Phase-locked loop stability constraint optimal power flow sequential linearization method, device and medium

Abstract

The application belongs to the field of power system optimal operation, and specifically discloses a sequential linearization method for optimal power flow with phase-locked loop stability constraints, equipment and medium. First, a scaled factor is constructed for the phase-locked loop synchronization stability constraint of the grid-connected converter, and an initial reference point is obtained by solving a traditional power flow model; then, the synchronization stability constraint is linearized to the first order, embedded into the power flow model and solved, and finally, the linearization reference point is updated according to the iteration result until the convergence condition is met, and the optimization result is output. The application realizes the conversion of the nonlinear phase-locked loop synchronization stability constraint with a scaling factor into an iterative and updateable linear constraint, which reduces the difficulty of solving the model while ensuring the accuracy of solving the original nonlinear model. Compared with the traditional method, the application can reduce the sensitivity of the model to the initial point and nonlinear constraints, and improve the solvability and engineering applicability of the model in large-scale power systems or multi-converter grid-connected scenarios.

Description

Technical Field

[0001] This application belongs to the field of power system optimization operation, specifically involving an optimal power flow sequential linearization method, device, and medium with phase-locked loop stability constraints. Background Technology

[0002] With the large-scale integration of renewable energy sources such as photovoltaics, wind power, and energy storage into the power system via grid-connected converters, the dynamic coupling between these converters and the grid is increasingly strengthened. The synchronization stability problem dominated by phase-locked loops (PLLs) has gradually become a key consideration in the optimal operation of the power system. To balance system operating economy with PLL synchronization stability, existing research incorporates the PLL synchronization stability boundary into the optimal power flow model, forming an optimization operation method that considers PLL synchronization stability constraints at the system level.

[0003] Currently, optimal power flow methods for phase-locked loop (PLL) synchronization stability constraints typically rely on equivalent models of PLLs connected to grid-connected converters and the system's equivalent generalized damping matrix. Distributed criteria such as Gell's disk theorem are used to characterize the PLL synchronization stability constraints, which are then embedded into the optimal power flow model for solution. Furthermore, to alleviate the conservatism of Gell's disk theorem, some studies have introduced a diagonal scaling mechanism into these methods, constructing PLL synchronization stability constraints with scaling factors. This improves the feasible output region of the grid-connected converter while maintaining PLL synchronization stability. However, the PLL synchronization stability constraints characterized by these methods often involve multivariate product coupling and higher-order terms, resulting in highly nonlinear models. Directly solving these models requires nonlinear solvers such as IPOPT, which are extremely sensitive to the initial points of the variables and the nonlinearity of the constraints. While good results can be obtained in small-scale examples, convergence failure or getting trapped in local optima is a significant challenge in large-scale power systems or multi-converter grid-connected scenarios. In contrast, linear solvers like GUROBI provide globally unique solutions and are widely used in engineering practice, but they require the model constraints to be linear expressions. Therefore, it is necessary to develop a sequential linearization method for optimal power flow models with phase-locked loop synchronization stability constraints containing scaling factors to adapt to linear solvers. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this application is to provide a sequential linearization method, device, and medium for optimal power flow with phase-locked loop stability constraints. This aims to solve the problem that the current lack of a sequential linearization method for optimal power flow models with phase-locked loop synchronous stability constraints with scaling factors leads to the inability to adapt to linear solvers and the high difficulty in solving the problem.

[0005] The first aspect of this application relates to a sequential linearization method for optimal power flow with phase-locked loop (PLL) stability constraints, comprising: Step S10, constructing PLL synchronization stability constraints for grid-connected converters with diagonal scaling factors based on power system operating data and grid-connected converter control parameters; Step S20, solving the optimal power flow model without PLL synchronization stability constraints to obtain system node voltages and grid-connected converter outputs, and using the system node voltages, grid-connected converter outputs, and preset scaling factors as the initial reference point for sequential linearization; Step S30, performing first-order linearization on the PLL synchronization stability constraints based on the current reference point to obtain linearized synchronization stability constraints; Step S40, embedding the linearized synchronization stability constraints into the optimal power flow model and solving it to obtain system node voltages, grid-connected converter outputs, and scaling factors to update the current reference point, and returning to step S30 if the current reference point does not meet the iteration conditions, until the current reference point meets the iteration conditions and the current reference point is output as the optimization result.

[0006] In one embodiment, step S10 includes: extracting the operating data of the power system and the control parameters of the grid-connected converter; the operating data includes node voltage amplitude, node active load, node self-conductance, and inter-node mutual conductance; the control parameters include the proportional coefficient and integral coefficient of the phase-locked loop controller; based on the operating data and control parameters, obtaining the converter dynamic response term and the network electrical coupling term; and performing combined calculations based on the converter dynamic response term, the network electrical coupling term, and the diagonal scaling factor to construct a synchronization stability margin function to establish synchronization stability constraints; the synchronization stability margin function characterizes the synchronization stability boundary between the grid-connected converter and the power grid by introducing the diagonal scaling factor.

[0007] In one embodiment, the synchronization stability constraint is: the synchronization stability margin function is greater than 0.

[0008] In one embodiment, step S20 includes: solving the optimal power flow model without phase-locked loop synchronous stability constraints to obtain the sum of squared voltage magnitudes of each node and the active power output of the grid converter; the initial optimal power flow model takes minimizing system network losses as the optimization objective and includes node power balance constraints, branch power flow constraints, voltage magnitude constraints, and grid converter output constraints; and combining the initial values ​​of the squared voltage magnitudes, the initial values ​​of the active power output of the grid converter, and a preset scaling factor into an initial reference vector, which serves as the initial reference point.

[0009] In one embodiment, step S30 includes: obtaining the partial derivatives of the synchronization stability margin function with respect to each decision variable at the current reference point, the decision variables including the square of the node voltage magnitude, the active power output of the grid converter, and the diagonal scaling factor; based on the partial derivatives, linearly approximating the synchronization stability margin function through a first-order Taylor expansion to obtain a linearized synchronization stability constraint, the linearized synchronization stability constraint being a linear combination of each decision variable.

[0010] In one embodiment, step S40, which involves embedding the linearized synchronous stability constraint into the optimal power flow model and solving it, includes: adding the linearized synchronous stability constraint to the optimal power flow model to form an optimal power flow model containing the linearized stability constraint; and using a linear solver to solve the optimal power flow model containing the linearized stability constraint to obtain the square of the node voltage magnitude, the active power output of the grid converter, and the diagonal scaling factor under the current iteration.

[0011] In one embodiment, step S40, when the current reference point does not meet the iteration conditions, returns to step S30 until the current reference point meets the iteration conditions and the current reference point is output as the optimization result. This includes: calculating the change in the reference point between two adjacent iterations; if the change is greater than a preset threshold, it is determined that the iteration conditions are not met, and the square of the node voltage amplitude, the active power output of the grid converter, and the diagonal scaling factor obtained in the current iteration are used as new reference points, and the process returns to step S30; if the change is less than or equal to the preset threshold, it is determined that the iteration conditions are met, and the reference point of the current iteration is output as the optimization result.

[0012] In one embodiment, the preset scaling factor is set to 1 or is obtained based on historical data.

[0013] In a second aspect, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0014] Thirdly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0015] Fourthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0016] It is understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0017] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: This application constructs a phase-locked loop synchronous stability constraint with a diagonal scaling factor, uses the solution results of the traditional optimal power flow model as the initial reference point for sequential linearization, and then performs first-order linearization on the nonlinear constraint based on the current reference point. The linearized constraint is then embedded into the optimal power flow model for iterative solution until convergence.

[0018] By adopting the above-mentioned sequential linearization strategy, the originally highly nonlinear synchronous stability constraints with scaling factors are transformed into a series of iteratively updated linear constraints. This allows complex models that could only be solved by nonlinear solvers to be adapted to linear solvers, significantly reducing the difficulty of solving the model while ensuring the accuracy of the original nonlinear model solution.

[0019] Meanwhile, since linearization is based on a local approximation of the current benchmark point and gradually approximates the original nonlinear solution through iteration, it effectively reduces the sensitivity to the selection of the initial point and the form of nonlinear constraints, and avoids the problems of convergence failure or getting trapped in local optima that are easy to occur when directly solving nonlinear models.

[0020] Compared with existing technologies, this application significantly improves the solvability and engineering applicability of the model in large-scale power systems or multi-converter grid-connected scenarios while ensuring solution accuracy. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the optimal power flow sequential linearization method with phase-locked loop stability constraints provided in the embodiments of this application. Figure 2 This is a topology diagram of a 39-node system provided in an embodiment of this application; Figure 3 This is a schematic diagram comparing the active power output of the grid converter obtained by solving the optimal power flow model with synchronous stability constraints of the phase-locked loop with scaling factor and the linearized optimal power flow model with synchronous stability constraints of the phase-locked loop with scaling factor provided in the embodiments of this application. Figure 4 This is a schematic diagram comparing the reactive power output of the grid converter obtained by solving the optimal power flow model with synchronous stability constraints of the phase-locked loop containing scaling factors and the linearized optimal power flow model with synchronous stability constraints of the phase-locked loop containing scaling factors, as provided in the embodiments of this application. Figure 5 This is a schematic diagram comparing the node voltage magnitudes obtained by solving the optimal power flow model with scaling factor and synchronous stability constraint of phase-locked loop provided in the embodiments of this application with the linearized optimal power flow model with scaling factor and synchronous stability constraint of phase-locked loop. Figure 6 This is a schematic diagram of the active power output error of the grid converter compared with the optimal power flow model with synchronous stability constraints of the phase-locked loop and scaling factor provided in the embodiments of this application. Figure 7 This is a schematic diagram of the reactive power output error of the grid converter compared to the optimal power flow model with synchronous stability constraints of the phase-locked loop and scaling factor provided in the embodiments of this application. Figure 8 This is a schematic diagram of the node voltage error between the linearized phase-locked loop synchronous stability constrained optimal power flow model with scaling factor and the phase-locked loop synchronous stability constrained optimal power flow model with scaling factor provided in the embodiments of this application. Figure 9 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0023] In this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A existing alone, A and B existing simultaneously, and B existing alone. In this application, the symbol " / " indicates that the related objects are in an "or" relationship, for example, A / B means A or B.

[0024] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0025] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0026] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0027] Based on the background technology, this application proposes an embodiment of an optimal power flow sequential linearization method with phase-locked loop stability constraints. Please refer to... Figure 1 , Figure 1This is a flowchart illustrating the optimal power flow sequential linearization method with phase-locked loop stability constraints provided in this application embodiment.

[0028] In this embodiment, the method includes: Step S10: Construct synchronization stability constraints for the grid-connected converter phase-locked loop with a diagonal scaling factor based on the power system's operating data and the grid-connected converter's control parameters.

[0029] It should be noted that in the field of power system optimization operation, the phase-locked loop (PLL) synchronization stability constraints of grid-connected converters typically originate from the analysis of small-signal models. Specifically, by establishing the closed-loop transfer function of the PLL, the dynamic equation of the phase difference between the converter output current and the grid voltage can be derived, thereby obtaining the critical condition for the system to maintain synchronization. This condition often manifests as a nonlinear inequality concerning node voltage amplitude, converter active power output, and network admittance parameters. However, constraints directly constructed based on this critical condition are often overly conservative, limiting the converter's output capacity.

[0030] Therefore, the phase-locked loop (PLL) synchronization stability constraint refers to the stability margin condition derived from the dynamic characteristics of the PLL controller of the grid-connected converter, used to determine whether the converter and the grid can maintain synchronous operation. The diagonal scaling factor introduced in this constraint is an adjustable weighting coefficient used to weight certain terms in the stability criterion. This mitigates the conservatism brought about by distributed criteria such as Gell's disk theorem, thereby appropriately relaxing the constraint boundary and expanding the feasible domain of converter output while ensuring stability.

[0031] When constructing this constraint, two types of data need to be collected: first, real-time operating data of the power system, such as the voltage amplitude, active load, node self-conductance, and line mutual conductance of each node obtained from the SCADA system; second, the control parameters of the grid-connected converter, namely the proportional coefficient and integral coefficient of the phase-locked loop controller. These parameters are combined in a specific algebraic way (for example, combining the phase-locked loop parameters into several intermediate coefficients, and then multiplying and summing them with node parameters such as voltage and admittance). Finally, a synchronization stability margin function is formed.

[0032] It should be noted that by combining these parameters, a form like this can be constructed. = f ( ， ， The synchronous stability margin function is defined, and it is set to be greater than zero as a stability constraint. For synchronization stability margin function; To provide power output for grid-connected converters; This refers to the node voltage amplitude. Indicates angular frequency; This represents the scaling factor. Finally, by using a function greater than zero as a constraint, the construction of the phase-locked loop synchronization stability constraint with the scaling factor is completed.

[0033] Understandably, this method will use a diagonal scaling factor. The scaling factor is explicitly incorporated into the optimization model and treated as an optimizable variable alongside node voltage and converter output. This means that the scaling factor no longer depends on offline experience or fixed values ​​(such as the identity matrix), but is dynamically adjusted during the iteration process, adaptively relaxing the constraint boundaries. This design allows the relaxation of stability constraints to vary flexibly according to the actual operating conditions of the system (such as voltage level and load conditions), thereby maximizing the feasible region of converter output while ensuring synchronous stability. This construction process provides the necessary mathematical model foundation for subsequent optimization solutions.

[0034] Step S20: Solve the optimal power flow model without phase-locked loop synchronous stability constraints to obtain the system node voltage and grid-connected converter output, and use the system node voltage, grid-connected converter output and preset scaling factor values ​​as the initial reference point for sequential linearization.

[0035] It should be noted that step S20 first solves an optimal power flow model without phase-locked loop (PLL) synchronization stability constraints. An optimal power flow model is a mathematical model that optimizes control variables such as generator active and reactive power output, transformer taps, and reactive power compensation devices within a power system, guided by objective functions such as minimizing generation cost, minimizing network loss, or other objectives, while satisfying conventional constraints such as power balance, node voltage limits, and branch transmission capacity.

[0036] The phase-locked loop (PLL) synchronization stability constraint is intentionally excluded here to obtain an initial feasible solution without considering PLL synchronization stability. This initial solution includes the voltage magnitude and phase angle of each node in the system, as well as the active power output of the grid converter. These quantities, along with the preset scaling factor, constitute the reference point required for subsequent linearization.

[0037] It should be noted that the preset scaling factor refers to a diagonal matrix set in the initial stage, whose diagonal elements serve as weighting coefficients for subsequently weighting certain terms in the phase-locked loop synchronization stability constraints. The initial value of this scaling factor is usually the diagonal element corresponding to the identity matrix, that is, each diagonal element has a value of 1, representing that no additional scaling effect is applied initially; it can also be pre-calibrated based on historical operating data or offline simulation results to reflect the expected adjustment requirements for stability margin under specific operating conditions.

[0038] It should be noted that the reference point is defined as the reference operating point of the Taylor expansion during the sequential linearization process. The effect of this step is that it quickly obtains a reasonable operating state without introducing nonlinear stability constraints, avoiding the convergence difficulties that may be caused by directly solving from a fully constrained nonlinear model; at the same time, this reference point provides accurate local derivative information for subsequent linearization, thereby improving the stability and efficiency of the entire iterative process.

[0039] Step S30: Based on the current reference point, perform first-order linearization on the phase-locked loop synchronization stability constraint to obtain the linearized synchronization stability constraint.

[0040] It should be noted that the phase-locked loop (PLL) synchronization stability constraint is itself a nonlinear inequality (of the form of) concerning variables such as node voltage magnitude, converter active power output, scaling factor, and angular frequency. H >0). First-order linearization refers to using Taylor series expansion to transform nonlinear functions. H Expanding at the current reference point and retaining the first-order terms while ignoring higher-order terms, yields a linear inequality regarding the variable increment. This process is equivalent to approximating the shape of the original nonlinear surface near the reference point using a hyperplane. The device required to achieve this linearization can be a processor with numerical computation capabilities, coupled with automatic or symbolic differentiation tools to calculate partial derivatives. Alternative options include piecewise linearization (dividing the nonlinear region into multiple sub-intervals and linearizing them separately) or a second-order Taylor expansion (retaining quadratic terms to form quadratic constraints), the latter offering higher accuracy but increasing the difficulty of solving.

[0041] Understandably, the effect of this step is to transform nonlinear constraints that are originally difficult to directly embed into the framework of linear programming or quadratic programming into linear constraints, so that the overall optimal power flow problem remains in a convex optimization or easily solvable form, greatly reducing the computational complexity. At the same time, since linearization is based on a local approximation of the current benchmark point, as long as the benchmark point is continuously updated during the iteration process, the final approximation error can be controlled within an allowable range.

[0042] Step S40: Embed the linearized synchronous stability constraint into the optimal power flow model and solve it to obtain the system node voltage, grid converter output and scaling factor to update the current reference point. If the current reference point does not meet the iteration conditions, return to step S30 until the current reference point meets the iteration conditions and output the current reference point as the optimization result.

[0043] It should be noted that in step S40, the linearized synchronous stability constraints obtained in step S30 are embedded into the optimal power flow model, and the extended model is solved to obtain new values ​​for system node voltages, grid-connected converter outputs, and scaling factors, which are used to update the current reference point. Then, it is determined whether the current reference point meets the iteration conditions. Typical iteration conditions include the change in solution between two adjacent iterations being less than a preset threshold, the residual between the linearized constraint and the original constraint being sufficiently small, or reaching the maximum number of iterations. If these conditions are not met, the process returns to step S30, and linearization and solving are performed again on the new reference point, forming a loop; if the conditions are met, the current reference point is output as the final optimization result.

[0044] Understandably, by iteratively linearizing and solving, the true optimal solution under the original nonlinear constraints is gradually approximated. This retains the computational efficiency brought by linearization while overcoming the drawback of excessive error in a single linearization through iterative correction. Furthermore, the scaling factor is dynamically optimized during iteration, further expanding the safe output range of the converter. The final output benchmark point is the optimal operating scheme of the system that satisfies the phase-locked loop synchronization stability constraints, which can be directly used for dispatching decisions in actual power systems.

[0045] In this embodiment, the nonlinear phase-locked loop synchronization stability constraint with scaling factor can be transformed into an iteratively updated linear constraint, which reduces the difficulty of solving the model while ensuring the accuracy of the original nonlinear model solution. Compared with directly using a nonlinear solver to solve the original nonlinear model, this application can reduce the model's sensitivity to initial points and nonlinear constraints, and improve the model's solvability and engineering applicability in large-scale power systems or multi-converter grid-connected scenarios.

[0046] Based on the above embodiments, this application provides a specific implementation method.

[0047] In this embodiment, step S10 includes: extracting the operating data of the power system and the control parameters of the grid-connected converter. The operating data includes node voltage amplitude, node active load, node self-conductance, and inter-node mutual conductance. The control parameters include the proportional coefficient and integral coefficient of the phase-locked loop controller. Based on the operating data and control parameters, the converter dynamic response term and the network electrical coupling term are obtained. Based on the converter dynamic response term, the network electrical coupling term, and the diagonal scaling factor, a combined calculation is performed to construct a synchronization stability margin function to establish synchronization stability constraints. The synchronization stability margin function characterizes the synchronization stability boundary between the grid-connected converter and the power grid by introducing a diagonal scaling factor.

[0048] It should be noted that operational data can be collected in real time from the SCADA system of the power system dispatch center. For example, voltage amplitude can be obtained through phasor measurement units, and node load and admittance matrix elements can be obtained through state estimation. Node self-conductance refers to the conductance component of the injected current at a node that is in phase with the voltage, reflecting the active power loss of that node to ground; inter-node mutual conductance characterizes the active power transmission characteristics of the line between two nodes. The proportional coefficient and integral coefficient determine the dynamic response speed and steady-state accuracy of the phase-locked loop in tracking the grid voltage phase. The proportional coefficient affects the speed of response, while the integral coefficient eliminates steady-state phase errors. These control parameters are usually stored in the firmware configuration of the converter controller and can be read through the communication interface.

[0049] Understandably, incorporating the static topology parameters of the power system and the dynamic control parameters of the converter into the basic dataset for constraint construction provides the necessary input for the subsequent calculation of the stability margin function, ensuring that the constraints can simultaneously reflect the power grid structure and the converter control characteristics.

[0050] It should be noted that the converter dynamic response term is an algebraic expression determined by the phase-locked loop control parameters, reflecting the dynamic characteristics of the phase difference between the converter output current and the grid voltage. It typically includes a combination of proportional and integral coefficients. The network electrical coupling term, on the other hand, is an algebraic combination quantifying the strength of the electrical interaction between grid nodes through line impedance, based on parameters such as node voltage amplitude, self-conductance, mutual conductance, and active load.

[0051] It should be noted that this step, through specific combination operations of the above two items and the diagonal scaling factor, essentially constructs a decision function for quantifying the system's disturbance rejection capability. The diagonal scaling factor, acting as a weighting coefficient, applies to specific parts of the converter dynamic response term and the network electrical coupling term, making the relative importance of each item adjustable in subsequent combination operations. It considers whether the converter's own dynamic potential energy for maintaining synchronization can withstand electrical interference imposed by the power grid under the worst operating conditions.

[0052] Crucially, the diagonal scaling factor acts as a weighting coefficient, applying it to specific parts of the converter dynamic response term and the network electrical coupling term, making the relative importance of each term adjustable in subsequent combined calculations. By introducing the diagonal scaling factor into this combined calculation, this embodiment endows the traditional rigid stability criterion with flexible adjustment capabilities. This scaling factor functions as a dynamic weighting coefficient in the calculation, making the boundary represented by the stability margin function no longer a fixed physical limit, but a soft boundary that can be adaptively adjusted according to the real-time operating state of the system. This design allows the optimization algorithm to actively explore the optimal relaxation point of the constraints while ensuring that the system does not exceed the limits.

[0053] Finally, the obtained synchronization stability constraints of the grid-connected converter phase-locked loop, including the scaling factor, are as follows: (1).

[0054] in, (2).

[0055] It should be noted that equation (1) is a synchronization stability constraint for the grid-connected converter phase-locked loop containing a scaling factor. This is the synchronization stability margin function of the phase-locked loop. Represents angular frequency. Represents a node The grid-connected converter has active power output. For nodes Active load, For nodes voltage amplitude, Represents a node Self-conductivity, For system nodes and The electrical conductance of the lines between them For nodes The diagonal scaling factor, For nodes The diagonal scaling factor, and These are the integral coefficient and proportional coefficient of the phase-locked loop controller for the grid-connected converter, respectively.

[0056] In this embodiment, step S20 includes: solving the optimal power flow model without phase-locked loop synchronous stability constraints to obtain the sum of squared voltage magnitudes of each node and the active power output of the grid converter; the initial optimal power flow model takes minimizing system network losses as the optimization objective and includes node power balance constraints, branch power flow constraints, voltage magnitude constraints and grid converter output constraints; the initial values ​​of the squared voltage magnitudes, the initial values ​​of the active power output of the grid converter, and the preset scaling factor are combined into an initial reference vector, which is used as the initial reference point.

[0057] Specifically, the traditional optimal power flow model without phase-locked loop (PLL) synchronization stability constraints includes the following equations (3) to (11). Wherein, the system node set is... The set of branches is Synchronous generator sets are Combined with grid-type energy storage converter , with nodes The set of connected nodes is .

[0058] (3); It should be noted that equation (3) is the optimization objective function, representing the minimization of system network loss. and They are nodes and The active power flow injected at both ends of the line.

[0059] (4); It should be noted that equation (4) represents the node power balance constraint. , and System nodes The active power output of the synchronous generator unit, the active power output of the grid converter, and the system nodes Active load at the location, , and System nodes The reactive power output of the synchronous generator unit, the reactive power output of the grid converter, and the system nodes reactive load at the location, Represents a node Flow to Node The unproductive current.

[0060] (5); It should be noted that equation (5) represents the branch power flow constraint. The square of the node voltage magnitude is: , and Both are auxiliary functions, and their sizes are: , , and System nodes and The conductance and susceptance of the lines between them. and System nodes and voltage amplitude, For system nodes and The voltage phase difference between them.

[0061] (6); It should be noted that equation (6) is a second-order cone constraint between the voltage product variable and the phase difference variable, used to ensure the auxiliary variable and Square of node voltage magnitude and The physical relationship between them satisfies the AC power flow equation.

[0062] (7); (8); (9); (10); (11); It should be noted that equation (7) is a small-angle approximation constraint for the voltage phase difference, used to establish the relationship between the auxiliary variable and the node voltage phase. Equation (8) is the output constraint for the synchronous generator unit. and The first The upper and lower limits of the active power output of the synchronous generator unit. and The first The upper and lower limits of reactive power output of the synchronous generator unit. Equation (9) is the output constraint of the grid-connected converter. and The first The power output of the converter in the Taiwan and the grid has an upper and lower limit. and The first The upper and lower limits of reactive power output of the converters connected to the grid. Equation (10) is the system node voltage amplitude constraint. and System nodes The upper and lower limits of the square of the voltage amplitude. Equation (11) is the transmission capacity constraint of the line. For system nodes and The maximum apparent power capacity of the line between them.

[0063] After solving the above model, the initial reference point for sequential linearization is: (12); in, This represents the initial reference vector for sequential linearization. , and These represent the nodes obtained from solving the traditional optimal power flow model. The initial values ​​of the active power output and the square of the voltage amplitude of the grid-connected converter at the location, as well as the node... Preset diagonal scaling factor (set to 1). Represents a node The preset diagonal scaling factor (also set to 1).

[0064] In this embodiment, step S30 includes: obtaining the partial derivatives of the synchronization stability margin function with respect to each decision variable at the current reference point, the decision variables including the square of the node voltage magnitude, the active power output of the grid converter, and the diagonal scaling factor; based on the partial derivatives, linearly approximating the synchronization stability margin function through a first-order Taylor expansion to obtain a linearized synchronization stability constraint, the linearized synchronization stability constraint being a linear combination of each decision variable.

[0065] It is understandable that performing first-order linearization on the phase-locked loop (PLL) synchronization stability constraint is essentially a local linear approximation of the PLL synchronization stability constraint based on the current iteration reference point and using a first-order Taylor expansion.

[0066] Furthermore, the linearization constraint under the initial reference point in step S3 is as follows: (13).

[0067] The partial derivatives of each are: (14); (15); (16); (17).

[0068] It should be noted that, This is the linearized phase-locked loop synchronization stability margin function at the initial reference point.

[0069] In this embodiment, step S40, which involves embedding the linearized synchronous stability constraint into the optimal power flow model and solving it, includes: adding the linearized synchronous stability constraint into the optimal power flow model to form an optimal power flow model containing the linearized stability constraint; and using a linear solver to solve the optimal power flow model containing the linearized stability constraint to obtain the square of the node voltage magnitude, the active power output of the grid converter, and the diagonal scaling factor under the current iteration.

[0070] It should be noted that the optimal power flow model at this point is: (18); (19); (20); (twenty one); (twenty two); (twenty three); (twenty four); (25); (26); (27).

[0071] The system node set is as follows: The set of branches is Synchronous generator sets are Combined with grid-type energy storage converter , with nodes The set of connected nodes is .

[0072] It should be noted that equation (18) is the optimization objective function, representing the minimization of system network loss. and They are nodes and The active power flow injected at both ends of the line.

[0073] It should be noted that equation (19) represents the node power balance constraint. , and System nodes The active power output of the synchronous generator unit, the active power output of the grid converter, and the system nodes Active load at the location, , and System nodes The reactive power output of the synchronous generator unit, the reactive power output of the grid converter, and the system nodes reactive load at the location, Represents a node Flow to Node The unproductive current.

[0074] It should be noted that equation (20) represents the branch power flow constraint. The square of the node voltage magnitude is: , and Both are auxiliary functions, and their sizes are: , , and System nodes and The conductance and susceptance of the lines between them. and System nodes and voltage amplitude, For system nodes and The voltage phase difference between them.

[0075] It should be noted that equation (21) is a second-order cone constraint between the voltage product variable and the phase difference variable, used to ensure the auxiliary variable and Square of node voltage magnitude and The physical relationship between them satisfies the AC power flow equation.

[0076] It should be noted that equation (22) is a small-angle approximation constraint for the voltage phase difference, used to establish the relationship between the auxiliary variable and the node voltage phase. Equation (23) is the output constraint for the synchronous generator unit. and The first The upper and lower limits of the active power output of the synchronous generator unit. and The first The upper and lower limits of reactive power output of the synchronous generator unit. Equation (24) is the output constraint of the grid-connected converter. and The first The power output of the converter in the Taiwan and the grid has an upper and lower limit. and The first The upper and lower limits of reactive power output of the converters in the system and the grid. Equation (25) is the system node voltage amplitude constraint. and System nodes The upper and lower limits of the square of the voltage amplitude. Equation (26) is the transmission capacity constraint of the line. For system nodes and The maximum apparent power capacity of the line between them.

[0077] It should be noted that Equation (27) is a linearized constraint of the synchronous stability constraint of the grid converter phase-locked loop with scaling factor at the initial reference point.

[0078] In this embodiment, step S40, when the current reference point does not meet the iteration conditions, returns to step S30 until the current reference point meets the iteration conditions and outputs the current reference point as the optimization result. This includes: calculating the change in the reference point between two adjacent iterations; if the change is greater than a preset threshold, it is determined that the iteration conditions are not met, and the square of the node voltage amplitude, the active power output of the grid converter, and the diagonal scaling factor obtained in the current iteration are taken as new reference points, and the process returns to step S30; if the change is less than or equal to the preset threshold, it is determined that the iteration conditions are met, and the reference point of the current iteration is output as the optimization result.

[0079] Specifically, let the first The second iteration and the first The linearization reference points for the next iteration are respectively and The threshold is If satisfied If the optimization variables converge, then the optimization variables are considered to have converged.

[0080] If satisfied If so, return to step S30.

[0081] The sequential linearization model for optimal power flow with phase-locked loop synchronization stability constraints proposed in this application requires solving for the following variables: , , , , , and When using a commercial solver to solve a sequential linearization method for optimal power flow with phase-locked loop synchronous stability constraints, the solution obtained is the unique global optimum. Other methods can also be used to solve the problem.

[0082] Based on this, this application provides a specific example.

[0083] This embodiment was tested in an improved 39-node system. The topology of the 39-node system is as follows: Figure 2 As shown, the system contains 39 nodes. Nodes 31 and 39 are thermal power unit nodes, nodes 30 and 37 are photovoltaic integrated power stations with DC-side energy storage, nodes 36 and 38 are centralized energy storage power stations, and nodes 32, 33, 34 and 35 are wind-storage integrated power stations with DC-side energy storage. The aforementioned renewable energy sources such as photovoltaic, energy storage and wind power are all connected to the grid through grid-connected converters.

[0084] Two scenarios are set up to illustrate the validity of this application: the first scenario is to use IPOPT to solve the optimal power flow model with scaling factor and synchronous stability constraint of phase-locked loop; the second scenario is to use GUROBI to solve the linearized optimal power flow model with scaling factor and synchronous stability constraint of phase-locked loop.

[0085] Figure 3 The results comparing the active power output of the grid converter are presented in two different scenarios. Figure 4 The results comparing the reactive power output of the grid converter are given in two different scenarios. Figure 5 The comparison results of node voltage magnitudes under two different conditions are presented. Figures 3 to 5 It can be seen that the results obtained from the linearized optimal power flow model with scaling factor and synchronous stability constraint of the phase-locked loop are basically consistent with the results obtained from the original optimal power flow model with scaling factor and synchronous stability constraint of the phase-locked loop. Furthermore, Figure 6 The error in the active power output of the grid converter is given in two cases. Figure 7 The error of reactive power output of the grid converter is given in two cases. Figure 8 The errors in the node voltage magnitude are given in two cases. Figures 6 to 8 It can be seen that the solution results of the linearized PLL synchronous stability constraint optimal power flow model with scaling factor have a small error compared with the original PLL synchronous stability constraint optimal power flow model with scaling factor. Therefore, it can be concluded that the linearized synchronous stability constraint constructed in this application can approximate the original synchronous stability constraint with high accuracy, and its solution results are highly consistent with the solution results of the PLL synchronous stability optimal power flow model with scaling factor.

[0086] It should be noted that the technical advantage of this application lies in improving the solver adaptability and engineering deployability of the optimal power flow model with scaling factors and synchronous stability constraints of PLLs. The optimal power flow model with scaling factors and synchronous stability constraints of PLLs is a nonlinear optimization problem, typically requiring nonlinear solvers such as IPOPT. The solution process is extremely sensitive to the initial points of variables and the nonlinearity of constraints, facing convergence difficulties or getting trapped in local optima in large-scale systems or multi-converter grid-connected scenarios. In contrast, this application transforms the nonlinear stability constraints involving multivariable coupling and higher-order terms into iteratively updated linear constraints by performing first-order linearization on the synchronous stability constraints of PLLs with scaling factors, and then uses a linear solver such as GUROBI for the solution. Specifically, the solution obtained by a solver like GUROBI is the unique global optimum.

[0087] Therefore, the sequential linearization solution method for optimal power flow with phase-locked loop synchronous stability constraints proposed in this application can improve the solvability and applicability of the model in practical engineering applications while ensuring the solution accuracy.

[0088] Based on the methods in the above embodiments, please refer to Figure 9 This application provides an electronic device that may include a processor, a communications interface, a memory, and a communication bus. The processor, communications interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions stored in the memory to execute the methods described in the above embodiments.

[0089] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0090] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0091] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0092] It is understood that the processor in the embodiments of this application 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, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0093] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0094] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0095] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0096] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A sequential linearization method for optimal power flow with phase-locked loop stability constraints, characterized in that, include: Step S10: Construct synchronization stability constraints for the grid-connected converter phase-locked loop containing a diagonal scaling factor based on the power system's operating data and the grid-connected converter's control parameters; Step S20: Solve the optimal power flow model without the phase-locked loop synchronous stability constraint to obtain the system node voltage and grid-connected converter output, and use the system node voltage, the grid-connected converter output and the value of the preset scaling factor as the initial reference point for sequential linearization. Step S30: Based on the current reference point, perform first-order linearization on the phase-locked loop synchronization stability constraint to obtain the linearized synchronization stability constraint; Step S40: Embed the linearized synchronous stability constraint into the optimal power flow model and solve it to obtain the system node voltage, grid converter output and scaling factor to update the current reference point. If the current reference point does not meet the iteration conditions, return to step S30 until the current reference point meets the iteration conditions and output the current reference point as the optimization result.

2. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in claim 1, characterized in that, Step S10 includes: Extract the operating data of the power system and the control parameters of the grid-connected converter. The operating data includes node voltage amplitude, node active load, node self-conductance, and inter-node mutual conductance. The control parameters include the proportional coefficient and integral coefficient of the phase-locked loop controller. Based on the operating data and the control parameters, obtain the converter dynamic response term and the network electrical coupling term; Based on the combined calculation of the converter dynamic response term, the network electrical coupling term, and the diagonal scaling factor, a synchronization stability margin function is constructed to establish the synchronization stability constraint; the synchronization stability margin function characterizes the synchronization stability boundary between the grid-connected converter and the power grid by introducing the diagonal scaling factor.

3. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in claim 2, characterized in that, The synchronization stability constraint is: the synchronization stability margin function is greater than 0.

4. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in claim 2, characterized in that, Step S20 includes: Solve the optimal power flow model without the phase-locked loop synchronization stability constraint to obtain the sum of squared voltage magnitudes of each node and the active power output of the grid converter; the initial optimal power flow model takes minimizing system network loss as the optimization objective and includes node power balance constraints, branch power flow constraints, voltage magnitude constraints and grid converter output constraints. The initial value of the square of the voltage amplitude, the initial value of the active power output of the grid converter, and the preset scaling factor are combined into an initial reference vector, which serves as the initial reference point.

5. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in claim 4, characterized in that, Step S30 includes: Obtain the partial derivatives of the synchronization stability margin function with respect to each decision variable at the current reference point. The decision variables include the square of the node voltage magnitude, the active power output of the grid converter, and the diagonal scaling factor. Based on the partial derivatives, the synchronization stability margin function is linearly approximated by the first-order Taylor expansion to obtain the linearized synchronization stability constraint, which is a linear combination of the decision variables.

6. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in claim 1, characterized in that, The step S40, which involves embedding the linearized synchronization stability constraint into the optimal power flow model and solving it, includes: The linearized synchronization stability constraint is added to the optimal power flow model to form an optimal power flow model with linearized stability constraints; The optimal power flow model with linearized stability constraints is solved using a linear solver to obtain the squared node voltage magnitude, active power output of the grid converter, and diagonal scaling factor under the current iteration.

7. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in any one of claims 1 to 6, characterized in that, Step S40, which returns to step S30 when the current reference point does not meet the iteration condition, continues until the current reference point meets the iteration condition and the current reference point is output as the optimization result, including: Calculate the change in the baseline point between two consecutive iterations; If the change is greater than the preset threshold, it is determined that the iteration condition is not met. The square of the node voltage amplitude, the active power output of the grid converter and the diagonal scaling factor obtained in the current iteration are used as the new reference point, and the process returns to execute step S30. If the change is less than or equal to a preset threshold, the iteration condition is determined to be met, and the benchmark point of the current iteration is output as the optimization result.

8. The optimal power flow sequential linearization method with phase-locked loop stability constraints as described in claim 1, characterized in that, The preset scaling factor is set to 1 or is obtained based on historical data.

9. An electronic device, characterized in that, Includes memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to execute the sequential linearization method for optimal power flow with phase-locked loop stability constraints as described in any one of claims 1 to 8.

10. A computer-readable storage medium comprising instructions, characterized in that: When the instruction is executed on an electronic device, the electronic device performs the sequential linearization method for optimal power flow with phase-locked loop stability constraints as described in any one of claims 1 to 8.

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