Clearing and electricity price incentive methods for the combined market of electricity and ancillary services under strong uncertainty

Abstract

The present invention discloses a method for clearing and electricity price incentives in a joint market of electric energy and ancillary services under strong uncertainty, and sequentially constructs a fuzzy set of system uncertainty power, a joint market clearing model considering uncertainty power, and an electricity joint market price system. The present invention obtains node marginal prices of electric energy, standby, frequency regulation, and uncertainty power based on the marginal pricing principle. Price incentives are provided for flexible resources through the node marginal prices of standby and frequency regulation, and market entities that generate uncertainty are penalized through the node marginal prices of uncertainty power. In solving the clearing model, the distributed robust bilateral chance constraint is converted into a mixed integer second-order cone programming through convex reconstruction. The present invention aims to transfer the penalty cost amount of the uncertainty power generated by new energy stations to traditional power generation units and energy storage companies that provide standby capacity and frequency regulation power through a market pricing mechanism, and verifies the practical application value of the uncertainty power price mechanism.

Description

Technical Field

[0001] The present invention relates to a joint market clearing technology for electric energy, reserve and frequency regulation and a power market price system, and in particular to an uncertainty pricing method based on a joint market clearing model. Background Art

[0002] The large-scale integration of highly uncertain wind and solar power sources poses a significant challenge to the safe and reliable operation of the power grid. Inaccurate power forecasts for wind and solar power and loads lead to power imbalances between sources and loads, resulting in a continuous increase in the system's flexible regulation capabilities and reserve requirements, posing a significant challenge to power market clearing.

[0003] However, the current design of a combined market for electricity and ancillary services primarily targets PCE market participants, to the detriment of ECE market participants, who play a crucial role in system safety. In developing market mechanisms and pricing rules, ECE market participants, including energy storage, should be allowed equal participation in electricity, ancillary services, and capacity markets. Currently, many regions have permitted energy storage to participate in ancillary services markets, but research on clearing coordination mechanisms for a combined market for spot electricity and frequency regulation ancillary services that takes into account the characteristics of energy storage is limited.

[0004] The joint market for electric energy, reserve and frequency regulation auxiliary services can not only reduce the total cost of all markets, but also take into account the capacity constraints of the units and can simultaneously handle the coupling of units participating in different products. Joint optimization has gradually developed into a clearing method for mature markets.

[0005] The current electricity market establishes clearing models based on forecasted wind and solar power and load power. Due to increased system uncertainty, this can lead to low or even non-existent execution of market clearing results. Therefore, incorporating system uncertainty into the joint market clearing model can mitigate the impact of wind and solar power on market clearing to some extent. Furthermore, reflecting uncertain power through market pricing can reflect the scarcity of flexible regulatory resources.

[0006] To guide the optimal allocation of scarce resources, pricing uncertain power through a clearing model can provide price incentives for the market, helping to encourage SMEs such as wind and solar energy stations to reduce their own uncertainties. Similar to node marginal prices, this paper innovatively proposes node marginal prices for uncertain power (ULMP), defining it as the change in system marginal cost caused by a unit increment of actual power at a node deviating from predicted power. Mathematically, ULMP can be represented by the mean and standard deviation of uncertain power; physically, ULMP describes the impact of uncertain power changes of market entities on the total market cost. Summary of the Invention

[0007] Purpose of the Invention: The purpose of the present invention is to address the deficiencies in the prior art and provide a method for clearing and incentivizing electricity prices in a joint market for electricity and ancillary services under strong uncertainty, thereby achieving node marginal price pricing for electricity, backup, frequency regulation, and uncertain power. The proposed joint market clearing model can quantify the market cost of SMEs generating uncertain power, as well as the market benefits of PCE and ECE participating in regulating system power balance, providing price signals for multiple types of market players to participate in the highly uncertain electricity market. The technology of the present invention can enhance the system's flexible regulation capabilities, promote the reduction of uncertainty in highly random enterprises such as new energy, and ensure that regulatory enterprises such as energy storage obtain relatively substantial benefits.

[0008] Technical solution: The present invention provides a method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty. The method is characterized in that market participants are divided into deterministic market participants (DMEs) and stochastic market participants (SMEs). The deterministic market participants (DMEs) include power constraint participants (PCEs) and energy constraint participants (ECEs). The method includes the following steps:

[0009] Step 1: To solve the uncertainty problem involving random variables, construct the system uncertainty power ξ i,t Fuzzy set Uncertain power ξ i,t It refers to the difference between the uncertainty power of renewable energy and the uncertainty power of load at all nodes. The load uncertainty power fuzzy set is modeled as a fuzzy set based on deterministic statistical moment information, and the renewable energy uncertainty power fuzzy set is modeled as an ellipsoidal fuzzy set considering the correlation between renewable energy sites. Here, by constructing a fuzzy set of the actual probability distribution of uncertain power, the distributed robust optimization method is used to solve the uncertainty problem containing random variables and achieve decision-making under the worst probability distribution. The specific method is as follows:

[0010] First, calculate the new energy uncertainty power of the random market entity SME and load uncertainty power Then, the mean value of the random variable and the moment information of the covariance matrix are determined through historical data, and the fuzzy set of load uncertainty power is constructed based on At the same time, the expectation and moment information of the covariance matrix of random variables are determined through historical data to construct the fuzzy set of new energy uncertainty power Finally, the load uncertainty power fuzzy set of all nodes is Fuzzy Sets of Uncertain Power of New Energy The union of is the fuzzy set of the uncertainty power of the system

[0011] Step 2: Construct a joint market clearing model considering uncertain power:

[0012] Obj.min a T x

[0013] stb T x≤U

[0014]

[0015] The joint market clearing objective function of the above model is: minimizing the total market cost of the combined electricity, reserve, and frequency regulation ancillary services. The constraints of the model include PCE operation constraints that consider uncertain power, ECE operation constraints, and system-level opportunity constraints. The opportunity constraints include power balance constraints, system flow opportunity constraints, reserve demand opportunity constraints, and frequency regulation demand opportunity constraints. ξ is an uncertain random variable; Ξ is a fuzzy set of random variables ξ; a(x) and b(x) are affine mappings; U is the constraint limit; 1-ε is the minimum probability that the opportunity constraint holds. Among them, for opportunity constraints, it is necessary to transform them into deterministic constraints through convex reconstruction, solve the market clearing model, and obtain the winning bid results of each market player until the joint market is cleared.

[0016] Step 3: Construct a joint electricity market price system and determine marginal pricing;

[0017] The price system includes deterministic power prices and uncertain power prices. The deterministic power prices include the marginal prices of PCE and ECE electric energy nodes, the marginal prices of standby nodes, and the marginal prices of frequency regulation nodes; the uncertain power prices include the system marginal prices and node marginal prices of uncertain power.

[0018] Furthermore, the detailed method of step 1 is:

[0019] Step 1.1, Uncertain power refers to the deviation between the actual power of the random market entity SME and the predicted power. New energy uncertainty power and load uncertainty power The calculation formula is as follows:

[0020]

[0021] Where, They are respectively the predicted power of new energy and the predicted power of load at node i during period t. They are the actual power of new energy and the actual power of load respectively;

[0022] Step 1.2: Determine the moment information of the random variable through historical data, and determine the load uncertainty power based on the moment information of the mean and covariance matrix Fuzzy set As shown in formula (3);

[0023]

[0024] Where, is the probability distribution function; express The set of all probability distributions of the above uncertainty power random variables; N is the dimension of the random variable; is the expected value of the probability distribution; is the first-order moment of the uncertainty power of the load at node i, that is The mean of , characterizes its position; is the second-order moment of the load uncertainty power of node i during period t, that is, The covariance matrix of , characterizing its divergence;

[0025] At the same time, the expectation and moment information of the covariance matrix of random variables are determined through historical data to construct the fuzzy set of new energy uncertainty power As shown in formula (4);

[0026]

[0027] Where: is the uncertainty power of the new energy station during period t fuzzy sets; is the first-order moment of the uncertainty power of the new energy station; is the second-order moment of the uncertainty power of the new energy station at node i during period t; β1 is the limiting parameter of the radius of the ellipsoid uncertainty set; γ2 is the limiting parameter of the semidefinite cone uncertainty set; is less than or equal to in the sense of semi-positive definite cone space;

[0028] Step 1.3: Calculate the uncertainty power ξ of the system first i,t The first and second moments of , as shown in equations (5)-(7);

[0029]

[0030] Where: is the first-order moment of the system uncertainty power; is the second-order moment of the system uncertainty power during period t;

[0031] Then the uncertainty power ξ of the system i,t The second-order moment of is expressed in the form of standard deviation, as shown in formula (8):

[0032]

[0033] Where: is the standard deviation of the system uncertainty power; P:{ρ i,j},ρ i,j is the Pearson correlation coefficient, ⊙ is the multiplication operation of the corresponding elements of the matrix;

[0034] Step 1.4: Obtain the system uncertainty power ξ i,t Fuzzy set As shown in formula (9),

[0035]

[0036] Furthermore, for the joint market clearing model of uncertain power of steps, the expressions of its objective function and constraint function are as follows:

[0037] Obj.min a T x

[0038] stb T x≤U

[0039]

[0040] (1) The objective function is to minimize the total market cost C, as shown in formula (11):

[0041]

[0042] Where: They are the standby quotes for PCE and ECE respectively; These are the frequency modulation quotations of PCE and ECE respectively; are the electric energy reported by PCE and ECE at node i during period t; are the frequency modulation powers reported by PCE and ECE at node i during period t; The operational reserves declared by PCE and ECE respectively;

[0043] (2) Constraints include PCE operation constraints, ECE operation constraints, system power flow constraints, and system-level opportunity constraints considering uncertain power.

[0044] 1) The PCE operation constraint considering uncertain power is calculated as follows:

[0045] After considering the uncertainty of power, the PCE power constraints are (12)-(14), and the ramp constraints are (14)-(15). In particular, the backup capacity and frequency regulation power bid by the PCE also need to meet the ramp constraints, as shown in (15);

[0046]

[0047] Where: is the active power output of the unit at node i during period t; They are the upper and lower limits of the unit’s active output respectively; They are the upward and downward climbing rates of the unit respectively;

[0048] 2) The ECE operation constraint considering the uncertainty power is calculated as follows:

[0049] The ECE operating power constraints are as follows: (16)-(22). Among them, the actual power of the ECE is as follows: (18), the operating state is as follows: (19), and the initial and final energy constraints are as follows: (20)-(21). Equation (22) is the energy constraint of the ECE after considering the uncertainty of power.

[0050]

[0051] Where: and are the active charging and discharging powers of ECE at node i in period t, respectively; and are the upper limits of active charging and discharging power of energy storage ECE at node i in period t, respectively; is the power of ECE participating in the electric energy market at node i in period t; and are 0-1 variables representing the active charging and discharging power of ECE at node i during period t; is the energy of ECE in period t; and e i are the upper and lower limits of ECE energy, respectively; and are the ECE charge and discharge loss coefficients respectively; β i,τ is the contribution factor of the uncertainty power of the ECE balance system at node i in the τ period; is the energy state of the ECE at node i during period t;

[0052] 3) The system power flow constraint considering the uncertainty of power is calculated as follows:

[0053] The system uncertainty power is jointly addressed by the spare capacity and frequency regulation power of the PCE and ECE bids, and the total uncertainty power is shared by the contribution factors of the PCE and ECE of each node. When the uncertainty power is not considered, the system power flow constraint is shown in Equation (26);

[0054]

[0055] After considering the uncertainty power, the system power balance constraints are (24)-(25);

[0056]

[0057] Where: α i,t is the contribution factor of the uncertainty power of the ECE balance system at node i during period t; α t is the α of all nodes i,t Constitute a column vector; β t is the β of all nodes i,t Construct a column vector;

[0058] 4) The system opportunity constraint considering the uncertainty power is calculated as follows:

[0059] The system constraints considering uncertain power are transformed into chance constraints to ensure that the probability of the constraints being established is not less than 1-ε. The chance constraints of ECE energy are shown in Equation (27), the chance constraints of line flow are shown in Equation (28), and the chance constraints of the relationship between uncertain power and system reserve capacity and frequency modulation power are shown in Equations (29)-(30).

[0060]

[0061] in, is the system reserve capacity and frequency modulation power in period t, as shown in equations (31)-(32);

[0062]

[0063] Where: o is the margin coefficient for the additional reserve capacity required to take into account the covariance factor of the uncertain power; ε is the risk tolerance threshold of the opportunity constraint; the opportunity constraints in equations (27)-(30) all contain uncertain power To maintain generality, we unify them into bilateral opportunity constraints.

[0064] Furthermore, to convert the distributed robust optimization model with bilateral chance constraints into a non-convex problem, it is necessary to transform the chance constraints into deterministic constraints through convex reconstruction. The specific steps are as follows:

[0065] Step A) Convert the bilateral opportunity constraint into two unilateral opportunity constraints to obtain equation (33);

[0066]

[0067] Step B) Model the random variables as fuzzy sets that satisfy certain statistical moment information, and directly transform the chance constraints into deterministic constraints through convex reconstruction; thereby, transforming the distributed robust optimization problem with bilateral chance constraints into a second-order cone programming (SOCP);

[0068]

[0069] Where: Σ is the covariance matrix of the random variable ξ;

[0070] Step C), according to formula (35), the bilateral distributed robust chance constraint is expressed as a set of deterministic inequalities, and the optimization problem containing the bilateral chance constraint is transformed into a second-order cone programming problem SOCP;

[0071]

[0072] Where: y and z is an auxiliary variable;

[0073] Therefore, equations (27)-(30) are transformed into the following four sets of deterministic inequalities respectively;

[0074]

[0075]

[0076] Where: and They are auxiliary variables of ECE energy opportunity constraint, power flow security opportunity constraint, reserve capacity opportunity constraint and frequency regulation power opportunity constraint.

[0077] Furthermore, the pricing method in step 3 includes the following four parts:

[0078] I. Node marginal price of electric energy: The partial derivative of the Lagrangian function of the market clearing model with respect to the node load power is zero, as shown in Equation (36). The marginal price of each node in the system consists of two parts: the electric energy cost and the system congestion cost, as shown in Equation (37).

[0079]

[0080] Where: is the node marginal price of electricity at node i in period t; and is the Lagrange multiplier corresponding to the power flow constraint of the system constructed without considering the uncertainty of power;

[0081] In the joint market clearing model of electric energy, reserve capacity and frequency regulation, the demand constraints of system reserve capacity and frequency regulation power are shown in Equations (38) and (39). The right side of the inequality is the minimum demand.

[0082]

[0083] II. The marginal price of the standby node and the marginal price of the frequency regulation node is the increase in system operating cost corresponding to each unit increase in demand capacity;

[0084] The Lagrange multipliers corresponding to the constraints of formulas (38) and (39) are the node marginal prices of standby and frequency regulation, respectively. The partial derivatives of the Lagrange function of the joint market clearing model with respect to demand can be used to obtain the node marginal clearing price expressions of standby and frequency regulation, as shown in formulas (40) and (41), respectively.

[0085] The marginal price of each node's backup and frequency regulation and the balance factor variable α between PCE and ECE i,t , β i,t directly related;

[0086]

[0087] Where: is the node marginal price of spare capacity at node i in period t; is the node marginal price of frequency modulation power at node i in period t;

[0088] III. The system marginal price of uncertainty power is the change in system marginal cost caused by a unit increment of system uncertainty power, including the unit mean increment and standard deviation increment, which will increase the system operation cost, that is, the partial derivatives of the Lagrangian function with respect to the mean and standard deviation of system uncertainty power, as shown in Equations (42) and (43) respectively. The marginal price of system uncertainty power is directly related to the scarcity of the corresponding flexible adjustment resources.

[0089]

[0090] Where: is the Lagrange multiplier of the first equation of the deterministic inequality corresponding to the chance constraint in equation (29); is the Lagrange multiplier of the first equation of the deterministic inequality corresponding to the chance constraint in equation (30).

[0091] IV. The node marginal price of uncertain power is the incremental marginal cost of the system caused by the unit standard deviation increment, which is the partial derivative of the Lagrangian function with respect to the standard deviation of the node uncertainty power. As shown in Equation (43), the node marginal price of uncertain power has three components;

[0092]

[0093] Where: Indicates the marginal cost of power reserved by the PCE; represents the marginal cost of the energy constraint required to be reserved by ECE; It represents the marginal cost of reserving available transmission power on the line;

[0094]

[0095] Where: represents the node marginal price of spare capacity; Represents the node marginal price of frequency modulation power.

[0096] Furthermore, the above process has improved the fairness of ECE's participation in the electricity market by calculating the marginal price of uncertain power. Due to its own uncertain power, SME needs to pay the cost settlement of backup capacity and frequency regulation power to PCE and ECE, and pay the cost of reserved line available transmission power to the grid. Therefore, after obtaining the marginal price of the node, the penalty cost amount C generated by the new energy station is calculated. i , as shown in formula (45);

[0097]

[0098] Where: C i The total cost that the SME of the i-node needs to pay;

[0099] By calculating C i This amount will flow to traditional power generation units and energy storage companies that provide backup capacity and frequency regulation power, thereby improving the fairness of benefits for all market players and ensuring long-term and stable operation of the market.

[0100] Beneficial effects: The present invention adopts the distributed blue stick-bilateral opportunity constraint method to solve the optimization problem with uncertain random variables. Based on the joint market clearing model and marginal pricing principle, it innovatively proposes a multi-category price mechanism including node marginal prices of electric energy, backup, frequency regulation, and uncertain power, which helps to promote SMEs such as wind and solar energy stations to reduce their own uncertainties and provide price incentives and technical guarantees for the long-term operation of the market. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 It is the overall flow chart of the present invention;

[0102] Figure 2 The topology of the IEEE 39-node system is shown in FIG.

[0103] Figure 3 This is a schematic diagram of the electric energy clearing results of the joint market in the embodiment;

[0104] Figure 4 Schematic diagram of node marginal price with uncertain power in an embodiment. DETAILED DESCRIPTION

[0105] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0106] like Figure 1As shown, the method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty of the present invention divides market participants into deterministic market participants DME and stochastic market participants SME, and the deterministic market participants DME include power constraint participants PCE and energy constraint participants ECE, and include the following steps:

[0107] Step 1: Construct system uncertainty power ξ i,t Fuzzy set Uncertain power ξ i,t It refers to the difference between the uncertainty power of new energy and the uncertainty power of load at all nodes. The uncertainty power fuzzy set of load is modeled as a fuzzy set based on deterministic statistical moment information, and the uncertainty power fuzzy set of new energy is modeled as an ellipsoidal fuzzy set considering the correlation of new energy sites. The specific method is:

[0108] First, calculate the new energy uncertainty power of the random market entity SME and load uncertainty power Then, the mean value of the random variable and the moment information of the covariance matrix are determined through historical data, and the fuzzy set of load uncertainty power is constructed based on At the same time, the expectation and moment information of the covariance matrix of random variables are determined through historical data to construct the fuzzy set of new energy uncertainty power Finally, the load uncertainty power fuzzy set of all nodes is Fuzzy Sets of Uncertain Power of New Energy The union of is the fuzzy set of the uncertainty power of the system

[0109] Step 2: Construct a joint market clearing model considering uncertain power:

[0110] Obj.min a T x

[0111] stb T x≤U

[0112]

[0113] The joint market clearing objective function of the above model is: minimizing the total market cost of the combined electricity, reserve, and frequency regulation ancillary services. The constraints of the model include PCE operation constraints that consider uncertain power, ECE operation constraints, and system-level opportunity constraints. The opportunity constraints include power balance constraints, system flow opportunity constraints, reserve demand opportunity constraints, and frequency regulation demand opportunity constraints. ξ is an uncertain random variable; Ξ is a fuzzy set of random variables ξ; a(x) and b(x) are affine mappings; U is the constraint limit; 1-ε is the minimum probability that the opportunity constraint holds. Among them, for opportunity constraints, it is necessary to transform them into deterministic constraints through convex reconstruction, solve the market clearing model, and obtain the winning bid results of each market player until the joint market is cleared.

[0114] Step 3: Construct a joint electricity market price system and determine marginal pricing;

[0115] The price system includes deterministic power prices and uncertain power prices. The deterministic power prices include the marginal prices of PCE and ECE electric energy nodes, the marginal prices of standby nodes, and the marginal prices of frequency regulation nodes; the uncertain power prices include the system marginal prices and node marginal prices of uncertain power.

[0116] The detailed method of step 1 of this embodiment is:

[0117] Step 1.1, Uncertain power refers to the deviation between the actual power of the random market entity SME and the predicted power. New energy uncertainty power and load uncertainty power The calculation formula is as follows:

[0118]

[0119] Where: They are respectively the predicted power of new energy and the predicted power of load at node i during period t. They are the actual power of new energy and the actual power of load respectively;

[0120] Step 1.2: Determine the moment information of the random variable through historical data, and determine the load uncertainty power based on the moment information of the mean and covariance matrix Fuzzy set As shown in formula (3);

[0121]

[0122] Where: is the probability distribution function; express The set of all probability distributions of the above uncertainty power random variables; N is the dimension of the random variable; is the expected value of the probability distribution; is the first-order moment of the uncertainty power of the load at node i, that is The mean of , characterizes its position; is the second-order moment of the load uncertainty power of node i during period t, that is, The covariance matrix of , characterizing its divergence;

[0123] At the same time, the expectation and moment information of the covariance matrix of random variables are determined through historical data to construct the fuzzy set of new energy uncertainty power As shown in formula (4);

[0124]

[0125] Where: is the uncertainty power of the new energy station during period t fuzzy sets; is the first-order moment of the uncertainty power of the new energy station; is the second-order moment of the uncertainty power of the new energy station at node i during period t; γ1 is the limiting parameter of the radius of the ellipsoid uncertainty set; γ2 is the limiting parameter of the semidefinite cone uncertainty set; is less than or equal to in the sense of semi-positive definite cone space;

[0126] Step 1.3: Calculate the uncertainty power ξ of the system first i,t The first and second moments of , as shown in equations (5)-(7);

[0127]

[0128]

[0129] Where: is the first-order moment of the system uncertainty power; is the second-order moment of the system uncertainty power during period t;

[0130] Then the uncertainty power ξ of the system i,t The second-order moment of is expressed in the form of standard deviation, as shown in formula (8):

[0131]

[0132] Where: is the standard deviation of the system uncertainty power; P:{ρ i,j},ρ i,j is the Pearson correlation coefficient, ⊙ is the matrix multiplication operation;

[0133] Step 1.4: Obtain the system uncertainty power ξ i,t Fuzzy set As shown in formula (9),

[0134]

[0135] In this embodiment, for the joint market clearing model of the uncertain power of the steps, the expressions of the objective function and constraint function are as follows:

[0136] Obj.min a T x

[0137] stb T x≤U

[0138]

[0139] (1) The objective function is to minimize the total market cost C, as shown in formula (11):

[0140]

[0141] Where: They are the standby quotes for PCE and ECE respectively; These are the frequency modulation quotations of PCE and ECE respectively; are the electric energy reported by PCE and ECE at node i during period t; are the frequency modulation powers reported by PCE and ECE at node i during period t; The operational reserves declared by PCE and ECE respectively;

[0142] (2) Constraints include PCE operation constraints considering uncertain power, ECE operation constraints, system power flow constraints, and system-level opportunity constraints:

[0143] 1) The PCE operation constraint considering uncertain power is calculated as follows:

[0144] After considering the uncertainty of power, the PCE power constraints are (12)-(14), and the ramp constraints are (14)-(15). In particular, the backup capacity and frequency regulation power bid by the PCE also need to meet the ramp constraints, as shown in (15);

[0145]

[0146] Where, is the active power output of the unit at node i during period t; They are the upper and lower limits of the unit’s active output respectively; They are the upward and downward climbing rates of the unit respectively;

[0147] 2) The ECE operation constraint considering the uncertainty power is calculated as follows:

[0148] The ECE operating power constraints are as follows: (16)-(22); where the actual power of the ECE is as follows: (18), the operating state is as follows: (19), and the initial and final energy constraints are as follows: (20)-(21). Equation (22) is the energy constraint of the ECE after considering the uncertainty of power.

[0149]

[0150] Where, and are the active charging and discharging powers of ECE at node i in period t, respectively; and are the upper limits of active charging and discharging power of energy storage ECE at node i in period t, respectively; is the power of ECE participating in the electric energy market at node i in period t; and are 0-1 variables representing the active charging and discharging power of ECE at node i during period t; is the energy of ECE in period t; and e i are the upper and lower limits of ECE energy, respectively; and are the ECE charge and discharge loss coefficients respectively; β i,τ is the contribution factor of the uncertainty power of the ECE balance system at node i in the τ period; is the energy state of the ECE at node i during period t;

[0151] 3) The system power flow constraint considering the uncertainty of power is calculated as follows:

[0152] The system uncertainty power is jointly addressed by the spare capacity and frequency regulation power of the PCE and ECE bids, and the total uncertainty power is shared by the contribution factors of the PCE and ECE of each node. When the uncertainty power is not considered, the system power flow constraint is shown in Equation (26);

[0153]

[0154] After considering the uncertainty power, the system power balance constraints are (24)-(25);

[0155]

[0156] Where, α i,t is the contribution factor of the uncertainty power of the ECE balance system at node i during period t; α t is the α of all nodes i,t Constitute a column vector; β t is the β of all nodes i,tConstruct a column vector;

[0157] 4) The system opportunity constraint considering the uncertainty power is calculated as follows:

[0158] The system constraints considering uncertain power are transformed into chance constraints to ensure that the probability of the constraints being established is not less than 1-ε. The chance constraints of ECE energy are shown in Equation (27), the chance constraints of line flow are shown in Equation (28), and the chance constraints of the relationship between uncertain power and system reserve capacity and frequency modulation power are shown in Equations (29)-(30).

[0159]

[0160] in, is the system reserve capacity and frequency modulation power in period t, as shown in equations (31)-(32);

[0161]

[0162] Where o is the margin coefficient for the additional reserve capacity required to take into account the covariance factor of the uncertain power; ε is the risk tolerance threshold of the opportunity constraint; the opportunity constraints in equations (27)-(30) all contain uncertain power To maintain generality, we unify them into bilateral opportunity constraints.

[0163] This embodiment considers converting the distributed robust optimization model with bilateral chance constraints into a non-convex problem. It is necessary to convert the chance constraints into deterministic constraints through convex reconstruction. The specific steps are as follows:

[0164] Step A) Convert the bilateral opportunity constraint into two unilateral opportunity constraints to obtain equation (33);

[0165]

[0166] Step B) Model the random variables as fuzzy sets that satisfy certain statistical moment information, and directly transform the chance constraints into deterministic constraints through convex reconstruction; thereby, transforming the distributed robust optimization problem with bilateral chance constraints into a second-order cone programming (SOCP);

[0167]

[0168] Where: Σ is the covariance matrix of the random variable ξ;

[0169] Step C), according to formula (35), the bilateral distributed robust chance constraint is expressed as a set of deterministic inequalities, and the optimization problem containing the bilateral chance constraint is transformed into a second-order cone programming problem SOCP;

[0170]

[0171] Where: y and z is an auxiliary variable;

[0172] Therefore, equations (27)-(30) are transformed into the following four sets of deterministic inequalities respectively;

[0173]

[0174] Where: and They are auxiliary variables of ECE energy opportunity constraint, power flow security opportunity constraint, reserve capacity opportunity constraint and frequency regulation power opportunity constraint.

[0175] The pricing method in step 3 of this embodiment includes the following four parts:

[0176] I. Node marginal price of electric energy: The partial derivative of the Lagrangian function of the market clearing model with respect to the node load power is zero, as shown in Equation (36). The marginal price of each node in the system consists of two parts: the electric energy cost and the system congestion cost, as shown in Equation (37).

[0177]

[0178]

[0179] Where: is the node marginal price of electricity at node i in period t; and is the Lagrange multiplier corresponding to the power flow constraint of the system constructed without considering the uncertainty of power;

[0180] In the joint market clearing model of electric energy, reserve capacity and frequency regulation, the demand constraints of system reserve capacity and frequency regulation power are shown in Equations (38) and (39). The right side of the inequality is the minimum demand.

[0181]

[0182] II. The marginal price of the standby node and the marginal price of the frequency regulation node is the increase in system operating cost corresponding to each unit increase in demand capacity;

[0183] The Lagrange multipliers corresponding to the constraints of formulas (38) and (39) are the node marginal prices of standby and frequency regulation, respectively. The partial derivatives of the Lagrange function of the joint market clearing model with respect to demand can be used to obtain the node marginal clearing price expressions of standby and frequency regulation, as shown in formulas (40) and (41), respectively.

[0184] The marginal price of each node's backup and frequency regulation and the balance factor variable α between PCE and ECE i,t , β i,t directly related;

[0185]

[0186] Where: is the node marginal price of spare capacity at node i in period t; is the node marginal price of frequency modulation power at node i in period t;

[0187] III. The system marginal price of uncertainty power is the change in system marginal cost caused by a unit increment of system uncertainty power, including the unit mean increment and standard deviation increment, which will increase the system operation cost, that is, the partial derivatives of the Lagrangian function with respect to the mean and standard deviation of system uncertainty power, as shown in Equations (42) and (43) respectively. The marginal price of system uncertainty power is directly related to the scarcity of its corresponding flexible adjustment resources.

[0188]

[0189] Where: is the Lagrange multiplier of the first equation of the deterministic inequality corresponding to the chance constraint in equation (29); is the Lagrange multiplier of the first equation of the deterministic inequality corresponding to the chance constraint in equation (30).

[0190] IV. The node marginal price of uncertain power is the incremental marginal cost of the system caused by the unit standard deviation increment, which is the partial derivative of the Lagrangian function with respect to the standard deviation of the node uncertainty power. As shown in Equation (43), the node marginal price of uncertain power has three components;

[0191]

[0192] Where: Indicates the marginal cost of power reserved by the PCE; represents the marginal cost of the energy constraint required to be reserved by ECE; It represents the marginal cost of reserving available transmission power on the line;

[0193]

[0194] Where: represents the node marginal price of spare capacity; Represents the node marginal price of frequency modulation power.

[0195] After obtaining the marginal price of the node, this embodiment calculates the uncertainty power penalty cost amount generated by the new energy station as follows:

[0196]

[0197] Example

[0198] This embodiment adopts the IEEE 39-node system, and the topology is as follows: Figure 2 Specifically, PCE represents traditional thermal power units, ECE represents energy storage, and SME represents wind farms or photovoltaic power plants. Market clearing occurs on a 1-hour cycle, with a total of 24 clearing periods. The standard deviation of the uncertainty power of each node's load is set to 5% of its predicted power. The power ranges of each market entity are shown in Table 1.

[0199] Table 1 Power range of market entities (MW)

[0200]

[0201] Figure 3 The results of electricity energy clearing in the proposed joint market are presented, in which ECE mainly plays the role of power balancing. Figure 4 The proposed node marginal price for uncertain power is presented. The ULMP reflects the marginal cost of market operations imposed by the uncertain power generated by SMEs. Consequently, the cost of uncertain power generated by SMEs flows to PCE and ECE companies that provide backup capacity and frequency regulation, resulting in an 18.5% reduction in revenue for new energy companies and a 26% increase in revenue for energy storage companies. Compared to traditional clearing models based on forecasted power, this reduces market operating costs by 25.5%.

Claims

1. A method for clearing and incentivizing electricity prices in a combined market of electricity and ancillary services under strong uncertainty, characterized by: The market participants are divided into deterministic market participants (DME) and stochastic market participants (SME). The deterministic market participants (DME) include power constraint participants (PCE) and energy constraint participants (ECE). The following steps are included: Step 1: Construct system uncertainty power ξ i,t Fuzzy set Uncertain power ξ i,t It refers to the difference between the uncertainty power of new energy and the uncertainty power of load at all nodes. The load uncertainty power fuzzy set is modeled as a fuzzy set based on deterministic statistical moment information, and the new energy uncertainty power fuzzy set is modeled as an ellipsoidal fuzzy set considering the correlation of new energy. The specific method is: First, calculate the new energy uncertainty power of the random market entity SME and load uncertainty power Then, the mean value of the random variable and the moment information of the covariance matrix are determined through historical data, and the fuzzy set of load uncertainty power is constructed based on At the same time, the expectation and moment information of the covariance matrix of random variables are determined through historical data to construct the fuzzy set of new energy uncertainty power Finally, the load uncertainty power fuzzy set of all nodes is Fuzzy Sets of Uncertain Power of New Energy The union of is the fuzzy set of the uncertainty power of the system Step 2: Construct a joint market clearing model considering uncertain power based on distributed robust bilateral opportunity constraints: Obj.min a T x s.t. b T x≤U The joint market clearing objective function of the above model is: minimizing the total market cost of the combined electricity, reserve, and frequency regulation ancillary services. The constraints of the model include PCE operation constraints that consider uncertain power, ECE operation constraints, and system-level opportunity constraints. The opportunity constraints include power balance constraints, system flow opportunity constraints, reserve demand opportunity constraints, and frequency regulation demand opportunity constraints. ξ is an uncertain random variable; Ξ is a fuzzy set of random variables ξ; a(x) and b(x) are affine mappings; U is the constraint limit; 1-ε is the minimum probability that the opportunity constraint holds. Among them, for opportunity constraints, they are converted into deterministic constraints through convex reconstruction, and the market clearing model is solved to obtain the winning bid results of each market player until the joint market is cleared. Step 3: Construct a power market price system based on the marginal pricing principle and determine the marginal pricing; The price system includes deterministic power prices and uncertain power prices. The deterministic power prices include the marginal prices of PCE and ECE electric energy nodes, the marginal prices of standby nodes, and the marginal prices of frequency regulation nodes; the uncertain power prices include the system marginal prices and node marginal prices of uncertain power.

2. The method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty according to claim 1, characterized in that: The detailed method of step 1 is: Step 1.1, Uncertain power refers to the deviation between the actual power of the random market entity SME and the predicted power. New energy uncertainty power and load uncertainty power The calculation formula is as follows: Where: They are respectively the predicted power of new energy and the predicted power of load at node i during period t. They are the actual power of new energy and the actual power of load respectively; Step 1.2: Determine the moment information of the random variable through historical data, and determine the load uncertainty power based on the moment information of the mean and covariance matrix Fuzzy set As shown in formula (3); Where: is the probability distribution function; express The set of all probability distributions of the above uncertainty power random variables; N is the dimension of the random variable; is the expected value of the probability distribution; is the first-order moment of the uncertainty power of the load at node i, that is The mean of , characterizes its position; is the second-order moment of the load uncertainty power of node i during period t, that is, The covariance matrix of , characterizing its divergence; At the same time, the expectation and moment information of the covariance matrix of random variables are determined through historical data to construct the fuzzy set of new energy uncertainty power As shown in formula (4); Where: is the uncertainty power of new energy in period t fuzzy sets; is the first-order moment of the uncertainty power of new energy; is the second-order moment of the uncertainty power of the new energy at node i during period t; γ1 is the limiting parameter of the radius of the ellipsoid uncertainty set; γ2 is the limiting parameter of the semidefinite cone uncertainty set; ≤ is less than or equal to in the sense of the semidefinite cone space; Step 1.3: Calculate the uncertainty power ξ of the system first i,t The first and second moments of , as shown in equations (5)-(7); Where: is the first-order moment of the system uncertainty power; is the second-order moment of the system uncertainty power during period t; Then the uncertainty power ξ of the system i,t The second-order moment of is expressed in the form of standard deviation, as shown in formula (8): Where: is the standard deviation of the system uncertainty power; P:{ρ i,j },ρ i,j is the Pearson correlation coefficient, ⊙ is the matrix multiplication operation; Step 1.4: Obtain the system uncertainty power ξ i,t Fuzzy set As shown in formula (9), 3. The method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty according to claim 2, characterized in that: For the joint market clearing model with uncertain power of steps, the expressions of its objective function and constraint function are as follows: Obj.min a T x s.t. b T x≤U (1) The objective function is to minimize the total market cost C, as shown in formula (11): Where: They are the standby quotes for PCE and ECE respectively; These are the frequency modulation quotations of PCE and ECE respectively; are the electric energy reported by PCE and ECE at node i during period t; are the frequency modulation powers reported by PCE and ECE at node i during period t; The operational reserves declared by PCE and ECE respectively; (2) Constraints include PCE operation constraints, ECE operation constraints, system power flow constraints, and system-level opportunity constraints considering uncertain power.

1. The PCE operation constraint considering uncertain power is calculated as follows: After considering the uncertainty power, the PCE power constraint is Equation (12)-(14), and the ramp constraint is Equation (14)-(15). The backup capacity and frequency regulation power bid by the PCE also need to meet the ramp constraint, as shown in Equation (15); Where, is the active power output of the unit at node i during period t; They are the upper and lower limits of the unit’s active output respectively; They are the upward and downward climbing rates of the unit respectively; 2. The ECE operation constraint considering the uncertainty power is calculated as follows: The ECE operating power constraints are as follows: (16)-(22); where the actual power of the ECE is as follows: (18), the operating state is as follows: (19), and the initial and final energy constraints are as follows: (20)-(21). Equation (22) is the energy constraint of the ECE after considering the uncertainty of power. Where, and are the active charging and discharging powers of ECE at node i in period t, respectively; and are the upper limits of active charging and discharging power of energy storage ECE at node i in period t, respectively; is the power of ECE participating in the electric energy market at node i in period t; and are 0-1 variables representing the active charging and discharging power of ECE at node i during period t; is the energy of ECE in period t; and e i are the upper and lower limits of ECE energy, respectively; and are the ECE charge and discharge loss coefficients respectively; β i,τ is the contribution factor of the uncertainty power of the ECE balance system at node i in the τ period; is the energy state of the ECE at node i during period t; 3. The system power flow constraint considering the uncertainty of power is calculated as follows: The system uncertainty power is jointly addressed by the spare capacity and frequency regulation power of the PCE and ECE bids, and the total uncertainty power is shared by the contribution factors of the PCE and ECE of each node. When the uncertainty power is not considered, the system power flow constraint is shown in Equation (26); After considering the uncertainty power, the system power balance constraints are (24)-(25); Where: α i,t is the contribution factor of the uncertainty power of the PCE balance system at node i during period t; α t is the α of all nodes i,t Constitute a column vector; β i,t is the contribution factor of the uncertainty power of the ECE balance system at node i during period t; 4. The system opportunity constraint considering the uncertainty of power is calculated as follows: The system constraints considering uncertain power are transformed into chance constraints to ensure that the probability of the constraints being established is not less than 1-ε. The chance constraints of ECE energy are shown in Equation (27), the chance constraints of line flow are shown in Equation (28), and the chance constraints of the relationship between uncertain power and system reserve capacity and frequency modulation power are shown in Equations (29)-(30). in, is the system reserve capacity and frequency modulation power in period t, as shown in equations (31)-(32); Where ε is the risk tolerance threshold of the opportunity constraint.

4. The method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty according to claim 3 is characterized in that: To convert the distributed robust optimization model with bilateral chance constraints into a non-convex problem, the chance constraints need to be transformed into deterministic constraints through convex reconstruction. The specific steps are as follows: Step A: Convert the bilateral opportunity constraint into two unilateral opportunity constraints to obtain equation (33); Step B: Model the random variables as fuzzy sets that satisfy certain statistical moment information, and directly transform the chance constraints into deterministic constraints through convex reconstruction; thereby, the distributed robust optimization problem with bilateral chance constraints is transformed into a second-order cone programming (SOCP); Where: Σ is the covariance matrix of the random variable ξ; Step C: According to formula (35), the bilateral distributed robust chance constraint is expressed as a set of deterministic inequalities, and the optimization problem with bilateral chance constraints is transformed into a second-order cone programming problem SOCP; Where: y and z are auxiliary variables; Therefore, equations (27)-(30) are transformed into the following four sets of deterministic inequalities respectively; Where: and They are auxiliary variables of ECE energy opportunity constraint, power flow security opportunity constraint, reserve capacity opportunity constraint and frequency regulation power opportunity constraint.

5. The method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty according to claim 1, characterized in that: The pricing method in step 3 includes the following four parts: I. Node marginal price of electric energy: The partial derivative of the Lagrangian function of the market clearing model with respect to the node load power is zero, as shown in Equation (36). The marginal price of each node in the system consists of two parts: the electric energy cost and the system congestion cost, as shown in Equation (37). Where: is the node marginal price of electricity at node i in period t; and is the Lagrange multiplier corresponding to the power flow constraint of the system constructed without considering the uncertainty of power; In the joint market clearing model of electric energy, reserve capacity and frequency regulation, the demand constraints of system reserve capacity and frequency regulation power are shown in Equations (38) and (39). The right side of the inequality is the minimum demand. o is the margin coefficient for additional reserve capacity to take into account the covariance factor of uncertain power; ε is the risk tolerance threshold of the opportunity constraint; II. The marginal price of the standby node and the marginal price of the frequency regulation node is the increase in system operating cost corresponding to each unit increase in demand capacity; The Lagrange multipliers corresponding to the constraints in equations (38) and (39) are the node marginal prices of standby and frequency regulation, respectively. Taking the partial derivative of the Lagrange function of the joint market clearing model with respect to demand, we can obtain the node marginal clearing price expressions of standby and frequency regulation, as shown in equations (40) and (41). The marginal price of each node's backup and frequency regulation and the balance factor variable α between PCE and ECE i,t , β i,t directly related; Where: is the node marginal price of spare capacity at node i in period t; is the node marginal price of frequency modulation power at node i in period t; III. The system marginal price of uncertain power is the change in system marginal cost caused by a unit increment of system uncertainty power, as shown in equations (42)-(43); Where: is the Lagrange multiplier of the first equation of the deterministic inequality corresponding to the chance constraint in equation (29); is the Lagrange multiplier of the first equation of the deterministic inequality corresponding to the chance constraint in equation (30); IV. The node marginal price of uncertain power is the incremental marginal cost of the system caused by the unit standard deviation increment as shown in formula (44); Where, Indicates the marginal cost of power reserved by the PCE; represents the marginal cost of the energy constraint required to be reserved by ECE; It represents the marginal cost of reserving available transmission power on the line; Where, represents the node marginal price of spare capacity; Represents the node marginal price of frequency modulation power.

6. The method for clearing and incentivizing electricity prices in a combined market of electric energy and ancillary services under strong uncertainty according to claim 5, characterized in that: After obtaining the marginal price of the node, calculate the uncertainty power penalty cost amount C generated by the new energy i , as shown below: Where C i The total cost that the SME of the i-node needs to pay.

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