the other functions are the same as those in the second embodiment shown in FIG.

  The processing of the electric power procurement plan creating unit 1004 according to the present embodiment is shown in the flowcharts of FIGS. 12 and 10B. In step S102, it is necessary to incorporate the electric power portfolio into the emission credit market price 121 and the weather derivative 122. Is different from the embodiment of the present invention. Other processing steps are common.

By combining emission rights such as carbon dioxide with the owned power portfolio, profits can be maximized while keeping the risk of fluctuations in power prices below an allowable value. If the power portfolio includes power plants that emit greenhouse gases, such as thermal power plants, and if these emissions trading is conducted in the market, the thermal power plants will be shut down and the emission credits will be sold at the same time. In some cases, profits can be further optimized. The emission rights in this case are not limited to carbon dioxide, but can be applied to other gases such as SO ₂ and NO _x .

  Weather derivatives are usually used to hedge weather risk, but power demand and prices are strongly correlated with the weather, and the potential to reduce the risk of the portfolio by properly incorporating weather derivatives into the portfolio .

  In assessing the future risks of electricity prices, the relationship with electricity demand cannot be ignored. Future electricity prices usually have a periodicity of one day, one week, and seasonality of one year. The regularly changing part is not a risk part and must be dealt with appropriately. However, the regularity of the electricity price is often not clear, and it is usually difficult to directly process the electricity price. On the other hand, the regularity of electricity demand is relatively clear because it reflects social activities. Therefore, it is more convenient to evaluate the regularity of the price from the regularity of the demand and the relationship between the demand and the price, instead of directly processing the regularity of the electricity price. However, since the relationship between demand and price is determined by the power supply configuration in the region, the type, quantity, configuration of power consumers, and the characteristics of the power system, a universal relationship cannot be determined in advance.

  FIGS. 13A and 13B show the relationship between the electricity price and demand of CalPX. FIG. 13A shows data of February 1999, and FIG. 13B shows data of August 1999. As can be seen from this figure, even in the same area, the relationship differs depending on the season. This is because the type of the activated power supply equipment differs depending on the demand level. In the relationship between demand and price, the so-called reserve capacity of the power source is important.

  On the other hand, FIGS. 14A and 14B are examples of the relationship between demand and price on the Leipzig Electricity Exchange. In this case, it can be seen that there is more variation than in California. This variation must be considered in the risk assessment as uncertainty.

  As mentioned above, the relationship between electricity demand and electricity price, which varies by country, region, and season, needs to be properly incorporated into risk assessment.

  FIG. 15 shows still another functional configuration of the power procurement plan creating unit 1004 in the power transaction risk management system according to the first embodiment as a fourth embodiment of the present invention. The present embodiment is characterized in that a portfolio is constructed using the relationship between power demand and power price, and the demand / price correlation measuring unit 133 performs regression analysis from past power demand data 131 and past power price data 132. , And outputs the obtained correlation equation and correlation coefficient to the covariance matrix creation unit 134 and the periodic component removal unit 135 (step S133).

  The covariance matrix creation unit 134 creates a covariance matrix (Step S134). Further, the periodic component removing unit 135 removes the periodic component of the electric power price, creates statistical data 104 such as appropriate volatility of the price from the price data from which the periodic component has been removed, and evaluates it (step S135). On the other hand, the correlation data between the demand and the price is also used for the composition of the power portfolio by the portfolio creating unit 102) (step S102). Other functions are the same as those of the second embodiment shown in FIG.

Electricity prices have a periodicity of one day, one week, or one year, depending on fluctuations in demand. This periodicity is essentially different from random fluctuations and is a regular fluctuation part. Therefore, if the data processing is performed as it is, there is a possibility that the fluctuation component (risk) is excessively (or underestimated). Therefore, when evaluating a future risk using past data, it is necessary to appropriately remove the periodic component from the past data. There are many methods of removing the periodic component. For example, there is a method of determining the coefficients (a _j , b _j ) by the least square method, assuming a function form as shown in Expression 23.

  Here, i is the time (or day), L is the length of the cycle (24 in a daily cycle, 7 in a weekly cycle), and m is about 12 for one day data, one week In the case of the above data, a value of about 3 is sufficient. FIG. 17 shows the result of removing the periodic component from the original data by such a method.

When assessing portfolio risk, it is necessary to consider the risk sensitivity E (exposure). This is defined by Equation 24.

  Here, Δx is a change in certain market data, and ΔP is a change in the portfolio at that time. For example, if x is an interest rate, E is (prior art) duration, if x is a stock index, E is the so-called beta value, if x is the underlying option and P is the option price, then E Corresponds to the optional delta. In this case, E is the first derivative, but it is also possible to consider up to the second order and to consider the amount corresponding to the convexity of interest rate risk and the optional gamma.

  Next, as a fifth embodiment of the present invention, another example of a risk evaluation method by the first power trading risk management system will be described. In the power transaction risk management system of the first embodiment described above, it is assumed that a normal distribution, which is generally used, is used as the distribution of the daily rate of return. However, as described above, in the case of electric power prices, the deviation of the distribution of the daily rate of return from the normal distribution is large. This in itself can be a significant risk. Therefore, it is necessary to always evaluate the deviation of the distribution of the daily rate of return from the normal distribution.

FIGS. 18A and 18B are diagrams plotting the change over time in the skewness a ₃ and the kurtosis a ₄ using the California Electric Power Exchange (CalPX) data. If daily return distribution is close to normal distribution a ₃ ~0, a ₄ ~3 is established. By monitoring these values, the deviation from the normal distribution can be checked. Further, the degree of deviation from the normal distribution can be evaluated by calculating a statistic JB (Jarque-Bera) defined by the following equation 25, for example.

Here, n is the number of data, and according to the theory of statistics, it is known that JB follows a χ ² distribution with ^two degrees of freedom, so if JB is 5.991 or more, 95% reliability is obtained. Indicates that it cannot be treated as a normal distribution. In the power transaction risk management system according to the first embodiment, the profit distribution evaluation unit 105 can perform risk evaluation more strictly by using these values. In this case, necessary data is registered in the statistical database 104 in advance.

  Next, as a sixth embodiment of the present invention, still another example of the risk evaluation method in the power trading risk management system of the first embodiment will be described. In the risk evaluation performed by the profit distribution evaluation unit 105, the distribution obtained from the market may be used as it is, but this is not strictly correct. The distribution of the daily rate of return must be obtained based on a consistent price fluctuation model.

  Therefore, the system according to the present embodiment uses a financial Boltzmann model (Y. Uenohara et. Al. Proc. 5th JAFEE Int. Nat. Conf. Pp. 18, 1999) as the price fluctuation model, and evaluates the fluctuation component. In the above, the calculation is performed according to the financial Boltzmann model, the risk-neutral probability distribution is obtained, and the risk measurement is performed.

The financial Boltzmann model is an extension of the diffusion model, and can evaluate derivative securities prices for a wide range of price distributions as well as normal distributions. The Boltzmann model incorporates a fat tail without loss of continuity, which guarantees reproducibility and facilitates risk hedging of derivative securities. The financial Boltzmann equation is represented by Equation 26.

Here, P is a risk-neutral probability measure of the underlying asset S, t is time, ν is log return, μ is the price change direction, Λ _T is the collision frequency, Λ _S is the scattering term representing the memory effect, and S ₀ is t = 0 at S. Further, P (S, t) is represented by Expression 27.

Scattering term lambda _S is calculated by assuming a functional form such as Eq. 28 as a few days following return distribution pair.

Further, T (v) is a parameter corresponding to temperature and is expressed by Expression 29.

Here, T ₀ , c ₀ , and g ₀ are constants.

FIG. 19A to FIG. 19D are calculation examples of the fluctuation of the electric power price by the financial Boltzmann model. The figure also shows the distribution of the corresponding daily rate of return. FIG. 19A is a calculation example when the distribution is close to the normal distribution, and FIG. 19B is a result when the daily rate of return is significantly different from the normal distribution. In the financial Boltzmann model, by selecting T ₀ , c ₀ , and g ₀ , the risk-neutral probability density of a wide range of distribution can be obtained.

  Since the financial Boltzmann model can handle distributions that deviate from the normal distribution as described above, it is easier to approximate the actual daily rate of return than the normal distribution, and is suitable for describing fluctuations in electricity prices You can see that.

  FIGS. 20A and 20B show the cumulative distribution functions obtained from the distribution of daily returns and the normal distribution obtained by the financial Boltzmann model in the case of FIG. In the case where the profit distribution evaluation unit 105 evaluates, for example, the value-at-risk with 95% reliability, it is sufficient to look at the daily profit rate at which the cumulative distribution becomes 0.05 in this figure. FIG. 20B is an enlarged view of FIG. 20A. From this figure, the value of the daily rate of return (corresponding to VaR) corresponding to a cumulative distribution of 5% is not significantly different between the financial Boltzmann model and the normal distribution. The probability of causing large losses is greater in the financial Boltzmann model. This corresponds to the actual situation as shown in FIG.

  In addition, the above result is a case where the value of VaR does not greatly differ due to a difference in distribution. However, when the reliability of VaR is 99% or 90%, a large difference appears between the two. .

In the above results, the method of selecting the parameters T ₀ , c ₀ , and g ₀ in the calculation of the financial Boltzmann model is not particularly specified. For example, a method of selecting to fit the market data can be adopted.

On the other hand, T ₀ , c ₀ , and g ₀ can be determined by a method such as that used in the field of financial securities. 21A and 21B show the relationship between the logarithmic daily rate of return and the demand (or trading volume) in the CalPX power price and the company A stock price. From these, it is possible to see a similar relationship, although not clear, where the demand or volume increases as the rate of return increases. At least, there is no clear characteristic difference between electricity prices and stock prices. Therefore, a method based on the memory effect of the daily rate of return as used in the field of financial securities (Y. Uenohara et. Al. Proc. 5th JAFEE Int. Nat. Conf. Pp. 18, 1999) is applicable. it is conceivable that.

FIG. 22 shows the relationship between the daily rate of return on the day and the daily rate of return on the previous day. This figure clearly shows that the larger the previous day's daily return rate is, the flatter the distribution of the daily return rate is on the current day. By fitting this distribution shape using Expressions 28 and 29, T ₀ , c ₀ , and g ₀ can be determined. FIG. 23 shows the result of the fitting. By using the financial Boltzmann model for the risk evaluation of the power portfolio by the above-described method, it is possible to perform risk management with higher accuracy.

  Next, a power trading risk management system according to a seventh embodiment of the present invention will be described. This embodiment is characterized by a profit maximization method at the time of portfolio creation performed by portfolio creating section 102 shown in FIG. 9 in the first power trading risk management system. Therefore, the system configuration is common to the first embodiment shown in FIG. The processing for creating the power portfolio is also similar to the flowcharts of FIGS. 10A and 10B.

  FIG. 24 shows a power portfolio creation function of portfolio creation section 102 in the present embodiment. In this case, the power of the plurality of power generation facilities (1) to (n) having different costs is distributed to the plurality of customers (1) to (m) having different prices and demands.

Conventionally, when determining the optimum generator output of each generator for a given power demand, the generator output is distributed according to Equations 9 to 13 so that the incremental fuel costs become equal, as described above. I was However, when the power trade is liberalized, the power price may be different for each time and for each partner. Which generator is allocated to which demand is determined by the ALM concept and the portfolio optimization method described in each of the above-described embodiments. In this case, too, which generator generates power and how much power is generated It must be determined using a fuel cost function. However, conventionally, the power generation is allocated so as to minimize the fuel cost, but in the present invention, the power is allocated so as to maximize the profit. Here, for simplicity of explanation, consider the simplest case in which the number of generators is 2, the number of consumers is 2, the generator 1 supplies power to demand 1, and the generator 2 supplies power to demand 2. In this case, the equation (11), under the condition of P ₁ + P ₂ = P _0, is replaced by the problem of determining the P ₁ and P ₂ to maximize the number 30 expression.

Here, T is the contract period, P ₁ and P ₂ are the power amounts of demand 1 and demand 2, S ₁ and S ₂ are the prices per unit power of demand 1 and demand 2, and generally, It is a function of the amount of demand and time, which varies from customer to customer. Further, f ₁ and f ₂ is the power cost function.

Here, for simplicity, the effects of the present invention will be shown based on an example in which S ₁ and S ₂ are constant with time (no risk), regardless of the demand level. In this case, since the equation (30) does not depend on time, the integral can be removed, and the equation (31) is obtained.

Therefore, the conditions for maximizing revenue are:

In this case, Expression 33 is obtained.

Solving this case _{f 1 (P 1) = a} 1 P 1 2, f 2 (P 2) = a 2 P 2 2, get the number 34 expression.

These results coincide with the results of the above-described equations (11) to (13) when S ₁ = S ₂ . The above results were obtained when S ₁ and S ₂ did not depend on time or demand level. However, when S ₁ and S ₂ depended on time or demand level, the conventional method and the present method did not. It is clear that the results are different and that the results of the present invention yield greater revenue.

Above was the example in the absence of risk, in fact, it S ₁ and S ₂ are time varying (i.e., the risk is present). Also in this case, the optimal solution can be similarly obtained by using Expression 30. Since overall risk in the case variance (sigma ²⁾ is equal to the random fluctuations of S ₁ and S ₂ are determined only by sigma and P _0, decide P ₀ to be equal to or less than the risk (eg VaR) an acceptable level, Then, P ₁ and P ₂ may be optimized to maximize the profit. If the risk of S ₁ and S ₂ are different, it is necessary to calculate the value of risk and return to the combination of a number P ₁ and P _2. Although optimization is possible in principle when the number of demands increases, the amount of calculation increases rapidly. In this case, calculation in a realistic time can be performed by using a dynamic programming method or the like. Further, when considering fluctuations in fuel cost, f ₁ and f ₂ are functions of time, but a similar method can be applied.

  FIG. 25 shows an example of a screen layout of the power portfolio risk management system according to the present invention. 301 is a target period, 302 is a new asset, 303 is an asset entered in the past, 304 is a position up to the present, 305 is a relationship between price and demand, 306 is a distribution of a daily rate of return, Reference numeral 307 denotes an VaR evaluation portion, 308 denotes an option period, 309 denotes an option type, 310 denotes a change in past demand, and 311 denotes a change in past price. This is a specification in which either the operation using the Black-Scholes equation or the operation using the Boltzmann model can be selected.

  In the present invention, the above-described power transaction risk management system is realized by a single computer or a network system in which a plurality of computers are connected to a network and computers distributed in various places are connected to each other by an information network. In addition, the technical scope includes a software program installed in one computer or a computer network system to realize the functions of the system.

It is the graph which showed the electric power price of the California Electric Power Exchange (CalPX) in 1999 by the average value per day. It is the graph which showed the electric power price of the California Electric Power Exchange (CalPX) in 2000 by the average value per day. FIG. 2 is a graph showing the power prices of the German Leipzig Electricity Exchange (LPX) in 2001 as a daily average. 3 is a graph showing a change in the closing price of a company A stock price in 2001. FIG. 4 is a distribution graph of a daily average power rate of return of the California Electric Power Exchange (CalPX). It is a distribution graph of the daily rate of return of the stock of company A. 11 is a graph showing a loss amount (VaR) when the value of an asset falls to _XL1 or less with a probability of 1%, assuming that the price fluctuates in accordance with a normal distribution having an average μ and a standard deviation σ. If the price varies according to the probability distribution with fat tails, is a graph showing the loss in the case of price 1% chance drops X _L2 below. Figure 4 is a graph of the California Power Exchange (CalPX) daily average power price revenue and VaR one day later with 95% confidence. It is the elements on larger scale of FIG. 5A. FIG. 2 is a block diagram illustrating a functional configuration according to the first embodiment of this invention. It is explanatory drawing of a portfolio of electric power demand. It is an explanatory view of a conventional power procurement portfolio. FIG. 2 is an explanatory diagram of a power procurement portfolio according to the first embodiment. It is a table showing the concept of power asset and liability management. FIG. 4 is a block diagram of a detailed internal functional configuration of a power procurement plan creation unit in the power transaction risk evaluation system according to the first embodiment as a second embodiment of the present invention. It is the first half part of the flow chart showing the processing of the electric power procurement plan creation unit of the second embodiment. It is the second half part of the flowchart which shows the process of the electric power procurement plan preparation part of 2nd Embodiment. FIG. 14 is a block diagram illustrating another detailed internal functional configuration of a power procurement plan creation unit in the power transaction risk evaluation system according to the first embodiment as a third embodiment of the present invention. It is a flowchart which shows the process of the electric power procurement plan preparation part of 3rd Embodiment. It is a graph which shows the relationship between the electric power demand and electric power price of the California Electric Power Exchange (CalPX) of February, 1999. It is a graph which shows the relationship between the electricity demand of California Electricity Exchange (CalPX) of August, 1999, and an electricity price. It is a graph which shows the relationship between the electric power demand of the Leipzig Electricity Exchange (LPX) and an electric power price of February, 2001. It is a graph which shows the relationship between the electric power demand of the Leipzig Electricity Exchange (LPX) of August 2001, and an electric power price. FIG. 14 is a block diagram illustrating a functional configuration according to a fourth embodiment of the present invention. 13 is a flowchart illustrating a process of a power procurement plan creating unit according to a fourth embodiment. It is a figure showing the method of removing periodicity from an electricity price. It is the figure which plotted the time change of skewness using California Electric Power Exchange (CalPX) data. It is the figure which plotted the time change of kurtosis using California Electric Power Exchange (CalPX) data. 15 is a graph illustrating a power price fluctuation close to a normal distribution calculated by the financial Boltzmann model according to the fifth embodiment of the present invention. 15 is a graph showing a power price fluctuation largely deviated from a normal distribution calculated by the financial Boltzmann model according to the fifth embodiment. It is a graph of the daily rate of return corresponding to the electric power price fluctuation shown in FIG. 19A. It is a graph of the daily rate of return corresponding to the electric power price fluctuation shown in FIG. 19B. It is a graph which shows the difference of VaR value of 95% reliability in a normal distribution model and a financial Boltzmann model. It is the elements on larger scale of FIG. 20A. It is a graph which shows the relationship between the absolute value of the daily rate of return in CalPX, and demand. It is a graph which shows the relationship between the daily rate of return and trading volume in the stock price of company A. It is a graph which shows the relationship between the absolute value of the daily return of the day in CalPX, and the daily return of the previous day. 9 is a graph showing a fitting result of a temperature function. FIG. 16 is a block diagram illustrating a power port format area creation method according to a sixth embodiment of the present invention. It is explanatory drawing which shows the output screen of the comprehensive electric power trading risk management system which mounts the functions of the 1st-6th embodiment of this invention.

Explanation of reference numerals

100: Market data 100A: Power generation cost function data 100B: Demand data 100C: Electricity price data 100D of spot market: Fuel price data 101: Portfolio creation unit 101A: Total demand curve calculation unit 102: Portfolio creation unit 103: Power generation plan formulation unit 104: Statistical data 105: Revenue distribution evaluation unit 107: Risk amount allowable value determination unit 107-1: Revenue maximization determination unit 108: Portfolio rearrangement unit 109: Power generation / procurement plan execution unit 110A: Position index data 110B: Risk index Data 110C: ALM data 111: Position review unit 112: Current index data 113: Output unit 114: Risk hedging processing unit 121: Emissions credit market price data 122: Weather derivative price data 131: Past power demand data 132 : Excessive Power price data 133: demand / price correlation measurement unit 134: variance / covariance matrix creation unit 135: periodic component removal unit 301: target period setting unit 302: new asset setting unit 303: asset of past input Display unit 304: Display position to date Window 305: Relationship between price and demand Display unit 306: Daily return rate distribution display unit 307: VaR evaluation setting unit 308: Option period setting unit 309: Option type setting unit 310: past demand change display unit 311: past price change display unit 1000: individual demand time, quantity, risk index data 1001: demand data input unit 1002: demand curve creation Unit 1003: Total power generation / procurement curve creation unit 1004: Electricity procurement plan creation unit 1005: Power generation / procurement target data

Claims (13)

Power demand plan creating means for creating an electric power demand plan by using data of related contract conditions such as contract power amount, contract period, contract type, and the like,
Based on the power demand plan, a total power generation / procurement curve creating means for creating a target total power generation / procurement curve,
Power portfolio creation means for creating a power portfolio combining in-house generated power and procured power corresponding to the total power generation / procurement curve,
Risk amount evaluation means for evaluating the risk amount of the power portfolio,
A profit calculating means for calculating a power sales profit based on the power portfolio;
A power transaction risk management system comprising: a power maximizing portfolio determining unit that rearranges the power portfolio and determines a power portfolio that maximizes the power sales profit while maintaining a risk amount in the power sales profit for a certain period of time at or below an allowable value. .   2. The power transaction risk management system according to claim 1, further comprising a generator combination determining unit that determines a combination of generators that operate so as to maximize profits generated by the in-house power generation. Power demand for a certain period in the past, price data and power demand / price relational expression and forecast data of future demand fluctuations, comprising power price fluctuation estimation means for estimating future fluctuations in power prices,
The power portfolio creating means combines the power portfolio with carbon dioxide emission credit prices,
The profit maximizing portfolio determining means determines an electric power portfolio that maximizes the electric power sales revenue while maintaining a risk in the electric power sales income for a certain period of time equal to or less than an allowable value for the electric power portfolio combining the carbon dioxide emission credit prices. The power trading risk management system according to claim 1, wherein Power demand for a certain period in the past, price data and power demand / price relational expression and forecast data of future demand fluctuations, comprising power price fluctuation estimation means for estimating future fluctuations in power prices,
The power portfolio creation means combines the power portfolio with financial products related to the weather in the corresponding region,
The profit maximizing portfolio determination means, for the power portfolio combining the financial products related to the weather, the power portfolio maximizing the power sales revenue while maintaining the risk amount in the power sales revenue for a certain period of time at or below an allowable value. The power transaction risk management system according to claim 1, wherein the determination is made.   The said risk evaluation means calculates the position management or the risk index of the said power portfolio using the electric power demand / price relational expression different for every country, area | region, and time when the said system is operated, The claim 1 characterized by the above-mentioned. The described power trading risk management system.   The risk evaluation means may include, in position management of the power portfolio or calculation of a risk index, volatility, risk sensitivity (exposure), risk index such as delta, skewness of return rate distribution, kurtosis, return rate and price distribution. The power trading risk management system according to claim 5, wherein a percentage point, value at risk, or learning at risk is used.   The power trading risk management system according to any one of claims 1 to 6, wherein the risk evaluation unit uses a probability distribution other than a normal distribution as a profit rate distribution by the power trading in the risk evaluation of the power portfolio.   7. The risk evaluation unit according to claim 1, wherein in the risk evaluation of the power portfolio, a probability distribution obtained by a financial Boltzmann model is used as a probability distribution that is not a normal distribution as a rate of return due to power trading. The power trading risk management system described in Crab. A power generation risk parameter evaluation unit that simulates fluctuations in profits of individual power plants based on the power plant profit data and fuel price fluctuation data, and evaluates power generation risk parameters from the fuel price fluctuations,
An external procurement risk parameter evaluation means for evaluating external procurement risk parameters of electric power procured from the power market;
A demand power risk parameter evaluation means for evaluating risk parameters of an individual customer's power contract;
Power portfolio creation means for creating a power portfolio including the ratio of the power generation amount of the power plant and the amount of power procured from the power market, the power generation risk parameter, the external procurement risk parameter, and the power contract risk parameter;
Risk amount evaluation means for evaluating the risk amount of the power portfolio,
Power portfolio rearranging means for rearranging the power portfolio by adjusting the ratio of the amount of power generated by the power plant and the amount of power procured from the power market so as to maximize profit while keeping the risk amount below an allowable value,
Optimum power generation plan creation means for outputting a power generation plan that optimally combines the ratio of the power generation amount of the power plant and the amount of power procured from the power market to maximize profit while keeping the risk amount below an allowable value. Power trading risk management system.   The power transaction risk management system according to claim 9, further comprising: means for determining a combination of generators that operate so as to maximize profits from in-house power generation.   The said risk amount evaluation means uses ALM methods, such as a maturity ladder analysis, a period gap analysis, and a duration gap analysis, for the evaluation of the risk amount of the said power portfolio, The claim 9 characterized by the above-mentioned. Power trading risk management system. Creating an electric power demand plan using the relevant contract conditions such as contract electric energy, contract period, contract type, and the like,
Creating a target total power generation and procurement curve using the power demand plan,
Creating a power portfolio combining in-house generated power and procured power corresponding to the total power generation / procurement curve;
Evaluating the amount of risk in the power portfolio;
Calculating power sales revenue based on the power portfolio;
Rearranging the power portfolio and determining a power portfolio that maximizes the power sales revenue while maintaining a risk amount in the power sales profit for a certain period of time equal to or less than an allowable value. Simulating the fluctuations in the profits of the individual power plants based on the power generation data and the fuel price fluctuation data, and evaluating a power generation risk parameter from the fuel price fluctuations;
Assessing external procurement risk parameters for electricity procured from the electricity market;
Assessing the risk parameters of the individual customer's power contract;
Creating a power portfolio including the ratio of the amount of power generated by the power plant and the amount of power procured from the power market, the power generation risk parameter, the external procurement risk parameter, and the power contract risk parameter;
Evaluating the amount of risk in the power portfolio;
Adjusting the ratio between the amount of power generated by the power plant and the amount of power procured from the power market so as to maximize profit while keeping the amount of risk below an allowable value, and rearranging the power portfolio;
A step of outputting the power generation plan as a power generation plan by optimally combining the ratio between the power generation amount of the power plant and the amount of power procured from the power market to maximize the profit while keeping the risk amount below an allowable value. Risk management method.

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