Scheduling method and system of power system based on sequential convex approximation technology

Abstract

The invention discloses a power system scheduling method and system based on a sequential convex approximation technology. The method comprises the steps of obtaining load information of each node in a power system and a new energy unit output prediction value; inputting the load information and the new energy unit output predicted value into a preset scheduling model, and processing non-convex opportunity constraints in the scheduling model by using a sequential convex approximation technology to obtain an updated convex scheduling model, and projecting the distribution of random variables of the convex scheduling model to a polynomial space by using a distribution projection technology to obtain an approximation problem, and solving the approximation problem by combining a Benders decomposition technology and taking the minimization of a total cost expected value of the power system as a target until an iteration difference value obtained by calculation meets a preset condition, so as to obtain a convex scheduling model. And outputting the target output value of the thermal power unit and the wind and light abandoning amount of the new energy unit to realize power system scheduling. According to the invention, the accuracy and applicability of the power system scheduling method can be improved.

Description

Technical Field

[0001] This invention relates to the field of power systems, and more particularly to a scheduling method and system for power systems based on sequential convex approximation technology. Background Technology

[0002] As the scale of new energy (such as wind and solar) grid connection gradually expands, the complexity and uncertainty of the power system have increased significantly. The intermittency and uncertainty of new energy power generation pose a huge challenge to the supply and demand balance of the power system, and also increase the safety risks of grid operation. Therefore, day-ahead dispatching of the power system needs to predict the output and load demand data of renewable energy in each time period of the next day, and based on this, arrange the power generation plan of each unit in each time period of the next day according to certain economic principles while meeting the load demand of the next day, thereby achieving economic operation and low-carbon development of the power system, while ensuring the reliability and stability of power supply.

[0003] Existing power system dispatching methods have several shortcomings when facing the uncertainty of renewable energy output and the dispatching requirements of a low-carbon economy. On the one hand, traditional dispatching methods typically assume that random variables follow a Gaussian distribution. This assumption fails to guarantee the accuracy of solutions when dealing with non-Gaussian uncertainties, potentially leading to dispatching results that deviate from actual needs and impacting the economic efficiency and security of the power system. On the other hand, existing methods are computationally inefficient when solving chance-constrained programming problems, especially when large-scale scenario sampling is involved, where computational complexity increases significantly, making it difficult to meet the demands of real-time dispatching. Furthermore, existing methods are often overly conservative when dealing with complex nonlinear and probabilistic constraints, resulting in insufficient economic efficiency in dispatching schemes, failure to fully utilize renewable energy resources, and limitations on the flexibility and adaptability of the power system. Summary of the Invention

[0004] This invention provides a power system scheduling method and system based on sequential convex approximation technology, which can improve the accuracy and applicability of power system scheduling methods.

[0005] An embodiment of the present invention provides a power system scheduling method based on sequential convex approximation technique, comprising:

[0006] Obtain load information of each node in the power system and the predicted output of new energy generating units;

[0007] The load information and the predicted output of the new energy units are input into a preset scheduling model. The non-convex opportunity constraints in the scheduling model are processed using the sequential convex approximation technique to obtain an updated convex scheduling model. The distribution projection technique is used to project the distribution of the random variables of the convex scheduling model onto the multinomial space to obtain an approximation problem. The approximation problem is then solved using the Benders decomposition technique with the goal of minimizing the expected total cost of the power system until the calculated iterative difference satisfies the preset conditions. The target output of the thermal power units and the amount of wind and solar curtailment of the new energy units are then output. The scheduling model is obtained by transforming the low-carbon economic scheduling model with uncertainty into an opportunity constraint form.

[0008] The power system is dispatched based on the target output of the thermal power units and the amount of wind and solar power curtailment of the new energy units.

[0009] This application's embodiments, by acquiring load information of each node in the power system and predicted output values ​​of new energy units, can understand the operating status of the power system in the coming day, providing a basic data basis for scheduling the following day. Through sequential convex approximation, non-convex opportunity constraints are transformed into convex constraints, making the model easier to solve and improving the operability of the scheduling method. It can also adapt to different types of uncertainty (such as the non-Gaussian distribution of new energy output), enhancing the applicability of the scheduling method. Distributed projection technology can accurately describe the distribution of random variables, avoiding the inefficiency of large-scale sampling in traditional methods and significantly improving computational efficiency. By rationally arranging the target output values ​​of the thermal power units and the amount of wind and solar curtailment of the new energy units, wind and solar curtailment is reduced, improving the utilization rate of new energy and optimizing the operating efficiency of thermal power units, achieving rational resource allocation. Compared with existing technologies, this application, based on the actual needs of "electricity-carbon" coordinated scheduling in the power system, utilizes sequential convex approximation technology to handle non-convex opportunity constraints and proposes distributed projection technology to improve computational efficiency, solving the problem of traditional methods being limited by random distribution forms, thereby improving the accuracy and applicability of power system scheduling methods.

[0010] Furthermore, the construction process of the aforementioned low-carbon economic dispatch model with uncertainty is as follows:

[0011] Obtain load information, predicted output values ​​of new energy generating units, upper and lower limits of line transmission power, upper and lower limits of voltage amplitude, upper and lower limits of active power of thermal power units, and upper and lower limits of reactive power of thermal power units at each node in the power system.

[0012] Based on the load information, the predicted output of the new energy units, the upper and lower limits of the transmission power of the lines, the upper and lower limits of the voltage amplitude, the upper and lower limits of the active power of the thermal power units, and the upper and lower limits of the reactive power of the thermal power units, a low-carbon economic dispatch model is established with the objective function of minimizing the expected value of the total cost of the power system. The total cost includes the power generation cost of thermal power units, the cost of wind and solar curtailment, and the cost of carbon emission trading. The constraints of the low-carbon economic dispatch model include AC power flow constraints, power generation control constraints, generator output limit constraints, transmission power constraints, and voltage amplitude constraints.

[0013] By constructing a low-carbon economic dispatch model with uncertainties, the power system dispatch method can be ensured to comprehensively consider various actual operating constraints and cost factors, thereby improving the accuracy and applicability of the dispatch method and better adapting to the complexity and uncertainty of power system operation.

[0014] Furthermore, the expression for the scheduling model is specifically as follows:

[0015] The objective function is:

[0016]

[0017] The current flow constraint is:

[0018]

[0019] The power generation control constraints are:

[0020]

[0021] The output limit constraint is:

[0022]

[0023] The transmission power constraint is:

[0024]

[0025] The voltage amplitude constraint is as follows:

[0026]

[0027] In the formula, C represents the total cost of the power system; ω represents the actual system scenario; P g,i (ω) represents the active power output information of thermal power unit i in scenario ω; P i loss (ω) and P i real (ω) represent the wind and solar curtailment and power output information of renewable energy unit i in scenario ω; C G CCUR and These are the power generation cost of the thermal power unit, the cost of wind and solar curtailment, and the cost of carbon emission trading, respectively; a g,i b g,i and c g,i η is the power generation cost coefficient of thermal power unit i; Δt is the dispatch period length; η i Cost per unit of wind and solar curtailment; For carbon trading prices; E p With E d These represent carbon quotas and carbon emissions, respectively; h is the carbon emission allocation per unit of electricity (unit: tons CO2 / MWh); ρ is the carbon emission factor for coal; μ i This represents the unit coal consumption of thermal power unit i. x is the upper limit of the active power of thermal power unit i; i y i With z i e is the unit coal consumption coefficient; i (ω) and f i (ω) represent the real and imaginary parts of the voltage phasor at node i under scenario ω, respectively; G ij With B ij These are the real and imaginary parts of the element at position (i,j) in the node admittance matrix, respectively. A set of nodes; Ω represents the set of lines; ω represents the set of actual scene ω. and Let P represent the sets of nodes for thermal power units and new energy power generation units, respectively; i Load (ω) and These represent the active and reactive loads of node i in scenario ω, respectively; Q g,i (ω) represents the reactive power output of thermal power unit i in scenario ω; ρ i dp represents the automatic generation control coefficient of generator i; D(ω) represents the change in total net load under scenario ω; i (ω) and dq i (ω) represents the change in active and reactive power losses under scenario ω; ω0 is the baseline scenario, under which D(ω0) and dp i (ω0) and dq i (ω0) are all equal to 0; This represents the upper limit of the transmission power of line ij; V i and These represent the lower and upper limits of the voltage amplitude at node i; P g,i and These are the lower and upper limits of the active power of thermal power unit i; Q g,i and These are the lower and upper limits of the reactive power of thermal power unit i; ε represents the probability; ε is the acceptable violation probability.

[0028] Furthermore, the sequential convex approximation technique is used to process the non-convex opportunity constraints in the scheduling model to obtain an updated convex scheduling model, specifically as follows:

[0029] The non-convex opportunity constraints in the scheduling model are redescribed in analytical form using a unit step function. Then, the unit step function in the analytical form is replaced with a convex piecewise linear function to obtain the first approximate convex constraint.

[0030] By minimizing the convex piecewise linear function in the first approximate convex constraint to reduce the approximation deviation, a second approximate convex constraint is obtained. The feasible domain of the convex piecewise linear function parameter in the second approximate convex constraint is relaxed to the real number domain to obtain a relaxed constraint. The relaxed constraint is simplified by introducing auxiliary variables to obtain a simplified relaxed constraint.

[0031] A non-negative relaxation parameter vector is added to the simplified relaxation constraint to obtain a third approximate convex constraint. The relaxation parameter vector of the third approximate convex constraint is updated using the fixed-point iteration technique until the relaxation parameter vector satisfies the preset convergence condition, and the updated convex scheduling model is determined.

[0032] By transforming non-convex opportunity constraints into convex constraints and further improving the accuracy and adaptability of the constraints through optimization parameters and iterative techniques, the accuracy and applicability of power system dispatching methods in dealing with uncertain problems are significantly enhanced.

[0033] Furthermore, the sequential convex approximation technique is used to process the non-convex opportunity constraints in the scheduling model to obtain the relevant formulas of the updated convex scheduling model, specifically as follows:

[0034] The original form of nonconvex opportunity constraints:

[0035]

[0036] In the formula, Indicates probability; l i (ω) is the i-th element of the inequality constraint auxiliary variable vector l(ω); ε is the acceptable violation probability; This is the index set for soft inequality constraints;

[0037] Analytical form of nonconvex chance constraints:

[0038]

[0039] In the formula, It is a unit step function;

[0040] Replacement of the unit step function:

[0041]

[0042] First approximate convex constraint:

[0043]

[0044] In the formula, α is a parameter; It is a convex piecewise linear function;

[0045] Minimizing the convex piecewise linear function yields the second approximate convex constraint:

[0046]

[0047] The feasible region of the relaxation parameters yields the relaxation constraints:

[0048]

[0049] Simplify and relax constraints:

[0050]

[0051] In the formula, u i (ω) represents the i-th auxiliary variable;

[0052] Adding nonnegative relaxation parameters yields the third approximate convex constraint:

[0053]

[0054] Update the relaxation parameters:

[0055]

[0056] In the formula, For the k-th iteration, δ i The value of δ (k) for ; and α obtained in the k-th iteration i with u i The optimal value of (ω); and This is the index set of active opportunity constraints and overly relaxed opportunity constraints at the k-th iteration;

[0057] Updated convex scheduling model:

[0058]

[0059] In the formula, x is the baseline decision vector; ω is the actual scenario of the system; α and u(ω) are the base decision vectors. i and u i The vector of (ω); δ * The optimal non-negative relaxation parameter The vector; l(ω) is the auxiliary variable vector of the inequality constraints; This is the feasible region.

[0060] Furthermore, the distribution projection technique is used to project the random variables of the convex scheduling model onto the multinomial space to obtain an approximate problem, specifically:

[0061] Define basis functions and inner product operations for the Bernstein polynomial space, wherein the basis functions are constructed based on tensor products and the inner product operations depend on the cumulative distribution function;

[0062] The inner product operation projects the distribution of random variables in the convex scheduling model onto the multinomial space, and the random distribution projected onto the multinomial space is re-described based on the basis functions to obtain the updated convex scheduling model.

[0063] The equality constraints in the updated convex scheduling model are projected to obtain equivalent equality constraints in the Bernstein polynomial space. The inequality constraints in the updated convex scheduling model are reconstructed, and the deviation introduced by the reconstruction process is reduced by strengthening the control points to obtain approximate inequality constraints.

[0064] The equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space are integrated to generate the approximate problem corresponding to the convex scheduling model.

[0065] By projecting the distribution of random variables onto the Bernstein multinomial space and processing the equality and inequality constraints accordingly, an approximate problem that is easy to solve can be generated, thereby significantly improving the accuracy and applicability of the power system dispatching method, enabling it to handle uncertainties more efficiently and adapt to complex scenarios.

[0066] Furthermore, the distribution projection technique is used to project the random variables of the convex scheduling model onto the multinomial space to obtain the relevant formulas for the approximation problem, specifically as follows:

[0067] The basis functions of the Bernstein polynomial space are:

[0068]

[0069] In the formula, Φ j(ω) is the j-th multivariable Bernstein polynomial basis function; basis function Φ j The index vector of (ω); Let j be the set; For tensor product operators; N ω B is the base of ω; j,n (ω w ) is the basis function of the j-th n-th single-variable Bernstein polynomial; ω w Let w be the w-th element of ω;

[0070] The inner product operation in Bernstein polynomial space is:

[0071]

[0072] In the formula, a(ω) represents an arbitrary random distribution; F(ω) represents the cumulative distribution function of ω;

[0073] The inner product operation in Bernstein polynomial space is:

[0074]

[0075] In the formula, a(ω) represents an arbitrary random distribution; F(ω) represents the cumulative distribution function of ω;

[0076] The re-description of the random distribution is as follows:

[0077]

[0078] In the formula, y i (ω), l i (ω) and u i (ω) represents the i-th element of y(ω), l(ω), and u(ω), respectively; y ij l ij with u ij y i (ω), l i (ω) and u i The j-th coefficient of (ω); N y N l With N u Let be the cardinalities of y(ω), l(ω), and u(ω), respectively;

[0079] The equivalent equality constraints obtained by projection are:

[0080]

[0081] The approximate inequality constraints obtained by projection are:

[0082]

[0083] In the formula, Let J be the set; K jk For l ik and l ij The composite relationship coefficient between them is the product of the relationship coefficients of all dimensions of ω; For index The set of k, where k w =0,1,...,m, w=1,2,...,N ω J k For use in calculation The kth coefficient.

[0084] Another embodiment of the present invention provides a power system dispatching system based on sequential convex approximation technology, comprising: an acquisition module, a calculation module, and a dispatching module;

[0085] The acquisition module is used to acquire load information of each node in the power system and the predicted output value of new energy units;

[0086] The calculation module is used to input the load information and the predicted output value of the new energy units into a preset scheduling model, process the non-convex opportunity constraints in the scheduling model using sequential convex approximation technology to obtain an updated convex scheduling model, project the distribution of the random variables of the convex scheduling model onto a multinomial space using distribution projection technology to obtain an approximation problem, and solve the approximation problem with the goal of minimizing the expected total cost of the power system using Benders decomposition technology until the calculated iterative difference satisfies the preset conditions, and output the target output value of thermal power units and the amount of wind and solar curtailment of new energy units. The scheduling model is obtained by converting the low-carbon economic scheduling model with uncertainty into an opportunity constraint form.

[0087] The scheduling module is used to schedule the power system based on the target output value of the thermal power unit and the amount of wind and solar curtailment of the new energy unit.

[0088] This application's embodiments, by acquiring load information of each node in the power system and predicted output values ​​of new energy units, can understand the operating status of the power system in the coming day, providing a basic data basis for scheduling the following day. Through sequential convex approximation, non-convex opportunity constraints are transformed into convex constraints, making the model easier to solve and improving the operability of the scheduling method. It can also adapt to different types of uncertainty (such as the non-Gaussian distribution of new energy output), enhancing the applicability of the scheduling method. Distributed projection technology can accurately describe the distribution of random variables, avoiding the inefficiency of large-scale sampling in traditional methods and significantly improving computational efficiency. By rationally arranging the target output values ​​of the thermal power units and the amount of wind and solar curtailment of the new energy units, wind and solar curtailment is reduced, improving the utilization rate of new energy and optimizing the operating efficiency of thermal power units, achieving rational resource allocation. Compared with existing technologies, this application, based on the actual needs of "electricity-carbon" coordinated scheduling in the power system, utilizes sequential convex approximation technology to handle non-convex opportunity constraints and proposes distributed projection technology to improve computational efficiency, solving the problem of traditional methods being limited by random distribution forms, thereby improving the accuracy and applicability of power system scheduling methods.

[0089] Furthermore, the calculation module includes a replacement unit, a calculation unit, and an update unit;

[0090] The replacement unit is used to re-describe the non-convex opportunity constraints in the scheduling model into an analytical form using a unit step function, and then replace the unit step function in the analytical form with a convex piecewise linear function to obtain the first approximate convex constraint.

[0091] The calculation unit is used to reduce the approximation deviation by minimizing the convex piecewise linear function in the first approximate convex constraint to obtain the second approximate convex constraint, relax the feasible domain of the convex piecewise linear function parameter in the second approximate convex constraint to the real number domain to obtain the relaxation constraint, and simplify the relaxation constraint by introducing auxiliary variables to obtain the simplified relaxation constraint.

[0092] The updating unit is used to add a non-negative relaxation parameter vector to the simplified relaxation constraint to obtain a third approximate convex constraint, and to update the relaxation parameter vector of the third approximate convex constraint using a fixed-point iteration technique until the relaxation parameter vector satisfies a preset convergence condition, thereby determining the updated convex scheduling model.

[0093] Furthermore, the calculation module also includes a definition unit, an update unit, a projection unit, and an integration unit;

[0094] The defining unit is used to define the basis functions and inner product operations of the Bernstein polynomial space, wherein the basis functions are constructed based on tensor products, and the inner product operations depend on the cumulative distribution function;

[0095] The updating unit is used to project the distribution of random variables of the convex scheduling model onto the multinomial space through the inner product operation, and to re-describe the random distribution projected onto the multinomial space based on the basis functions to obtain the updated convex scheduling model.

[0096] The projection unit is used to project the equality constraints in the updated convex scheduling model to obtain equivalent equality constraints in the Bernstein polynomial space, and to reconstruct the inequality constraints in the updated convex scheduling model. By strengthening the control points, the deviation introduced by the reconstruction process is reduced to obtain approximate inequality constraints.

[0097] The integration unit is used to integrate the equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space to generate an approximate problem corresponding to the convex scheduling model. Attached Figure Description

[0098] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0099] Figure 1 This is a flowchart illustrating an embodiment of the power system scheduling method based on sequential convex approximation technology provided in this application;

[0100] Figure 2 This is a flowchart illustrating steps S201 to S203 provided in this application;

[0101] Figure 3 This is a flowchart illustrating steps S301 to S304 provided in this application;

[0102] Figure 4 This is a schematic diagram of the complete iterative process of the scheduling method provided in this application;

[0103] Figure 5 This is a schematic diagram of an embodiment of the dispatching system for a power system based on the sequential convex approximation technique provided in this application. Detailed Implementation

[0104] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0105] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0106] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0107] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0108] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0109] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).

[0110] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0111] The expansion of renewable energy grid connection has increased the complexity and uncertainty of the power system, posing challenges to supply-demand balance and grid security. Power system dispatching requires real-time monitoring of operating status, rational allocation of unit output, optimization of transmission paths, and achievement of economical and low-carbon operation, ensuring reliability and stability. Existing dispatching methods have shortcomings in handling the uncertainties of renewable energy and low-carbon demands: First, traditional methods assume that random variables follow a Gaussian distribution, which cannot cope with non-Gaussian uncertainties, leading to inaccurate dispatching results and affecting economic efficiency and security; second, the computational efficiency is low when solving chance-constrained programming, and large-scale scenario sampling increases complexity, making it difficult to meet real-time dispatching requirements; third, they are too conservative in handling complex constraints, lacking economic efficiency and limiting flexibility and adaptability.

[0112] See Figure 1 To improve the accuracy and applicability of power system dispatching methods, an embodiment of the present invention provides a power system dispatching method based on sequential convex approximation technology, including steps S101 to S103.

[0113] Step S101: Obtain the load information of each node in the power system and the predicted output of the new energy generating units;

[0114] In some embodiments, firstly, the forecasting center obtains high-precision numerical weather forecast data from meteorological service providers; secondly, renewable energy power plants generate power output forecasts based on numerical weather forecast data and local data, and report them to the dispatching agency; then, the power grid forecasting center generates a total system load forecast based on historical load, numerical weather forecast data, calendar data, and other data; finally, the dispatching agency receives the power plant forecasts and load forecasts, integrates, verifies, and corrects them using its own model, and may consider power grid constraints, ultimately forming load forecasts and renewable energy output forecasts for each node or region of the system used for day-ahead dispatching decisions.

[0115] Step S102: Input the load information and the predicted output value of the new energy units into a preset scheduling model. Use the sequential convex approximation technique to process the non-convex opportunity constraints in the scheduling model to obtain an updated convex scheduling model. Use the distribution projection technique to project the distribution of the random variables of the convex scheduling model to the multinomial space to obtain an approximation problem. Combine the Benders decomposition technique to solve the approximation problem with the goal of minimizing the expected value of the total cost of the power system until the calculated iterative difference satisfies the preset conditions. Output the target output value of the thermal power units and the amount of wind and solar curtailment of the new energy units. The scheduling model is obtained by converting the low-carbon economic scheduling model with uncertainty into an opportunity constraint form.

[0116] In some embodiments, the construction process of the low-carbon economic dispatch model with uncertainty specifically involves: acquiring load information of each node in the power system, predicted output values ​​of new energy generating units, upper and lower limits of line transmission power, upper and lower limits of voltage amplitude, upper and lower limits of active power of thermal power units, and upper and lower limits of reactive power of thermal power units; based on the load information, the predicted output values ​​of new energy generating units, the upper and lower limits of line transmission power, the upper and lower limits of voltage amplitude, the upper and lower limits of active power of thermal power units, and the upper and lower limits of reactive power of thermal power units, establishing a low-carbon economic dispatch model with the objective function of minimizing the expected value of the total cost of the power system, wherein the total cost includes the power generation cost of thermal power units, the cost of wind and solar curtailment, and the cost of carbon emission trading, and the constraints of the low-carbon economic dispatch model include AC power flow constraints, power generation control constraints, generator output limit constraints, transmission power constraints, and voltage amplitude constraints. Specifically, firstly, load information of each node in the power system is obtained through smart meters, load monitoring equipment, etc., including the active and reactive loads of the nodes, to reflect the load demand of each node in different time periods; the upper and lower limits of active and reactive power of thermal power units are obtained; the output forecast values ​​of new energy units (such as wind power, photovoltaic, etc.) are obtained; the upper and lower limits of line transmission power are obtained, that is, the power range allowed to be transmitted by each line; the upper and lower limits of voltage amplitude at each node are obtained, that is, the allowable range of voltage amplitude at each node; the upper and lower limits of active power of thermal power units are obtained, that is, the allowable active power output range of thermal power units; and the upper and lower limits of reactive power of thermal power units are obtained, that is, the allowable reactive power output range of thermal power units. Secondly, the power generation cost of thermal power units is calculated based on their power generation output and cost coefficient. The cost coefficient is typically related to factors such as fuel prices and equipment operation and maintenance costs. Wind and solar curtailment costs are calculated based on the amount of wind and solar power curtailed and the cost per unit of curtailment. Carbon emission trading costs are calculated based on the carbon emissions of thermal power units and carbon trading prices. Carbon emissions can be calculated based on the active power output of thermal power units, the carbon emission factor of coal, and the carbon emission allocation per unit of electricity. The calculated power generation cost, wind and solar curtailment cost, and carbon emission trading cost are then added together to obtain the total cost of the power system. Next, based on the power system's network topology and the load and power generation status of each node, AC power flow equations are established. Based on the output of thermal power units and new energy units, power generation control constraints are established, limiting the active and reactive power output ranges of thermal power units and new energy units, i.e., determining the generator output limit constraints. The transmission power range of each line and the voltage amplitude range at each node are also constrained. Through the above steps, a low-carbon economic scheduling model with uncertainties was constructed, laying the foundation for subsequent solutions using sequential convex approximation and distributed projection techniques.

[0117] It should be noted that the predicted information of load and renewable energy output is included in the actual scenario ω. This application obtains the predicted information of load and renewable energy for the next day in the previous day, and makes the optimal scheduling decision under the predicted load and renewable energy situation (i.e. scenario).

[0118] It should be noted that the upper and lower limits of active power and reactive power of thermal power units are determined based on factors such as the equipment characteristics and operational safety requirements of the thermal power units; while the upper and lower limits of transmission power of each line in the power system are determined based on factors such as the thermal stability limit and voltage stability limit of the line, in order to ensure the safe operation of the line; the upper and lower limits of voltage amplitude at each node are determined based on the voltage quality requirements and equipment operation safety requirements of the power system, and this application does not impose any restrictions on them.

[0119] In some embodiments, the expression of the low-carbon economic dispatch model is specifically:

[0120] The objective function is:

[0121]

[0122] The current flow constraint is:

[0123]

[0124]

[0125] The power generation control constraints are:

[0126]

[0127] The output limit constraint is:

[0128]

[0129] The transmission power constraint is:

[0130]

[0131] The voltage amplitude constraint is as follows:

[0132]

[0133] In the formula, C represents the total cost of the power system; ω represents the actual system scenario; P g,i (ω) represents the active power output information of thermal power unit i in scenario ω; P i loss (ω) and P i real (ω) represent the wind and solar curtailment and power output information of renewable energy unit i in scenario ω; C G CCUR and These are the power generation cost of the thermal power unit, the cost of wind and solar curtailment, and the cost of carbon emission trading, respectively; a g,i b g,i and c g,i η is the power generation cost coefficient of thermal power unit i; Δt is the dispatch period length; η i Cost per unit of wind and solar curtailment; For carbon trading prices; E p With E d These represent carbon quotas and carbon emissions, respectively; h is the carbon emission allocation per unit of electricity; ρ is the carbon emission factor for coal; μ i This represents the unit coal consumption of thermal power unit i. x is the upper limit of the active power of thermal power unit i; i y i With z i e is the unit coal consumption coefficient; i (ω) and f i (ω) represent the real and imaginary parts of the voltage phasor at node i under scenario ω, respectively; G ij With B ij These are the real and imaginary parts of the element at position (i,j) in the node admittance matrix, respectively. A set of nodes; Ω represents the set of lines; ω represents the set of actual scene ω. and Let P represent the sets of nodes for thermal power units and new energy power generation units, respectively; i Load (ω) and These represent the active and reactive loads of node i in scenario ω, respectively; Q g,i (ω) represents the reactive power output of thermal power unit i in scenario ω; ρ i dp represents the automatic generation control coefficient of generator i; D(ω) represents the change in total net load under scenario ω; i (ω) and dq i (ω) represents the change in active and reactive power losses under scenario ω; ω0 is the baseline scenario, under which D(ω0) and dp i (ω0) and dq i (ω0) are all equal to 0; This represents the upper limit of the transmission power of line ij; V i and These represent the lower and upper limits of the voltage amplitude at node i; P g,i and These are the lower and upper limits of the active power of thermal power unit i; Q g,i and These represent the lower and upper limits of reactive power for thermal power unit i.

[0134] By constructing a low-carbon economic dispatch model with uncertainties, the power system dispatch method can be ensured to comprehensively consider various actual operating constraints and cost factors, thereby improving the accuracy and applicability of the dispatch method and better adapting to the complexity and uncertainty of power system operation.

[0135] In some embodiments, the power system dispatch model can be concisely described as follows:

[0136]

[0137] In the formula, x is the baseline decision vector, including P g,i (ω0), Q g,i (ω0), e i (ω0) and f i (ω0); y(ω) represents the adjustment decision under the actual scenario ω, including P g,i (ω), Q g,i (ω), e i (ω), f i (ω), dp i (ω) and dq i (ω); g(·) and h(·) represent equality constraints (9)-(12) and inequality constraints (13)-(16) respectively; l(ω) is the auxiliary variable vector of the inequality constraints.

[0138] In the above model, the decision made needs to strictly satisfy all constraints in all possible scenarios. Because the decision is too conservative, its economy is reduced. Therefore, it is necessary to establish a scheduling model with opportunity constraints to allow the decision to not satisfy the soft constraints of the system to a certain extent, and to precisely control the probability of violation of the soft constraints through opportunity constraints.

[0139] In some embodiments, the scheduling model is obtained by transforming a low-carbon economic scheduling model with uncertainty into an opportunity constraint form. Specifically, the constraints are divided into hard constraints (which must be strictly satisfied) and soft constraints (which allow a certain degree of violation). For soft constraints, an opportunity constraint form is introduced, allowing the constraint to be violated with a certain probability. The probability of violation of the soft constraint is calculated through a probability distribution, and it is ensured that it does not exceed a preset threshold. For example, P in formula (25) represents the probability. If ε is 5%, then (25) means that the probability of violating the soft constraint does not exceed 5%, that is, the probability of the constraint being satisfied is 95%.

[0140] In some embodiments, the expression for the scheduling model is specifically:

[0141]

[0142] In the formula, x is the baseline decision vector, including P g,i (ω0), Q g,i (ω0), e i (ω0) and f i (ω0); y(ω) represents the adjustment decision under the actual scenario ω, including P g,i (ω), Q g,i (ω), e i (ω), f i (ω), dp i (ω) and dq i (ω); g(·) and h(·) represent equality constraints (9)-(12) and inequality constraints (13)-(16) respectively; l(ω) is the auxiliary variable vector of the inequality constraints; l i (ω) is the i-th element of l(ω); Represents probability; and ε represents the index set of hard inequality constraints and soft inequality constraints, respectively; ε is the acceptable violation probability.

[0143] It should be noted that when (15) and (16) are modified to: the transmission power constraint is: The voltage amplitude constraint is as follows: This constitutes the power system dispatch model.

[0144] Please refer to Figure 2 In some embodiments, the step of using sequential convex approximation technique to process the non-convex opportunity constraints in the scheduling model to obtain an updated convex scheduling model includes steps S201 to S203.

[0145] Step S201: The non-convex opportunity constraint in the scheduling model is re-described in analytical form using a unit step function, and then the unit step function in the analytical form is replaced with a convex piecewise linear function to obtain the first approximate convex constraint.

[0146] In some embodiments, due to the non-convexity of the opportunity constraints involved in the probability calculation of the scheduling model, the model solution is difficult. Therefore, it is necessary to use a set of convex constraints to approximate the non-convex opportunity constraints, and further propose a sequential convex approximation technique to reduce the deviation between the original opportunity constraints and the approximate constraints. Specifically, firstly, by calculating constraint l i The probability of violating (ω)≤0 in all scenarios is used to reformulate the chance constraint (25) (i.e., the original form of the non-convex chance constraint) into an analytical form, namely:

[0147]

[0148] In the formula, It is a unit step function.

[0149] Then, due to the unit step function The nonconvexity of the constraint (26) still makes it difficult to handle. Therefore, a convex piecewise linear function with parameter α is introduced. approximation The replacement of the unit step function is:

[0150]

[0151] In the formula, [·] + =max{0, ·}.

[0152] By using replace That is, the replacement of the unit step function, constraint (26), this non-convex chance constraint, can be approximated as a convex constraint. The first approximate convex constraint is shown below:

[0153]

[0154] In the formula, α i For the i-th opportunity constraint The parameters are obtained, and thus the first approximate convex constraint (28) can be obtained.

[0155] Step S202: By minimizing the convex piecewise linear function in the first approximate convex constraint to reduce the approximation deviation, a second approximate convex constraint is obtained. The feasible domain of the convex piecewise linear function parameter in the second approximate convex constraint is relaxed to the real number domain to obtain a relaxed constraint. The relaxed constraint is simplified by introducing auxiliary variables to obtain a simplified relaxed constraint.

[0156] In some embodiments, due to the function Always greater than function Therefore, constraint (28) is actually a conservative approximation of constraint (26), meaning there is always a non-negative deviation between (28) and (26). To solve this problem, a minimization function is used. The method reduces the deviation, thereby improving the approximate effect of constraint (28), and obtains the second approximate convex constraint, namely:

[0157]

[0158] After rearranging the terms, constraint (29) can be simplified to the following form, which is also the simplified relaxation constraint:

[0159]

[0160] Equation (30) is actually a parameter optimization problem, aiming to find the optimal parameters. By constructing a parameter optimization problem (31), the deviation between the convex piecewise linear function and the unit step function can be minimized. To further improve the approximation accuracy, α i The feasible region (i.e., α) i >0) Relaxed to the entire real number domain, equation (30) can be rewritten in the following form, that is, the third approximate convex constraint is:

[0161]

[0162] It is worth noting that this relaxation operation does not affect the approximate validity of the chance constraint (25) (i.e., as long as constraint (31) is satisfied, the original chance constraint (25) will be satisfied), as proven below:

[0163] Let the left side of the above equation be L. i (α i ), L i (α i The derivative of is calculated as shown in the following formula:

[0164]

[0165] In the formula, F(l) i ) for l i The cumulative distribution function of (ω).

[0166] Because of L i (α i ) is a convex function, therefore when When (31) has an optimal solution It is easy to know from (32) The following conditions must be met:

[0167]

[0168] The above formula shows that the optimal solution Actually, it is l i The 1-ε quantile of (ω), i.e.:

[0169]

[0170] In the formula, It is a 1-ε quantile function.

[0171] According to (34), (31) can be rewritten in the following form:

[0172]

[0173] In the above formula, by Since it is always a non-negative number, the following conclusion can be easily drawn:

[0174]

[0175] The above conclusions are compared with the quantile representation of the original chance constraint (25). The comparison shows that even if the relaxation operation in (31) is performed, the original opportunity constraint still holds, that is, the relaxation operation does not affect the approximate validity of the opportunity constraint (25).

[0176] To facilitate application, the relaxed constraint (31) is further simplified by introducing auxiliary variables. The simplified result, i.e., the final convex constraint, is as follows:

[0177]

[0178] In the formula, u i (ω) represents the i-th auxiliary variable.

[0179] By replacing the non-convex chance constraint (25) with convex constraints (37)-(39), the scheduling model becomes easier to solve. Since the above approximation process does not depend on any assumptions about the random distribution, the approximated model is theoretically applicable to chance-constrained low-carbon economic scheduling problems under arbitrary random distributions.

[0180] Step S203: Add a non-negative relaxation parameter vector to the simplified relaxation constraint to obtain a third approximate convex constraint, and use fixed-point iteration technique to update the relaxation parameter vector of the third approximate convex constraint until the relaxation parameter vector satisfies the preset convergence condition, and determine the updated convex scheduling model.

[0181] In some embodiments, in the aforementioned convex approximation method, a deviation still exists between the original chance constraint and the approximation constraint, and in some cases the deviation may be too large. To address this issue, the present invention further proposes a sequential convex approximation technique. First, a non-negative relaxation parameter vector δ is introduced. i To improve the approximate accuracy of the opportunity constraint (37) pre-constructed by the aforementioned method, a convex opportunity constraint (37) is obtained, which can be rewritten as:

[0182]

[0183] In (40), if δ i When set correctly, it can accurately fill the gap between the original and approximate chance constraints. Then, the original chance constraints can be replaced by (40), and the updated convex scheduling model can be described as:

[0184]

[0185] In the formula, α and u(ω) are α i and u i The vector of (ω); For δi The optimal value, if δ i If the optimal value is taken, then when solving (41), the approximate chance constraint (40) will be equivalent to the original chance constraint; δ * for The vector corresponds to all approximate chance constraints; For constraints (22)-(24) and δ * The feasible region is constructed by the lower constraints (38)-(40).

[0186] To obtain the optimal nonnegative relaxation parameter vector δ * The approximate chance constraint in (41) is rewritten in quantile form, i.e.:

[0187] α * (δ * )≤0 (43)

[0188] In the formula, α * quantiles The vector that can be obtained through δ * Solving (41) yields the result.

[0189] Since non-positive opportunity constraints do not affect the solution of the optimization problem, we only need to focus on the positive opportunity constraints in (42), that is:

[0190]

[0191] In the formula, The set of indexes for active opportunity constraints.

[0192] Theoretically, δ * It can be obtained by solving (43), but due to α * Essentially, it is an implicit function defined by (41), so directly solving (43) is difficult. To solve this problem, this invention uses a fixed-point iteration technique to update the relaxation vector, as follows:

[0193]

[0194] In the formula, For the k-th iteration, δ i The value of δ (k) for ; and α is obtained by solving (41) in the k-th iteration. i with u i The optimal value of (ω); and Let δ be the index set of the active chance constraint and the overly relaxed chance constraint at the k-th iteration (during the iteration process, δ (k)From δ (0) =0 gradually increases and may become too large, leading to excessive relaxation of the chance constraint), when the iteration difference E gap =||δ (k+1) -δ (k) If the value is less than the preset threshold, stop the iteration.

[0195] The detailed steps of the sequential convex approximation technique are as follows:

[0196] ① Initialization: Input convergence threshold τ, maximum number of iterations k max ;

[0197] ② Set k = 1, δ (0) =0,E gap >τ;

[0198] ③while k≤k max &E gap >τ

[0199] ④ Utilizing δ (k) Solve problem (37);

[0200] ⑤ Construct a set based on (45) and (46) and

[0201] ⑥ Calculate δ based on (44) (k+1) ;

[0202] ⑦ Calculate E according to the following formula gap ;

[0203] E gap =||δ (k+1) -δ k( ||

[0204] ⑧k = k + 1;

[0205] ⑨end

[0206] ⑩ Output decision

[0207] Through the above steps, non-convex opportunity constraints can be transformed into convex constraints. Then, by using sequential convex approximation techniques and fixed-point iteration techniques, the scheduling model can be gradually optimized, ultimately resulting in a convex scheduling model that satisfies the preset convergence conditions.

[0208] By transforming non-convex opportunity constraints into convex constraints and further improving the accuracy and adaptability of the constraints through optimization parameters and iterative techniques, the accuracy and applicability of power system dispatching methods in dealing with uncertain problems are significantly enhanced.

[0209] Please refer to Figure 3In some embodiments, the random variable distribution of the convex scheduling model is projected onto the multinomial space using the distributed projection technique to obtain an approximate problem, including steps S301 to S304.

[0210] Step S301: Define the basis functions and inner product operation of the Bernstein polynomial space, wherein the basis functions are constructed based on the tensor product, and the inner product operation depends on the cumulative distribution function;

[0211] In some embodiments, the sequential convex approximation technique struggles to analytically obtain the distribution of random variables (i.e., y(ω), l(ω), and u(ω)) in the chance constraint (41). This problem becomes more pronounced when the random distribution of the original random variables is continuous and arbitrary. While traditional scene-based techniques can address this issue, they require large-scale sampling of the random scene, significantly reducing the computational efficiency of the sequential convex approximation technique. To address this problem, this invention further proposes a distribution projection technique to replace the scene-based technique. Since the distribution projection technique does not require scene sampling, it can significantly improve the solution speed of the sequential convex approximation technique. Specifically, firstly, to describe the random distribution of y(ω), l(ω), and u(ω) in (41), a Bernstein polynomial space is constructed using tensor products, i.e.:

[0212]

[0213] In the formula, Φ j (ω) is the j-th multivariable Bernstein polynomial basis function; basis function Φ j The index vector of (ω); Let j be the set; For tensor product operators; N ω B is the base of ω; j,n (ω w ) is the basis function of the j-th n-th single-variable Bernstein polynomial; ω w Let w be the w-th element of ω.

[0214] In some embodiments, in order to project an arbitrary random distribution into the Bernstein polynomial space, the inner product operation is defined as:

[0215]

[0216] In the formula, a(ω) represents any random distribution; F(ω) represents the cumulative distribution function of ω.

[0217] Step S302: Project the distribution of random variables of the convex scheduling model onto the multinomial space through the inner product operation, and re-describe the random distribution projected onto the multinomial space based on the basis functions to obtain the updated convex scheduling model.

[0218] In some embodiments, since each element is Φ in the Bernstein polynomial space j A linear combination of (ω), therefore, after projecting the random distributions of y(ω), l(ω) and u(ω) onto the Bernstein polynomial space according to (49), Φ can be used. j A linear combination of (ω) re-describes y(ω), l(ω), and u(ω). That is:

[0219]

[0220] In the formula, y i (ω), l i (ω) and u i (ω) represents the i-th element of y(ω), l(ω), and u(ω), respectively; y ij l ij with u ij y i (ω), l i (ω) and u i The j-th coefficient of (ω); N y N l With N u Let be the bases of y(ω), l(ω), and u(ω), respectively.

[0221] Step S303: Project the equality constraints in the updated convex scheduling model to obtain equivalent equality constraints in the Bernstein polynomial space, and reconstruct the inequality constraints in the updated convex scheduling model. Reduce the deviation introduced by the reconstruction process by strengthening the control points to obtain approximate inequality constraints.

[0222] In some embodiments, in model (41), equality constraints (22) and (23) are difficult to handle because they need to hold for all random scenarios. To solve this problem, this invention uses the Galerkin method to project the equality constraints (22) and (23) onto the Bernstein polynomial space. According to the Galerkin method, since the functions on the left side of (22) and (23) are equal to 0 for all scenarios, their projections into the Bernstein polynomial space are also equal to 0. This can be described by the Galerkin projection equation, that is, the equality constraints obtained by projection are:

[0223]

[0224] Using the Galerkin method, (22) and (23) can be transformed into (53) and (54), the latter being essentially a set of equations concerning the coefficients y. ij l ij with u ij Processable constraints.

[0225] In some embodiments, similar to equality constraints, inequality constraints (i.e., (24) and (38)-(40)) in model (41) are also difficult to handle. To address this problem, this invention reconstructs the inequality constraints based on the convex hull property of Bernstein polynomials. i Taking (ω) as an example, the convex hull property implies that the Bernstein polynomial It always lies within the convex hull formed by the control points. Since these control points are actually a set of points in the ω-l coordinate system, their l-coordinates are the coefficients l in (51). ij Therefore, l i The convex hull property of (ω) can be expressed as:

[0226]

[0227] According to (55), (24) l i (ω) can be replaced with This will not compromise its effectiveness. The resulting constraints can be simplified as follows:

[0228]

[0229] Similarly, constraints (38) and (39) can be restated as:

[0230]

[0231] For constraint (40) involving expectation calculation, it can be restated according to (52) as follows:

[0232]

[0233] In the formula, I j For use in calculation The j-th coefficient can be obtained in advance by (60).

[0234]

[0235] Based on the convex hull property of Bernstein polynomials, the inequality constraints that are difficult to handle in the opportunity-constrained low-carbon economic dispatch model (i.e. (24) and (38)-(40)) can be transformed into a set of easily handled constraints (i.e. (56)-(59)).

[0236] In some embodiments, the control points in the Bernstein polynomial space are enhanced to obtain target control points, specifically by: due to the inequality constraints projecting onto l i (ω) and This introduces a bias, so (56)-(58) are merely conservative approximations of (24), (38), and (39). To reduce this bias, further strengthening control points are introduced, which can be obtained by increasing the order of the Bernstein polynomial.

[0237]

[0238] In the formula, l ik Let l be the coordinate of the k-th reinforced control point; Ψ k (ω) is the kth multivariate Bernstein polynomial basis function, whose polynomial order is increased from the order n of the polynomial to the strengthening order m, where m is the strengthening order. For index The set of k, where k w =0,1,...,m, w=1,2,...,N ω .

[0239] According to the definition of the Bernstein polynomial in (48), l ik and l ij The relationship between them can be derived from (61), that is:

[0240]

[0241] In the formula, K jk For l ik and l ij The composite relationship coefficient between them, that is, the product of the relationship coefficients of all dimensions of ω, is calculated as follows:

[0242]

[0243] In the formula, ω represents the dimension w The relationship coefficients in the equation.

[0244] According to (62), the conservative constraints (i.e., (56)-(58)) can be further strengthened to (65)-(67), that is, the approximate inequality constraints obtained by projection are:

[0245]

[0246]

[0247] Similarly, constraint (59) can be redescribed by strengthening control points, i.e.:

[0248]

[0249] In the formula, J k For use in calculation The k-th coefficient can be obtained in advance by (69).

[0250]

[0251] Step S304: Integrate the equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space to generate the approximate problem corresponding to the convex scheduling model.

[0252] In some embodiments, the equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space are integrated to generate an approximate problem corresponding to the convex scheduling model. The relevant formula is: By combining sequential convex approximation techniques and distributed projection techniques, the difficult-to-solve non-convex chance-constrained low-carbon economic scheduling problem can be transformed into an easily solvable convex problem, that is:

[0253]

[0254] In (70), the size of constraints (65)-(68) will increase with the increase of control points, but most of these constraints are in an inactive state. This is because the acceptable probability of violation of opportunity constraints is usually set to a small value, and only the constraints corresponding to the violation will be in an active state in the low-carbon economic dispatch problem.

[0255] By projecting the distribution of random variables onto the Bernstein multinomial space and performing equivalent transformations and enhancements on the constraints, an approximate problem that is easy to solve is generated, thereby significantly improving the accuracy and applicability of the power system dispatching method, enabling it to handle uncertainties more efficiently and adapt to complex scenarios.

[0256] In some embodiments, the approximate problem is solved by combining Benders decomposition technology with the goal of minimizing the expected total cost of the power system until the calculated iterative difference satisfies the preset conditions, and the target output value of thermal power units and the amount of wind and solar curtailment of new energy units are output. Specifically, since non-active constraints do not play a role in solving the optimization problem, only active constraints can be considered to reduce the size of the problem (70). This operation can be achieved by Benders decomposition technology, that is, Benders cuts of active constraints (i.e., unsatisfied constraints) are dynamically added during the solution process of (70) until all constraints are satisfied.

[0257] After improvements using distributed projection and Benders decomposition techniques, please refer to [the original text]. Figure 4The complete iterative steps of the scheduling method in this application are as follows:

[0258] ① Initialization: Input convergence threshold τ, maximum number of iterations k max , polynomial order n, enhanced order m;

[0259] ② Set the iteration number k = 1, and the initial value δ of the non-negative relaxation parameter vector. (0) =0, iteration difference E gap >τ, where τ is the iteration step size of the relaxation parameter;

[0260] ③while k≤k max &E gap >τ

[0261] ④ Using the nonnegative relaxation parameter vector δ (k) Construct opportunity constraints (36);

[0262] ⑤ Construct an opportunity-constrained low-carbon economic dispatch model (37);

[0263] ⑥ Construct Bernstein polynomial basis functions;

[0264] ⑦ Construct an approximate chance-constrained low-carbon economic dispatch model using distributed projection techniques (70);

[0265] ⑧ Solve problem (70) based on Benders decomposition;

[0266] ⑨ Update the nonnegative relaxation parameter vector δ:

[0267] ⑩ First, construct the active opportunity constraint index set based on (45) and (46). and overly relaxed opportunity constraint index set

[0268] Secondly, the nonnegative relaxation parameter vector δ is calculated according to (44). (k+1) ;

[0269] The iterative difference E is calculated according to the following formula. gap ;

[0270] E gap =||δ (k+1) -δ k( ||

[0271] k = k + 1;

[0272] End;

[0273] Output decision.

[0274] Step S103: Dispatch the power system based on the target output value of the thermal power unit and the amount of wind and solar curtailment of the new energy unit.

[0275] In some embodiments, after calculating the target output value of thermal power units and the amount of wind and solar curtailment of renewable energy units, a dispatching instruction is generated to instruct the thermal power units to adjust their output to achieve the target value. The dispatching instruction can be issued to the control center of the thermal power units through the automatic generation control (AGC) system or manual dispatching instructions to gradually adjust the output of the thermal power units. At the same time, a dispatching instruction is generated to instruct renewable energy units to make adjustments. For the amount of wind and solar curtailment of renewable energy units, the dispatching instruction needs to clearly indicate which renewable energy units need to reduce their output and the specific amount of reduction.

[0276] It should be noted that during the dispatching process, the real-time monitoring system of the power system (such as SCADA system) is needed to monitor the actual output of thermal power units in real time and compare it with the target output value output by the optimization model. If there is a deviation between the actual output and the target output, the dispatching center needs to adjust the dispatching instructions in a timely manner according to the deviation. For thermal power units, the deviation can be corrected by adjusting their generating capacity or adjusting the output of standby units. During the adjustment process, the overall operating status of the power system needs to be considered to ensure that the adjusted output still meets the requirements for the safe and stable operation of the power system.

[0277] This application's embodiments, by acquiring load information of each node in the power system and predicted output values ​​of new energy units, can understand the operating status of the power system in the coming day, providing a basic data basis for scheduling the following day. Through sequential convex approximation, non-convex opportunity constraints are transformed into convex constraints, making the model easier to solve and improving the operability of the scheduling method. It can also adapt to different types of uncertainty (such as the non-Gaussian distribution of new energy output), enhancing the applicability of the scheduling method. Distributed projection technology can accurately describe the distribution of random variables, avoiding the inefficiency of large-scale sampling in traditional methods and significantly improving computational efficiency. By rationally arranging the target output values ​​of the thermal power units and the amount of wind and solar curtailment of the new energy units, wind and solar curtailment is reduced, improving the utilization rate of new energy and optimizing the operating efficiency of thermal power units, achieving rational resource allocation. Compared with existing technologies, this application, based on the actual needs of "electricity-carbon" coordinated scheduling in the power system, utilizes sequential convex approximation technology to handle non-convex opportunity constraints and proposes distributed projection technology to improve computational efficiency, solving the problem of traditional methods being limited by random distribution forms, thereby improving the accuracy and applicability of power system scheduling methods.

[0278] like Figure 5 As shown, based on the above method embodiments, corresponding apparatus embodiments are provided;

[0279] An embodiment of the present invention provides a power system dispatching system based on sequential convex approximation technology, comprising: an acquisition module 100, a calculation module 200, and a dispatching module 300;

[0280] The acquisition module is used to acquire load information of each node in the power system and the predicted output value of new energy units;

[0281] The calculation module is used to input the load information and the predicted output value of the new energy units into a preset scheduling model, process the non-convex opportunity constraints in the scheduling model using sequential convex approximation technology to obtain an updated convex scheduling model, project the distribution of the random variables of the convex scheduling model onto a multinomial space using distribution projection technology to obtain an approximation problem, and solve the approximation problem with the goal of minimizing the expected total cost of the power system using Benders decomposition technology until the calculated iterative difference satisfies the preset conditions, and output the target output value of thermal power units and the amount of wind and solar curtailment of new energy units. The scheduling model is obtained by converting the low-carbon economic scheduling model with uncertainty into an opportunity constraint form.

[0282] The scheduling module is used to schedule the power system based on the target output value of the thermal power unit and the amount of wind and solar curtailment of the new energy unit.

[0283] In some embodiments, the calculation module 200 includes a replacement unit, a calculation unit, and an update unit;

[0284] The replacement unit is used to re-describe the non-convex opportunity constraints in the scheduling model into an analytical form using a unit step function, and then replace the unit step function in the analytical form with a convex piecewise linear function to obtain an initial approximate convex constraint.

[0285] The computational unit is used to reduce the approximation deviation by minimizing the convex piecewise linear function, and combined with the initial approximate convex constraint, relax the feasible domain of the updated convex piecewise linear function to the real domain to obtain the relaxation constraint, and simplify the relaxation constraint by introducing auxiliary variables to obtain the approximate convex constraint.

[0286] The updating unit is used to add a non-negative relaxation parameter vector to the convex constraint to obtain a convex opportunity constraint, and to update the relaxation parameter vector using a fixed-point iteration technique until the convex opportunity constraint satisfies a preset convergence condition, thereby determining the updated convex scheduling model.

[0287] In some embodiments, the computing module 200 further includes a definition unit, an update unit, a projection unit, and an integration unit;

[0288] The defining unit is used to define the basis functions and inner product operations of the Bernstein polynomial space, wherein the basis functions are constructed based on tensor products, and the inner product operations depend on the cumulative distribution function;

[0289] The updating unit is used to project the distribution of random variables of the convex scheduling model onto the multinomial space through the inner product operation, and to re-describe the random distribution projected onto the multinomial space based on the basis functions to obtain the updated convex scheduling model.

[0290] The projection unit is used to project the equality constraints in the updated convex scheduling model to obtain equivalent equality constraints in the Bernstein polynomial space, and to reconstruct the inequality constraints in the updated convex scheduling model. By strengthening the control points, the deviation introduced by the reconstruction process is reduced to obtain approximate inequality constraints.

[0291] The integration unit is used to integrate the equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space to generate an approximate problem corresponding to the convex scheduling model.

[0292] It is understood that the above-described device embodiments correspond to the method embodiments of the present invention, and can implement the power system scheduling method based on sequential convex approximation technology provided by any of the above-described method embodiments of the present invention.

[0293] It should be noted that the device embodiments described above are merely illustrative, and some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can specifically be implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0294] Based on the above embodiments of the power system scheduling method based on sequential convex approximation technology, another embodiment of the present invention provides a terminal device, which includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the power system scheduling method based on sequential convex approximation technology of any embodiment of the present invention.

[0295] For example, in this embodiment, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the terminal device.

[0296] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0297] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device via various interfaces and lines.

[0298] Based on the above-described method embodiments, another embodiment of the present invention provides a computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to execute the power system scheduling method based on sequential convex approximation technology described in any of the above-described method embodiments of the present invention.

[0299] The modules / units integrated in the device / terminal equipment, if implemented as software functional units and sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0300] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A power system scheduling method based on sequential convex approximation technique, characterized in that, include: Obtain load information of each node in the power system and the predicted output of new energy generating units; The load information and the predicted output of the new energy units are input into a preset scheduling model. The non-convex opportunity constraints in the scheduling model are processed using the sequential convex approximation technique to obtain an updated convex scheduling model. The distribution projection technique is used to project the distribution of the random variables of the convex scheduling model onto the multinomial space to obtain an approximation problem. The approximation problem is then solved using the Benders decomposition technique with the goal of minimizing the expected total cost of the power system until the calculated iterative difference satisfies the preset conditions. The target output of the thermal power units and the amount of wind and solar curtailment of the new energy units are then output. The scheduling model is obtained by transforming the low-carbon economic scheduling model with uncertainty into an opportunity constraint form. The power system is dispatched based on the target output of the thermal power units and the amount of wind and solar power curtailment of the new energy units.

2. The power system scheduling method based on sequential convex approximation technology according to claim 1, characterized in that, The construction process of the low-carbon economic dispatch model containing uncertainty is as follows: Obtain load information, predicted output values ​​of new energy generating units, upper and lower limits of line transmission power, upper and lower limits of voltage amplitude, upper and lower limits of active power of thermal power units, and upper and lower limits of reactive power of thermal power units at each node in the power system. Based on the load information, the predicted output of the new energy units, the upper and lower limits of the transmission power of the lines, the upper and lower limits of the voltage amplitude, the upper and lower limits of the active power of the thermal power units, and the upper and lower limits of the reactive power of the thermal power units, a low-carbon economic dispatch model is established with the objective function of minimizing the expected value of the total cost of the power system. The total cost includes the power generation cost of thermal power units, the cost of wind and solar curtailment, and the cost of carbon emission trading. The constraints of the low-carbon economic dispatch model include AC power flow constraints, power generation control constraints, generator output limit constraints, transmission power constraints, and voltage amplitude constraints.

3. The power system scheduling method based on sequential convex approximation technology according to claim 2, characterized in that, The expression for the scheduling model is as follows: The objective function is: The current flow constraint is: The power generation control constraints are: The output limit constraint is: The transmission power constraint is: The voltage amplitude constraint is as follows: In the formula, C represents the total cost of the power system; ω represents the actual system scenario; P g,i (ω) represents the active power output information of thermal power unit i in scenario ω; P i loss (ω) and P i real (ω) represent the wind and solar curtailment and power output information of renewable energy unit i in scenario ω; C G C CUR and These are the power generation cost of the thermal power unit, the cost of wind and solar curtailment, and the cost of carbon emission trading, respectively; a g,i b g,i and c g,i Δt represents the power generation cost coefficient of thermal power unit i; Δt represents the length of the dispatch period. η i Cost per unit of wind and solar curtailment; For carbon trading prices; E p With E d These represent carbon quotas and carbon emissions, respectively; h is the carbon emission allocation per unit of electricity; ρ is the carbon emission factor for coal; μ i This represents the unit coal consumption of thermal power unit i. x is the upper limit of the active power of thermal power unit i; i y i With z i e is the unit coal consumption coefficient; i (ω) and f i (ω) represent the real and imaginary parts of the voltage phasor at node i under scenario ω, respectively; G ij With B ij These are the real and imaginary parts of the element at position (i,j) in the node admittance matrix, respectively. A set of nodes; For the set of routes; Ω represents the set of actual scene ω; and Let P represent the sets of nodes for thermal power units and new energy power generation units, respectively; i Load (ω) and These represent the active and reactive loads of node i in scenario ω, respectively; Q g,i (ω) represents the reactive power output of thermal power unit i in scenario ω; ρ i dp represents the automatic generation control coefficient of generator i; D(ω) represents the change in total net load under scenario ω; i (ω) and dq i (ω) represents the change in active and reactive power losses under scenario ω; ω0 is the baseline scenario, under which D(ω0) and dp i (ω0) and dq i (ω0) are all equal to 0; This represents the upper limit of the transmission power of line ij; V i and These are the lower and upper limits of the voltage amplitude at node i; P g,i and These are the lower and upper limits of the active power of thermal power unit i; Q g,i and These are the lower and upper limits of the reactive power of thermal power unit i; ε represents the probability; ε is the acceptable violation probability.

4. The power system dispatching method based on sequential convex approximation technology according to claim 1, characterized in that, The sequential convex approximation technique is used to process the non-convex opportunity constraints in the scheduling model to obtain an updated convex scheduling model, specifically as follows: The non-convex opportunity constraints in the scheduling model are redescribed in analytical form using a unit step function. Then, the unit step function in the analytical form is replaced with a convex piecewise linear function to obtain the first approximate convex constraint. By minimizing the convex piecewise linear function in the first approximate convex constraint to reduce the approximation deviation, a second approximate convex constraint is obtained. The feasible domain of the convex piecewise linear function parameter in the second approximate convex constraint is relaxed to the real number domain to obtain a relaxed constraint. The relaxed constraint is simplified by introducing auxiliary variables to obtain a simplified relaxed constraint. A non-negative relaxation parameter vector is added to the simplified relaxation constraint to obtain a third approximate convex constraint. The relaxation parameter vector of the third approximate convex constraint is updated using the fixed-point iteration technique until the relaxation parameter vector satisfies the preset convergence condition, and the updated convex scheduling model is determined.

5. The power system scheduling method based on sequential convex approximation technology according to claim 4, characterized in that, The sequential convex approximation technique is used to process the non-convex opportunity constraints in the scheduling model to obtain the relevant formulas of the updated convex scheduling model, specifically: The original form of nonconvex opportunity constraints: In the formula, Indicates probability; l i (ω) is the i-th element of the inequality constraint auxiliary variable vector l(ω); ε is the acceptable probability of violation; This is the index set for soft inequality constraints; Analytical form of nonconvex chance constraints: In the formula, It is a unit step function; Replacement of the unit step function: First approximate convex constraint: In the formula, α is a parameter; It is a convex piecewise linear function; Minimizing the convex piecewise linear function yields the second approximate convex constraint: The feasible region of the relaxation parameters yields the relaxation constraints: Simplify and relax constraints: In the formula, u i (ω) represents the i-th auxiliary variable; Adding nonnegative relaxation parameters yields the third approximate convex constraint: Update the relaxation parameters: In the formula, For the k-th iteration, δ i The value of δ (k) for ; and α obtained in the k-th iteration i with u i The optimal value of (ω); and This is the index set of active opportunity constraints and overly relaxed opportunity constraints at the k-th iteration; Updated convex scheduling model: In the formula, x is the baseline decision vector; ω is the actual scenario of the system; α and u(ω) are the base decision vectors. i and u i The vector of (ω); δ * The optimal non-negative relaxation parameter The vector; l(ω) is the auxiliary variable vector of the inequality constraints; This is the feasible region.

6. The power system scheduling method based on sequential convex approximation technology according to claim 1, characterized in that, The method of projecting the distribution of the random variables of the convex scheduling model onto the multinomial space using the distribution projection technique yields an approximate problem, specifically: Define basis functions and inner product operations for the Bernstein polynomial space, wherein the basis functions are constructed based on tensor products and the inner product operations depend on the cumulative distribution function; The inner product operation projects the distribution of random variables in the convex scheduling model onto the multinomial space, and the random distribution projected onto the multinomial space is re-described based on the basis functions to obtain the updated convex scheduling model. The equality constraints in the updated convex scheduling model are projected to obtain equivalent equality constraints in the Bernstein polynomial space. The inequality constraints in the updated convex scheduling model are reconstructed, and the deviation introduced by the reconstruction process is reduced by strengthening the control points to obtain approximate inequality constraints. The equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space are integrated to generate the approximate problem corresponding to the convex scheduling model.

7. The power system scheduling method based on sequential convex approximation technology according to claim 6, characterized in that, The distribution projection technique is used to project the random variables of the convex scheduling model onto the multinomial space to obtain the relevant formulas for the approximate problem, specifically: The basis functions of the Bernstein polynomial space are: In the formula, Φ j (ω) is the j-th multivariable Bernstein polynomial basis function; basis function Φ j The index vector of (ω); Let j be the set; For tensor product operators; N ω B is the base of ω; j,n (ω w ) is the basis function of the j-th n-th univariate Bernstein polynomial; ω w Let w be the w-th element of ω; The inner product operation in Bernstein polynomial space is: In the formula, a(ω) represents an arbitrary random distribution; F(ω) represents the cumulative distribution function of ω; The re-description of the random distribution is as follows: In the formula, y i (ω), l i (ω) and u i (ω) represents the i-th element of y(ω), l(ω), and u(ω), respectively; y ij l ij with u ij y i (ω), l i (ω) and u i The j-th coefficient of (ω); N y N l With N u Let be the cardinalities of y(ω), l(ω), and u(ω), respectively; The equivalent equality constraints obtained by projection are: The approximate inequality constraints obtained by projection are: In the formula, Let J be the set; K jk For l ik and l ij The composite relationship coefficient between them is the product of the relationship coefficients of all dimensions of ω; For index The set of k, where k w =0,1,...,m, w=1,2,...,N ω J k For use in calculation The kth coefficient.

8. A power system dispatching system based on sequential convex approximation technique, characterized in that, include: The module consists of an acquisition module, a calculation module, and a scheduling module. The acquisition module is used to acquire load information of each node in the power system and the predicted output value of new energy units; The calculation module is used to input the load information and the predicted output value of the new energy units into a preset scheduling model, process the non-convex opportunity constraints in the scheduling model using sequential convex approximation technology to obtain an updated convex scheduling model, project the distribution of the random variables of the convex scheduling model onto a multinomial space using distribution projection technology to obtain an approximation problem, and solve the approximation problem with the goal of minimizing the expected total cost of the power system using Benders decomposition technology until the calculated iterative difference satisfies the preset conditions, and output the target output value of thermal power units and the amount of wind and solar curtailment of new energy units. The scheduling model is obtained by converting the low-carbon economic scheduling model with uncertainty into an opportunity constraint form. The scheduling module is used to schedule the power system based on the target output value of the thermal power unit and the amount of wind and solar curtailment of the new energy unit.

9. The power system dispatching system based on sequential convex approximation technology according to claim 8, characterized in that, The calculation module includes a replacement unit, a calculation unit, and an update unit; The replacement unit is used to re-describe the non-convex opportunity constraints in the scheduling model into an analytical form using a unit step function, and then replace the unit step function in the analytical form with a convex piecewise linear function to obtain the first approximate convex constraint. The calculation unit is used to reduce the approximation deviation by minimizing the convex piecewise linear function in the first approximate convex constraint to obtain the second approximate convex constraint, relax the feasible domain of the convex piecewise linear function parameter in the second approximate convex constraint to the real number domain to obtain the relaxation constraint, and simplify the relaxation constraint by introducing auxiliary variables to obtain the simplified relaxation constraint. The updating unit is used to add a non-negative relaxation parameter vector to the simplified relaxation constraint to obtain a third approximate convex constraint, and to update the relaxation parameter vector of the third approximate convex constraint using a fixed-point iteration technique until the relaxation parameter vector satisfies a preset convergence condition, thereby determining the updated convex scheduling model.

10. The power system dispatching system based on sequential convex approximation technology according to claim 8, characterized in that, The calculation module also includes a definition unit, an update unit, a projection unit, and an integration unit; The defining unit is used to define the basis functions and inner product operations of the Bernstein polynomial space, wherein the basis functions are constructed based on tensor products, and the inner product operations depend on the cumulative distribution function; The updating unit is used to project the distribution of random variables of the convex scheduling model onto the multinomial space through the inner product operation, and to re-describe the random distribution projected onto the multinomial space based on the basis functions to obtain the updated convex scheduling model. The projection unit is used to project the equality constraints in the updated convex scheduling model to obtain equivalent equality constraints in the Bernstein polynomial space, and to reconstruct the inequality constraints in the updated convex scheduling model. By strengthening the control points, the deviation introduced by the reconstruction process is reduced to obtain approximate inequality constraints. The integration unit is used to integrate the equivalent equality constraints and the approximate inequality constraints in the Bernstein polynomial space to generate an approximate problem corresponding to the convex scheduling model.

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