An efficient tracing and optimization method for ac power flow calculation non-convergence problem based on linear optimal power flow

Abstract

The application discloses an efficient tracing and optimization adjustment method for AC power flow calculation non-convergence problems based on linear optimal power flow, and first, an operation condition of AC power flow non-convergence is acquired; second, an optimization adjustment model based on linear optimal power flow is constructed; then, a power flow non-convergence tracing constraint is introduced into the optimization adjustment model, so as to construct a power flow convergence optimization adjustment model; next, the operation condition of AC power flow non-convergence is input into the power flow convergence optimization adjustment model, and non-zero power relaxation amounts P1, P2, P3 and P4 are solved; finally, based on the non-zero power relaxation amounts P1, P2, P3 and P4, power compensation is performed on corresponding nodes, the power flow distribution is changed, and AC power flow convergence is realized.

Description

Technical Field

[0001] This invention relates to the field of power, specifically to an efficient method for tracing the source and optimizing the non-convergence problem of AC power flow calculation based on linear optimal power flow. Background Technology

[0002] AC power flow calculation is fundamental to crucial aspects of power system safety and economic dispatch, as well as operation mode calculation. By solving for voltage amplitude and phase angle, reliable AC power flow calculations accurately characterize the power system's operating conditions, determine whether the current system meets safety operating conditions, and directly impact the physical feasibility of dispatch decisions such as optimal power flow and unit combination. In actual power grid operation, AC power flow non-convergence frequently occurs. In such cases, dispatchers must manually probe and adjust the power flow distribution based on their extensive experience to meet AC power flow convergence requirements. With the rapid development of new power systems, the large-scale grid connection of renewable energy and energy storage equipment, and the surge in extreme operating scenarios, AC power flow non-convergence is becoming increasingly frequent. The difficulty and workload of traditional manual power flow adjustment are increasing daily, making it difficult to meet the high standards required for high-quality power grid development and refined, safe, and economical operation. Therefore, how to quickly trace the causes of power flow non-convergence through a series of optimization and adjustment methods and achieve automatic adjustment of power flow non-convergence has significant practical significance and application value.

[0003] Due to the strong random fluctuations on both the source and load sides of the new power system, the fluctuation range of node injected power increases accordingly. As a key boundary condition affecting the system power flow distribution and state variables, abnormal active or reactive power injection at nodes is an important reason for the non-convergence of AC power flow calculations. Therefore, the adjustment of non-convergent AC power flow based on operational boundary reconstruction mainly includes the optimization adjustment of the system's active and reactive power compensation.

[0004] Existing methods primarily employ linear programming to optimize and adjust power flow. However, these methods suffer from two main problems: First, most existing methods presuppose that power flow non-convergence is caused by improper active or reactive power allocation, and then adjust active or reactive power accordingly, failing to trace the root cause of non-convergence when its cause is unclear. Second, linear power flow models exhibit better convergence than nonlinear AC power flow models, with their Jacobian matrices typically being full-rank constant matrices. Linear power flow calculations always have a unique solution, leading to direct convergence in the linear programming problem, where the power compensation reflecting the adjustment in the optimization model is zero. This conclusion of "no adjustment required" contradicts the actual operating conditions of AC power flow non-convergence, thus failing to provide a direct and effective reference for power flow adjustment. Summary of the Invention

[0005] The purpose of this invention is to provide an efficient method for tracing the source and optimizing the non-convergence problem in AC power flow calculation based on linear optimal power flow, comprising the following steps:

[0006] Step 1) Obtain the operating condition where the AC power flow does not converge;

[0007] Step 2) Construct an optimization and adjustment model based on linear optimal power flow;

[0008] Step 3) Introduce the power flow non-convergence source tracing constraint into the optimization and adjustment model, thereby constructing a power flow convergence optimization and adjustment model;

[0009] Step 4) Input the non-convergent AC power flow operating condition into the power flow convergence optimization and adjustment model, and solve for the non-zero power relaxation amount. , , , ;

[0010] Step 5) Based on non-zero power relaxation , , , Power compensation is applied to the corresponding nodes to change the power flow distribution and achieve AC power flow convergence.

[0011] Furthermore, the operating conditions where AC power flow does not converge include nodal loads where AC power flow does not converge, generator output at PV nodes, and PV node voltage.

[0012] The methods for power compensation at the corresponding nodes include adjusting generator output, reactive power compensation, and load shedding.

[0013] Furthermore, the power flow non-convergence source tracing constraints include branch phase angle difference and node voltage correlation constraints, a mathematical model to identify whether the branch phase angle difference and node voltage correlation constraints are effective, and optimization space constraint;

[0014] Specifically, this refers to introducing branch phase angle difference and node voltage correlation constraints into the power flow convergence optimization model;

[0015] First, maintain the branch phase angle difference and node voltage within reasonable operating limits, as shown below:

[0016] (1)

[0017] (2)

[0018] In the formula, Ω L and I PQ These represent the sets of system branches and PQ nodes, respectively. Indicates the reasonable upper and lower limits of the phase angle difference of the branches; Indicates the reasonable upper and lower bounds for node voltage operation;

[0019] Secondly, establish identification constraints. - The mathematical model for determining whether it works is as follows:

[0020] (3)

[0021] (4)

[0022] (5)

[0023] (6)

[0024] In the formula, M is a sufficiently large positive number introduced by the Big M method, ε is the numerical tolerance introduced to avoid numerical problems, and z is a 0-1 variable representing whether the constraint takes effect. P,R With z P,L The effective states of the upper and lower limit operating boundary constraints of the branch phase angle difference in formula (1); z v,R With z v,L The active states of the upper and lower limit operating boundary constraints of the node voltage in formula (2) are respectively;

[0025] The optimized space constraints are shown below:

[0026] (7)

[0027] (8)

[0028] (9)

[0029] In the formula, Ω L Represents the set of system branches. , These represent sufficiently large positive numbers corresponding to the non-zero constraints of active and reactive slack variables in the Big M method, respectively.

[0030] Furthermore, a mathematical model for identifying whether the branch phase angle difference and node voltage correlation constraints are effective is used to trace the set of parameters Γ that needs to be adjusted through the 0-1 variable z. A ;

[0031] Regarding constraints - If z=1 exists, it indicates that there is a branch phase angle difference θ within the system. ij If the absolute value is too large, then the active power injection of all nodes will be included in the optimization adjustment scope, as shown below:

[0032] (10)

[0033] In the formula, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. P is a set containing all input parameters. in =P d -P G Q represents the input active power for power flow calculation. in =Q d -Q G This represents the input reactive power for power flow calculation, (P) d Q d ) is the node load injection vector, (P G Q G ( ) represents the known generator setpoint;

[0034] Regarding constraints - If z=1 exists, it indicates that the voltage of node i is too low or too high. The reactive power injection of node i will be adjusted within the scope of optimization, as shown below:

[0035] (11)

[0036] In the formula, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. It is a set containing all input parameters.

[0037] Furthermore, the reasonable operating boundaries for branch phase angle difference and node voltage. and The parameters are determined based on historical operating data or under extreme operating conditions when the power flow is about to fail to converge, as shown below:

[0038] (12)

[0039] (13)

[0040] In the formula, θ ij,0 and v i,0 These represent the system branch phase angle difference and the initial value of the node voltage, respectively; γ and β are proportionality coefficients with values ​​between [0, 1], used to characterize the degree of tightening of the operating boundary; and These represent the maximum deviation of the branch (i, j) phase angle difference and the node i voltage relative to the initial value, determined based on the historical operating boundary.

[0041] Maximum deviation and As shown below;

[0042] (14)

[0043] In the formula, This represents the branch phase angle difference and node voltage extreme values ​​derived from historical operating data.

[0044] Furthermore, in step 2), the objective function of the optimization adjustment model based on linear optimal power flow is as follows:

[0045] (15)

[0046] In the formula, and Let Ω represent the active and reactive slack variables at node i, respectively. B A set of system nodes. , These are sufficiently large positive numbers representing the penalty terms corresponding to the active and reactive power relaxation amounts in the objective function, respectively.

[0047] Furthermore, the constraints of the optimization adjustment model based on linear optimal power flow include active power balance constraints of PQ and PV nodes, reactive power balance constraints of PQ node, voltage magnitude constraints of PV node and slack node, and voltage phase angle constraints of slack node.

[0048] The active power balance constraints for PQ and PV nodes are shown below:

[0049] (16)

[0050] (17)

[0051] The reactive power balance constraints of the PQ node are as follows:

[0052] (18)

[0053] (19)

[0054] The voltage magnitude constraints for PV nodes and slack nodes are as follows:

[0055] (20)

[0056] The voltage phase angle constraint of the slack node is shown below:

[0057] (twenty one)

[0058] (twenty two)

[0059] In the formula, and Let i represent the active and reactive slack variables, respectively. and Let these represent the load and voltage at node i, respectively. and Represents the linearized form of branch power flow. and I represents the given output values ​​for generator output and power flow calculation, respectively. PQ I PV I Vθ Let I represent the sets of system nodes, PQ nodes, PV nodes, and balancer nodes, respectively. L I G These represent the branch and generator set connected to node i, respectively.

[0060] Furthermore, when constructing the power flow convergence optimization adjustment model, with ( Let ,θ) be variables, and convert the active power balance constraint (16) and reactive power balance constraint (18) of node PQ into linear power flow equations, that is:

[0061] (twenty three)

[0062] (twenty four)

[0063] Among them, network loss and As shown below:

[0064] (25)

[0065] (26)

[0066] (27)

[0067] In the formula, , , This represents the phase angle difference of system branches and the initial value of node voltage; , Indicates admittance;

[0068] In the formula, This is the state variable function form used for Taylor expansion at different nodes in a linear power flow model, with the exponent term k. i These are decision variables.

[0069] Furthermore, the decision variable k i It is obtained through an optimization process based on historical data;

[0070] The optimization process based on historical data aims to minimize the error between the linear branch power flow and the AC power flow in historical data, that is:

[0071] (28)

[0072] In the formula, , These represent the active and reactive power flows of a linear branch, respectively. , Let k represent the active and reactive power flows of the branch in the AC form, respectively. i Substituting into model (23)-(27), we can obtain the linear power flow model that minimizes the error. Equations (15)-(27) are power flow non-convergence optimization adjustment models based on linear optimal power flow.

[0073] Furthermore, the power flow convergence optimization adjustment model is shown below:

[0074] (29).

[0075] The technical effectiveness of this invention is undeniable. Addressing the problem of non-convergence in AC power flow calculations caused by unreasonable active or reactive power injection in power systems, this invention proposes an efficient source tracing and optimization method based on high-precision linear optimal power flow. This invention traces the non-convergence to active or reactive power overload based on the distribution characteristics of power system state variables, describes the source tracing process in the form of mathematical constraints, and directly embeds it into the optimization model to guide the solution of power compensation. This achieves accurate location and rapid compensation for unreasonable power injections that lead to AC power flow non-convergence. Attached Figure Description

[0076] Figure 1 The active power adjustment amount for restoring power flow convergence in this invention is defined as follows: a is the active power adjustment amount comparison (node ​​group I), and b is the active power adjustment amount comparison (node ​​group II).

[0077] Figure 2 This refers to the reactive power adjustment amount for restoring power flow convergence in this invention. Detailed Implementation

[0078] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0079] Example 1:

[0080] See Figures 1 to 2 An efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow includes the following steps:

[0081] Step 1) Obtain the operating condition where the AC power flow does not converge;

[0082] Step 2) Construct an optimization and adjustment model based on linear optimal power flow;

[0083] Step 3) Introduce the power flow non-convergence source tracing constraint into the optimization and adjustment model, thereby constructing a power flow convergence optimization and adjustment model;

[0084] Step 4) Input the non-convergent AC power flow operating condition into the power flow convergence optimization and adjustment model, and solve for the non-zero power relaxation amount. , , , ;

[0085] Step 5) Based on non-zero power relaxation , , , Power compensation is applied to the corresponding nodes to change the power flow distribution and achieve AC power flow convergence.

[0086] Example 2:

[0087] The main structure of this embodiment is the same as that of embodiment 1. Furthermore, the operating conditions where the AC power flow does not converge include the node loads where the AC power flow does not converge, the generator output connected to the PV node, and the PV node voltage.

[0088] The methods for power compensation at the corresponding nodes include adjusting generator output, reactive power compensation, and load shedding.

[0089] Example 3:

[0090] The main structure of this embodiment is the same as any one of embodiments 1 to 2. Furthermore, the power flow non-convergence source tracing constraint includes branch phase angle difference and node voltage correlation constraint, a mathematical model for identifying whether the branch phase angle difference and node voltage correlation constraint are effective, and optimization space constraint.

[0091] Specifically, this refers to introducing branch phase angle difference and node voltage correlation constraints into the power flow convergence optimization model;

[0092] First, maintain the branch phase angle difference and node voltage within reasonable operating limits, as shown below:

[0093] (1)

[0094] (2)

[0095] In the formula, Ω L and I PQ These represent the sets of system branches and PQ nodes, respectively. Indicates the reasonable upper and lower limits of the phase angle difference of the branches; Indicates the reasonable upper and lower bounds for node voltage operation;

[0096] Secondly, establish identification constraints. - The mathematical model for determining whether it works is as follows:

[0097] (3)

[0098] (4)

[0099] (5)

[0100] (6)

[0101] In the formula, M is a sufficiently large positive number introduced by the Big M method, ε is the numerical tolerance introduced to avoid numerical problems, and z is a 0-1 variable representing whether the constraint takes effect. P,R With z P,L The effective states of the upper and lower limit operating boundary constraints of the branch phase angle difference in formula (1); z v,R With z v,L The active states of the upper and lower limit operating boundary constraints of the node voltage in formula (2) are respectively;

[0102] The optimized space constraints are shown below:

[0103] (7)

[0104] (8)

[0105] (9)

[0106] In the formula, Ω L Represents the set of system branches. , These represent sufficiently large positive numbers corresponding to the non-zero constraints of active and reactive slack variables in the Big M method, respectively.

[0107] Example 4:

[0108] The main structure of this embodiment is the same as any one of embodiments 1 to 3. Furthermore, the mathematical model for identifying whether the branch phase angle difference and node voltage correlation constraints are effective is used to trace the parameter set Γ that needs to be adjusted through the 0-1 variable z. A ;

[0109] Regarding constraints - If z=1 exists, it indicates that there is a branch phase angle difference θ within the system. ij If the absolute value is too large, then the active power injection of all nodes will be included in the optimization adjustment scope, as shown below:

[0110] (10)

[0111] In the formula, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. It is a set containing all input parameters. This represents the input active power for power flow calculation. This represents the input reactive power for power flow calculation. Inject vectors into node loads. Given the known generator setpoint;

[0112] Regarding constraints - If z=1 exists, it indicates that the voltage of node i is too low or too high. The reactive power injection of node i will be adjusted within the scope of optimization, as shown below:

[0113] (11)

[0114] In the formula, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. It is a set containing all input parameters.

[0115] Example 5:

[0116] The main structure of this embodiment is the same as any one of embodiments 1 to 4. Furthermore, the reasonable operating boundaries for branch phase angle difference and node voltage are defined. and The parameters are determined based on historical operating data or under extreme operating conditions when the power flow is about to fail to converge, as shown below:

[0117] (12)

[0118] (13)

[0119] In the formula, θ ij,0 and v i,0 These represent the system branch phase angle difference and the initial value of the node voltage, respectively; γ and β are proportionality coefficients with values ​​between [0, 1], used to characterize the degree of tightening of the operating boundary; and These represent the maximum deviation of the branch (i, j) phase angle difference and the node i voltage relative to the initial value, determined based on the historical operating boundary.

[0120] Maximum deviation and As shown below;

[0121] (14)

[0122] In the formula, This represents the branch phase angle difference and node voltage extreme values ​​derived from historical operating data.

[0123] Example 6:

[0124] The main structure of this embodiment is the same as any one of embodiments 1 to 5. Further, in step 2), the objective function of the optimization adjustment model based on linear optimal power flow is as follows:

[0125] (15)

[0126] In the formula, and Let i represent the active and reactive slack variables, respectively. For the set of system nodes, the objective function contains sufficiently large positive numbers for the penalty terms corresponding to the active and reactive power relaxations.

[0127] Example 7:

[0128] The main structure of this embodiment is the same as any one of embodiments 1 to 6. Furthermore, the constraints of the optimization adjustment model based on linear optimal power flow include active power balance constraints of PQ and PV nodes, reactive power balance constraints of PQ nodes, voltage amplitude constraints of PV nodes and slack nodes, and voltage phase angle constraints of slack nodes.

[0129] The active power balance constraints for PQ and PV nodes are shown below:

[0130] (16)

[0131] (17)

[0132] The reactive power balance constraints of the PQ node are as follows:

[0133] (18)

[0134] (19)

[0135] The voltage magnitude constraints for PV nodes and slack nodes are as follows:

[0136] (20)

[0137] The voltage phase angle constraint of the slack node is shown below:

[0138] (twenty one)

[0139] (twenty two)

[0140] In the formula, and Let i represent the active and reactive slack variables, respectively. and Let these represent the load and voltage at node i, respectively. and Represents the linearized form of branch power flow. and I represents the given output values ​​for generator output and power flow calculation, respectively. PQ I PV I Vθ Let I represent the sets of system nodes, PQ nodes, PV nodes, and balancer nodes, respectively. L I G These represent the branch and generator set connected to node i, respectively.

[0141] Example 8:

[0142] The main structure of this embodiment is the same as any one of embodiments 1 to 7. Furthermore, when constructing the power flow convergence optimization adjustment model, (… Let ,θ) be variables, and convert the active power balance constraint (16) and reactive power balance constraint (18) of node PQ into linear power flow equations, that is:

[0143] (twenty three)

[0144] (twenty four)

[0145] Among them, network loss and As shown below:

[0146] (25)

[0147] (26)

[0148] (27)

[0149] In the formula, , , This represents the phase angle difference of system branches and the initial value of node voltage; , Indicates admittance;

[0150] In the formula, This is the state variable function form used for Taylor expansion at different nodes in a linear power flow model, with the exponent term k. iThese are decision variables.

[0151] Example 9:

[0152] The main structure of this embodiment is the same as any one of embodiments 1 to 8. Furthermore, the decision variable k... i It is obtained through an optimization process based on historical data;

[0153] The optimization process based on historical data aims to minimize the error between the linear branch power flow and the AC power flow in historical data, that is:

[0154] (28)

[0155] In the formula, , These represent the active and reactive power flows of a linear branch, respectively. , Let k represent the active and reactive power flows of the branch in the form of AC, respectively. i Substituting into model (23)-(27), we can obtain the linear power flow model that minimizes the error. Equations (15)-(27) are power flow non-convergence optimization adjustment models based on linear optimal power flow.

[0156] Example 10:

[0157] The main structure of this embodiment is the same as any one of embodiments 1 to 9. Furthermore, the power flow convergence optimization adjustment model is as follows:

[0158] (29).

[0159] Example 11:

[0160] An efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow includes the following steps:

[0161] 1) A method for tracing the source of power flow non-convergence based on the distribution characteristics of state variables is proposed.

[0162] The steps for tracing the source of power flow non-convergence based on the distribution characteristics of state variables are as follows:

[0163] 1.1) Introduce branch phase angle difference and node voltage correlation constraints into the power flow convergence optimization model, and restrict them within a reasonable operating boundary. By using the state in which these constraints are in effect, trace the key parameters that cause power flow non-convergence.

[0164] First, the branch phase angle difference and node voltage are maintained within reasonable operating boundaries, and the constraint form is as follows:

[0165] (30)

[0166] (31)

[0167] In the formula, Ω L and I PQ These represent the sets of system branches and PQ nodes, respectively. and These represent the reasonable upper and lower limits of branch phase angle difference and node voltage, respectively.

[0168] When the absolute value of the phase angle difference of a branch is too large or the voltage of a node is too low, it will be limited by constraints (30)-(31) and reach the limit. At this time, the constraint is an active constraint. By identifying the active constraint, unreasonable phase angle difference or voltage can be determined, and then the source of the unreasonable active or reactive power arrangement of the state variable can be traced. This section adopts the Big M method and introduces an auxiliary 0-1 variable z to establish a mathematical model for identifying whether the constraint (30)-(31) is active. The specific form is as follows:

[0169] (32)

[0170] (33)

[0171] (34)

[0172] (35)

[0173] Where M is a sufficiently large positive number introduced by the Big M method, and ε is a numerical tolerance introduced to avoid numerical problems, taken as ε=10. -6 z is a 0-1 variable representing whether the constraint is active or not. Taking constraint (34) as an example, when z=1, , ,Right now This constraint takes effect, indicating that the voltage at node i is low and near the reasonable lower bound, requiring adjustment of the reactive power arrangement; when z=0, , Meanwhile, constrained by constraint (31), the node voltage is within the normal range, and constraint (31) has no effect. The dimension of the 0-1 variable z introduced by the proposed method is (2NL+2NB). PQ )×1, where NL and NB PQ represents the number of system branches and PQ nodes, respectively. In actual operation, since only a few constraints (30)-(31) are effective, the variable z has high sparsity. This characteristic enables commercial solvers such as Gurobi and CPLEX to fully leverage their algorithmic advantages to solve this mixed-integer linear programming problem, and maintain good computational performance even when facing large-scale systems.

[0174] For constraints (32)-(33), if z=1 exists, it indicates that there is a phase angle difference θ in the system at this time. ij For branches with excessively large absolute values ​​of phase angle difference, the system's active power allocation needs adjustment. Since the active power flow of branch (i,j) is closely related not only to the active power injection at nodes i and j, but also to the active power distribution of the rest of the network, simply adjusting the active power injection at nodes i and j to address the excessively large absolute value of the branch phase angle difference cannot fully account for the impact of the active power flow of each branch on the branch phase angle difference θ. ij The impact. To ensure the accuracy of source tracing and subsequent active power optimization adjustments, when the absolute value of the branch phase angle difference in the system is too large, the active power injection of all nodes is included in the optimization adjustment scope, that is:

[0175] (36)

[0176] in, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. P is a set containing all input parameters. in = P d -P G , representing the input parameter value for power flow calculation; similarly, Q in =Q d -Q G (P) d Q d ) is the node load injection vector, (P G Q G The part contains known generator setpoints (such as P at node PQ). G and Q G ), some of which are variables to be determined (such as Q of PV nodes). G ).

[0177] Unlike the overall network balance of active power, reactive power exhibits significant local balance characteristics. Therefore, for constraints (34)-(35), if z=1 exists, it indicates that the voltage of node i is too low or too high. In this case, the reactive power injection of node i needs to be adjusted and included in the subsequent optimization adjustment range, that is:

[0178] (37)

[0179] In summary, the constraints used to trace the causes of non-convergence of power flow are shown in (30)-(37).

[0180] 1.2) Determine the reasonable operating boundary of state variables based on historical operating data.

[0181] Reasonable operating boundary parameters for different systems and The parameter values ​​can be determined based on historical system operating data or under extreme operating conditions when the power flow is on the verge of non-convergence. Specifically, they are defined as follows:

[0182] (38)

[0183] (39)

[0184] Where, θ ij,0 and v i,0 γ and β represent the system branch phase angle difference and the initial value of the node voltage, respectively; γ and β are proportionality coefficients with values ​​between [0,1], representing the degree of tightening of the operating boundary. and These represent the maximum deviation of the branch (i,j) phase angle difference and the node i voltage relative to the initial value, determined according to the historical operating boundary. Their expressions are shown in (40), which are used to describe the reasonable operating boundary constraint range in equations (38)-(39).

[0185] (40)

[0186] In the formula, This represents the branch phase angle difference and node voltage extreme values ​​derived from historical operating data.

[0187] Selecting appropriate scaling factors (γ, β) is crucial for effectively tracing the source of power injection at key nodes. If (γ, β) is too small, it will negatively impact the node voltage v and branch phase angle difference θ in the optimization model. ij If the feasible region is too tight, it may force some non-critical nodes to participate in the injection power adjustment, resulting in an increase in the node injection power compensation amount, causing unnecessary compensation costs, and in severe cases, it may even lead to the model having no feasible solution due to excessive constraints. Conversely, if the value of (γ,β) is too large, although it improves the feasibility of the optimization model, the overly broad operating boundary will weaken the model's ability to identify abnormal state variables, making it difficult to accurately trace the source of abnormal voltage or phase angle distribution nodes or branches through constraints (30)-(35).

[0188] 2) A linear modeling method for power flow optimization adjustment based on power flow non-convergence source tracing is proposed.

[0189] The steps of the linear modeling method for power flow optimization adjustment based on power flow non-convergence source tracing are as follows:

[0190] 2.1) Construct an optimization adjustment model based on linear optimal power flow

[0191] The power flow convergence optimization problem can be modeled as an optimization problem with minimizing node power compensation as the objective function, the power equations of each type of node in the power flow calculation as the constraints, and the unknown state variables of each type of node (such as v and θ of PQ node) and the active and reactive power relaxation of each node as variables. The specific expression is shown below.

[0192] Objective function:

[0193] (41)

[0194] Constraints:

[0195] (42)

[0196] (43)

[0197] (44)

[0198] (45)

[0199] (46)

[0200] (47)

[0201] (48)

[0202] Equations (41)-(48) are power flow non-convergence optimization adjustment models based on linear optimal power flow, where equations (42)-(43) represent the active power balance constraints of PQ and PV nodes, equations (44)-(45) represent the reactive power balance constraints of PQ node, equation (46) represents the voltage magnitude constraints of PV node and slack node, and equation (47) represents the voltage phase angle constraints of slack node. and These represent the active and reactive slack variables of node i, respectively, which are the power compensation amounts required to achieve power flow convergence. With v i / θ i Let PF represent the load and voltage at node i, respectively. L and QF L P represents the linearized form of branch power flow. G / Q G With P G,0 / Q G,0 These represent the generator output and the given output values ​​for power flow calculations, respectively. Ω B I PQ I PV I Vθ These represent the sets of system nodes, PQ nodes, PV nodes, and balance nodes, respectively.

[0203] 2.2) Use high-precision linear power flow modeling that takes into account reactive power and voltage.

[0204] The non-convergent optimization problem of power flow based on optimal power flow is a typical nonlinear and non-convex problem, which is difficult to solve. Therefore, this invention adopts (… The high-precision linear power flow model, which considers reactive power and voltage as variables (θ), transforms the nonlinear programming problem into an easily solvable linear programming problem. The linear power flow equations in equations (42) and (44) are as follows:

[0205] (49)

[0206] (50)

[0207] To improve the accuracy of the linear approximation, the model considers network losses modeled using a hot-start approach. and That is, using the initial value point of a warm start. Instead of (v=1, θ=0) as the initial value point for the Taylor expansion in the linear approximation model of network loss, its expression is as follows:

[0208] (51)

[0209] (52)

[0210] In the formula, As The linearized form is expressed as follows:

[0211] (53)

[0212] This refers to the state variable function form used for Taylor expansion at different nodes in a linear power flow model, which has the "optimal" form that minimizes the error. A precise high-precision linear power flow model can be obtained through an optimization process based on historical data. Historical data near the non-convergence boundary of the power flow under active or reactive power overload conditions are selected for linear model construction, ensuring a high degree of matching between the application scenario and the training scenario. The objective function (54) of this optimization process is to minimize the error between the linear branch power flow and the AC power flow based on historical data, with the decision variable being the exponential term k. i .

[0213] (54)

[0214] The optimized k iSubstituting into model (49)-(53), we can obtain the linear power flow model that minimizes the error. Equations (41)-(53) are the proposed non-convergent power flow optimization adjustment models based on linear optimal power flow.

[0215] 2.3) Improved linear optimization model with source tracing constraints.

[0216] By introducing the power flow non-convergence source tracing constraint proposed in this patent into the linear optimization adjustment model, the set of parameters Γ that needs to be adjusted can be obtained. A and the set of parameters Г that do not require adjustment NA This source constraint is restated here into an analytical form that can be used to optimize the model, ensuring that parameter tuning is limited to Γ. A Inside.

[0217] Equations (32)-(35) trace the origin of Г through the 0-1 variable z. A Similarly, this section also constructs information about the slack variable (S) using different values ​​of z. P ,S Q The constraints are used to limit the optimization space, as follows:

[0218] (55)

[0219] (56)

[0220] (57)

[0221] Combined with constraint (48) requirement (S) P ,S Q Non-negative, with respect to active power relaxation S P In other words, when z exists in the entire system P,R =1 or z P,L When = 1, the active power relaxation on all nodes in the system is within the optimization space. Therefore, the source constraint of node active power injection is expressed as the total network constraint form shown in equation (55). In contrast, constraints (56)-(57) control the reactive power optimization space at the node level, when =1 or When =1, , Only the reactive power relaxation at node i is included in the optimization space. hour, That is, reactive power relaxation at node i is not considered. Based on the z-value, the proposed method can determine the power injection of key nodes that need to participate in power adjustment, reducing the power relaxation variable (S). P ,S QThe effective optimization dimension of ) reduces the size of nodes involved in power adjustment. In addition, through the 0-1 variable z and its related constraints (32)-(35) and (55)-(57), an explicit correlation between "constraint in action state" and "node power relaxation non-zero" is established within the optimization model, ensuring that equation (55)-(57) accurately traces the cause of power flow non-convergence.

[0222] In summary, the improved linear optimization model incorporating source constraints is a mixed-integer linear programming problem, summarized as follows:

[0223] (58)

[0224] The steps for adjusting the AC power flow to a convergent state using this model are detailed below:

[0225] 1. Input the operating condition of non-convergent AC power flow. Based on the node type and characteristics of the power flow calculation, use the node load, generator output of PV node connections, and PV node voltage as inputs to the optimization model.

[0226] 2. Based on the linear optimal power flow considering reactive power and voltage, a power flow convergence optimization adjustment model is established (58), and a power flow non-convergence source tracing constraint is introduced.

[0227] 3. Solve the proposed linear optimization model to obtain the non-zero power relaxation. , , , .

[0228] 4. Based on the results obtained in step 3 , , , By adjusting generator output, reactive power compensation, and load shedding, power compensation is applied to the corresponding nodes to change the power flow distribution and achieve AC power flow convergence.

[0229] This model can reduce slack variables (S P ,S Q By narrowing the feasible region of the optimization model to make it closer to the feasible region of the nonlinear optimization model based on AC optimal power flow, the power compensation amount obtained at this time is more valuable for achieving AC power flow convergence.

[0230] Example 12:

[0231] As a further optimization of Embodiment 11, this embodiment also includes the following technical features based on Embodiment 11:

[0232] This invention was validated on the IEEE 118-node standard test system. The results were compared with those of the proposed method M1, the nonlinear optimization method M2 based on AC optimal power flow, and the linear programming method M3 based on the existing linear power flow model in terms of power flow convergence optimization and adjustment, respectively, for typical scenarios of power flow non-convergence caused by active or reactive power overload.

[0233] Figures 1 to 2 Three methods for calculating power adjustment amounts to restore power flow convergence are presented. It can be observed that the adjustment amounts of the proposed method M1 and the nonlinear optimization method M2 are very close at most nodes. In contrast, the power adjustment amounts calculated using M3 are zero at all nodes, failing to provide a direct reference for AC power flow convergence.

Claims

1. An efficient method for tracing the source and optimizing the non-convergence problem in AC power flow calculation based on linear optimal power flow, characterized in that, Includes the following steps: Step 1) Obtain the operating condition where the AC power flow does not converge; Step 2) Construct an optimization and adjustment model based on linear optimal power flow; Step 3) Introduce the power flow non-convergence source tracing constraint into the optimization and adjustment model, thereby constructing a power flow convergence optimization and adjustment model; Step 4) Input the non-convergent AC power flow operating condition into the power flow convergence optimization and adjustment model, and solve for the non-zero power relaxation amount. , , , ; Step 5) Based on non-zero power relaxation , , , Power compensation is applied to the corresponding nodes to change the power flow distribution and achieve AC power flow convergence.

2. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 1, is characterized in that: Operating conditions where AC power flow does not converge include nodal loads where AC power flow does not converge, generator output at PV nodes, and PV node voltage. The methods for power compensation at the corresponding nodes include adjusting generator output, reactive power compensation, and load shedding.

3. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 1, is characterized in that: The constraints for tracing the non-convergence of power flow include branch phase angle difference and node voltage correlation constraints, a mathematical model to identify whether the branch phase angle difference and node voltage correlation constraints are effective, and optimization space constraints. Specifically, this refers to introducing branch phase angle difference and node voltage correlation constraints into the power flow convergence optimization model; First, maintain the branch phase angle difference and node voltage within reasonable operating limits, as shown below: In the formula, Ω L and I PQ These represent the sets of system branches and PQ nodes, respectively. Indicates the reasonable upper and lower limits of the phase angle difference of the branches; Indicates the reasonable upper and lower bounds for node voltage operation; Secondly, establish identification constraints. - The mathematical model for determining whether it works is as follows: where M is a sufficiently large positive number introduced by the Big-M method, ε is a numerical tolerance introduced to avoid numerical problems, z is a 0-1 variable indicating whether the constraint is active or not, z P,R and z P,L respectively indicate the active status of the upper and lower operating boundary constraints of the branch phase angle difference in equation (1); z v,R and z v,L respectively indicate the active status of the upper and lower operating boundary constraints of the node voltage in equation (2). The optimized space constraints are shown below: (7) (8) (9) In the formula, Represents the set of system branches. , These represent sufficiently large positive numbers corresponding to the non-zero constraints of active and reactive slack variables in the Big M method, respectively.

4. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 3, is characterized in that: A mathematical model for identifying whether the branch phase angle difference and node voltage correlation constraints are effective is used to trace the set of parameters that need to be adjusted through the 0-1 variable z. ; Regarding constraints - If z=1 exists, it indicates that there is a branch phase angle difference θ within the system. ij If the absolute value is too large, then the active power injection of all nodes will be included in the optimization adjustment scope, as shown below: (10) In the formula, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. P is a set containing all input parameters. in =P d -P G Q represents the input active power for power flow calculation. in =Q d -Q G This represents the input reactive power for power flow calculation, (P) d Q d ) is the node load injection vector, (P G Q G ( ) represents the known generator setpoint; Regarding constraints - If z=1 exists, it indicates that the voltage of node i is too low or too high. The reactive power injection of node i will be adjusted within the scope of optimization, as shown below: (11) In the formula, For the set of parameters that need to be adjusted, This is a set of parameters that do not require adjustment. It is a set containing all input parameters.

5. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 3, is characterized in that: Reasonable operating boundaries for branch phase angle difference and node voltage and The parameters are determined based on historical operating data or under extreme operating conditions when the power flow is about to fail to converge, as shown below: (12) (13) In the formula, θ ij,0 and v i,0 These represent the system branch phase angle difference and the initial value of the node voltage, respectively; γ and β are proportionality coefficients with values ​​between [0, 1], used to characterize the degree of tightening of the operating boundary; and These represent the maximum deviation of the branch (i, j) phase angle difference and the node i voltage relative to the initial value, determined based on the historical operating boundary. Maximum deviation and As shown below; (14) In the formula, This represents the branch phase angle difference and node voltage extreme values ​​derived from historical operating data.

6. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 1, is characterized in that... In step 2), the objective function of the optimization adjustment model based on linear optimal power flow is as follows: (15) In the formula, and Let Ω represent the active and reactive slack variables at node i, respectively. B A set of system nodes. , These are sufficiently large positive numbers representing the penalty terms corresponding to the active and reactive power relaxation amounts in the objective function, respectively.

7. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 1, is characterized in that... The constraints of the optimization adjustment model based on linear optimal power flow include active power balance constraints of PQ and PV nodes, reactive power balance constraints of PQ node, voltage magnitude constraints of PV node and slack node, and voltage phase angle constraints of slack node. The active power balance constraints for PQ and PV nodes are shown below: (16) (17) The reactive power balance constraints of the PQ node are as follows: (18) (19) The voltage magnitude constraints for PV nodes and slack nodes are as follows: (20) The voltage phase angle constraint of the slack node is shown below: (21) (22) In the formula, and Let i represent the active and reactive slack variables, respectively. and Let these represent the load and voltage at node i, respectively. and Represents the linearized form of branch power flow. and I represents the given output values ​​for generator output and power flow calculation, respectively. PQ I PV I Vθ Let I represent the sets of system nodes, PQ nodes, PV nodes, and balancer nodes, respectively. L I G These represent the branch and generator set connected to node i, respectively.

8. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 7, is characterized in that... When constructing the power flow convergence optimization adjustment model, with ( Let ,θ) be variables, and convert the active power balance constraint (16) and reactive power balance constraint (18) of node PQ into linear power flow equations, that is: (23) (24) Among them, network loss and As shown below: (25) (26) (27) In the formula, , , This represents the phase angle difference of system branches and the initial value of node voltage; , Indicates admittance; In the formula, This is the state variable function form used for Taylor expansion at different nodes in a linear power flow model, with the exponent term k. i These are decision variables.

9. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 8, is characterized in that: Decision variable k i It is obtained through an optimization process based on historical data; The optimization process based on historical data aims to minimize the error between the linear branch power flow and the AC power flow in historical data, that is: (28) In the formula, , These represent the active and reactive power flows of a linear branch, respectively. , Let k represent the active and reactive power flows of the branch in the form of AC, respectively. i Substituting into model (23)-(27), we can obtain the linear power flow model that minimizes the error. Equations (15)-(27) are power flow non-convergence optimization adjustment models based on linear optimal power flow.

10. The efficient source tracing and optimization method for non-convergence problems in AC power flow calculation based on linear optimal power flow, as described in claim 1, is characterized in that... The power flow convergence optimization adjustment model is shown below: (29)。

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