JP4679910B2 - Determinant analysis method of contract price in power trading market and computer program for analysis - Google Patents

Description

  The present invention relates to an analysis of a power trading market in a power system, and more particularly to a method for analyzing a determinant of a contract price in a power transaction market of a power system and a computer program for analyzing a determinant of a contract price.

  In recent years, the electric power market has been liberalized in countries around the world, mainly in the United States and Europe, and as part of this, an electric power trading market has been established. Typical examples include Nord Europe's Nord Pool, US PJMISO and NYISO energy markets, and German EEX power trading markets. In Japan, a wholesale power exchange is scheduled to open in April 2005 in preparation for the introduction of a power trading system. As a trading method (contract method) in these electric power trading markets, a single price auction method is basically adopted.

FIG. 1 is a schematic diagram showing a configuration of an electric power system when an electric power trading system is introduced. As shown in FIG. 1, the power system 1 includes a generator SG12 (SG means a set of generators SG ₁ , SG ₂ ,..., SG _NG ) and a load SD 13 (SD Is a set of loads SD ₁ , SD ₂ ,..., SD _ND ), and a generator G14 of a person who does not participate in the power trading market (G is a set of generators G ₁ , G _{2 ,.} And D15 (D means a set of loads D ₁ , D ₂ ,..., D _Nd ). A generator G14 of a person who does not participate in the power trading market provides power to the power system 1 at a fixed price, and a load D15 of a person who does not participate in the power trading market consumes power from the power system 1 at a fixed price. On the other hand, those who participate in the power trading market (generator SG12, load SD13) determine the selling price of power by bidding through the power exchange. However, the load (the load in SD13) of the person who did not complete the transaction can buy power from the generator G14.

  Generally, the power trading market is the spot market, the participants selling the power to the market (for example, the generator SG12) as the seller (spot supplier), and the participants purchasing the power from the market (for example, the load SD13) as the buyer (Spot consumer), the transaction amount determined in the spot market is referred to as a fixed amount, and the price (MCP) settled in the spot market is referred to as a contract price. Further, a power supplier (G14) who does not participate in the power trading market is referred to as a non-spot supplier, and a power consumer (D15) is referred to as a non-spot consumer.

  When performing a transaction by the single price auction method, first, each seller (SG12) and buyer (SD13) submit their bid data (that is, bid price and bid amount) to the power exchange. All bid data is stacked to create the market supply curve shown in FIG. 2a and the market demand curve shown in FIG. 2b. The price (contract price) and quantity (approx. Quantified) (FIG. 2c) at the intersection of the market supply curve and the market demand curve are the transaction results of the auction. That is, in the single price auction, in accordance with the principle of price priority, a contract is determined in advance from a seller with a low bid price and a buyer with a high bid price, and a single bid price with a balance between supply and demand is settled as the contract price of the entire market. As a result, it is possible to realize efficient resource allocation that maximizes the social surplus, which is the sum of the power consumer surplus and the power supplier surplus.

  However, when the amount of distributed power between areas in the power system exceeds the amount that can be transferred by the interconnection facility (transmission line between areas), the amount of power that can be transferred is a constraint (the amount of distributed power between areas can be transferred) It is only possible to adopt a market division method in which the contract processing is performed again for each area and the power system is divided into a plurality of auctions. As a result of adopting the market division method, the contract price in the sending area of the congested interconnection line is reduced and the contract price in the receiving area of the congested interconnection line is increased. In addition, in an actual power system, congestion due to restrictions such as voltage and reactive power may occur in addition to congestion due to power transmission capacity. Therefore, if the configuration of the power system including the generator and the buyer's load determined by the contract price and the contract amount does not satisfy the constraints such as stability and reliability of power system operation, The new auction is added and the auction is executed again, and such an adjustment process is repeated until all the constraint conditions are satisfied.

  On the other hand, when the single price auction method described above is adopted, the main factors related to the operation of the power system (balance between active power and reactive power, voltage limit, power transmission capacity) are the limiting conditions, A method has been proposed for calculating the contract price and contract quantity so that the social surplus, which is the sum of the power supplier surpluses, is maximized. Next, the calculation method will be described.

First, a simulation model of a single price auction will be described.

In equation (1), F (X) is a goal function indicating the surplus of power consumers and all surplus of power suppliers, and G '(X) in equation (2) is an equation constraint in the power system. (That is, power flow equation), and H (X) in equation (3) is an inequality constraint condition in power system (that is, active / reactive power upper / lower limit, voltage upper / lower limit, power flow upper / lower limit, etc.). ) Medium K (X) is the spot market balance (liberalized power generation including transmission loss and demand-supply balance) equality constraint condition, X is an independent variable indicating bus voltage, and all P _gi, P _Gi , P _Di is a function of X.

  Equations (1) to (4) are the optimal solutions that maximize the objective function F (X) after satisfying the equality constraints G '(X) and K (X) and the inequality constraint H (X). It represents the problem of solving X (generally referred to as a single price auction problem).

In equation (1), the amount of power consumed by the load in the non-spot market and its electricity rate are given in advance, so π _di and P _di are constants and do not affect the optimal solution X. ω _i (P _gi ) is an incremental fuel cost function of the generator and can be expressed by a linear function of P _gi . φ _i (P _Gi ) and θ _i (P _Di ) are the linear functions or piecewise linear functions shown in FIGS. 3a and 3b, respectively. The bid function (supply curve) shown in FIG. 3a shows that seller i sells power up to the maximum P _Gi at a price of φ _i (P _Gi ) or more, and the bid function (demand curve) shown in FIG. , Indicates that buyer i buys power up to P _Di at a price less than θ _i (P _Di ). The bid price for the amount of electric power at the time of contract (when the optimum solution is reached) is called the limit bid price.

By solving Equation (1) and finding the optimal solution X (ie, by a single price auction using the SPA model), each seller, each buyer's approximately fixed amount P _Gi (X), P _Di (X) and non-spot A generator output P _gi (X) is obtained. Furthermore, if each seller and each buyer's approximately fixed amounts P _Gi (X) and P _Di (X) are substituted into the bid functions φ _i (P _Gi ) and θ _i (P _Di ), respectively, the marginal bid price of each seller ( π _Gi ) and the limit bid price (π _Di ) of each buyer is calculated (since φ _i (P _Gi ) and θ _i (P _Di ) are given).

If the supply curve (FIG. 3a) and the demand curve (FIG. 3b) intersect as shown in FIG. Is determined by the highest limit bid price (π _Gmax ) of each seller's limit bid price (π _Gi ) or the lowest limit bid price (π _Dmin ) of each buyer's limit bid price (π _Di ) (ie, , Π = Π _Gmax = π _Dmin ), the contract price is a single price.

However, when there are a plurality of intersections between the supply curve (FIG. 3a) and the demand curve (FIG. 3b) (ie, π _Gmax ≠ π _Dmin ), the contract price π needs to be calculated by the following equations (9) to (11) There is.

但し、ｃ（０≦ｃ≦１）は約定価格決定係数であり、最も安価な点を約定する場合、ｃを１とする。

However, c (0 ≦ c ≦ 1) is a contract price determination coefficient, and c is set to 1 when the cheapest point is executed.

In the case of dividing the market into a plurality of cases (in the case of market division), the maximum selling price π _{Gmax, k} (π _{Gmax, k} = max {π _{Gi, k} = φ _i (P _{Gi, k} ): i _{, k} = 1,…, N _{G, k} , P _{G, k} ≠ 0}) and buy minimum execution price π _{Dmin, k} (π _{Dmin, k} = min {π _{Di, k} = θ _i (P _{Di, k} ): i _{, k} = 1,..., N _{D, k} , P _{Di, k} ≠ 0}) and the respective contract prices (π _k ) are determined as described above.

Therefore, using the simulation model of the single price auction described above, it is possible to calculate the contract price and contract quantity that maximize the social surplus, with the main factors related to the operation of the power system as the constraint condition. Evaluate what element the value of price (π or π _k ) is composed of, and how much the bid data of each seller / buyer and the constraints of each power system affect the value of the contract price Can not.

  However, in order to improve the efficiency of interconnection operation and congestion management of the power system, or to make it possible to evaluate bid data in the spot market, it is required to clarify detailed information regarding the contract price.

  So far, many analysis methods have been proposed for the derivation and evaluation of electricity charges in power systems. These methods can basically be classified into a method for evaluating the equivalent value of various costs and constraints using a Lagrange multiplier as a shadow price, and a method for decomposing a nodal price at the bus. When evaluating the equivalent value of various costs and constraints using the Lagrange multiplier as a shadow price, there was a problem that the contract price could not be evaluated directly.

  On the other hand, in the nodal price decomposition method, a nodal price decomposition method that realizes quantitatively evaluating the influence of each power source and the constraint condition on the nodal price is disclosed in Patent Document 1 below. . The decomposition method directly associates each factor of the power system with a nodal price, and decomposes each nodal price into detailed components. Each item in the decomposed nodal price is not heuristic, but the degree of influence of each factor in the nodal price of the bus. It is used for network operation, congestion management efficiency, and investment evaluation of shipping power facilities.

However, the nodal price disassembly method disclosed in Patent Document 1 does not consider the configuration of the power system when the power trading system is introduced. There was a problem that the influence on the judgment price by each factor of the included electric power system could not be directly evaluated.
JP 2001-268790 A

Means for solving the problems and their effects

  The present invention has been made in view of the above problems, and elucidates the factors that determine the contract price in the power trading market, and derives detailed components of the contract price, thereby providing power including bid information, voltage constraints, etc. The purpose is to make it possible to quantitatively evaluate the influence of various factors of the system on the contract price.

  In order to achieve the above object, a determinant analysis method (1) of a contract price in a power trading market according to the present invention includes a generator of a seller selling power at a contract price settled by a bid in the power trading market, Electricity comprising a load of a buyer who purchases power at a contract price, a non-spot market generator that provides power at a fixed electricity rate, and a non-spot market load that consumes electricity at the fixed electricity rate In the determinant analysis method of the contract price in the power trading market of the grid, an equality constraint condition including the power flow equation in the power grid and the relation between the liberalized power generation including transmission loss and the supply-demand balance relation of demand, Include inequality constraints including reactive power upper and lower limits, voltage upper and lower limits, and power flow upper and lower limits, and include all power consumer surpluses and all power supplier surpluses. A single price auction optimal solution that maximizes the value of the target function indicating social surplus and its dual solution are obtained, and a contract pricing bus is searched based on the optimal solution and the bid function of each of the seller and the buyer. The equality constraint condition and the inequality constraint condition are divided into a value constraint condition whose value is positively evaluated for the contract price and a non-value constraint condition whose value is not explicitly evaluated for the contract price, By calculating the voltage sensitivity at the contract pricing bus based on the value constraint, the valueless constraint, the optimal solution and the dual solution, the contract price is related to the non-spot market load consumption cost. A term relating to power generation costs of the non-spot market generator, a term relating to the bid function of the buyer, a term relating to the bid function of the seller, The value of each term is calculated by decomposing into a linear polynomial composed of a term relating to the equivalent value of the security constraint condition, a term relating to the upper limit constraint on the bid amount, and a term relating to the lower limit constraint on the bid amount. It is said.

  According to the determinant analysis method (1) of the contract price in the power trading market, the generator of the seller who sells power at the contract price settled by bidding in the power trading market and the buyer who purchases the power at the contract price. Contract price in the power trading market of a power system comprising a load of a non-spot market that provides power at a fixed electricity rate, and a load on a non-spot market that consumes power at the fixed electricity rate In the determinant analysis method, there are equality constraints including the power flow equation in the power system and the relation between the liberalized power generation and demand balance including transmission loss, the active / reactive power upper and lower limits, and the voltage upper and lower limits. And an inequality constraint that includes the upper and lower limits of the tidal current, and a social function surplus that includes all power consumer surpluses and all power supplier surpluses. A single price auction optimal solution and a dual solution thereof are searched, and a contract pricing bus is searched based on the optimal solution and each bid function of the seller and the buyer, and the equality constraint and the The inequality constraint condition is divided into a value constraint condition whose value is explicitly evaluated at the contract price and a value constraint condition whose value is not evaluated explicitly at the contract price, and the value constraint condition and the value constraint By calculating the voltage sensitivity at the contract pricing bus based on the condition, the optimal solution and the dual solution, the contract price is calculated in terms of the consumption cost of the non-spot market load; A term relating to the power generation cost of the generator, a term relating to the bid function of the buyer, a term relating to the bid function of the seller, and the equivalent value of the value constraint In order to calculate the value of each term by decomposing it into a linear polynomial composed of a term relating to the upper limit constraint on the bid amount, and a term relating to the lower limit constraint on the bid amount. Factors that determine prices (detailed information) are elucidated, and quantitative evaluation of the impact on the contract price due to factors including bid information, non-spot market generator and load operation information, voltage and power constraints, etc. Can be realized.

  Also, the determinant analysis method (2) of the contract price in the power trading market according to the present invention is the following determinant analysis method (1) of the contract price in the power transaction market. The equality constraint condition is expressed by the following formulas (2) and (4), and the inequality constraint condition is expressed by the following formula (3).

  According to the determinant analysis method (2) of the contract price in the power trading market, the target function is expressed by the following formula (1), and the equality constraint condition is expressed by the following formulas (2) and (4). Since the inequality constraint condition is expressed by the following equation (3), the simulation model of the single price auction is formulated by a mathematical formula, and the optimal solution of the single price auction can be obtained.

また、本発明に係る電力取引市場における約定価格の決定要因分析方法（３）は、上記電力取引市場における約定価格の決定要因分析方法（１）又は（２）において、前記最適解での入札価格が一番高い売り手の発電機に接続されている母線と、前記最適解での入札価格が一番安い買い手の負荷に接続されている母線をそれぞれ前記約定価格決定母線とすることを特徴としている。

Also, the determinant analysis method (3) of the contract price in the power trading market according to the present invention is the bidding price at the optimal solution in the determinant analysis method (1) or (2) of the contract price in the power transaction market. The bus connected to the generator with the highest seller and the bus connected to the load of the buyer with the lowest bid price at the optimal solution are used as the contract pricing buses, respectively. .

  In general, in a single price auction, the contract price is determined by the highest limit bid price of each seller's limit bid price or the lowest limit bid price of each buyer's limit bid price.

  According to the determinant analysis method (3) of the contract price in the power trading market, the bus connected to the generator of the seller with the highest bid price at the optimal solution and the bid price at the optimal solution are Since each bus connected to the cheapest buyer's load is used as the contract price determination bus, the contract price determination bus is a bus that determines the contract price.

  Further, the contract factor determining factor analysis method (4) in the power trading market according to the present invention is connected to the seller's generator in the contract price determining factor analysis method (2) or (3) in the power trading market. The voltage sensitivity at the contracted pricing bus is calculated by the following formulas (5) and (7), and the voltage sensitivity at the contracted pricing bus connected to the generator of the buyer is expressed by the following formula (6): It is characterized by calculating by (7).

  According to the determinant analysis method (4) of the contract price in the power trading market, the voltage sensitivity at the contract price determination bus connected to the generator of the seller is calculated by the following equations (5) and (7). Since the voltage sensitivity at the contract pricing bus connected to the generator of the buyer is calculated by the following equations (6) and (7), the voltage sensitivity values can be calculated respectively.

  In addition, the determinant analysis method (5) of the contract price in the power trading market according to the present invention is the same as the determinant analysis method (4) of the contract price in the power transaction market. A linear combination of the highest bid price among the seller's bid prices and the lowest bid price among the buyers in the optimal solution, and it is decomposed and calculated as shown in Equation (8) below. It is characterized by.

  According to the determinant analysis method (5) of the contract price in the power trading market, the contract price is calculated by using the highest bid price among the bid prices of each seller in the optimal solution and each buyer in the optimal solution. In order to make a linear combination with the lowest bid price among the bid prices, and to decompose and calculate as shown in the following equation (8), the contract price is a term related to the consumption cost of the load of the non-spot market, and the non-spot A term relating to the power generation cost of the generator in the market, a term relating to the bid function of the buyer, a term relating to the bid function of the seller, a term relating to the equivalent value of the value constraint, a term relating to the upper limit constraint of the bid amount, and bidding It can be decomposed into a linear polynomial composed of terms relating to the lower limit constraint of the quantity, and the value of each term can be calculated.

  The computer program (1) for analyzing determinants of contract prices in the power trading market according to the present invention includes a generator of a seller that sells power at a contract price contracted by bidding in the power trading market, and the contract. In a power system comprising a load of a buyer who purchases electricity at a price, a non-spot market generator that provides power at a fixed electricity rate, and a non-spot market load that consumes electricity at a fixed electricity rate , An equality constraint condition including a tidal current equation expressed by the following equation (2) and a liberalized power generation including transmission loss expressed by the following equation (4) and a demand-supply balance relation equation, and the following equation ( 3) After satisfying the inequality constraints that include the upper and lower limits of active and reactive power, the upper and lower limits of voltage, and the upper and lower limits of power flow, all power consumer surpluses and all expressed by the following formula (1) Power of A step of obtaining an optimal solution and a dual solution of a single price auction that maximizes the value of a target function indicating a social surplus including a surplus of surplus, and a bid price at the optimal solution serving as a contract price determination bus is the highest. Searching for the bus connected to the generator of the seller and the bus connected to the buyer's load with the lowest bid price in the optimal solution, and the equality and inequality constraints Based on the value constraint that the value is positively evaluated for the contract price divided from the above, the value constraint that the value is not explicitly evaluated for the contract price, the optimal solution and the dual solution, the seller The voltage sensitivity at the contract pricing bus connected to the generator is calculated by the following equations (5) and (7), and the contract pricing bus connected to the buyer's generator is calculated. Calculating the voltage sensitivity according to the following formulas (6) and (7), the following formula (8) to calculate the contract price as a term relating to the consumption cost of the load of the non-spot market, and the non-spot market: A term relating to the power generation cost of the generator, a term relating to the bid function of the buyer, a term relating to the bid function of the seller, a term relating to the equivalent value of the value constraint, a term relating to the upper limit constraint of the bid amount, and a bid amount The computer is caused to execute a step of calculating by decomposing into a term relating to the lower limit constraint.

  According to the determinant analysis program (1) of the contract price in the above power trading market, the power supply and demand balance including the power flow equation represented by the following equation (2) and the transmission loss represented by the following equation (4) After satisfying the equality constraint condition including the relational expression and the inequality constraint condition including the active / reactive power upper / lower limit, voltage upper / lower limit, and power flow upper / lower limit expressed by the following equation (3) Then, the optimal solution of the single price auction that maximizes the value of the target function indicating the social surplus including all the power consumer surpluses and all the power supplier surpluses expressed by the following formula (1) and its dual solution are obtained. Connected to the generator connected to the generator of the seller with the highest bid price at the optimal solution as the contract price determination bus and the buyer's load with the lowest bid price at the optimal solution And the bus Retrieval step, valuable constraint condition whose value is positively evaluated for the contract price divided from the equality constraint condition and the inequality constraint condition, and a non-value constraint whose value is not explicitly evaluated for the contract price Based on the conditions, the optimal solution and the dual solution, the voltage sensitivity at the contract pricing bus connected to the seller's generator is calculated by the following equations (5) and (7), Calculating the voltage sensitivity at the contract pricing bus connected to the machine by the following formulas (6) and (7), and the formula (8) below, the contract price is calculated as the load of the non-spot market. A term relating to consumption costs, a term relating to power generation costs of generators in the non-spot market, a term relating to the bid function of the buyer, a term relating to the bid function of the seller, In order to cause the computer to execute the step of decomposing and calculating the term relating to the value and value, the term relating to the upper limit constraint on the bid amount, and the term relating to the lower limit constraint on the bid amount, the proportion of the respective terms in the contract price, From the degree of influence of each item, it is possible to quantitatively analyze and evaluate the influence of various factors in the power system including bid information on the contract price.

FIG. 1 is a configuration diagram schematically illustrating a main part of an electric power system to which a determinant analysis method for a contract price in an electric power market according to an embodiment of the present invention is applied. Figure 1 shows the power system in the case of introducing electric power trading system, the power system 1, the generator SG12 (SG of the spot market to participate in the electricity trading market power generator _{SG 1, SG 2, ...,} SG _NG means a set of _NG ) and spot market load SD13 (SD means a set of loads SD ₁ , SD ₂ ,..., SD _ND ), and a non-spot market generator G14 (G _Includes a generator G ₁ , G ₂ ,..., _GNg ) and a non-spot market load D15 (D means a set of loads D ₁ , D ₂ ,..., D _Nd ). Has been. The non-spot market generator G14 provides power to the power grid 1 at a fixed price, and the non-spot market load D15 consumes power from the power grid 1 at a fixed price. On the other hand, those who participate in the power trading market (generator SG12, load SD13) determine the selling price of power by bidding through the power exchange. However, it is also possible to buy electric power from the generator G14 as the load (the load in the SD 13) of the person who did not complete the transaction.

In the power system 1 shown in FIG. 1, when a single price auction is performed, a simulation model of the single price auction is expressed by equations (1) to (4).
In Formula (1), F (X) is a target function indicating the social surplus that is the sum of the power supplier surplus and the power demand surplus, and the first term thereof is the consumption cost (known amount) of the load D15 in the non-spot market. The second term represents the power generation cost of the generator G14 in the non-spot market, the third term represents the purchase cost of the spot market buyer (load SD13), and the fourth term The term shows the selling cost of the spot market seller (generator SG12). Since the non-spot market load consumption and its charge are given in advance, the first term is a known amount and does not affect the optimal solution of the target function. ω _i (P _gi ) is usually expressed as a linear function of P _gi because of the incremental fuel cost function of the generator. The buyer's bid function θ _i (P _Di ) and the seller's bid function φ _i (P _Gi ) can be generally expressed by a linear function or a piecewise linear function.

  G '(X) is the equality constraint in the power system, that is, the power flow equation, and H (X) is the inequality constraint in the power system, that is, the upper and lower limits of the effective and reactive power generation, the voltage upper and lower limits, and the power flow upper and lower limits. K (X) is a spot market balance equation constraint, that is, a supply-demand balance equation of liberalized power generation and demand including transmission loss.

X is an independent variable of the target function F (X), the equation constraint G ′ (X), the inequality constraint H (X), and the equation constraint K (X) described above, and the power shown in FIG. It is a vector composed of a real part and an imaginary part of the bus voltage in the system 1. Further, the amounts of power P _gi, P _Gi , P _Di are also functions of X.

Moreover, in Formula (1), since the amount of power consumption of the load (D15) of the non-spot market and the electricity charge are given in advance, π _di and P _di are constants and do not affect the optimal solution X. ω _i (P _gi ) is an incremental fuel cost function of the generator (G14), and can be expressed by a linear function of P _gi . The bid function θ _i (P _Di ) of the buyer (SD13) and the bid function φ _i (P _Gi ) of the seller (SG12) are the linear functions or piecewise linear functions shown in FIGS. 3b and 3a, respectively. The bidding function (supply curve) shown in FIG. 3a shows that seller i (SG _{i in} SG12) sells power up to P _Gi at a price greater than φ _i (P _Gi ) and is shown in FIG. 3b. The bid function (demand curve) indicates that buyer i (SD _i in SD 13) buys power up to the maximum P _Di at a price equal to or less than θ _i (P _Di ).

By solving equation (1), it is possible to obtain an optimal solution X that maximizes the social surplus that is the sum of the surplus of power suppliers (SG12 and G14) and the surplus of power consumers (SD13 and D15). Furthermore, the optimal solution X gives approximately fixed amounts P _Gi (X) and P _Di (X) of each seller (SG12) and each buyer (SD13) and the output P _gi (X) of the non-spot generator (G14). It is done. Further, by substituting approximately fixed amounts P _Gi (X) and P _Di (X) into bid functions φ _i (P _Gi ) and θ _i (P _Di ), respectively, the limit bid price (π _Gi ) of each seller (SG12) And the limit bid price (π _Di ) of each buyer (SD13) is calculated by the respective bid functions φ _i (P _Gi ) and θ _i (P _Di ).

If the supply curve (FIG. 3a) and the demand curve (FIG. 3b) intersect as shown in FIG. 3c, the contract price (MCP) π Is the highest limit bid price (π _Gmax ) in the limit bid price (π _Gi ) of each seller (SG12) or the lowest limit bid price (π _Dmin ) in the limit bid price (π _Di ) of each buyer (SD13) _I.e. , π = π _Gmax = π _Dmin .

When there are a plurality of intersections between the supply curve (FIG. 3a) and the demand curve (FIG. 3b) (that is, π _Gmax ≠ π _Dmin ), the contract price π can be calculated by the equations (9) to (11).

  Here, it was possible to calculate the contract price π using the simulation model of the single model price auction described above, but the calculation result is only the value of the contract price π, and the factors of the bid information and each power system are It is still unclear how much it affects the value of the contract price.

但し、λ、ρは双対解である。 Next, in order to decompose the contract price π, a parameter P = (P ₁ , ..., P _n ) representing the amount of market selling bids (that is, bids with arbitrary bid prices) is introduced, and the formula ( 1) Goal function F, constraint G (constraint G is the combination of constraint G ′ in equation (2) and constraint K in equation (4)), and H in equation (3) A function of X and P, and its Lagrangian function L is expressed by equation (12).

Where λ and ρ are dual solutions.

但し、μ_PGKはスポット市場母線GKのSPAノーダルプライスとなる。 式（１）〜（４）により、目標関数F、制約条件GとHには、わずかの項のみ特定のスポット市場の母線の成行売り入札量P_GKに直接関係しているため、特定の成行売り入札量P_GKでLを偏微分した後に、式（１３）の項はほとんど消去されて式（１４）となる。 If the Lagrangian function L in Expression (12) is partially differentiated by P _Gk that is an element of P, Expression (13) is obtained.

However, μ _PGK is the SPA nodal price of the spot market bus GK. According to Equations (1) to (4), the target function F and the constraints G and H are directly related to the market bid amount P _GK of a specific spot market bus because only a few terms are directly related. After partial differentiation of L with the selling bid amount P _GK , the term of equation (13) is almost eliminated to become equation (14).

式（１３）において、φ (P_GK)はスポット市場の母線GKの売り手の入札関数であり、ρ_Gmax、ρ_Gminは売り手の入札量上限制約および下限制約のラグランジュ乗数であり、その限界値に引っかからない場合０となる。

In equation (13), φ (P _GK ) is a bid function of the seller of the spot market bus GK, and ρ _Gmax and ρ _Gmin are Lagrange multipliers of the seller's upper limit and lower limit of the bid amount of the seller, and 0 when the limit value is not caught.

In equation (14), if P _GK is the bid amount of the spot market generator (one in SG12) that connects to the contract pricing bus GK, then φ (P _GK ) is the seller's maximum marginal price π _Gmax . That is, the seller's maximum marginal price π _Gmax can be expressed by equation (15).

Using the same method, if P _DK is the bid amount of the spot market load (one in SD13) that connects to the contract pricing bus DK, the buyer's minimum limit price π _Dmin is derived and expressed by equation (16) be able to. Furthermore, the contract price π can be expressed by Expression (18) by Expression (9).

但し、ｃは約定価格決定係数であり、ρ_Gmax、ρ_Gminは売り手の入札量上限制約および下限制約のラグランジュ乗数であり、ρ_Dmax、ρ_Dminは買い手の入札量上限制約および下限制約のラグランジュ乗数であり、その限界値に引っかからない場合０となる。

Where c is a contract pricing factor, ρ _Gmax and ρ _Gmin are Lagrange multipliers for the seller's upper and lower bounds, and ρ _Dmax and ρ _Dmin are Lagrange multipliers for the buyer's upper and lower bounds. It is 0 when the limit value is not caught.

Therefore, if the SPA nodal price μ _PGK of the bus GK and the SPA nodal price μ _{PDK of the} bus DK in Formula (18) are decomposed, the contract price π can be decomposed. That is, the contract price π includes the marginal equivalent social surplus of the contract pricing buses GK and DK and the Lagrange multiplier of the bid volume upper and lower limit constraints, and the buses GK and DK are not subject to the bid volume upper and lower limit constraints (ρ _Gmax , Ρ _Gmin , ρ _Dmax , ρ _Dmin are 0), and the contract price π represents the marginal equivalent social surplus, that is, the increase in social surplus when a small amount of market bids are placed on the buses GK and DK I understand.

Next, disassembly of the SPA nodal price _μPGK of the bus GK and the SPA nodal price _μPDK of the bus DK will be described.
If H is an activation constraint in the optimum solution X of equation (1), the optimum solution satisfies equations (19) to (21).

  On the other hand, in order to break down the contract price in more detail, it is necessary to determine which constraint factors are specifically reflected in the contract price. Each factor or constraint in power system operation can be classified into a factor that has a market value and can be traded, a factor that has no market value and cannot be traded, or a constraint that can be relaxed and a constraint that cannot be relaxed. For example, power transmission line power constraints and bus voltage constraints can be relaxed by technological innovation and capital investment, and therefore belong to factors that can be traded according to market needs. On the other hand, the power balance constraint in which the total bus injection power is zero belongs to a non-transactional factor that cannot be relaxed because of Kirchhoff's physical law. In the present invention, among the constraint conditions G and H, a constraint expression (non-transaction factor) that does not express the price explicitly is defined as a non-value constraint condition M, and the remaining constraint expression, that is, a constraint expression that expresses the charge explicitly ( The factor that can be traded) is the value constraint condition N. Further, if α is a Lagrange multiplier in the non-value constraint M, and β is a Lagrange multiplier in the value constraint N, the second and third items (λ∂G / ∂X + ρ∂H / ∂X) in Equation (19) Can be replaced by α∂M / ∂X + β∂N / ∂X. That is, Expression (19) can be rewritten as Expression (22).

制約条件M、NとUは全て列ベクトルであり、ラグランジュ乗数αとβは行ベクトルである。
また、式（２２）〜（２４）はラグランジュ関数Lが常に最大値となるための必要条件である。

The constraints M, N and U are all column vectors, and the Lagrange multipliers α and β are row vectors.
Expressions (22) to (24) are necessary conditions for the Lagrangian function L to always have the maximum value.

Next, in order to disassemble the configuration of the contract price, it is assumed that the condition indicated by the equation (25) is satisfied in the optimal solution X of the equation (1).

  That is, if the condition expressed by the equation (25) is satisfied, there is only one function [X (P), a (P)] in the vicinity of the given variable P. Therefore, as long as the equations (22) to (24) hold, the variable (X, a) is not independent of P, but is a function of P. By substituting X (P) and a (P) into equations (22) and (24), equations (26) and (27) are obtained.

さらに、Pの要素であるP_GKで式（２６）を偏微分すれば、式（２８）が得られる。

Furthermore, if the equation (26) is partially differentiated by P _GK which is an element of P, the equation (28) is obtained.

但し、F_XX=∂²F(X, P)/∂X²、F_XPGK=∂²F(X, P)/∂X∂P_GK、U_x=∂U(X, P)/∂X、 U_α=∂U(X, P)/∂α、U_PGK=∂U(X, P)/∂P_GK、M_X=∂M(X, P)/∂X、M_PGk=∂M(X, P)/∂Ｐ_GK、X_PGk=∂X/∂P_GK、α_PGk=∂α/∂P_GKとする。
式（２５）が成立すれば、式（２８）を式（２９）に書き換え、約定価格決定母線GKにおける電圧感度X_PGkとラグランジュ乗数α_PGkを求めることができる。
同じ方法により、約定価格決定母線DKにおける電圧感度X_PDkとラグランジュ乗数α_PDkを表す式（３０）を導出することができる。

However, F _XX = ∂ ² F (X, P) / ∂X ² , F _XPGK = ∂ ² F (X, P) / ∂X∂P _GK , U _x = ∂U (X, P) / ∂X, U _α = ∂U (X, P) / ∂α, U _PGK = ∂U (X, P) / ∂P _GK , M _X = ∂M (X, P) / ∂X, M _PGk = ∂M (X _{, P) / ∂P GK, X} PGk = ∂X / ∂P GK, and α _PGk = ∂α / ∂P _GK.
If Expression (25) is established, Expression (28) can be rewritten to Expression (29), and the voltage sensitivity X _PGk and Lagrange multiplier α _PGk at the contract price determination bus GK can be obtained.
By the same method, the expression (30) representing the voltage sensitivity X _PDk and the Lagrange multiplier α _PDk in the contract pricing bus DK can be derived.

但し、F_XX=∂²F(X, P)/∂X²、F_XPDK=∂²F(X, P)/∂X∂P_DK、U_X=∂U(X, P)/∂X、U_α=∂U(X, P)/∂α、U_PDK=∂U(X, P)/∂P_DK 、M_X=∂M(X, P)/∂X、M_PDk=∂M(X, P)/∂Ｐ_GK、X_PDk=∂X/∂P_DK 、α_PDk=∂α/∂P_DKとする。

However, F _XX = ∂ ² F (X, P) / ∂X ² , F _XPDK = ∂ ² F (X, P) / ∂X∂P _DK , U _X = ∂U (X, P) / ∂X, U _α = ∂U (X, P) / ∂α, U _PDK = ∂U (X, P) / ∂P _DK , M _X = ∂M (X, P) / ∂X, M _PDk = ∂M (X _{, P) / ∂P GK, X} PDk = ∂X / ∂P DK, and α _PDk = ∂α / ∂P _DK.

On the other hand, when the variable X, the target function F, the constraint conditions M and N, and the Lagrangian multiplier are all displayed as functions of P, the Lagrangian function L is rewritten into Expression (31).

Therefore, if partial differential Lagrange function L of the formula (31) in Shigeyuki selling bid amount P _GK, equation (32) is obtained.

Since the optimal solution X is F _X = 0, M = 0, and M _X X _PGK + M _PGK = 0 (from Expression (28)), Expression (33) is obtained.
By the same method, Expression (34) can be derived in the contract pricing bus DK.

式（３５）において、電圧感度X_PGKとX_PDKはそれぞれ式（２９）と式（３０）により求められる。 If μ _PGK and μ _PDK in equations (33) and (34) are substituted into equation (18), the decomposition formula for the contract price becomes equation (35).

In the equation (35), the voltage sensitivities X _PGK and X _PDK are obtained by the equations (29) and (30), respectively.

Therefore, the expansion formula (formula (35)) of the decomposed contract price π is a term related to the consumption cost of the load (D15) in the non-spot market, a term related to the power generation cost of the generator (G14) in the non-spot market, the buyer ( SD13) for bid function θ _i , for seller (SG12) for bid function φ _i, for equivalent value of constraint N, for seller, buyer's maximum bid, and for seller, buyer's minimum bid It is a linear combination of terms.

Note that if the constraint condition N includes all of the equality constraint condition G and the inequality constraint condition H, all elements appearing in the Lagrangian function L are not zero, and therefore are represented explicitly in the contract price. On the other hand, if the constraint M includes all of the equality constraint G and the inequality constraint H, all terms except the target function F are eliminated from the decomposition formula of the contract price π.
That is, if the setting of the constraint condition N with market value is determined, the contract price π can be obtained uniquely, but the decomposition formula of the contract price π may differ depending on how the constraint condition N is determined.

Next, the processing of the determinant analysis program for the contract price in the above-mentioned power trading market will be described based on the flowchart shown in FIG. First, in step S1, in the power system 1 shown in FIG. 1, the bid function φ _i of each seller (SG12), the bid function θ _i of the buyer (SD 13), and a transmission line (not shown) constant in the power system, Set data such as voltage, active power, and reactive power constraints. Subsequent to step S1, in step S2, the optimal solution X and its dual solution (λ, ρ) are obtained by solving equations (1) to (4). Subsequent to step S2, in step S3, the bid price of each seller is calculated with the optimal solution by equation (10), and the bus GK connected to the generator of the seller with the highest bid price is detected. Subsequent to step S3, in step S4, the bid price of each buyer is calculated with the optimal solution according to equation (11), and the bus DK connected to the buyer's load with the lowest bid price is detected. Subsequent to step S4, in step S5, the voltage sensitivity X _PGK at the bus GK is calculated by the equation (29) based on the valuable constraint condition N and the non-value constraint condition M. Subsequent to step S5, in step S6, the voltage sensitivity X _PDK at the bus DK is calculated from the equation (30) based on the valuable constraint condition N and the non-value constraint condition M. Subsequent to step S6, in step S7, the value of the component of the contract price is obtained by the equation (35).

  According to the method for analyzing the determinants of the contract price in the power trading market and the computer program for the analysis according to the above-described embodiment, the contract price π in the single price auction is the term relating to the bid function of the buyer (SD13), and the seller ( SG12) a term relating to the bid function, a term relating to the power generation cost of the generator (G14) in the non-spot market, a term relating to the consumption cost of the load (D15) in the non-spot market, and the equivalent value of the value constraint N Divides into a linear polynomial consisting of a term on the upper limit constraint on the bid amount, a term on the lower limit constraint on the bid amount, and a term on the lower limit constraint on the bid amount, so detailed information on the factors that determine the contract price π from the decomposed polynomial is clarified In addition, since the values of the above terms are calculated, bid information, non-spot market generators and load It is possible to quantitatively evaluate the effect on the contract price due to factors including constraints such as utility information, voltage and power. Therefore, the determinant analysis method of contract prices in the power trading market and the computer program for the analysis according to the present invention can be used not only for the efficiency of power operation management, power supply and transmission network operation and congestion management, but also for investment risk. It can also be used for strengthening management and bidding decisions.

  Next, an embodiment using the determinant analysis method of the contract price in the power trading market of the present invention and the computer program for the analysis will be shown.

  FIG. 5 is a diagram showing an electric power system according to an embodiment using the determinant analysis method of the contract price in the power trading market according to the present invention. In FIG. 5, reference numeral 2 denotes an electric power system. The electric power system 2 includes a first seller (generator) 21, a second seller (generator) 22, and a first buyer (load) that participate in the power trading market. 31, a second buyer (load) 32, a non-spot market generator 23 not participating in the power trading market, a non-spot market load 33, a first bus 41 connected to the generator 21, and a load 31, a second bus 42 connected to 31, a third bus 43 connected to the load 33, a fourth bus 44 connected to the generator 22, and a fifth bus 45 connected to the load 32. And a sixth bus 46 connected to the generator 23, and a power transmission line 51 connecting the buses.

  The non-spot market generator 23 provides power to the power grid 2 at a fixed electricity rate, and the non-spot market load 33 consumes power from the power grid 2 at a fixed electricity rate, while the first seller 21 and the second The seller 22 provides the electric power system 2 with the electric power produced by each of the generators at the contract price (electricity charge) contracted in the single price auction via the power exchange, and the first buyer 31 and the second buyer. No. 32 purchases electric power from the electric power system 2 at a contract price (electricity charge) contracted in a single price auction via the power exchange. The generators 21 to 23 inject the generated power into the electric power system 2 through the connected bus 41, bus 44, and bus 46, respectively, and the loads 31 to 33 are connected to the bus 42, the bus 43, Power consumption is absorbed from the electric power system 1 via the bus 45, and each power transmission line 51 delivers power between the buses 41 to 46 in response to demands for supply and demand.

FIG. 6 a is a table showing the values of resistance r, reactance x, and transmission line admittance y / 2 of each transmission line in the power system 2. FIG. 6b is a table showing the respective bid functions and amounts of power for sellers 21 and 22 and buyers 31 and 32 participating in the power transaction.
The incremental fuel cost function of the non-spot market generator 23 connected to the bus 46 is ω ₆ (P _g6 ) = 7.0P _g6 , and the valid / invalid output upper and lower limits are 0.0 ≦ P _g6 ≦ 1.0. The upper and lower limits of the invalid output are 0.0 ≦ Q _g6 ≦ 0.5. The effective load of the non-spot customer 33 connected to the bus 43 is P _d3 = 0.3, and the invalid load is Q _d3 = 0.18. The lower limit of the reactive power output for sellers and buyers is 0.0, and the upper limit is 1/2 of the bid amount. The upper and lower limits of the voltages for all the buses 41 to 46 are 0.95 ≦ V _k ≦ 1.05, and the upper and lower limits of the active power flow of the transmission line 51 between the buses 43 and 42 are −0.05 ≦ Pf _3-2 ≦ 0.05. The electricity rate π _di of the non-spot consumer 33 is 15.0, and the spot market transmission loss rate k Is 0.0. All values are in pu notation.

  Based on the data described above, a simulation model of a single price auction of formulas (1) to (4) is created, and by solving formula (1), the voltage X of buses 41 to 46 that is the optimum solution obtained is obtained. The real part, the imaginary part and the social surplus F are shown in FIG.

  From the results shown in FIG. 7, the limit bid price of the first seller 21 is 14.969, the limit bid price of the second seller 22 is 9.586, the limit bid price of the first buyer 31 is 19.284, and the limit bid price of the second buyer 32 is 14.969. Therefore, from the formulas (9) to (10), the contract price is 14.969, and the contract price determination bus is connected to the first bus 41 connected to the generator 21 of the first seller and the load 32 of the second buyer. The fifth bus 45 is present.

Further, if three constraint conditions in the constraint condition G are non-value constraint conditions M, six activation constraint conditions in the inequality constraint condition H are valuable constraint conditions N, and the contract price determination coefficient c is 1, the contract price π Can be decomposed into equation (36).

Where φ ₁ (P _G1 ) is the bid price of the first seller 21, θ ₂ (P _D2 ) is the bid price of the first buyer 31, π _d3 is the electricity price of the non-spot load 33, φ ₄ (P _G4 ) is the bid price of the second seller 22, θ ₅ (P _D5 ) is the bid price of the second buyer 32, and ω ₆ (P _g6 ) is the incremental fuel of the generator 23 in the non-spot market. Ρ _V4 , ρ _V6 are Lagrange multipliers for the voltage upper limit constraints of the fourth bus 44 and the sixth bus 46, and ρ _pf3-2 is the upper limit constraint for the current flowing from the third bus 43 to the second bus 42. It is a Lagrange multiplier, and ∂ / ∂p ₁ is a partial differential of the first bus 41 according to the amount of a bid for market selling.

Further, if the voltage sensitivity X _PGK of the first bus is calculated according to equation (29) and substituted into equation (36), the contract price π and its components are calculated as shown in equation (37). . FIG. 8 shows the degree of influence and the proportion of each component in the calculated contract price.

但し、φ₁=14.969、θ₂=19.284、π_d3=15.0、φ₄= 9.586、θ₅=14.969、ω₆=7.0、ρ_V4=0.002、ρ_V6=0.006、ρ_Pf3-2=13.800である。

However, φ ₁ = 14.969, θ ₂ = 19.284, π _d3 = 15.0, φ ₄ = 9.586, θ ₅ = 14.969, ω ₆ = 7.0, ρ _V4 = 0.002, ρ _V6 = 0.006, ρ _Pf3-2 = 13.800. .

  According to the numerical results shown in FIG. 8, it can be seen that the influence degree of the value constraint conditions 1 and 2 is large in each element, and the ratio occupied by the bid function is large.

It is the schematic diagram which showed roughly the principal part of the electric power system with which the computer program for the determination factor analysis method and analysis of the contract price in the electric power transaction market which concerns on embodiment of this invention was applied. It is a figure which shows the market supply curve in the computer program for the determination factor analysis method and analysis of the contract price in the electric power transaction market which concerns on embodiment. It is a figure which shows the market demand curve in the computer program for the determinant analysis method of the contract price in the electric power transaction market which concerns on embodiment, and an analysis. It is a figure which shows the determinant analysis method of the contract price in the electric power transaction market which concerns on embodiment, and the contract price determination curve in the computer program for an analysis. It is a figure which shows the bid function of the seller in the determinant analysis method of the contract price in the electric power transaction market which concerns on embodiment, and the computer program for analysis. It is a figure which shows the bid function of the buyer in the determinant analysis method of the contract price in the electric power transaction market which concerns on embodiment, and the computer program for analysis. It is a figure which shows the supply factor and demand curve of the spot market in the determinant analysis method of the contract price in the electric power transaction market which concerns on embodiment, and the computer program for analysis. It is a flowchart which shows the processing operation of the decision factor analysis program of the contract price in the electric power transaction market which concerns on embodiment. BRIEF DESCRIPTION OF THE DRAWINGS It is a systematic diagram which shows roughly the principal part of the electric power grid | system in the Example to which the determinant analysis method of the contract price in the electric power transaction market which concerns on this invention and the computer program for an analysis were applied. It is a table | surface which shows the transmission line constant of the electric power grid | system in an Example. It is a table | surface which shows the bid information in an Example. It is a table | surface which shows the active power and reactive power of each bus in the optimal solution in an Example. It is a table | surface which shows the calculation result of each component of the contract price in an Example.

Explanation of symbols

1, 2 Power system 12 Spot market generator SG
13 Spot Market Load SD
14 Non-spot market generator G
15 Non-spot market load D
16 Operation & Display Means 21 First Seller 22 Second Seller 23 Non-Spot Market Generator 31 First Buyer 32 Second Buyer 33 Non-Spot Market Load 41 First Bus 42 Second Bus 43 Third Bus 44 Fourth Bus 45 5th bus 46 6th bus 51 Transmission line

Claims (6)

A generator of a seller who sells power at a contract price settled by a bid in the power trading market, a load of a buyer who purchases power at the contract price, and a generator in a non-spot market that provides power at a fixed electricity rate In the determinant analysis method of the contract price in the power trading market of the power system configured to include the load of the non-spot market that consumes power at the fixed electricity rate,
Including the power flow equation in the power system and the equality constraints including the power supply / demand balance relational expression including power transmission loss, including the active / reactive power upper and lower limits, the voltage upper and lower limits, and the power flow upper and lower limits An optimal solution for a single price auction that satisfies the configured inequality constraints and maximizes the value of the target function indicating the social surplus including all power demand surplus and all power surplus, and its dual Seeking a solution
Based on the optimal solution and the bid function of each of the seller and the buyer, search for a contract pricing bus,
The equality constraint and the inequality constraint are divided into a value constraint whose value is positively evaluated for the contract price and a valueless constraint whose value is not explicitly evaluated for the contract price,
Based on the value constraint, the valueless constraint, the optimal solution and the dual solution, calculating the voltage sensitivity at the contract pricing bus,
The contract price, a term relating to a consumption cost of the non-spot market load, a term relating to a power generation cost of the non-spot market generator, a term relating to the bid function of the buyer, a term relating to the bid function of the seller, The value of each term is calculated by decomposing into a linear polynomial composed of a term relating to the equivalent value of the valuable constraint condition, a term relating to the upper limit constraint on the bid amount, and a term relating to the lower limit constraint on the bid amount. A determinant analysis method of contract prices in the electricity trading market. The target function is expressed by the following formula (1), the equality constraints are expressed by the following formulas (2) and (4), and the inequality constraint is expressed by the following formula (3). The determinant analysis method of a contract price in the power trading market according to claim 1.

  The contract price determination bus is connected to the bus connected to the generator of the seller with the highest bid price at the optimal solution and the bus connected to the load of the buyer with the lowest bid price at the optimal solution. The determinant analysis method of the contract price in the power trading market according to claim 1 or 2, wherein The voltage sensitivity at the contract pricing bus connected to the generator of the seller is calculated by the following formulas (5) and (7), and the voltage sensitivity at the contract pricing bus connected to the buyer's generator is calculated. The determinant analysis method of the contract price in the electric power trading market according to claim 2 or 3, wherein calculation is performed by the following formulas (6) and (7).

The contract price is a linear combination of the highest bid price of each seller's bid price in the optimal solution and the lowest bid price of each buyer's bid price in the optimal solution. 5. The determinant analysis method of the contract price in the power trading market according to claim 4, wherein the factor is analyzed and calculated as shown in FIG.

A generator of a seller who sells power at a contract price contracted in the electricity trading market, a load of a buyer who purchases power at the contract price, and a non-spot market generator which provides power at a fixed electricity rate In a power system that includes non-spot market loads that consume electricity at a fixed electricity rate,
An equality constraint condition including a power flow equation represented by the following equation (2) and a liberalized power generation including transmission loss represented by the following equation (4) and a demand-supply balance relation equation, and the following equation (3 ) And the inequality constraints that include the upper and lower limits of active and reactive power, the upper and lower limits of voltage, and the upper and lower limits of power flow, and all power consumer surpluses and all Obtaining an optimal solution and a dual solution of a single price auction that maximizes a value of a target function indicating a social surplus including a power supplier surplus;
A bus connected to the generator of the seller with the highest bid price at the optimal solution to be a contract price determination bus, and a bus connected to the load of the buyer with the lowest bid price at the optimal solution; Searching for each of the
A value constraint condition whose value is positively evaluated for the contract price divided from the equation constraint condition and the inequality constraint condition, a non-value constraint condition whose value is not explicitly evaluated for the contract price, the optimal solution and Based on the dual solution, the voltage sensitivity at the contract pricing bus connected to the generator of the seller is calculated by the following equations (5) and (7) and connected to the generator of the buyer. Calculating the voltage sensitivity at the contract pricing bus using the following equations (6) and (7):
According to the following equation (8), the contract price is a term relating to the consumption cost of the load in the non-spot market, a term relating to the power generation cost of the generator in the non-spot market, a term relating to the bid function of the buyer, and the seller. Causing the computer to execute a step of decomposing and calculating a term relating to a bid function, a term relating to the equivalent value of the value constraint condition, a term relating to an upper limit constraint on the bid amount, and a term relating to a lower limit constraint on the bid amount. A computer program for analyzing determinants of contract prices in a featured electricity trading market.

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