A bilateral random power grid dispatching method

Abstract

The present application belongs to the technical field of power system operation, and relates to a double-sided random power grid scheduling method. By analyzing historical data of wind power output, Gaussian mixture distribution fitting is carried out by using software. For determined power system parameters, a double-sided chance constraint random scheduling model is established. Then, the hyperbolic tangent function is used to analytically approximate the cumulative distribution function of random variables in the reserve demand constraint and the line flow constraint, so as to convert the double-sided chance constraint into a deterministic constraint, and convert the original problem into a convex optimization problem which is easy to solve. Finally, the scheduling model is solved to obtain the scheduling strategy. The present application has the advantage that the double-sided chance constraint containing the risk level and the random variable is converted into a solvable deterministic convex constraint by using the hyperbolic tangent function, which effectively improves the solving efficiency of the model and provides a more reasonable scheduling basis for decision makers. The present application can be applied to active power scheduling of a power system containing large-scale renewable energy grid-connected.

Description

Technical Field

[0001] This invention belongs to the field of power system operation technology and relates to a bilateral random power grid dispatching method. Background Technology

[0002] Developing and utilizing renewable energy and achieving sustainable energy development are major initiatives in my country's energy development strategy. With the large-scale integration of renewable energy sources such as wind power and photovoltaics into the power grid, their volatility and randomness have brought two challenges to the active power rolling dispatch of the power system.

[0003] On the one hand, accurate and flexible wind power output forecasting is the foundation for achieving safe and economical active power rolling dispatch. Traditional forecasting methods include interval description methods with given upper and lower limits of output and simple Gaussian probability density function description methods. Although models such as beta distribution and general distribution have also been used to fit the predicted output of renewable energy, they either cannot accurately fit the predicted wind power output or bring great difficulties to solving the active power rolling dispatch model. Therefore, an accurate and flexible forecasting model is urgently needed.

[0004] On the other hand, the volatility and randomness of renewable energy make traditional deterministic or robust scheduling methods difficult to apply. One-sided opportunity-constrained scheduling can balance system operation risks and generation costs, but modeling the upper and lower bounds of reserve capacity (line capacity) separately leads to overly relaxed optimization results that fail to meet pre-set safety levels. Two-sided opportunity-constrained stochastic scheduling overcomes the disadvantages of one-sided models by minimizing the objective function value to obtain the lowest-cost scheduling strategy. Solving two-sided opportunity-constrained stochastic scheduling is extremely difficult. Traditional sampling methods are computationally intensive and have poor convergence, while relaxation methods result in imprecise solutions, failing to achieve efficient scheduling.

[0005] In summary, modeling and rapidly solving bilateral opportunity-constrained scheduling that takes into account the stochasticity of renewable energy output remains a major challenge affecting the utilization rate of renewable energy. Summary of the Invention

[0006] The purpose of this invention is to propose a bilateral stochastic power grid dispatching method. Based on the accurate approximation of the Gaussian mixture distribution by the hyperbolic tangent function, the bilateral chance constraints are transformed into deterministic convex constraints and solved effectively. This fully utilizes the advantages of chance-constrained stochastic dispatching, effectively reduces system risk, and saves power grid dispatching costs.

[0007] The bilateral random power grid scheduling method proposed in this invention includes the following steps:

[0008] (1) Establish a bilateral stochastic power grid dispatch model based on the hyperbolic tangent function approximation. The bilateral stochastic power grid dispatch model consists of an objective function and constraints.

[0009] (2) Based on the standby demand constraints and line power flow constraints in step (1), perform analytical approximation on the mixture Gaussian distribution satisfied by the random variables appearing in the constraints to obtain the approximate expression of the random variables.

[0010] (3) Based on the approximation of random variables in the reserve demand constraint and power flow constraint of the power grid line in step (2), the bilateral opportunity constraint optimization model in step (1) is transformed into a deterministic optimization model.

[0011] (4) Using the interior point method, the deterministic optimization model obtained in steps (1) to (3) is solved to obtain the power generation plan of thermal power units and renewable energy power plants.

[0012] The bilateral stochastic scheduling method based on the hyperbolic tangent function approximation proposed in this invention has the following characteristics and advantages:

[0013] This invention first accurately characterizes the output characteristics and correlations of renewable energy sources such as wind and solar power through a mixture of Gaussian distributions of multiple random variables. Based on this distribution, this method establishes a cost-minimizing stochastic scheduling model considering deterministic constraints and bilateral opportunity constraints. The bilateral opportunity constraints simultaneously limit the uncertainty of reserve demand (line power flow) caused by the randomness of output from renewable energy power plants such as wind and solar power during the scheduling process to a safe upper and lower limit with a certain confidence level. Simultaneously, the cumulative distribution function of the random variables in the opportunity constraints is analytically approximated using the hyperbolic tangent function, thereby transforming the bilateral opportunity constraints into deterministic convex constraints. The stochastic scheduling model is effectively solved, and the optimization result is the optimal scheduling decision for the output of traditional thermal power units and renewable energy power plants such as wind and solar power under the conditions of controlling scheduling risk and reducing scheduling costs. The advantages of this invention are that by analytically approximating the cumulative distribution function of random variables, the bilateral opportunity constraints are transformed into deterministic convex constraints, effectively improving the solution efficiency of the model. At the same time, the bilateral opportunity constraint model with adjustable risk levels eliminates the conservatism of traditional robust scheduling, providing decision-makers with a more reasonable scheduling basis. The method of this invention can be applied to the dispatching of power systems that include large-scale renewable energy grid connections. Detailed Implementation

[0014] The bilateral random scheduling method based on the hyperbolic tangent function approximation proposed in this invention includes the following steps:

[0015] The bilateral random power grid scheduling method proposed in this invention includes the following steps:

[0016] (1) Establish a bilateral stochastic power grid dispatch model based on the hyperbolic tangent function approximation. The bilateral stochastic power grid dispatch model consists of an objective function and constraints.

[0017] (2) Based on the standby demand constraints and line power flow constraints in step (1), perform analytical approximation on the mixture Gaussian distribution satisfied by the random variables appearing in the constraints to obtain the approximate expression of the random variables.

[0018] (3) Based on the approximation of random variables in the reserve demand constraint and power flow constraint of the power grid line in step (2), the bilateral opportunity constraint optimization model in step (1) is transformed into a deterministic optimization model.

[0019] (4) Using the interior point method, the deterministic optimization model obtained in steps (1) to (3) is solved to obtain the power generation plan of thermal power units and renewable energy power plants.

[0020] The specific steps of step (1) in the above-mentioned bilateral random power grid dispatching method are as follows:

[0021] (1) The objective function for establishing the bilateral stochastic power grid dispatch model is:

[0022] The expression for minimizing the sum of the power generation cost of thermal power units and the costs of positive and negative spinning reserve capacity is as follows:

[0023]

[0024] Where T and N G Let c represent the number of scheduling periods t and the number of thermal power units, respectively, where t and i are the numbers of the scheduling periods and the thermal power units, respectively. up c represents the cost per unit of spinning reserve capacity. dn This represents the cost per unit of negative spinning reserve capacity. This represents the reserve capacity for positive rotation of the i-th thermal power unit during the dispatch period t. P represents the negative spinning reserve capacity reserved by the i-th thermal power unit during the t-period dispatching time. i t CF represents the planned power generation of the i-th thermal power unit during the t-period dispatch period. i Let P represent the fuel cost function of the i-th thermal power unit, where the fuel cost function of the thermal power unit is expressed as the unit output P. i t Quadratic function:

[0025] CF i (P i t ) = a i (P i t ) 2 +b i P i t +ci (26)

[0026] Among them, a i b i and c i These are the quadratic coefficient, linear coefficient, and constant term of the fuel cost for thermal power unit i, respectively.

[0027] (2) The constraints of the above bilateral stochastic power grid dispatch model include:

[0028] (2-1) Power balance constraint of the power grid, the expression is as follows:

[0029]

[0030] in, This represents the planned reference output of the j-th renewable energy power plant during dispatch period t. N represents the size of the k-th load during scheduling period t. W N represents the number of wind farms. D Indicates the quantity of load;

[0031] (2-2) Power output P of thermal power units in the power grid i t Upper bound constraints and lower bound constraints:

[0032]

[0033] Among them, P i and These are the upper and lower bounds of the output of the i-th thermal power unit, respectively.

[0034] (2-3) Planned wind power output of the power grid Upper bound constraints and lower bound constraints:

[0035]

[0036] This represents the upper bound of the allowable output of the j-th renewable energy power plant during scheduling period t;

[0037] (2-4) The ramping constraint of thermal power units in the power grid is expressed as follows:

[0038] P i t -P i t-1 ≥-RD i ΔT (30)

[0039] P i t -P i t-1 ≤RUi ΔT (31)

[0040] Among them, RU i and RD i Let be the upward and downward ramp rates of the i-th thermal power unit, respectively, and ΔT represent the scheduling interval between two adjacent scheduling periods.

[0041] (2-5) The maximum reserve capacity constraint that thermal power units in the power grid can provide is expressed as follows:

[0042]

[0043]

[0044] Here, the mathematical symbol min{·} represents the minimum value of the elements in the set;

[0045] (2-6) The reserve demand constraint in the power grid to cope with renewable energy fluctuations is expressed as follows:

[0046]

[0047] Wherein, the mathematical symbol Pr{·} represents the probability of the event occurring. Let represent the actual output of the j-th renewable energy power plant during dispatch period t. The superscript ~ indicates that this variable is a random variable. β represents the maximum risk level preset by the dispatcher, with the maximum risk level ranging from 0 to 0.5. The joint probability distribution of the actual output of all renewable energy power plants at any given time satisfies the following Gaussian mixture distribution:

[0048]

[0049]

[0050] in, This represents the set of planned outputs of all renewable energy power plants during scheduling period t. For random vectors, Y represents the probability density function of a random vector. The value of N(Y,μ) m ,Σ m ) represents the m-th component of the Gaussian mixture distribution, M is the number of components in the Gaussian mixture distribution, and ω m Let μ represent the weight coefficient of the m-th component of the Gaussian mixture distribution, and satisfy the condition that the sum of the weight coefficients of all components equals 1. m Σ represents the average vector of the m-th component. m Let det represent the covariance matrix of the m-th component, det denote the determinant of the matrix, and the superscript T denote the transpose of the matrix.

[0051] (2-7) Power flow constraints of power grid lines, expressed as follows:

[0052]

[0053] Among them, G l,i G is the transfer distribution factor of the active power output of the l-th line to the i-th thermal power generating unit in the power grid. l,j Let G be the active power transfer distribution factor from line l to the renewable energy power station j. l,k Let L be the transfer distribution factor of the l-th line to the k-th load. Each of these transfer distribution factors is obtained from the power grid dispatch center. l Here, η represents the upper limit of active power on line l, and η is the risk level of the active power on the power grid line exceeding the line's active power limit, set by the dispatcher. The actual output of the i-th thermal power unit during the dispatch period t is expressed as:

[0054]

[0055] Where α i Let be the power allocation factor of the i-th thermal power unit, determined by the ratio of its rated capacity to the total capacity of all participating thermal power units. To ensure power balance in the power grid at any given time, the sum of the power allocation factors of all thermal power units must equal 1. This represents the power difference between the actual output and the planned output of all renewable energy power plants; Substituting expression (14) into the power flow constraint (13), constraint (13) is transformed into:

[0056]

[0057] The specific steps of step (2) in the above bilateral random power grid dispatching method are as follows:

[0058] (1) The Gaussian mixture distribution is approximated using the following formula:

[0059]

[0060] Where ξ0 is any one-dimensional random variable that follows a Gaussian mixture distribution. Let ξ0 be the cumulative distribution function of the random variable, x be the independent variable of the cumulative distribution function, ω0 represent the possible values ​​of ξ0, uppercase M0 represent the number of Gaussian components of the distribution followed by the random variable ξ0, lowercase m0 represent the m0th component, and ω0 and μ0 represent the cumulative distribution function of the random variable ξ0. m0 and σ m0 Let a and b represent the weight coefficient, expected value, and standard deviation of the m0th component, respectively, where a and b are constants, and tanh is the hyperbolic tangent function in mathematical operations;

[0061] (2) Based on the Gaussian mixture distribution approximation method in step (1), the cumulative distribution function of the random variable in the standby demand constraint of the above formula (13) is approximated:

[0062]

[0063] in, Let be a random variable, representing the total actual output of all renewable energy power plants at time t, and 1 represents a column vector where all elements are 1. Represents a one-dimensional random variable The probability density function, where y is the cumulative distribution function. The independent variable represents Possible values, express An approximate expression for;

[0064] (3) Based on the Gaussian mixture distribution approximation method in step (1), the cumulative distribution function of the random variable in the power flow constraint of the power grid line in the above formula (15) is approximated:

[0065]

[0066] in, Let be a column vector, and let the j-th element of the vector be... Let be a random variable, representing the linear combination of the actual output of all renewable energy power plants at time t, with coefficients of the linear combination being... Represents a one-dimensional random variable The probability density function, z is the cumulative distribution function. The independent variable represents Possible values, express An approximate expression for;

[0067] The specific steps of step (4) in the above bilateral random power grid dispatching method are as follows:

[0068] (1) Based on the approximation of the random variables in the reserve requirement constraint, the opportunity constraint is transformed using the approximate expression (17) of the cumulative distribution function:

[0069]

[0070]

[0071]

[0072] in and As auxiliary variables, they represent the upper and lower quantiles of the standby demand constraint at time t, respectively.

[0073] (2) Based on the approximation of the random variables in the power flow constraints of the power grid lines, the power flow opportunity constraints of the power grid lines determined by formula (15) are transformed using the approximate expression (18) of the cumulative distribution function of the random variables in the power flow constraints of the power grid lines:

[0074]

[0075]

[0076]

[0077] in and As auxiliary variables, they represent the upper and lower quantiles of the power flow constraint of the l-th line at time t, respectively;

[0078] (4) Solving the bilateral stochastic scheduling model based on the hyperbolic tangent function approximation

[0079] Based on the above deterministic transformation of the bilateral opportunity constraint, the opportunity constraint shown in formula (13) is equivalently transformed into deterministic convex constraints (19)-(21); the opportunity constraint (15) is equivalently transformed into deterministic convex constraints (22)-(24). Since the other constraints are linear constraints related to the optimization variables and the objective function is a quadratic function, the bilateral stochastic scheduling problem is equivalently transformed into a convex optimization problem.

[0080] Using the interior point method, the optimization model consisting of the objective function (1)-(2) and constraints (3)-(9), (14), (19)-(24) in steps (1)-(3) above is solved to obtain the planned power generation of the i-th thermal power unit during the t-schedule period. and the planned reference output of the j-th renewable energy power plant during dispatch period t. Among them This represents the planned output of the i-th thermal power unit during scheduling period t. As the reference output of the j-th renewable energy power plant during scheduling period t, it realizes chance-constrained stochastic economic scheduling based on hyperbolic tangent function approximation.

Claims

1. A bilateral stochastic power grid dispatch method, characterized by The method comprises the following steps: (1) establishing a two-sided stochastic power grid scheduling model based on hyperbolic tangent function approximation, the two-sided stochastic power grid scheduling model comprising an objective function and constraint conditions; The objective function of the two-sided stochastic power grid scheduling model is to minimize the sum of the power generation cost of the thermal power unit and the positive spinning reserve capacity cost and the negative spinning reserve capacity cost, The constraint conditions of the two-sided stochastic power grid scheduling model comprise: (1-2-6) a spinning reserve demand constraint for coping with renewable energy fluctuation in the power grid, and the expression is as follows: (10) Among them, mathematical symbols Indicates the probability of an event occurring. express t The first during the scheduling period j The actual output of each renewable energy power plant, with the superscript ~ indicating that the variable is a random variable. This indicates the maximum risk level preset by the dispatcher, with the maximum risk level ranging from 0 to 0.

5. (1-2-7) a power grid line flow constraint, and the expression is as follows: (13) in, For the first in the power grid Line 1 to the 1st The transfer distribution factor of active power output of a thermal power generating unit. For the first Line 1 to the 1st The active power output transfer distribution factor of a renewable energy power plant For the first Line 1 to the 1st k The load transfer distribution factors are obtained from the power grid dispatch center. For the first The upper limit of active power on the line. The risk level of active power exceeding the line's active power limit is set by the dispatcher. Indicates the first i Taiwan thermal power units t Actual output during the scheduling period; (2) according to the spinning reserve demand constraint and the line flow constraint in step (1), performing analytical approximation on the mixed Gaussian distribution satisfied by the random variables appearing in the constraint to obtain an approximate expression of the random variables; The specific steps of step (2) are as follows: (2-1) performing approximation on the Gaussian mixed distribution by using the following formula: (16) wherein is a one-dimensional random variable subject to a Gaussian mixture distribution, is a cumulative distribution function of the random variable, is an argument of the cumulative distribution function, representing possible values, in capital letters represents a random variable subject to a distribution, in lower case represents the th component, , and represent a weight coefficient, an expectation and a standard deviation of the th component, respectively, a and b are constants, is a hyperbolic tangent function in mathematical operation; (3) according to the approximation of the random variables in the spinning reserve demand constraint and the power grid line flow constraint in step (2), converting the two-sided chance constraint optimization model in step (1) into a deterministic optimization model; (4) solving the deterministic optimization model converted in steps (1)-(3) by using an interior point method to obtain the power generation plan of the thermal power unit and the renewable energy power station.

2. The double-sided stochastic power grid dispatch method of claim 1, wherein, The specific steps of step (1) are as follows: (1-1) the objective function of the two-sided stochastic power grid scheduling model, and the expression is as follows: (1) wherein, T and denote the number of dispatch periods t and the number of thermal power units, respectively, t and i are the indices of the dispatch periods and the thermal power unit numbers, respectively, denotes the cost of unit positive spinning reserve capacity, denotes the cost of unit negative spinning reserve capacity, denotes the capacity of positive spinning reserve reserved for the i th thermal power unit in the t th dispatch period, denotes the capacity of negative spinning reserve reserved for the i th thermal power unit in the t th dispatch period, denotes the scheduled power generation of the i th thermal power unit in the t th dispatch period, denotes the fuel cost function of the i th thermal power unit, which is expressed as a quadratic function of the unit output . (2) wherein, are quadratic, linear and constant coefficients of fuel cost of thermal power generating units i respectively; (1-2) the constraint conditions of the two-sided stochastic power grid scheduling model further comprise: (1-2-1) a power grid power balance constraint, and the expression is as follows: (3) in, Indicates the first j A renewable energy power plant t Planned reference output during the scheduling period Indicates the first k A load in t The size of the scheduling period, Indicates the number of wind farms. Indicates the quantity of load; (1-2-2) Power output of thermal power generating units in power grid Upper and lower constraints (4) wherein, and are the upper and lower bounds of the power output of the thermal power unit, respectively. i the upper and lower bounds of the power output of the thermal power unit, respectively. (1-2-3) The grid wind power output planning value Upper and lower constraints: (5) express t Scheduling period j The upper limit of the permissible output of a renewable energy power plant; (1-2-4) a ramping constraint of the thermal power unit in the power grid, and the expression is as follows: (6) (7) wherein, and are the first i upward and downward ramping rates of the thermal power unit, denotes the scheduling interval between two adjacent scheduling periods. (1-2-5) a maximum spinning reserve capacity constraint of the thermal power unit in the power grid, and the expression is as follows: (8) (9) wherein the mathematical symbol denotes the minimum value of the elements in a set; The (1-2-6) further comprises: The joint probability distribution of the actual output of all renewable energy power stations at any time satisfies the following Gaussian mixed distribution: (11) (12) wherein, denotes t a set of scheduled outputs of all renewable energy power plants at a dispatch period, is a random vector, denotes a probability density function of the random vector, denotes a value of denotes a m th component of a mixture Gaussian distribution, M is a number of components of the mixture Gaussian distribution, denotes a weight coefficient of a m th component of the mixture Gaussian distribution, and satisfies a sum of weight coefficients of all components equal to 1, represents a mean vector of a m th component, represents a covariance matrix of a m th component, det represents a determinant of a matrix, and a superscript T represents a transpose of a matrix; The (1-2-7) further comprises: For whose expression is: (14) in For the first i The power allocation factor of a thermal power unit is determined by the ratio of its rated capacity to the total capacity of all participating thermal power units. To ensure power balance in the power grid at any given time, the sum of the power allocation factors of all thermal power units must equal 1. This represents the power difference between the actual output and the planned output of all renewable energy power plants; Substituting expression (14) into the power flow constraint (13), constraint (13) is transformed into: (15)。 3. The double-sided stochastic power grid dispatch method of claim 1, wherein, The specific steps of step (2) further comprise: (2-2) according to the Gaussian mixed distribution approximation method of step (2-1), performing approximation on the cumulative distribution function of the random variables in the spinning reserve demand constraint of the above formula (10): (17) wherein is a random variable representing t the sum of all renewable energy power plants actual outputs at time is a column vector with all elements equal to 1, is a one-dimensional random variable whose probability density function is is the argument of the cumulative distribution function whose possible values are is an approximate expression of ;​ (2-3) according to the Gaussian mixed distribution approximation method of step (2-1), performing approximation on the cumulative distribution function of the random variables in the power grid line flow constraint of the above formula (15): (18) wherein is a column vector, the i-th element of which is j , , is a random variable representing t a linear combination of the actual outputs of all renewable energy power plants at time instant t, the coefficients of the linear combination being , denotes the probability density function of the one-dimensional random variable , is the argument of the cumulative distribution function , denotes the possible values of denotes an approximate expression of .

4. The double-sided stochastic power grid dispatch method of claim 1, wherein, The specific steps of step (3) are as follows: (3-1) according to the approximation of the random variables in the spinning reserve demand constraint, converting the chance constraint by using the approximate expression (17) of the cumulative distribution function: (19) (20) (21) wherein and are auxiliary variables, respectively representing t upper and lower quantile of the reserve requirement at time (3-2) according to the approximation of the random variables in the power grid line flow constraint, converting the power grid line flow chance constraint determined by formula (15) by using the approximate expression (18) of the cumulative distribution function of the random variables in the power grid line flow constraint: (22) (23) (24) wherein and are auxiliary variables, respectively representing t the upper and lower quantile of the flow constraint of the i-th line at time t l the upper and lower quantile of the flow constraint of the i-th line at time t The specific steps of step (4) are as follows: (4-1) solving the two-sided stochastic scheduling model based on hyperbolic tangent function approximation Solve the optimization model composed of the objective functions (1)-(2) and the constraint conditions (3)-(9), (14), (19)-(24) in the above steps (1)-(3) by using the interior point method to obtain the planned output of the i-th thermal power unit in the dispatch period i The thermal power unit in t The planned generation power of the dispatch period And the planned reference output of the i-th renewable energy power station in the dispatch period j The planned reference output of the i-th renewable energy power station in the dispatch period t The planned output of the i-th thermal power unit in the dispatch period The reference output of the i-th renewable energy power station in the dispatch period The reference output of the i-th renewable energy power station in the dispatch period The reference output of the i-th renewable energy power station in the dispatch period The reference output of the i-th renewable energy power station in the dispatch period The reference output of the i-th renewable energy power station in the dispatch period t The reference output of the i-th renewable energy power station in the dispatch period j The reference output of the i-th renewable energy power station in the dispatch period

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