Hybrid integer convex relaxation method and system for power system optimal power flow

Abstract

The present application relates to the technical field of power system, specifically relates to a mixed integer convex relaxation solution method and system for power system optimal power flow, comprising the following steps: uniformly convex relaxation modeling is carried out on ordinary branch and transformer branch in power system, second-order cone constraint is converted from alternating current power flow constraint, and a tap position coupling model is constructed by using transformer tap position discrete representation rule, forming a mixed integer convex relaxation model; the mixed integer convex relaxation model is solved, and a convex relaxation power flow solution and corresponding transformer tap position solution are obtained, and a tap position influence branch set is constructed according to the transformer tap position solution.The present application, by binary tap position representation, tap side auxiliary variable and linearization reduction constraint, avoids non-convex product formed by transformer tap position and power flow variable directly, and realizes the collaborative solution of alternating current power flow non-convex constraint and discrete tap position constraint.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a hybrid integer convex relaxation solution method and system for optimal power flow in power systems. Background Technology

[0002] Optimal power flow is an important scheduling method that minimizes generation costs, line losses, or overall operation objectives under the conditions of satisfying power flow equations, node power balance, line thermal limits, node voltage upper and lower limits, and generator output constraints. Due to the nonlinear coupling relationship between voltage amplitude, voltage phase angle, branch current, active power, and reactive power in the AC power flow equations, the optimal power flow problem usually exhibits non-convex characteristics, which makes it difficult to solve.

[0003] Existing methods mostly use linear approximation or convex relaxation to handle power flow constraints. Linear approximation methods rely on the initial solution and the accuracy of the approximation. When the phase angle difference of the ring network is large, the line is heavily loaded, or the voltage is close to the boundary, infeasible power flow solutions are easily generated. Although convex relaxation methods can reduce the difficulty of solving the problem, the relaxed result may not strictly satisfy the original power flow equation.

[0004] Furthermore, transformer tap positions in power systems are typically discrete integers, and the turns ratio directly influences the relationship between branch voltage, current, and power. If only a penalty function is used to handle integer tap positions, the physical feasibility of the tap position results cannot be guaranteed. If a mixed-integer nonlinear model is directly established, the solution complexity is high and the convergence stability is poor. Therefore, there is an urgent need for an optimal power flow solution method that can simultaneously handle power flow non-convexity and transformer integer tap positions, and can perform power flow equation recovery and ring network phase angle consistency recovery on convex relaxation results. Summary of the Invention

[0005] This invention provides a hybrid integer convex relaxation solution method and system for optimal power flow in power systems.

[0006] A mixed-integer convex relaxation method for optimal power flow in power systems includes the following steps:

[0007] A unified convex relaxation model is performed on ordinary branches and transformer branches in the power system. The AC power flow constraints are transformed into second-order cone constraints. The tap position coupling model is constructed using the discrete representation rules of transformer tap positions, forming a hybrid integer convex relaxation model.

[0008] The mixed integer convex relaxation model is solved to obtain the convex relaxation power flow solution and the corresponding transformer tap position solution, and the set of tap position-affected branches is constructed based on the transformer tap position solution;

[0009] Using the set of branches affected by the tap position as the recovery object, power flow equality recovery and ring network phase angle consistency recovery are performed on the convex relaxation power flow solution to obtain the optimal power flow solution that satisfies the original power flow constraints and the transformer integer tap position constraints.

[0010] Preferably, the node voltages, currents, and branch power of ordinary branches are de-phased, and the voltage, current, and power relationships in the AC power flow equations are characterized using the square variables of node voltages, the square variables of branch currents, and the active and reactive power variables of the branches. The voltage constraint relationships of ordinary branches are then established based on Ohm's law as follows:

[0011] ;in, Represents a node The squared variable of the node voltage, Represents a node The squared variable of the node voltage, Indicates the branch resistance. Represents a node To node The active power of the branch circuit, Indicates branch reactance, Represents a node To node The reactive power of the branch circuit, This represents the squared variable of the branch current.

[0012] Furthermore, based on the active power, reactive power, squared variable of node voltage, and squared variable of branch current, a power constraint at the beginning of the branch is constructed, and the power constraint at the beginning of the branch is converted into a second-order cone form constraint as follows: ,in, Represents a node To node The active power of the branch circuit, Represents a node To node The reactive power of the branch circuit, Represents a node The squared variable of the node voltage, Represents the squared variable of the branch current. The 2-norm of a vector Indicates the node number at the beginning of the branch road. Indicates the branch terminal node number. Represents a node To node Branch active power variable twice as much, Represents a node To node Branch reactive power variable This is twice the size of the standard branch convex relaxation model, which is formed by combining node power balance constraints.

[0013] For transformer branches, the transformer tap position is represented as a discrete integer tap position, and the discrete integer tap position is encoded using binary variables. The correspondence between the transformer tap position and the branch parameters is established based on the normalized transformer ratio.

[0014] As a further aspect of the present invention, auxiliary variables for tap-side voltage and tap-side current are introduced on the transformer tap side, and the tap-side coupling relationship between the binary variables and the auxiliary variables for tap-side voltage and current is constructed as follows: ; ;in, Indicates the first The voltage coupling auxiliary variable introduced by multiplying the binary variable by the squared auxiliary variable of the tap-side voltage. Indicates the first The current coupling auxiliary variable introduced by multiplying the binary variable by the square auxiliary variable of the tap-side current. Indicates transformer branch The auxiliary variable is the square of the tap-side voltage. Indicates transformer branch The auxiliary variable is the square of the tap-side current. For the first The nonlinear product relationship between the gear position variable and the power flow variable is eliminated by linearizing the order reduction constraint;

[0015] Voltage consistency constraints and current consistency constraints between the transformer tap side and the line side are established using unified coupling variables. The ordinary branch convex relaxation model, tap coupling relationship, voltage consistency constraints, current consistency constraints, node power balance constraints, and operation safety constraints are combined to form the hybrid integer convex relaxation model.

[0016] Preferably, the objective function, ordinary branch convex relaxation model, transformer tap-coupled model, node power balance constraint, and line thermal limit constraint in the hybrid integer convex relaxation model are: The active power output constraint of the generator is: The reactive power output constraint of the generator is: The node voltage limit constraints and ring network phase angle constraints are input together into the mixed integer convex optimization solver to obtain the feasible solution object of the model. Indicates a branch The thermal limit of the circuit, Represents the squared variable of the branch current. This represents the square of the thermal limit of the circuit. , Representing generator nodes The lower limit and upper limit of active power output, , Representing generator nodes The lower limit and upper limit of reactive power output, Indicates generator node Those who have made contributions Indicates generator node The effort wasted.

[0017] Furthermore, based on the feasible solution object of the model, optimization is performed to obtain the convex relaxed power flow solution under the objectives of minimizing generator cost, minimizing line loss, or minimizing both generator cost and line loss:

[0018] ,in, This represents a convex relaxation power flow solution. This represents the squared variable of the node voltage obtained from the solution. This represents the squared variable of the branch current obtained from the solution. This represents the active power variable of the branch obtained from the solution. This represents the reactive power variable of the branch obtained from the solution. This represents the nodal active power injection variable obtained from the solution. The term "node reactive power injection variable" represents the obtained nodal reactive power injection variable. The convex relaxation power flow solution includes the node voltage square variable, branch current square variable, branch active power variable, branch reactive power variable, nodal active power injection variable, and nodal reactive power injection variable.

[0019] As a further technical solution of the present invention, the binary variable value corresponding to the transformer branch is read in the convex relaxation power flow solution, and the actual tap position integer value of the transformer is restored according to the binary variable value as follows: ;in, Indicates transformer branch The actual gear number (integer value) Indicates transformer branch The number of bits in the binary code. Represents the binary bit sequence number. Indicates the first The weight corresponding to the bit binary variable Indicates transformer branch The The value of the binary variable is obtained by solving the value of the actual tap position of the transformer, and then the normalized ratio of the transformer is determined according to the integer value of the actual tap position of the transformer to obtain the transformer tap position solution.

[0020] Based on the transformer tap position identification, transformer branches that have undergone tap position adjustments or have tap position coupling relationships are identified. These transformer branches and the ordinary branches connected to them are determined as tap position affected branches. All tap position affected branches are then summarized into a tap position affected branch set, represented as follows: ;in, This indicates that the gear position affects the branch set. Indicates the connection with the transformer branch A set of connected ordinary branches, This represents the set of transformer branches affected by the tap position. The set of branches affected by the tap position is used for subsequent power flow equation restoration and ring network phase angle consistency restoration.

[0021] Preferably, taking the set of branches affected by the gear position as the recovery target, the squared variable of the node voltage, the squared variable of the branch current, the active power variable of the branch, and the reactive power variable of the branch affected by the gear position are read from the convex relaxation power flow solution. It is then determined whether each branch affected by the gear position satisfies the branch power equation. Branches affected by the gear position that do not satisfy the branch power equation are identified as branches to be recovered, represented as follows: ;in, This represents the set of branches to be restored. Indicates a branch The second-order cone relaxation gap, This indicates that the gear position affects the set of branch lines;

[0022] For the branch to be restored, while keeping the corresponding node voltage square variable unchanged, the branch current square variable, branch active power variable and branch reactive power variable of the branch to be restored are restored by power flow equation, so that the restored branch active power variable, branch reactive power variable, node voltage square variable and branch current square variable satisfy the original branch power flow equation relationship.

[0023] Furthermore, when the endpoint node of the branch to be restored is connected to a generator node, the node power balance is maintained by adjusting the active power output variable and reactive power output variable of the corresponding generator node; when the endpoint node of the branch to be restored is not connected to a generator node, the connection path from the endpoint node to the generator node is found, and the branch power correction is passed step by step along the connection path until the generator node in the connection path completes the output compensation, and the power flow equation restoration solution is obtained.

[0024] Based on the power flow equation recovery solution, calculate the branch voltage phase angle difference in each loop, and determine whether the branch voltage phase angle difference in each loop meets the ring network phase angle consistency constraint; if not, under the condition of keeping the transformer tap position solution unchanged, perform phase angle consistency recovery on the branch power variable of the branch to be recovered in the loop to obtain the phase angle consistency recovery solution.

[0025] The phase angle consistency recovery solution is combined with the transformer tap position solution to generate the optimal power flow solution that satisfies the original power flow constraints, node power balance constraints, operation safety constraints, ring network phase angle consistency constraints, and transformer integer tap position constraints.

[0026] A hybrid integer convex relaxation solution system for optimal power flow in power systems includes the following modules:

[0027] A unified convex relaxation modeling module is used to perform unified convex relaxation modeling on ordinary branches and transformer branches in a power system. It converts AC power flow constraints into second-order cone constraints and uses the discrete representation rules of transformer tap positions to construct a tap position coupling model, forming a hybrid integer convex relaxation model.

[0028] A mixed integer solving module, which is connected to the unified convex relaxation modeling module, is used to solve the mixed integer convex relaxation model to obtain the convex relaxation power flow solution and the corresponding transformer tap position solution, and to construct a set of tap position influence branches based on the transformer tap position solution;

[0029] The power flow recovery module, connected to the mixed integer solution module, is used to perform power flow equality recovery and ring network phase angle consistency recovery on the convex relaxation power flow solution, taking the set of branches affected by the tap position as the recovery object, and generating the optimal power flow solution that satisfies the original power flow constraints, node power balance constraints, operation safety constraints, ring network phase angle consistency constraints, and transformer integer tap position constraints.

[0030] The beneficial effects of this invention are:

[0031] This invention unifies the second-order conical convex relaxation of ordinary branches with the coupled model of transformer integer tap positions. By using binary tap position representation, tap-side auxiliary variables, and linearized order reduction constraints, it avoids the direct non-convex product between transformer tap positions and power flow variables, and achieves the collaborative solution of AC power flow non-convex constraints and discrete tap position constraints.

[0032] This invention constructs a set of branches affected by transformer tap positions based on the transformer tap position solution, and uses this set as the recovery object to perform power flow equality recovery and ring network phase angle consistency recovery on the convex relaxation power flow solution. This makes the solution not only satisfy the mixed integer convex relaxation model, but also further satisfy the original power flow constraints and transformer integer tap position constraints. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the method flow of Embodiment 1 of the present invention;

[0035] Figure 2 This is a schematic diagram of a typical branch in Embodiment 1 of the present invention;

[0036] Figure 3 This is a schematic diagram of the transformer branch in Embodiment 1 of the present invention;

[0037] Figure 4 This is a schematic diagram of the system modules in Embodiment 2 of the present invention.

[0038] In the picture: , Indicates a branch End and The square of the terminal voltage magnitude , Indicates a branch End and End-injected power, Indicates a branch impedance, Indicates a branch Admittance. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. For some well-known technologies, those skilled in the art may also use other alternative methods to implement the invention. Moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0040] Example 1

[0041] As attached Figure 1 - Appendix Figure 3 As shown, the mixed-integer convex relaxation solution method for optimal power flow in power systems includes the following steps:

[0042] S1. Perform unified convex relaxation modeling on ordinary branches and transformer branches in the power system, convert AC power flow constraints into second-order cone constraints, and construct a tap coupling model using the discrete representation rules of transformer tap positions to form a mixed integer convex relaxation model.

[0043] S11, for ordinary branch lines Its node voltage is expressed as:

[0044] ; indicates a node The voltage is represented in polar coordinates to describe the node. The magnitude and phase state of voltage are fundamental electrical quantities in AC power flow calculations;

[0045] ; indicates a node The voltage is represented in polar coordinates to describe the node. The voltage state and the node The voltage of each component determines the voltage difference and power transmission on the branch.

[0046] Branch current is expressed as: ; indicates from node Flow to Node The branch currents are represented in polar coordinates to describe the magnitude and direction characteristics of the branch currents and to reflect the energy transfer state in the branch.

[0047] Branch power is expressed as: ; indicates from node Flow to Node The branch complex power characterizes the total power state transmitted on the branch, where active power reflects the actual electrical energy consumed or transmitted, and reactive power reflects the power exchange corresponding to the energy stored in the electric and magnetic fields.

[0048] in, Represents a node Voltage, Represents a node Voltage, Indicates a branch Current, Represents a node To node Branch complex power, Represents a node To node The active power of the branch circuit, Represents a node To node The reactive power of the branch circuit, , Indicates the phase angle of the node voltage. Indicates the phase angle of the branch current. Represents the imaginary unit. This indicates the phase information of the current.

[0049] To eliminate the non-convex coupling caused by phase angle variables, the AC power flow equations are dephase-angled, and the following definition is made:

[0050] ; ;in, Represents the squared variable of node voltage. This represents the squared variable of the branch current.

[0051] In AC power flow equations, node voltages and branch currents are typically represented in polar coordinates, which includes both magnitude and phase angle information. However, there are numerous trigonometric functions and complex product operations between voltage and current phase angles. The coupling relationship between these phase angle variables leads to a significant non-convex characteristic in the power flow equations. To reduce the difficulty of solving the equations, phase angle reduction is performed on the AC power flow equations. Instead of directly using voltage and current phase angles as optimization variables, the squares of node voltage magnitudes and branch current magnitudes are used to replace the original complex variable representations. Node voltages are converted into square node voltage variables, and branch currents are converted into square branch current variables. At the same time, the active and reactive power variables of the branches are retained as power transmission characteristics.

[0052] According to Ohm's Law: ;in, Indicates the branch impedance. Indicates the branch resistance. This indicates the branch circuit reactance.

[0053] After substituting the phase-diagonalized variables, the voltage constraint relationship of the ordinary branch can be expressed as follows:

[0054] ;in, Represents a node The squared variable of the node voltage.

[0055] The voltage constraint relationship described above is used to describe the relationship between the voltage at the beginning and end nodes of a common branch and the branch power and branch current.

[0056] S12, based on the power definition at the beginning of the branch: ;

[0057] Multiplying both sides by the conjugate term yields: ;

[0058] Further written as: ;

[0059] Since the above relationship is a non-convex constraint, a second-order cone relaxation method is used: ;

[0060] Further converted to the standard second-order cone constraint form, it can be expressed as: The above constraints constitute the second-order cone constraints of ordinary branches.

[0061] Simultaneously, the node power balance constraint is established as follows:

[0062] ;

[0063] ;

[0064] in, Indicates the active power injected into the node. Indicates the reactive power injected into the node. Represents the set of power grid branches. This represents the complex conjugate operation. Represents nodes Connected adjacent nodes, Indicates a branch The resistance, Indicates a branch The square variable of the current, Indicates from node Flow to Node The active power of the branch circuit, Indicates from node Flow to Node The reactive power of the branch circuit, Indicates a branch The reactance.

[0065] The node power balance constraint and the second-order cone constraint are combined to form a convex relaxation model for ordinary branches. Specifically, in the modeling process of ordinary branches, on the one hand, the second-order cone constraint limits the relationship between active power, reactive power, the square variable of node voltage, and the square variable of branch current on each branch, so that the originally non-convex branch power equation is transformed into a solvable convex constraint; on the other hand, the node power balance constraint limits the balance relationship between the power inflow, power outflow, line loss, and power injected at each node, so that the power flow results of each branch can maintain power conservation throughout the entire network. That is, the second-order cone constraint is responsible for describing the voltage, current, and power relationship within a single ordinary branch, and the node power balance constraint is responsible for describing the connection relationship and power distribution relationship of each ordinary branch at the node. After incorporating both into the same optimization model, the optimization model refers to the model formed by uniformly writing the voltage, current, and power relationship of ordinary branches and the node power balance relationship into the same mathematical solution framework, that is, forming a convex relaxation model for ordinary branches that satisfies both the branch electrical relationship and the node power conservation relationship.

[0066] S13, for the transformer branch, its turns ratio is expressed as: ;in, Indicates the actual ratio. This indicates the minimum turns ratio, which can be obtained from the transformer equipment parameters, nameplate information, and voltage regulation instructions. This represents the change in transformer ratio for a single tap, and is a fixed step size between adjacent taps within the transformer's voltage regulation range. This represents the integer value of the actual tap position of the transformer.

[0067] Gear position is represented by a binary variable:

[0068] ;

[0069] in, For the first Bit binary variable Indicates the number of bits in the gear position code. It is a binary bit sequence number. For the first Bit binary variable The corresponding positional weight.

[0070] Establish the normalized transformation ratio based on the transformer's rated parameters: ;in, Indicates the normalized ratio. Indicates the rated transformer ratio. This represents the actual transformer turns ratio; the normalized turns ratio is used to establish the correspondence between transformer tap positions and branch power flow variables.

[0071] S14, For the transformer branch, introduce an auxiliary variable for the tapped side voltage: ; and auxiliary variables for tap-side current: .

[0072] To eliminate the non-linear product relationship between binary variables and continuous variables, an auxiliary variable is introduced: ; ;in, Indicates the first The voltage coupling auxiliary variable introduced by multiplying the binary variable by the squared auxiliary variable of the tap-side voltage. Indicates the first The current coupling auxiliary variable introduced by multiplying the binary variable by the square auxiliary variable of the tap-side current. Indicates transformer branch The auxiliary variable is the square of the tap-side voltage. Indicates transformer branch The square of the tap-side current is an auxiliary variable.

[0073] Linearization is performed using the Big M method:

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] in, This indicates a pre-defined large constant, for , The auxiliary variable should not be less than the square of the tap-side voltage. To obtain the maximum possible value, first take the upper limit of the node voltage, then convert it to the tap side according to the transformer turns ratio relationship; this will give the maximum possible value of the auxiliary variable, the square of the tap side voltage. , The auxiliary variable should not be less than the square of the tap-side current. The maximum possible value of the auxiliary variable, the square of the branch current, can be obtained by taking the maximum value of the branch current square from the thermal limit of the line, and then amplifying and converting it in combination with the transformer ratio range.

[0083] The above constraints enable a linearized, reduced-order expression between the gear position variable and the power flow variable.

[0084] S15 ensures synchronous mapping of voltage and current variables on the same transformer branch, introducing a unified coupling variable: ;in, Indicates a branch The corresponding unified coupling variable.

[0085] Voltage consistency constraints are established using the aforementioned unified coupling variables: ;

[0086] And current consistency constraints: ;

[0087] This ensures that the tap-side variables and the line-side variables maintain a consistent mapping relationship.

[0088] The following constraints will be further combined:

[0089] (1) Convex relaxation model of ordinary branch;

[0090] (2) Transformer tap coupling relationship;

[0091] (3) Voltage consistency constraints;

[0092] (4) Current consistency constraint;

[0093] (5) Node power balance constraints;

[0094] (6) Line thermal stability constraints: ;in, Indicates the thermal stability limit of the line;

[0095] (7) Generator active power output constraints: ;

[0096] (8) Generator reactive power output constraint: ;

[0097] (9) Node voltage constraints: ;

[0098] The resulting hybrid integer convex relaxation model provides a foundation for subsequent solutions to convex relaxation power flow and transformer tap position problems.

[0099] S2. Solve the mixed integer convex relaxation model to obtain the convex relaxation power flow solution and the corresponding transformer tap position solution, and construct the tap position influence branch set based on the transformer tap position solution.

[0100] S21, the obtained mixed integer convex relaxation model is organized into a model feasible solution object that can be recognized by the mixed integer convex optimization solver. The model feasible solution object that can be recognized by the mixed integer convex optimization solver is composed of objective function, continuous variables, integer variables and constraints.

[0101] Continuous variables include: , , , , , ;in, Represents a node The squared variable of the node voltage, Indicates a branch The squared variable of the branch current, Indicates a branch The branch active power variable, Indicates a branch Branch reactive power variable, Represents a node The node's active power injection variable, Represents a node The reactive power injection power variable at the node.

[0102] For transformer branches, it also includes: ;in, Indicates transformer branch The auxiliary variable is the square of the tap-side voltage. Indicates transformer branch The auxiliary variable is the square of the tap-side current. Indicates transformer branch Unified coupling variables, Indicates the first The binary variable is a voltage-coupled auxiliary variable corresponding to the squared auxiliary variable of the tap-side voltage. Indicates the first The binary variable is a current-coupled auxiliary variable corresponding to the square auxiliary variable of the tap-side current.

[0103] Integer variables include: ;in, Indicates transformer branch The actual gear number (integer value) Indicates transformer branch The Bit binary variable.

[0104] The objective function can be a combination of the generator cost objective and the line loss objective.

[0105] The generator cost target is expressed as: ;in, Indicates the generator cost target; Represents the set of generator nodes. Indicates generator node Those who have made contributions Indicates generator node The fixed cost coefficient represents the fixed operating cost of the unit during the modeling period, and is obtained from the unit's operation and maintenance cost and no-load cost parameters. Indicates generator node The primary cost coefficient represents the portion of power generation cost that increases linearly with active power output, and can be obtained by fitting the primary term of the cost curve. Indicates generator node The quadratic cost coefficient represents the portion of power generation cost that increases non-linearly with active power output, and can be obtained by fitting the quadratic term of the cost curve.

[0106] The line loss target is expressed as: ;in, Indicates the line loss target. Represents the set of power grid branches. Indicates a branch The resistance.

[0107] The overall objective is expressed as: ;in, Indicates the overall objective. Indicates the target weight of generator cost. The target weights for line loss, generator cost, and line loss are determined by the power grid dispatching strategy, operational performance indicators, and economic dispatching requirements.

[0108] The mixed-integer convex optimization solver can also identify feasible solution objects for ordinary branch convex relaxation models:

[0109] ;

[0110] ;

[0111] Or it can be written in the equivalent form of a second-order cone:

[0112] ;

[0113] in: Indicates a branch The reactance.

[0114] The node power balance constraint is:

[0115] ;

[0116] ;

[0117] in, Represents nodes Connected adjacent nodes, They represent the nodes respectively Flow to Node The active power and reactive power of the branch circuit, , They represent the nodes respectively Flow to Node The active power and reactive power of the branch circuit, Representing branches Resistance and reactance, Indicates a branch The squared variable of the branch current.

[0118] The thermal limit constraint of the line is: ;in, Indicates a branch The thermal limit of the line is obtained from the allowable current carrying capacity of the branch equipment.

[0119] The active power output constraint of the generator is: ;

[0120] The reactive power output constraint of the generator is: ;

[0121] in, , Representing generator nodes The lower limit and upper limit of active power output, , Representing generator nodes The lower limit and upper limit of reactive power output, Indicates generator node Those who have made contributions Indicates generator node The effort wasted.

[0122] The node voltage over-limit constraint is: ;in, Represents a node The lower limit of the square of the voltage. Represents a node The upper limit of the square of the voltage.

[0123] The phase angle constraint of the ring network is:

[0124] ;

[0125] ;

[0126] in, Indicates a loop in the power grid. Indicates a branch voltage phase angle difference, Indicates a branch The direction coefficients in the loop direction are traversed sequentially according to the node numbers. Then, the relationship between the branch directions in the loop and the loop direction is determined one by one. If the branch direction is... If the direction of a branch is the same as the direction of the loop traversal, the direction coefficient is +1; if the direction of a branch is opposite to the direction of the loop traversal, the direction coefficient is -1. , Representing branches The lower limit and upper limit of the phase angle difference.

[0127] The objective function and constraints mentioned above together form a feasible solution object that can be recognized by the mixed integer convex optimization solver, and are then input into the mixed integer convex optimization solver.

[0128] A mixed-integer convex optimization solver is a mathematical tool capable of simultaneously handling continuous, integer, or binary variables, where the constraints and objective function satisfy convex optimization form. In this invention, node voltage square variables, branch current square variables, branch active power variables, and branch reactive power variables are continuous variables, while the actual transformer tap position integer and binary tap position variables are integer or binary variables. The second-order cone constraints of ordinary branches, node power balance constraints, line thermal limit constraints, generator output constraints, voltage over-limit constraints, and transformer tap position coupling constraints together constitute a convex constraint system. Therefore, the mixed-integer convex optimization solver is used to solve for minimizing generator cost, line loss, or overall objective while satisfying the above constraints, outputting a convex relaxation power flow solution and a transformer tap position solution. Common implementations can use solvers that support mixed-integer second-order cone programming, such as CPLEX, Gurobi, and MOSEK.

[0129] S21, using the obtained feasible solution object of the model as input, optimize the objective function; according to the actual scheduling requirements, the solution objective can be: , and ;in, This indicates that the goal is to minimize the cost of the generator. This indicates that the goal is to minimize line loss. This indicates that the goal is to minimize the combined cost of generators and line losses.

[0130] The solution obtained after solving is expressed as follows:

[0131] ;

[0132] in, This represents a convex relaxation power flow solution. This represents the squared variable of the node voltage obtained from the solution. This represents the squared variable of the branch current obtained from the solution. This represents the active power variable of the branch obtained from the solution. This represents the reactive power variable of the branch obtained from the solution. This represents the nodal active power injection variable obtained from the solution. This represents the reactive power injection variable obtained from the solution.

[0133] For any ordinary branch If its second-order cone relaxation relation satisfies: If the convex relaxation power flow solution of the branch satisfies the original power flow equation on that branch.

[0134] If it exists: This indicates that there is a slack gap in the branch, and this slack gap will be used to restore the power flow equation in the subsequent combination of the gear position and the branch set.

[0135] When the objective function is the line loss target, or the objective function is a non-decreasing target for the square variable of branch current, the convex relaxation power flow solution can serve as the basis for subsequent power flow equation recovery. That is, the above obtained is the optimal solution that satisfies the mixed integer convex relaxation model. Subsequently, through power flow equation recovery and ring network phase angle consistency recovery, it can be further satisfied to meet the original power flow constraints.

[0136] S23, Read the binary variable values ​​corresponding to each transformer branch from the obtained convex relaxation power flow solution: ;in, Indicates transformer branch The Solving for the value of a binary variable.

[0137] Reconstruct the actual tap position integer value of the transformer based on the binary variable value:

[0138] ;

[0139] in, Indicates transformer branch The actual gear number (integer value) Indicates transformer branch The number of bits in the binary code. Represents the binary bit sequence number. Indicates the first The weight corresponding to the bit binary variable.

[0140] When the actual tap position integer value of the transformer has a valid range, the following conditions must be met: ;in, Indicates transformer branch The total number of gears.

[0141] Then calculate the actual gear ratio based on the actual integer value of the gear: ;in, Indicates transformer branch The actual ratio, Indicates transformer branch The minimum change ratio, Indicates transformer branch The change in single-slot ratio refers to the ratio difference between two adjacent slots of a transformer, which is calculated based on the transformer's minimum ratio, maximum ratio, and total number of slots.

[0142] Further calculation of the normalized ratio:

[0143] ;

[0144] in, Indicates transformer branch The normalized ratio, Indicates transformer branch The rated ratio.

[0145] This leads to the transformer tap position solution: ;in, This indicates the transformer tap position solution. This represents the set of transformer branches.

[0146] The transformer tap position solution is used to characterize the discrete adjustment state of each transformer branch in the optimal power flow solution, and serves as the basis for subsequently constructing the set of branches affected by tap position.

[0147] S24, with the obtained transformer tap position solution As input, identify transformer branches where gear adjustment or gear coupling relationship exists.

[0148] For transformer branch If its actual gear integer value satisfies: Alternatively, if a transformer branch has a tap position coupling relationship, then the transformer branch is defined as a tap position-affected branch; among which, Indicates transformer branch The initial gear integer value.

[0149] The set of transformer branches affected by tap position is defined as follows:

[0150] ;

[0151] in, This represents the set of transformer branches affected by the tap position.

[0152] For any transformer branch affected by the tap position Identify its endpoint nodes or node Connected ordinary branches result in a set of connected ordinary branches:

[0153] ;

[0154] in, Indicates the connection with the transformer branch A set of connected ordinary branches, Represents the set of ordinary branches. , This represents the nodes at both ends of a normal branch.

[0155] The transformer branches affected by the tap position and their connected ordinary branches are collectively represented as the tap position affected branch set as follows:

[0156] ;

[0157] in, This indicates that the gear position affects the set of branch paths.

[0158] To facilitate subsequent power flow equation restoration and ring network phase angle consistency restoration, a restoration record unit is established for each branch in the set of branches affected by the gear position:

[0159] ;

[0160] in, Indicates a branch The recovery record unit, This represents the auxiliary variable representing the square of the tap-side voltage obtained from the solution. This represents the squared auxiliary variable of the tap-side current obtained from the solution. This represents the unified coupling variable obtained from the solution.

[0161] The gear affects the set of branch roads. This clarifies the branch scope for which subsequent power flow equation restoration and ring network phase angle consistency restoration need to be prioritized. This prevents the restoration process from being blindly implemented across the entire network, but instead prioritizes processing branches affected by transformer discrete tap positions and their adjacent ordinary branches, thereby improving the targeting and solution efficiency of the restoration process.

[0162] S3. Using the set of branches affected by the tap position as the recovery object, perform power flow equation recovery and ring network phase angle consistency recovery on the convex relaxed power flow solution to obtain the optimal power flow solution that satisfies the original power flow constraints and the transformer integer tap position constraints.

[0163] S31, the obtained gear affects the set of branches As the object of recovery, from the convex relaxation power flow solution Read each branch affected by gear position Corresponding variables: ;in, Indicates the nodes in the convex relaxation power flow solution The squared variable of the node voltage, Indicates the branch path in the solution of convex relaxation current. The squared variable of the branch current, Indicates the branch path in the solution of convex relaxation current. The branch active power variable, Indicates the branch path in the solution of convex relaxation current. Branch reactive power variable, This indicates that the gear position affects the set of branch paths.

[0164] For each branch affected by the gear Determine whether it satisfies the branch power equation:

[0165] ;

[0166] If satisfied, it means that the branch affected by the block has already satisfied the original branch power flow equation relationship in the convex relaxation power flow solution;

[0167] If it exists: If the result is negative, it indicates that the branch affected by the gear has a relaxation gap and belongs to the strict inequality branch after second-order cone relaxation. The branch affected by the gear is then identified as a branch to be restored.

[0168] The relaxation gap is defined as follows: ;in, Indicates a branch The second-order cone relaxation gap.

[0169] when At that time, the branch power equation holds true;

[0170] when When the branch power equation does not hold, the branch power equation will be applied. Record the branches to be restored in the set:

[0171] ;in, This represents the set of branches to be restored.

[0172] S32, Set of branches to be restored The branches to be restored are restored one by one using the power flow equation, while keeping the squared voltage of the corresponding node constant during restoration, i.e.: ; ;in, Indicates the node after recovery The squared variable of the node voltage, Indicates the node after recovery The squared variable of the node voltage, , This represents the squared variable of the node voltage in the convex relaxation power flow solution. This represents the variable after restoration.

[0173] The reason for keeping the squared variable of the node voltage constant is that the power of the branch to ground is mainly affected by the node voltage. If the node voltage is kept constant during the recovery process, the power of the branch to ground will not change, thus avoiding additional disturbance to the power of the branch to ground during the recovery process.

[0174] For the branch roads to be restored The restored variables are represented as follows: ;in, Indicates the restored branch The branch active power variable, Indicates the restored branch road Branch reactive power variable, Indicates the restored branch road The squared variable of the branch current.

[0175] The restored variables satisfy the original branch power flow equations: ;

[0176] Simultaneously satisfying the ordinary branch voltage constraint relationship: ;

[0177] in, Indicates a branch The resistance, Indicates a branch The reactance.

[0178] When the branch to be restored is a transformer branch, the transformer tap position solution is kept unchanged during the power flow equation restoration process, that is: ; ; ;in, Indicates the transformer branch after restoration The actual gear number (integer value) Indicates the transformer branch after restoration The actual ratio, Indicates the transformer branch after restoration The normalized ratio, This represents the obtained transformer tap position solution.

[0179] The above method only restores the continuous power flow variables without changing the already solved transformer integer tap positions, thus ensuring that the restoration result still satisfies the transformer integer tap position constraints.

[0180] When the objective function is the line loss target, or the objective function is relative to the square of the branch current variable When the objective is non-decreasing, if a strict inequality exists: If the branch current square variable is reduced and the branch power variable is corrected, the branch power equation can be made to hold. Otherwise, if the strict inequality persists for a long time, it means that the objective function value can still be reduced by decreasing the branch current square variable, which contradicts the optimality of the convex relaxation optimal solution. Therefore, it is possible to obtain the restored branch variables that satisfy the original branch power flow equation.

[0181] S33, after completing the power equality restoration of the branch to be restored, further maintain the node power balance and restore the node. The active power balance relationship is as follows:

[0182] ;

[0183] After recovery node The reactive power balance relationship is as follows:

[0184] ;

[0185] in, Represents the set of power grid branches. Indicates the node after recovery The node's active power injection variable, Indicates the node after recovery The reactive power injection variable at the node, Represents nodes Connected adjacent nodes, , These represent the nodes after recovery. Flow to Node The branch active power variable and the branch reactive power variable, , These represent the nodes after recovery. Flow to Node The branch active power variable and the branch reactive power variable, Representing branches Resistance and reactance, Indicates the restored branch road The squared variable of the branch current.

[0186] Branch road to be restored endpoint nodes or node When connecting generator nodes, the power correction amount generated during the recovery process is absorbed by adjusting the active and reactive power output variables of the corresponding generator nodes; if the node If the node is a generator node, then: ; ;in, Indicates the generator node after recovery The active power output variable, Indicates the generator node after recovery The reactive power output variable, Represents a node Active load, Represents a node The reactive load.

[0187] When the endpoint node of the branch to be restored is not connected to the generator node, find the connection path from the endpoint node to the generator node.

[0188] For example, when the node If no generator node is connected, find the slave generator node. To node Connection path:

[0189] ;in, Indicates from generator node To the node The connection path; Indicates the generator node. Indicates the connection path with the node The adjacent upstream node.

[0190] For branches in the connection path According to the node The power correction amount is used to update the branch power variable:

[0191] ; ;in, , These represent the branches after restoration. The branch active power variable and the branch reactive power variable, , They represent the branches in the solution of convex relaxed power flow, respectively. The branch active power variable and the branch reactive power variable, Represents a node The active power correction is obtained by comparing the active power balance difference between the node to be restored in the convex relaxed power flow solution state and the power flow equation restoration state. Represents a node The reactive power correction is determined by first determining the original reactive power balance state of the node based on the branch reactive power, the square variable of the branch current, and the line reactance in the convex relaxation power flow solution; then determining the restored reactive power balance state based on the restored branch reactive power, the square variable of the branch current, and the line reactance according to the power flow equation. The reactive power difference between the two is the reactive power correction for that node.

[0192] Then along the connection path The power correction is transmitted upstream node by node until it reaches the generator node. and by generator node Compensation is achieved by adjusting the active power output variables and reactive power output variables.

[0193] Since power systems typically use balancing nodes or generator nodes as the starting nodes for power flow, and in actual operation each load node is usually connected to at least one generator node via a network path, the restored node power balance can be maintained through the above-mentioned path transmission method.

[0194] After the above processing, the recovered solution of the power flow equation is obtained: ;in, This indicates the solution to the power flow equation.

[0195] S34, Recovering the solution based on the obtained power flow equation Calculate the phase angle difference of the branch voltage for each branch; for ordinary branches... The branch voltage phase angle difference, calculated based on the restored node voltage squared variable, branch active power variable, branch reactive power variable, and branch parameters, is expressed as follows:

[0196] ;

[0197] in, Indicates the restored branch road The branch voltage phase angle difference, This represents the arctangent function that determines the quadrant based on the numerator and denominator terms.

[0198] For transformer branches, the restored normalized transformer ratio is used when calculating the branch voltage phase angle difference. The variables on the tap side are calculated while keeping the transformer tap solution unchanged.

[0199] For any loop in the power grid Determine whether it satisfies the ring network phase angle consistency constraint:

[0200] ;

[0201] Or, within the allowable error range, the following conditions must be met: ;

[0202] in, Indicates a loop in the power grid. Indicates a branch The directional coefficient in the loop direction, This indicates the allowable error for phase angle consistency, which is preset based on the power flow calculation accuracy, solver numerical tolerance, and power grid operation verification requirements.

[0203] If a certain loop does not meet the ring network phase angle consistency constraint, then under the condition of keeping the transformer tap position solution unchanged, the branch power variable of the branch to be restored in the loop is restored to phase angle consistency.

[0204] That is, to maintain: ; and for the ring road , , Make corrections to ensure that the corrections simultaneously satisfy the branch power flow equations and the ring network phase angle consistency constraints.

[0205] After completing the phase angle consistency recovery, the phase angle consistency recovery solution is obtained:

[0206] ;

[0207] in, This represents the phase angle consistency recovery solution.

[0208] S35, obtain the phase angle consistency recovery solution With the obtained transformer tap position solution By combining the results, the optimal power flow solution is generated: ;in, This represents the final optimal power flow solution. This represents the phase angle consistency recovery solution. This indicates the transformer tap position solution.

[0209] Specifically, the optimal power flow solution includes:

[0210] ;

[0211] in, Indicates transformer branch The actual gear number (integer value) Indicates transformer branch The actual ratio, Indicates transformer branch The normalized ratio.

[0212] Before outputting the optimal power flow solution, perform constraint checks on it:

[0213] Verify the original branch power flow equations:

[0214] ;

[0215] Verify the voltage constraint relationship of ordinary branches:

[0216] ;

[0217] Verification of node power balance constraints:

[0218] ;

[0219] ;

[0220] Verify operational safety constraints:

[0221] ;

[0222] in, Indicates a branch The thermal limit of the circuit, , Representing generator nodes The lower limit and upper limit of active power output, , Representing generator nodes The lower limit and upper limit of reactive power output, , Representing nodes respectively The lower limit of the square of the node voltage and the upper limit of the square of the node voltage.

[0223] Finally, check the integer tap constraints of the transformer:

[0224] ;

[0225] ;

[0226] ;

[0227] ;

[0228] in, Represents a set of integers. Indicates transformer branch The minimum gear integer value, Indicates transformer branch The maximum gear integer value, Indicates transformer branch The change in single-gear ratio. Indicates transformer branch The rated ratio.

[0229] When all the above checks are satisfied, the optimal power flow solution is output. The optimal power flow solution simultaneously satisfies the original power flow constraints, node power balance constraints, operational safety constraints, ring network phase angle consistency constraints, and transformer integer tap constraints, thereby completing the recovery from the convex relaxation power flow solution to the feasible optimal power flow solution.

[0230] Example 2

[0231] like Figure 4 The mixed integer convex relaxation solution system for optimal power flow in a power system, shown below, includes the following modules:

[0232] A unified convex relaxation modeling module is used to perform unified convex relaxation modeling on ordinary branches and transformer branches in a power system. It converts AC power flow constraints into second-order cone constraints and uses the discrete representation rules of transformer tap positions to construct a tap position coupling model, forming a hybrid integer convex relaxation model.

[0233] A mixed integer solving module, which is connected to the unified convex relaxation modeling module, is used to solve the mixed integer convex relaxation model to obtain the convex relaxation power flow solution and the corresponding transformer tap position solution, and to construct a set of tap position influence branches based on the transformer tap position solution;

[0234] The power flow recovery module, connected to the mixed integer solution module, is used to perform power flow equality recovery and ring network phase angle consistency recovery on the convex relaxation power flow solution, taking the set of branches affected by the tap position as the recovery object, and generating the optimal power flow solution that satisfies the original power flow constraints, node power balance constraints, operation safety constraints, ring network phase angle consistency constraints, and transformer integer tap position constraints.

[0235] Example 3

[0236] The optimal power flow model of this invention was tested in IEEE Case 9, IEEE Case 14, IEEE Case 30, IEEE Case 57, IEEE Case 118, and IEEE Case 300, and the effectiveness of the invention was demonstrated by the maximum phase angle difference and line loss.

[0237] Table 1 shows the maximum phase angle difference on each branch of the power flow solution before and after optimization, in degrees. This invention uses phase angle relaxation to obtain a convex optimization model and adds phase angle difference constraints using an approximation method. If the branch phase angle difference is too large, it will lead to instability in the power grid operation. The maximum phase angle difference of the optimized power flow solution is smaller than that of the unoptimized power flow solution, thus ensuring the effectiveness of the power flow solution.

[0238] Table 1 Maximum phase angle difference of branches

[0239]

[0240] Table 2 shows the line loss of the power flow solution before and after optimization. The line loss of the optimized power flow solution is significantly smaller than that of the unoptimized solution. Since the cone relaxation can be accurately recovered, this invention can provide a better power flow solution.

[0241] Table 2 Line loss before and after optimization

[0242]

[0243] Test results on the IEEE test set show that the optimized results are significantly better than the unoptimized results, proving the effectiveness of the present invention.

[0244] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0245] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A mixed-integer convex relaxation solution method for optimal power flow in power systems, characterized in that, Includes the following steps: A unified convex relaxation model is performed based on ordinary branches and transformer branches in the power system, transforming AC power flow constraints into second-order cone constraints. A tap coupling model is constructed using the discrete representation rules of transformer tap positions to obtain a mixed integer convex relaxation model; The mixed integer convex relaxation model is solved to obtain the convex relaxation power flow solution and the corresponding transformer tap solution, and the set of tap-affected branches is constructed based on the transformer tap solution. Based on the set of branches affected by the gear position as the recovery object, power flow equation recovery and ring network phase angle consistency recovery are performed on the convex relaxed power flow solution; Obtain the optimal power flow solution that satisfies the original power flow constraints and the transformer integer tap constraints; The binary variable values ​​corresponding to the transformer branch are read from the convex relaxation power flow solution, and the actual tap position integer value of the transformer is restored based on the binary variable values ​​as follows: ;in, Indicates transformer branch The actual gear position integer value, Indicates transformer branch The number of bits in the binary code. Represents the binary bit sequence number. Indicates the first The weights corresponding to the binary variables are then used to determine the normalized transformer ratio based on the actual integer value of the transformer tap position, thus obtaining the transformer tap position solution. Based on the transformer tap position identification, transformer branches that have undergone tap position adjustment or have tap position coupling relationships are identified. These transformer branches and the ordinary branches connected to them are determined as tap position affected branches. All tap position affected branches are then summarized into a tap position affected branch set, represented as follows: ;in, This indicates that the gear position affects the set of branch paths. Indicates the connection with the transformer branch A set of connected ordinary branches, This represents the set of transformer branches affected by the tap position, and the set of branches affected by the tap position is used for subsequent power flow equation restoration and ring network phase angle consistency restoration; Taking the set of branches affected by the gear position as the recovery object, the squared variables of node voltage, squared variables of branch current, active power, and reactive power of each branch affected by the gear position are read from the convex relaxation power flow solution. It is then determined whether each branch affected by the gear position satisfies the branch power equation. Branches affected by the gear position that do not satisfy the branch power equation are identified as branches to be recovered, represented as follows: ;in, This represents the set of branches to be restored. Indicates a branch The second-order cone relaxation gap; For the branch to be restored, while keeping the corresponding node voltage square variable unchanged, the branch current square variable, branch active power variable and branch reactive power variable of the branch to be restored are restored by power flow equation, so that the restored branch active power variable, branch reactive power variable, node voltage square variable and branch current square variable satisfy the original branch power flow equation relationship.

2. The hybrid integer convex relaxation solution method for optimal power flow in power systems according to claim 1, characterized in that, The node voltages, currents, and power of ordinary branches are de-phased. The voltage, current, and power relationships in the AC power flow equations are characterized using the square variables of node voltages, the square variables of branch currents, and the active and reactive power variables of the branches. The voltage constraint relationship of the ordinary branches is established according to Ohm's law as follows: ;in, Represents a node The squared variable of the node voltage, Represents a node The squared variable of the node voltage, Indicates the branch resistance. Represents a node To node The active power of the branch circuit, Indicates branch reactance, Represents a node To node The reactive power of the branch circuit, This represents the squared variable of the branch current.

3. The hybrid integer convex relaxation solution method for optimal power flow in power systems according to claim 2, characterized in that, Based on the active power, reactive power, squared variable of node voltage, and squared variable of branch current, a power constraint at the beginning of the branch is constructed, and the power constraint at the beginning of the branch is converted into a second-order cone form constraint as follows: ,in, Represents a node To node The active power of the branch circuit, Represents a node To node The reactive power of the branch circuit, Represents a node The squared variable of the node voltage, This represents the squared variable of the branch current, and is combined with the node power balance constraint to form a general branch convex relaxation model; For transformer branches, the transformer taps are represented as discrete integer taps, and binary variables are used to encode the discrete integer taps. The correspondence between the transformer taps and the branch parameters is established based on the normalized transformer ratio.

4. The hybrid integer convex relaxation solution method for optimal power flow in power systems according to claim 3, characterized in that, Auxiliary variables for tap-side voltage and tap-side current are introduced on the transformer tap side, and the tap-side coupling relationship between these binary variables and the auxiliary variables for tap-side voltage and current is constructed as follows: ; ;in, Indicates the first The voltage coupling auxiliary variable introduced by multiplying the binary variable by the squared auxiliary variable of the tap-side voltage. Indicates the first The current coupling auxiliary variable introduced by multiplying the binary variable by the square auxiliary variable of the tap-side current. Indicates transformer branch The auxiliary variable is the square of the tap-side voltage. Indicates transformer branch The auxiliary variable is the square of the tap-side current. For the first The nonlinear product relationship between the gear position variable and the power flow variable is eliminated by linearizing the order reduction constraint; Voltage consistency constraints and current consistency constraints between the transformer tap side and the line side are established using unified coupling variables. The ordinary branch convex relaxation model, tap coupling relationship, voltage consistency constraints, current consistency constraints, node power balance constraints, and operation safety constraints are combined to form the hybrid integer convex relaxation model.

5. The hybrid integer convex relaxation solution method for optimal power flow in power systems according to claim 1, characterized in that, The objective function, ordinary branch convex relaxation model, transformer tap coupling model, node power balance constraint, and line thermal limit constraint in the hybrid integer convex relaxation model are defined as follows: The active power output constraint of the generator is: The reactive power output constraint of the generator is: The node voltage limit constraints and ring network phase angle constraints are input together into the mixed integer convex optimization solver to obtain the feasible solution object of the model. Indicates a branch The thermal limit of the circuit, , Representing generator nodes The lower limit and upper limit of active power output, , Representing generator nodes The lower limit and upper limit of reactive power output, Indicates generator node Those who have made contributions Indicates generator node The effort wasted.

6. The hybrid integer convex relaxation solution method for optimal power flow in power systems according to claim 5, characterized in that, Based on the feasible solution object of the aforementioned model, optimization is performed to obtain the convex relaxed power flow solution under the objectives of minimizing generator cost, minimizing line loss, or minimizing both generator cost and line loss: ,in, This represents a convex relaxation power flow solution. This represents the squared variable of the node voltage obtained from the solution. This represents the squared variable of the branch current obtained from the solution. This represents the active power variable of the branch obtained from the solution. This represents the reactive power variable of the branch obtained from the solution. This represents the nodal active power injection variable obtained from the solution. The term "node reactive power injection variable" represents the obtained nodal reactive power injection variable. The convex relaxation power flow solution includes the node voltage square variable, branch current square variable, branch active power variable, branch reactive power variable, nodal active power injection variable, and nodal reactive power injection variable.

7. The hybrid integer convex relaxation solution method for optimal power flow in power systems according to claim 6, characterized in that, When the endpoint node of the branch to be restored is connected to the generator node, the node power balance is maintained by adjusting the active power output variable and reactive power output variable of the corresponding generator node; when the endpoint node of the branch to be restored is not connected to the generator node, the connection path from the endpoint node to the generator node is found, and the branch power correction is passed step by step along the connection path until the generator node in the connection path completes the output compensation, and the power flow equation restoration solution is obtained. Based on the power flow equation recovery solution, calculate the branch voltage phase angle difference in each loop, and determine whether the branch voltage phase angle difference in each loop meets the ring network phase angle consistency constraint; if not, under the condition of keeping the transformer tap solution unchanged, perform phase angle consistency recovery on the branch power variable of the branch to be recovered in the loop to obtain the phase angle consistency recovery solution. The phase angle consistency recovery solution is combined with the transformer tap position solution to generate the optimal power flow solution that satisfies the original power flow constraints, node power balance constraints, operation safety constraints, ring network phase angle consistency constraints, and transformer integer tap position constraints.

8. A hybrid integer convex relaxation solution system for optimal power flow in power systems, used to implement the hybrid integer convex relaxation solution method for optimal power flow in power systems as described in any one of claims 1-7, characterized in that, Includes the following modules: A unified convex relaxation modeling module is used to perform unified convex relaxation modeling on ordinary branches and transformer branches in a power system. It converts AC power flow constraints into second-order cone constraints and uses the discrete representation rules of transformer taps to construct a tap coupling model, forming a hybrid integer convex relaxation model. A mixed integer solving module, which is connected to the unified convex relaxation modeling module, is used to solve the mixed integer convex relaxation model to obtain the convex relaxation power flow solution and the corresponding transformer tap solution, and to construct a set of tap-influenced branches based on the transformer tap solution; The power flow recovery module, connected to the mixed integer solution module, is used to perform power flow equality recovery and ring network phase angle consistency recovery on the convex relaxation power flow solution, taking the set of branches affected by the tap position as the recovery object, and generating the optimal power flow solution that satisfies the original power flow constraints, node power balance constraints, operation safety constraints, ring network phase angle consistency constraints, and transformer integer tap position constraints.

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