New-power-system power grid restoration method and apparatus based on second-order cone transformation

Abstract

A new-power-system power grid restoration method and apparatus based on second-order cone transformation. The method comprises: acquiring power data of a new power system (101); on the basis of the power data and taking the output uncertainty of a new energy unit into consideration, constructing a mixed-integer nonlinear two-stage robust optimization model based on a multi-state uncertainty set (102), wherein the model comprises an alternating-current power flow constraint; using a second-order cone relaxation technique to simplify the alternating-current power flow constraint, and converting the mixed-integer nonlinear two-stage robust optimization model into a mixed-integer second-order cone two-stage robust optimization model (103); decomposing the mixed-integer second-order cone two-stage robust optimization model into a main question and a sub-question, and solving the main question and the sub-question, so as to obtain an optimization result (104); and on the basis of the optimization result, generating a power grid restoration scheme for the new power system (105).

Description

New power system grid restoration method and device based on second-order cone transformation

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on December 25, 2023, with application number 202311798821.X. The entire contents of this application are incorporated by reference into this application. Technical Field

[0002] The present application relates to the field of electric power technology, and in particular to a novel method and device for restoring an electric power system grid based on second-order cone transformation. Background Art

[0003] With the advancement of policies related to "carbon peak and carbon neutrality," the integration and output of renewable energy sources such as wind power and photovoltaics into power grids across the country are increasing. The construction of new power systems primarily based on renewable energy generation has been rapidly underway and is showing signs of accelerating development. Due to the unavoidable occurrence of grid failures and large-scale power outages, coupled with the volatility and poor controllability of renewable energy generation, the risk of localized or even large-scale power outages in these new systems is significant. While no serious large-scale power outages have occurred, many regions have been forced to implement varying degrees of orderly power consumption and peak-shifting measures to ensure safe grid operation while prioritizing power supply to critical loads. Therefore, the gradual increase in the integration and output of renewable energy sources, which is closely linked to meteorological conditions, while achieving greener, more environmentally friendly, and sustainable grid operation and development, also increases the risk of localized or even large-scale power outages. Active responses are therefore necessary to minimize the risk and losses of these devastating events.

[0004] A scientific and rational emergency plan centered around black start and system recovery solutions is the best response to large-scale power outages. This plan can quickly restore power to the grid and significantly reduce the political and economic losses caused by outages. With the development of new power systems, renewable energy units can operate independently in a network, providing active support and autonomous operation for the grid, making them potential black start power sources. Therefore, in regional power grids with a high proportion of renewable energy installed, the black start support capabilities of renewable energy units can be fully utilized. Research on using renewable energy units as black start power sources after severe grid failures not only provides a new solution for system recovery and accelerates grid and load recovery after major power outages, but also plays a significant role in shortening outage duration and ensuring national energy security and social stability.

[0005] In new power systems, the randomness of renewable energy output and load recovery increases the volatility of the power grid. In system recovery optimization problems, when the uncertainty variables fluctuate greatly, the objective function decision is difficult and the solution cannot meet the actual needs. Currently, considering the uncertainty of renewable energy unit output and load demand during system recovery, the commonly used methods are stochastic optimization and robust optimization. Stochastic optimization methods require a scenario reduction strategy to obtain their approximate solutions, and the quality and speed of the solution are difficult to meet the requirements at the same time. Compared with stochastic optimization models, robust optimization methods have the obvious advantages of not requiring the probability information of uncertain variables that are difficult to accurately grasp, but only the operating range information of uncertain variables, and fast calculation speed. However, they can only adapt to linear constraints, and the current linearization processing technology is not efficient, which affects its performance. Therefore, there is an urgent need for an optimization method that considers the probability information of the uncertainty variables of renewable energy output to solve the problem of low efficiency of the linearization processing technology of conventional power grid recovery methods.

[0006] Summary of the Invention

[0007] The embodiments of the present application provide a novel power system grid restoration method and device based on second-order cone transformation, which considers the probability information of uncertainty variables of new energy output to solve the problem of low efficiency of linear processing technology of conventional grid restoration methods.

[0008] In a first aspect, an embodiment of the present application provides a novel power system grid restoration method based on second-order cone transformation, comprising:

[0009] Obtain power data for new power systems;

[0010] Based on power data and considering the uncertainty of renewable energy unit output, a two-stage robust optimization model of the new power system based on mixed integer nonlinearity and multi-state uncertainty sets is constructed. The two-stage robust optimization model of the mixed integer nonlinearity includes AC power flow constraints.

[0011] The second-order cone relaxation technique is used to simplify the AC power flow constraints and transform the mixed-integer nonlinear two-stage robust optimization model into a mixed-integer second-order cone two-stage robust optimization model.

[0012] The two-stage robust optimization model of mixed integer second-order cone is decomposed into a main problem and sub-problems, and the main problem and sub-problems are solved to obtain the optimization results;

[0013] Based on the optimization results, a grid restoration plan for the new power system is generated.

[0014] In a second aspect, an embodiment of the present application provides a power grid restoration device in a power system based on a second-order cone transformation, comprising:

[0015] A data acquisition module configured to acquire power data of a new power system;

[0016] The model building module is set up to build a two-stage robust optimization model of the new power system based on mixed integer nonlinearity and multi-state uncertainty sets based on power data and considering the uncertainty of the output of new energy units. The two-stage robust optimization model of the mixed integer nonlinearity includes AC power flow constraints.

[0017] The first calculation module is configured to simplify the AC power flow constraints by using a second-order cone relaxation technique, and transform the two-stage robust optimization model as a mixed integer nonlinearity into a two-stage robust optimization model of a mixed integer second-order cone;

[0018] The second computing module is configured to decompose the two-stage robust optimization model of mixed integer second-order cone into a main problem and sub-problems, solve the main problem and the sub-problems, and obtain an optimization result;

[0019] The scheme generation module is configured to generate a grid restoration scheme for a new power system based on the optimization results. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to illustrate the embodiments of the present application, the drawings required for use in the description of the embodiments will be introduced below. The drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0021] FIG1 is a flow chart of a novel power system grid restoration method based on second-order cone transformation provided by an embodiment of the present application;

[0022] FIG2A is a schematic diagram of the state of the daily power value of the first wind farm provided by an embodiment of the present application;

[0023] FIG2B is a schematic diagram of the state of the second wind farm daily power value provided by an embodiment of the present application;

[0024] FIG2C is a schematic diagram of the state of the third wind farm daily power value provided by an embodiment of the present application;

[0025] FIG3 is a schematic diagram of the IEEE39 node system recovery provided in an embodiment of the present application;

[0026] FIG4 is a schematic diagram of the IEEE118 node system recovery provided in an embodiment of the present application;

[0027] FIG5A is a diagram of an embodiment of the present application, which takes the IEEE118 node system as the research object, and the order of magnitude is 10 -16 Schematic diagram of low nonlinearity error of all branches;

[0028] FIG5B is a diagram of an embodiment of the present application, which takes the IEEE118 node system as the research object, and the order of magnitude is 10 -8 Schematic diagram of low nonlinearity error of all branches;

[0029] FIG6 is a schematic diagram of relaxation errors of voltage and phase angle provided in an embodiment of the present application;

[0030] FIG7 is a schematic structural diagram of a power grid restoration device in an electric power system based on second-order cone transformation according to an embodiment of the present application. DETAILED DESCRIPTION

[0031] In the following description, details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these details. In other cases, descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0032] The following will be described through embodiments with reference to the accompanying drawings.

[0033] FIG1 is a flow chart of a novel power system grid restoration method based on second-order cone transformation provided in an embodiment of the present application, which includes the following steps.

[0034] Step 101: Acquire power data of a new power system.

[0035] First, the predicted generator start-up sequence, bus and line charging sequence, and load recovery sequence in the decision-making power grid are obtained, and the unit output and load recovery amount including new energy units are obtained. These data are used as the first-stage power data of the new power system under the expected scenario.

[0036] Secondly, the output of the re-dispatched units and the restored load are obtained as the second-stage power data of the new power system under the worst energy fluctuation scenario.

[0037] Step 102 : Based on the power data and taking into account the uncertainty of the output of the new energy units, a two-stage robust optimization model based on a mixed integer nonlinear multi-state uncertainty set is constructed.

[0038] Among them, the mixed integer nonlinear two-stage robust optimization model includes AC power flow constraints.

[0039] For example, a mixed-integer nonlinear two-stage robust optimization model for a novel power system is established, with the goals of minimizing power outage losses under a desired scenario and minimizing system power outage losses and load adjustment under a worst-case energy fluctuation scenario. The mixed-integer nonlinear two-stage robust optimization model includes a first-stage objective function and a second-stage objective function.

[0040] The objective function of the two-stage robust optimization model with mixed integer nonlinearity is expressed as:

[0041] in, represents the first stage objective function; represents the second stage objective function; N T The number of time periods in the new power system restoration process is represented by ΔT, and the total restoration time is N. S , and assume that the black start unit and the node where it is located are restored at time 0; represents the state of the i-th busbar node in time period s, A value of 1 indicates that the i-th busbar node has been restored. A value of 0 indicates that the i-th busbar node has not been restored; represents the state of the i-th load node in period s, A value of 1 indicates that the i-th load node has recovered. A value of 0 indicates that the i-th load node has not recovered; represents the state of the i-th unit node in time period s, A value of 1 indicates that the i-th unit node has recovered. A value of 0 indicates that the i-th unit node has not recovered. Here, The i-th unit node in is for all units, including conventional units and new energy units. When it is for new energy units, i=r; Indicates whether the line connecting node (i, j) is restored in time period s, A value of 1 indicates that the node has recovered. A value of 0 indicates that the node has not recovered; represents the active power output of the i-th conventional unit in time period s under the expected scenario; represents the reactive power output of the i-th conventional unit in time period s under the expected scenario; represents the actual active power output of the rth renewable energy unit in time period s; W represents the load restored by the i-th load node in period s, i，d represents the load weight coefficient of the i-th load node; represents the active power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; represents the reactive power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; It represents the actual active power output of the rth renewable energy unit in time period s after adjustment in the rescheduling stage; represents the load restored by the i-th load node in time period s after adjustment in the rescheduling phase; N BUS Indicates the total number of all bus nodes; The outer optimization variable of the second stage objective function.

[0042] As mentioned above, under the expected scenario, the output of units including conventional units and new energy units and the restored load are all predicted values.

[0043] The mixed integer nonlinear two-stage robust optimization model also includes conventional unit output characteristic constraints, new energy unit output uncertainty constraints based on multi-state uncertainty sets, new energy unit actual output constraints, node voltage constraints, line transmission power constraints, equipment recovery state constraints, line allowed recovery time constraints, system frequency constraints and node power balance constraints.

[0044] Among them, the output characteristic constraints of conventional units include output constraints before conventional units are connected to the grid, output ramp constraints of conventional units, output constraints of conventional units and cold / hot start time constraints of conventional units.

[0045] The output constraint of conventional units before grid connection is expressed as:

[0046] in, represents the active power output of the i-th conventional unit in time period s under the expected scenario; represents the reactive power output of the i-th conventional unit in period s under the expected scenario, t 1，i = represents the time when the i-th conventional unit starts to be connected to the grid. Formula (2) shows that the active output and reactive output of the i-th conventional unit are both 0 before being connected to the grid.

[0047] The output ramp constraint of conventional units is expressed as:

[0048] t 2，i Indicates the moment when the output of the i-th conventional unit reaches the minimum output; Rm i Indicates the ramp rate of conventional unit i. represents the active power output of the i-th conventional unit in period s-1 under the expected scenario, where period s-1 is the period before period s; j represents the j-th period, j = 0, 1, ..., s; Formula (3) indicates that after the i-th conventional unit is connected to the grid and before it reaches the minimum power output, the active power of the i-th conventional unit must meet the one-way ramp constraint; Formula (4) represents the upper and lower limit constraints of the active power after the i-th conventional unit reaches the minimum power output.

[0049] The output constraint of conventional units is expressed as:

[0050] in, represents the upper limit of the active power output of the i-th conventional unit; p i，g represents the lower limit of the active power output of the i-th conventional unit; represents the upper limit of reactive power output of the i-th conventional unit; q i，g represents the lower limit of the reactive power output of the i-th conventional unit; Equation (5) represents the upper and lower limit constraints of the reactive power after the i-th conventional unit is connected to the grid; Equation (6) represents the ramp constraint that must be met after the active power of the i-th conventional unit reaches the minimum output.

[0051] The cold / hot start time constraint of conventional units is expressed as:

[0052] in, represents the time that the i-th conventional unit has been shut down before the black start time 0; Indicates the maximum startup time limit of the i-th conventional unit from shutdown to restart. If the i-th conventional unit has no hot start time limit, then Take a very large number, in this embodiment is the minimum startup time limit of the i-th conventional unit from shutdown to restart. If the i-th conventional unit has no cold start time limit, then represents the state of the i-th unit node in time period s+1, A value of 1 indicates that the i-th unit node has recovered. The value of 0 indicates that the node of the i-th unit has not been restored, and the period s+1 is the next period of period s. Formula (7) indicates that the i-th conventional unit to be hot-started should be restored within its maximum hot-start time limit. The cold-start unit must be shut down for a minimum of time, and then it can be started again. Formula (8) is its corresponding constraint expression.

[0053] In view of the uncertainty constraints of the output of new energy units, a multi-state uncertainty set U is constructed to describe the uncertainty of the output of new energy units. The multi-state uncertainty set U of the uncertainty constraints of the output of new energy units is expressed as:

[0054] in, It represents the predicted value of the active power output of the rth renewable energy unit in time period s under the expected scenario; is the output corresponding to the zth state of the rth new energy unit in time period s; is 0 or 1, Indicates that the output of the rth new energy unit is in state z during period s, Indicates that the output of the rth renewable energy unit is not in state z during time period s; N is the total number of states; Γ g，p The budget value of renewable energy power generation is the limit of fluctuation within the recovery period; Ω E is the set of nodes connected to the new energy generating units; R is a set of rational numbers. Formula (9) indicates that the power of the rth new energy generating unit at time t is the power value of all states The linear combination of ; Formula (10) indicates that at the same time, the output of the new energy unit can only be in one state, such as the minimum value, maximum value, expected value or average value, and the state can even be further refined to take into account more states; Formula (11) is a generalized budget constraint, which is used to limit the fluctuation of the output of the new energy unit.

[0055] For example, the output data of three wind farms within a period of time are selected, with the horizontal axis representing time (hours) and the vertical axis representing output value (megawatts). FIG2A is a state diagram of the output value of the first wind farm per day, FIG2B is a state diagram of the output value of the second wind farm per day, and FIG2C is a state diagram of the output value of the third wind farm per day. The uncertainty variable (wind power output) is subjected to historical statistical analysis and quantile regression approximation technology to obtain the state value corresponding to each state (s=1, 2, 3; t=1, ..., 24). Considering that the number of output states of the wind farm in each period is 3, namely the maximum value (Max), average value (Avg) and minimum value (Min), the curves from top to bottom represent the state values ​​corresponding to the output of new energy.

[0056] The actual output constraint of new energy units is expressed as:

[0057] Formula (12) indicates that the actual active power output of the rth renewable energy unit in time period s does not exceed the predicted value

[0058] The node voltage constraint is expressed as:

[0059] in, represents the voltage amplitude of the connection node i in time period s; represents the voltage amplitude of the connection node j in time period s, V minRepresents the lower limit of all node amplitudes, V max Indicates the upper limit of all node amplitudes. Equation (13) indicates that the node voltage should be guaranteed to be within the normal operating range.

[0060] The line transmission power constraint is expressed as:

[0061] represents the active power flowing through the line between the connecting nodes (i, j) in time period s, p ij，max Represents the upper limit of the active power flowing through the line between the connecting nodes (i, j); Ω L Represents the line set. Equation (14) indicates that the power transmitted by the line should not exceed its specified maximum power.

[0062] The device recovery state constraint is expressed as:

[0063] Equations (15) and (16) indicate that the generator and load can only be started after the busbar to which they are connected is energized; Equations (17) and (18) indicate that if the line is restored in period s, then at least one of the buses to which it is connected has been restored in period s; Equation (19) indicates that when an end node i (or j) of branch 1 is restored in period s, if branch 1 is restored in period s, then the other node j (or i) of branch 1 must also be restored in period s, and the end node of the line is restored at the same time as the line, thereby speeding up the subsequent network recovery process; Equation (20) indicates that if a busbar is restored in period s, then at least one of the lines connected to the busbar is restored in period s; Equation (21) indicates that once the busbar is restored, it will not be cut off; Equation (22) indicates that once the line is restored, it will not be cut off; Equation (23) indicates that once the load is restored, it will not be cut off; Equation (24) indicates that once the generator is restored, it will not be cut off.

[0064] The allowed restoration time constraint of the line is expressed as:

[0065] This embodiment introduces the maximum number of recoverable layers k allowed in each time period to prevent the calculation from being too long due to the number of recovery layers being too large and the corresponding search range being too large. In the formula, N BS-l is the set of nodes included in each feasible path from the black start power source to line l, Indicates a ceiling operation.

[0066] The system frequency constraint is expressed as:

[0067] Where ΔP is the total power or load required by the units to be started during the current period; Kg i , Kl i，dare the frequency power effect coefficients of the i-th conventional unit and the load respectively; Kl i，d Take 1 to 3, Kl i，d The value depends on the load type. Equation (26) indicates that the sum of all auxiliary power (or maximum load) of the units to be started must be less than or equal to the maximum power that can be used to start the equipment under the maximum allowable frequency drop of the restored network in the current period.

[0068] The node power balance constraint is expressed as:

[0069] Equations (27) and (28) are the active power and reactive power of each node in the line loss between nodes (i, j) in time period s.

[0070] The AC power flow constraint is expressed as:

[0071] Among them, G ij represents the conductance value of the line connecting nodes (i, j), B ij represents the susceptance value of the line connecting nodes (i, j); represents the active power flowing through the line between the connecting nodes (i, j) in time period s; represents the reactive power flowing through the line between the connecting nodes (i, j) in time period s; represents the active power flowing through the line between the connecting nodes (j, i) in time period s; represents the reactive power flowing through the line between the connecting nodes (j, i) in time period s; represents the loss of active power of the line between the connecting nodes (i, j) in time period s; represents the reactive power loss of the line between nodes (i, j) in time period s; represents the state of the line connecting nodes (i, j) in time period s, A value of 1 indicates that the node has recovered. A value of 0 indicates that the node has not recovered; represents the voltage amplitude of the connection node i in time period s; represents the voltage amplitude of the connection node j in time period s; express and The phase angle.

[0072] Step 103 , using the second-order cone relaxation technique to simplify the AC power flow constraints, transforming the mixed-integer nonlinear two-stage robust optimization model into a mixed-integer second-order cone two-stage robust optimization model.

[0073] The second-order cone relaxation technique is used to simplify the AC power flow constraints, including: performing variable substitution on the voltage phase angle cross term of the AC power flow constraints of the two-stage robust optimization model for system recovery to obtain the AC power flow constraints after variable substitution.

[0074] Among them, and Denotes the voltage phase angle cross term, using and represents the voltage squared term.

[0075] The second-order cone relaxation constraint is added to the AC power flow constraint after variable substitution to obtain the simplified AC power flow constraint.

[0076] The second-order cone relaxation constraint is expressed as:

[0077] The simplified AC power flow constraint is expressed as:

[0078] in, represents the voltage amplitude of the connection node i in time period s; represents the voltage amplitude of the connection node j in time period s; express and The phase angle; express The square of express The square of G ij represents the conductance value of the line connecting nodes (i, j), B ij represents the susceptance value of the line connecting nodes (i, j); represents the active power flowing through the line between the connecting nodes (i, j) in time period s; represents the reactive power flowing through the line between the connecting nodes (i, j) in time period s; represents the active power flowing through the line between the connecting nodes (j, i) in time period s; represents the reactive power flowing through the line between the connecting nodes (j, i) in time period s; represents the active power loss of the line between nodes (i, j) in time period s; It represents the reactive power loss of the line between the connecting nodes (i, j) in time period s.

[0079] The second-order cone relaxation technique requires tightening the second-order cone relaxation through a directional objective function, minimizing the relaxation amount while satisfying the corresponding power flow constraints and ensuring the correctness of the solution. The objective function constructed in this embodiment can meet this requirement of the second-order cone relaxation technique.

[0080] Step 104 : Decompose the two-stage robust optimization model of the mixed integer second-order cone into a main problem and sub-problems, solve the main problem and the sub-problems, and obtain an optimization result.

[0081] The objective function f of the main problem MP Expressed as:

[0082] Among them, α is an auxiliary variable.

[0083] Given the solution to the main problem, the sub-problem is to minimize the load loss and load adjustment in the worst scenario. The outer optimization variables are uncertain parameters. The outer problem seeks the worst scenario, that is, maximizing the load loss and load regulation. The inner optimization variable is the rescheduling variable The inner problem is to re-dispatch to reduce load loss when the value of the outer optimization variable is given (that is, after the output status of new energy is given). The objective function f of the sub-problem is SP Expressed as:

[0084] The constraints of the main problem include:

[0085] Among them, the constraints of the main problem still use the output characteristic constraints of conventional units, the output uncertainty constraints of new energy units, the actual output constraints of new energy units, the node voltage constraints, the line transmission power constraints, the equipment recovery state constraints, the line allowed recovery time constraints, the system frequency constraints and the node power balance constraints. Then formula (37) includes formulas (2)-(8), formulas (12)-(28) and formulas (33)-(34). represents the cutting plane generated by solving the subproblem, Indicates that the output forecast value of the rth renewable energy unit in the main problem is the expected value.

[0086] Exemplarily, before iteratively solving the master problem (MP) and the subproblem (SP), the iteration lower limit is set to LB=0, and the iteration upper limit is set to UB=+∞, the number of iterations is initialized to k=1, and the auxiliary variable α=0.

[0087] Exemplarily, solving the main problem and sub-problems to obtain optimization results includes: adopting a solution acceleration strategy, eliminating the line transmission power constraints and unit output climbing constraints of the two-stage robust optimization model of the mixed integer second-order cone, solving the main problem without line transmission power constraints and unit output climbing constraints, and obtaining the solution results; fixing the load required to be restored at each node in the main problem, and obtaining the optimal solution of the integer variables under the expected scenario, including the load node recovery order, the unit start-up and shutdown order, and the bus and line charging order, as well as the output value of the conventional unit in the expected scenario, and passing the solution results to the sub-problems.

[0088] The above solution results are compared with the line transmission power constraints and the unit output ramp constraints to verify the problematic conventional units that violate the line transmission power constraints or the unit output ramp constraints.

[0089] For example, if the output size of the conventional unit in the above solution result is not within the line transmission power constraint or the unit output climbing constraint, it means that the unit corresponding to the conventional unit output size violates the line transmission power constraint or the unit output climbing constraint.

[0090] For problematic conventional units, the transmission power constraint and the unit output ramp constraint are added to the constraints of the sub-problem to form additional constraints, and the main problem and sub-problems are solved based on the additional constraints to obtain the optimization results.

[0091] Exemplarily, the optimization results obtained by solving the main problem and subproblems based on adding constraints include:

[0092] Solve the main problem based on the added constraints and get the optimal solution x of the main problem * And the corresponding first objective function value

[0093] Updating the Iterative Lower Bound of a Two-Stage Robust Optimization Model Based on the First Objective Function Value

[0094] Based on the optimal solution x of the master problem * , solve the sub-problem and get the optimal solution of the sub-problem And the corresponding second objective function value and worst-case energy fluctuation scenario set The worst energy fluctuation scenario set includes the expected output value of each new energy unit in each period

[0095] Based on the second objective function value Updating the Iteration Upper Bound of a Two-Stage Robust Optimization Model with Mixed Integer Second-Order Cones

[0096] Based on the difference between the updated iteration lower limit and the updated iteration upper limit, and the ratio of the updated iteration lower limit |UB-LB| / |LB|≤ε, iteration is performed. If the ratio is greater than the preset threshold ε, that is, |UB-LB| / |LB|>ε, the second objective function value is updated, and the worst energy fluctuation scenario set is updated. Based on the updated second objective function value and the updated worst energy fluctuation scenario set, the added constraint is updated. According to the updated added constraint, the method goes to the main problem solved based on the added constraint and continues to iteratively solve until the ratio is less than or equal to the preset threshold ε, that is, |UB-LB| / |LB|≤ε, then the iteration is stopped to obtain the optimization result.

[0097] The additional constraints for the subproblems include:

[0098] And formulas (9)-(28), formulas (33)-(34).

[0099] Among them, Rm i represents the ramp rate of the i-th conventional unit; represents the upper limit of active output of the i-th conventional unit in time period s; It represents the lower limit of active output of the i-th conventional unit in time period s; represents the upper limit of reactive power output of the i-th conventional unit in time period s; It represents the lower limit of reactive power output of the i-th conventional unit in time period s; represents the reactive power of the i-th load node in time period s; represents the reactive power of the i-th load node in time period s after adjustment in the rescheduling phase; N represents the upper limit of reactive power output of the i-th load node in time period s; T The number of time periods in the new power system restoration process is represented by ΔT, and the total restoration time is N. S , and assume that the black start unit and the node where it is located are restored at time 0; represents the state of the i-th busbar node in time period s, A value of 1 indicates that the i-th busbar node has been restored. A value of 0 indicates that the i-th busbar node has not been restored; represents the state of the i-th load node in period s, A value of 1 indicates that the i-th load node has recovered. A value of 0 indicates that the i-th load node has not recovered; represents the state of the i-th unit node in time period s, A value of 1 indicates that the i-th unit node has recovered. A value of 0 indicates that the i-th unit node has not recovered; Indicates whether the line connecting node (i, j) is restored in time period s, A value of 1 indicates that the node has recovered. A value of 0 indicates that the node has not recovered; represents the active power output of the i-th conventional unit in time period s under the expected scenario; represents the reactive power output of the i-th conventional unit in time period s under the expected scenario; represents the actual active power output of the rth renewable energy unit in time period s; It represents the predicted value of the active power output of the rth renewable energy unit in time period s under the expected scenario; represents the load amount restored by the i-th load node in period s, is the load in the expected scenario, that is, the predicted value of the load restored by the i-th load node in time period s, W i，d represents the load weight coefficient of the i-th load node; represents the active power output of the i-th conventional unit at time s after adjustment in the rescheduling phase; represents the reactive power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; It represents the actual active power output of the rth renewable energy unit in time period s after adjustment in the rescheduling stage; represents the load restored by the i-th load node in time period s after adjustment in the rescheduling phase; N BUS Indicates the total number of all bus nodes; The outer optimization variable of the second stage objective function.

[0100] Step 105: Generate a grid restoration plan for the new power system based on the optimization result.

[0101] For example, the load node recovery sequence, unit start-up and shutdown sequence, bus and line charging sequence, and the output value of conventional units in the expected scenario are solved, and based on these contents, a grid restoration plan for the new power system is formed.

[0102] In an embodiment of the present application, in order to verify the effectiveness of the method of the present application, Table 1 gives the basic parameters of the example calculation of the method proposed in the present application, including the maximum number of recovery layers, the maximum frequency offset, the node voltage upper limit, the node voltage lower limit, the phase angle difference upper limit, the total recovery period, the recovery period interval and the iteration deviation.

[0103] Table 1 Basic parameters of the example

[0104] This example demonstrates the recovery of the IEEE 39-node system and the IEEE 118-node system, as shown in Figures 3 and 4 (where G represents a thermal power unit and WT represents a wind turbine). Table 2 shows the power outage losses and network losses during the recovery period. During the unit recovery phase, the introduction of new energy can accelerate the startup of coal-fired units, minimizing the total unit recovery time and thus reducing unit recovery costs. During the grid and load recovery phase, the simultaneous introduction of new energy, based on a large number of already started units, can accelerate grid and load recovery. Overall, this can significantly reduce system recovery time and substantially minimize economic losses.

[0105] This embodiment constructs an analysis of the error solved by low nonlinearization and second-order cone transformation technology by using voltage phase angle cross-term replacement error and second-order cone relaxation error.

[0106] The calculation formula for the voltage phase angle cross term replacement error is:

[0107] The calculation formula for the second-order cone relaxation error is:

[0108] Figure 5A and Figure 5B show the low nonlinearity error of all branches in the IEEE118 node system as the research object, where the horizontal axis Node represents the node and the vertical axis error represents the error. Figure 5A shows the order of magnitude of 10 -16 The low nonlinearity error of all branches is shown in Figure 5B, which is on the order of 10 -8 It can be found that the errors after replacing the voltage and phase angle variables are less than 10 -16 and 10 -8 The relaxation error of voltage and phase angle is shown in Figure 6. It can be found that the relaxation error is less than 10 -12 This is because although the second-order cone relaxation expands the feasible domain, the objective function is a minimization problem, and what is found is the lower limit in the feasible domain. Therefore, the solution of the model after the second-order cone relaxation is the same as the solution of the original model, and its accuracy can meet the requirements in practical applications.

[0109] Table 2 Optimization results of the proposed method in IEEE 39-node and IEEE 118-node systems

[0110] The embodiment of the present application proposes a new power system grid restoration method based on second-order cone transformation. By constructing a two-stage robust optimization model of mixed integer nonlinearity based on multi-state uncertainty sets and using second-order cone relaxation technology to process the AC power flow constraints of the model, the mixed integer nonlinear model is converted into a mixed integer second-order cone model; finally, the line transmission power constraints and unit output ramp constraints of the two-stage robust optimization model of the mixed integer second-order cone are eliminated, thereby shortening the time required for generating a grid restoration plan for the new power system, and then decomposing the two-stage robust model into a main problem and sub-problems. The solution is achieved through alternating iteration of the main and sub-problems to ensure the accuracy of the model solution. A system restoration emergency plan that meets the actual grid operation requirements can be generated in the shortest time, thereby reducing the political and economic losses caused by large-scale power outages and having good engineering promotion value.

[0111] The order of execution of each step in the above embodiment does not imply the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0112] The following are device embodiments of the present application. For details not described therein, please refer to the corresponding method embodiments described above.

[0113] Figure 7 shows a structural diagram of a power grid restoration device in an electric power system based on second-order cone transformation provided in an embodiment of the present application. For ease of explanation, only the parts related to the embodiment of the present application are shown, see below.

[0114] As shown in FIG7 , the power grid restoration device 200 based on second-order cone transformation includes: a data acquisition module 201 , a model building module 202 , a first calculation module 203 , a second calculation module 204 and a solution generation module 205 .

[0115] The data acquisition module 201 is configured to acquire power data of the new power system.

[0116] The model building module 202 is configured to construct a two-stage robust optimization model of the new power system based on a mixed integer nonlinearity and a multi-state uncertainty set based on power data and taking into account the uncertainty of the output of the new energy units, wherein the two-stage robust optimization model of the mixed integer nonlinearity includes AC power flow constraints.

[0117] The first calculation module 203 is configured to simplify the AC power flow constraints by using a second-order cone relaxation technique, and transform the two-stage robust optimization model as a mixed integer nonlinearity into a two-stage robust optimization model as a mixed integer second-order cone.

[0118] The second calculation module 204 is configured to decompose the two-stage robust optimization model of the mixed integer second-order cone into a main problem and sub-problems, solve the main problem and the sub-problems, and obtain an optimization result.

[0119] The solution generation module 205 is configured to generate a grid restoration solution for the new power system based on the optimization results.

[0120] For the beneficial effects of the power grid restoration device based on second-order cone transformation in the power system proposed in the embodiment of the present application, please refer to the beneficial effects of the new power system power grid restoration method based on second-order cone transformation.

[0121] In a possible implementation, in the model building module 202 , the mixed integer nonlinear two-stage robust optimization model includes a first-stage objective function and a second-stage objective function.

[0122] The objective function of the two-stage robust optimization model with mixed integer nonlinearity is expressed as:

[0123] in, represents the first stage objective function; represents the second stage objective function; N T The number of time periods in the new power system restoration process is represented by ΔT, and the total restoration time is N. S , and assume that the black start unit and the node where it is located are restored at time 0; represents the state of the i-th busbar node in time period s, A value of 1 indicates that the i-th busbar node has been restored. A value of 0 indicates that the i-th busbar node has not been restored; represents the state of the i-th load node in period s, A value of 1 indicates that the i-th load node has recovered. A value of 0 indicates that the i-th load node has not recovered; represents the state of the i-th unit node in time period s, A value of 1 indicates that the i-th unit node has recovered. A value of 0 indicates that the i-th unit node has not recovered; Indicates whether the line connecting node (i, j) is restored in time period s, A value of 1 indicates that the node has recovered. A value of 0 indicates that the node has not recovered; represents the active power output of the i-th conventional unit in time period s under the expected scenario; represents the reactive power output of the i-th conventional unit in time period s under the expected scenario; represents the actual active power output of the rth renewable energy unit in time period s; W represents the load restored by the i-th load node in period s, i，d represents the load weight coefficient of the i-th load node; represents the active power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; represents the reactive power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; It represents the actual active power output of the rth renewable energy unit in time period s after adjustment in the rescheduling stage; represents the load restored by the i-th load node in time period s after adjustment in the rescheduling phase; N BUS Indicates the total number of all bus nodes; The outer optimization variable of the second stage objective function.

[0124] In one possible implementation, in the model building module 202, the mixed integer nonlinear two-stage robust optimization model also includes conventional unit output characteristic constraints, new energy unit output uncertainty constraints, new energy unit actual output constraints, node voltage constraints, line transmission power constraints, equipment recovery state constraints, line allowed recovery time constraints, system frequency constraints and node power balance constraints; among them, the unit output characteristic constraints include conventional unit output constraints before grid connection, conventional unit output climbing constraints, conventional unit output constraints and conventional unit cold / hot start time limit constraints.

[0125] The multi-state uncertainty set U with uncertainty constraints on the output of new energy units is expressed as:

[0126] in, It represents the predicted value of the active power output of the rth renewable energy unit in time period s under the expected scenario; is the output corresponding to the zth state of the rth new energy unit in time period s; is 0 or 1, Indicates that the output of the rth new energy unit is in state z during period s, Indicates that the output of the rth renewable energy unit is not in state z during time period s; N is the total number of states; Γ g，p The budget value of renewable energy power generation is the limit of fluctuation within the recovery period; Ω E is the set of nodes connected to the new energy generating units; R is a set of rational numbers; N T The number of time periods representing the restoration process of the new power system;

[0127] The actual output constraint of new energy units is expressed as:

[0128] in, represents the actual output value of the rth new energy unit in time period s, represents the state of the i-th unit node in time period s, A value of 1 indicates that the i-th unit node has recovered. A value of 0 indicates that the i-th unit node has not recovered.

[0129] In one possible implementation, in the model building module 202, the AC power flow constraint is expressed as:

[0130] Among them, G ij represents the conductance value of the line connecting nodes (i, j), B ij represents the susceptance value of the line connecting nodes (i, j); represents the active power flowing through the line between the connecting nodes (i, j) in time period s; represents the reactive power flowing through the line between the connecting nodes (i, j) in time period s; represents the active power flowing through the line between the connecting nodes (j, i) in time period s; represents the reactive power flowing through the line between the connecting nodes (j, i) in time period s; represents the active power loss of the line between nodes (i, j) in time period s; represents the reactive power loss of the line between nodes (i, j) in time period s; represents the state of the line connecting nodes (i, j) in time period s, A value of 1 indicates that the node has recovered. A value of 0 indicates that the node has not recovered; represents the voltage amplitude of the connection node i in time period s; represents the voltage amplitude of the connection node j in time period s; express and The phase angle.

[0131] In a possible implementation, in the first calculation module 203, a second-order cone relaxation technique is used to simplify the AC power flow constraints, including:

[0132] The voltage phase angle cross terms of the AC power flow constraint of the two-stage robust optimization model for system recovery are replaced by variables to obtain the AC power flow constraint after variable replacement; the second-order cone relaxation constraint is added to the AC power flow constraint after variable replacement to obtain the simplified AC power flow constraint.

[0133] In a possible implementation, in the first calculation module 203, the simplified AC power flow constraint is expressed as:

[0134] in, represents the voltage amplitude of the connection node i in time period s; represents the voltage amplitude of the connection node j in time period s; express and The phase angle; express The square of express The square of G ij represents the conductance value of the line connecting nodes (i, j), B ij represents the susceptance value of the line connecting nodes (i, j); represents the active power flowing through the line between the connecting nodes (i, j) in time period s; represents the reactive power flowing through the line between the connecting nodes (i, j) in time period s; represents the active power flowing through the line between the connecting nodes (j, i) in time period s; represents the reactive power flowing through the line between the connecting nodes (j, i) in time period s; represents the active power loss of the line between nodes (i, j) in time period s; It represents the reactive power loss of the line between the connecting nodes (i, j) in time period s.

[0135] In a possible implementation, in the second calculation module 204, solving the main problem and the sub-problems to obtain an optimization result includes:

[0136] A solution acceleration strategy is adopted to eliminate the line transmission power constraint and unit output ramping constraint of the two-stage robust optimization model of mixed integer second-order cone, solve the main problem without the line transmission power constraint and unit output ramping constraint, obtain the solution result, and pass the solution result to the sub-problem; compare the solution result with the line transmission power constraint and unit output ramping constraint, and verify the problematic conventional units that violate the line transmission power constraint or the unit output ramping constraint; for the problematic conventional units, the transmission power constraint and the unit output ramping constraint are added to the constraints of the sub-problem to form additional constraints, and solve the main problem and sub-problems based on the additional constraints to obtain the optimization results.

[0137] In a possible implementation, in the second calculation module 204, the main problem and the sub-problems are solved based on the added constraints to obtain the optimization results, including:

[0138] Solve the main problem based on the added constraints to obtain the optimal solution of the main problem and the corresponding first objective function value; update the iteration lower limit of the two-stage robust optimization model of the mixed integer second-order cone based on the first objective function value; solve the subproblem based on the optimal solution of the main problem to obtain the optimal solution of the subproblem and the corresponding second objective function value, as well as the worst energy fluctuation scenario set; update the iteration upper limit of the two-stage robust optimization model of the mixed integer second-order cone based on the second objective function value; calculate the ratio of the difference between the updated iteration lower limit and the updated iteration upper limit to the updated iteration lower limit, and update the second objective function value and the worst energy fluctuation scenario set in response to the ratio being greater than a preset threshold; update the added constraints based on the updated second objective function value and the updated worst energy fluctuation scenario set; according to the updated added constraints, switch to the main problem solved based on the added constraints and continue to iteratively solve until the ratio is less than or equal to the preset threshold, stop the iteration, and obtain the optimization result.

[0139] In a possible implementation, in the second calculation module 204, the objective function f of the main problem MP Expressed as:

[0140] The objective function f of the subproblem SP Expressed as:

[0141] The additional constraints for the subproblems include:

[0142] Among them, α is an auxiliary variable; Rm i represents the ramp rate of the i-th conventional unit; represents the upper limit of active output of the i-th conventional unit in time period s; It represents the lower limit of active output of the i-th conventional unit in time period s; represents the upper limit of reactive power output of the i-th conventional unit in time period s; It represents the lower limit of reactive power output of the i-th conventional unit in time period s; represents the reactive power of the i-th load node in time period s; represents the reactive power of the i-th load node in time period s after adjustment in the rescheduling phase; N represents the upper limit of reactive power output of the i-th load node in time period s; T The number of time periods in the new power system restoration process is represented by ΔT, and the total restoration time is N. S , and assume that the black start unit and the node where it is located are restored at time 0; represents the state of the i-th busbar node in time period s, A value of 1 indicates that the i-th busbar node has been restored. A value of 0 indicates that the i-th busbar node has not been restored; represents the state of the i-th load node in period s, A value of 1 indicates that the i-th load node has recovered. A value of 0 indicates that the i-th load node has not recovered; represents the state of the i-th unit node in time period s, A value of 1 indicates that the i-th unit node has recovered. A value of 0 indicates that the i-th unit node has not recovered; Indicates whether the line connecting node (i, j) is restored in time period s, A value of 1 indicates that the node has recovered. A value of 0 indicates that the node has not recovered; represents the active power output of the i-th conventional unit in time period s under the expected scenario; represents the reactive power output of the i-th conventional unit in time period s under the expected scenario; represents the actual active power output of the rth renewable energy unit in time period s; It represents the predicted value of the active power output of the rth renewable energy unit in time period s under the expected scenario; W represents the load restored by the i-th load node in period s, i，d represents the load weight coefficient of the i-th load node; represents the active power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; represents the reactive power output of the i-th conventional unit in time period s after adjustment in the rescheduling stage; It represents the actual active power output of the rth renewable energy unit in time period s after adjustment in the rescheduling stage; represents the load restored by the i-th load node in time period s after adjustment in the rescheduling phase; N BUS Indicates the total number of all bus nodes; The outer optimization variable of the second stage objective function.

[0143] In some embodiments, the embodiments of the present application provide a new power system grid restoration method and device based on second-order cone transformation, taking into account the uncertainty of the output of new energy units, by constructing a two-stage robust optimization model of mixed integer nonlinearity based on multi-state uncertainty sets, and using second-order cone relaxation technology to process the AC flow constraints of the model, thereby converting the mixed integer nonlinear model into a mixed integer second-order cone model; finally, the two-stage robust model is decomposed into a main problem and sub-problems, and the solution is achieved through alternating iteration of the main and sub-problems, thereby ensuring the accuracy of the model solution, reducing the political and economic losses caused by large-scale power outages, and having good engineering promotion value.

[0144] In the above embodiments, the description of each embodiment has its own emphasis. For parts not described in one embodiment, reference can be made to the relevant descriptions of other embodiments.

[0145] Those skilled in the art will appreciate that the templates, units, and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0146] If the module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present application implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by the processor, it can implement the steps of the above-mentioned embodiments of the new power system grid restoration method based on second-order cone transformation. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form, etc. Computer-readable media may include: any entity or device that can carry computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electric carrier signal, telecommunication signal and software distribution medium, etc.

Claims

1. A novel power system grid restoration method based on second-order cone transformation, comprising: Obtaining power data of the novel power system; Based on the power data, considering the uncertainty of the output of new energy units, constructing a two-stage robust optimization model of the novel power system based on a multi-state uncertain set, which is a mixed-integer non-linear two-stage robust optimization model, wherein the mixed-integer non-linear two-stage robust optimization model includes AC power flow constraints; Using the second-order cone relaxation technique to simplify the AC power flow constraints, and transforming the mixed-integer non-linear two-stage robust optimization model into a mixed-integer second-order cone two-stage robust optimization model; Decomposing the mixed-integer second-order cone two-stage robust optimization model into a master problem and a sub-problem, solving the master problem and the sub-problem, and obtaining an optimization result; Based on the optimization result, generating a grid restoration plan for the novel power system.

2. The novel power system grid restoration method based on second-order cone transformation according to claim 1, wherein, The mixed-integer non-linear two-stage robust optimization model includes a first-stage objective function and a second-stage objective function; The objective function of the mixed-integer non-linear two-stage robust optimization model is expressed as: Represents the objective function of the first stage; Denote the objective function of the second stage; N T Denote the number of time periods in the restoration process of the new power system. The time length of each time period is ΔT, and the total restoration time is N S , and it is assumed that the black-start unit and the node where it is located are restored at the 0th moment; Indicates the state of the i-th bus node in period s, A value of 1 indicates that the i-th bus node has been restored. A value of 0 indicates that the i-th bus node has not been restored; Indicates the state of the i-th load node at time period s, A value of 1 indicates that the i-th load node has been restored. A value of 0 indicates that the i-th load node is not restored; Indicates the state of the i-th unit node at time period s, A value of 1 indicates that the i-th unit node has been restored. A value of 0 indicates that the i-th unit node has not been restored; Indicates whether the line connecting nodes (i, j) is restored during period s A value of 1 indicates that the node has been restored, A value of 0 indicates that the node has not been restored; Denote the active power output of the $i$-th conventional unit in period $s$ under the expected scenario; Denote the reactive power output of the i-th conventional unit at time period s in the expected scenario; Indicates the actual active power output of the r-th new energy unit in period s; Indicates the amount of load restored by the i-th load node during period s, W i,d Indicates the load weight coefficient of the i-th load node; Denote the active power output of the i-th conventional unit after adjustment in the rescheduling stage at time period s; Denote the reactive power output of the \(i\)-th conventional unit after adjustment in the rescheduling stage at time period \(s\); Indicates the actual active power output of the r-th new energy unit after adjustment in the rescheduling stage at time period s; denotes the restored load of the \(i\)-th load node after adjustment in the rescheduling stage at time period \(s\); \(N\) BUS denotes the total number of all bus nodes; is the outer-layer optimization variable of the second-stage objective function.

3. The novel power system grid restoration method based on second-order cone transformation according to claim 1, wherein, The mixed-integer non-linear two-stage robust optimization model further includes conventional unit output characteristic constraints, new energy unit output uncertainty constraints, new energy unit actual output constraints, node voltage constraints, line transmission power constraints, equipment restoration state constraints, line allowed restoration time constraints, system frequency constraints, and node power balance constraints; among them, the unit output characteristic constraints include conventional unit output constraints before grid connection, conventional unit output ramp constraints, conventional unit output constraints, and conventional unit cold / hot start time limit constraints; The multi-state uncertainty set U representing the uncertainty constraint of the new energy unit output is expressed as: Among them, Denote the predicted value of the active power output of the r-th new energy unit in the s-th time period under the expected scenario; is the power output corresponding to the z-th state of the r-th new energy unit in period s; is 0 or 1, Indicates that the output of the r-th new energy unit is in state z during period s, Indicates that the output of the r-th new energy unit is not in state z during period s; N is the total number of states; Γ g,p is the budget value of new energy power generation, which is a limit on the fluctuation amount during the recovery period; Ω E is the set of power generation nodes accessing new energy units; R is the set of rational numbers; NT represents the number of periods in the recovery process of the new power system; The actual output constraint of the new energy unit is expressed as: Among them, Indicates the actual output value of the r-th new energy unit in period s, Indicates the state of the i-th unit node at time period s, A value of 1 indicates that the node has recovered, A value of 0 indicates that the node has not been restored.

4. The novel power system grid restoration method based on second-order cone transformation according to claim 1, wherein, The AC power flow constraint is expressed as: Among them, G ij represents the conductance value of the line connecting nodes (i, j), and B ij represents the susceptance value of the line connecting nodes (i, j); Indicates the active power flowing through the line between connection nodes (i, j) during time period s; Denotes the reactive power flowing through the line between connection nodes (i, j) during time period s; Indicates the active power flowing through the line connecting nodes (j, i) during time period s; Denotes the reactive power flowing through the line between connection nodes (j, i) during time period s; Indicates the active power loss of the line between nodes (i, j) connected during period s; Denote the reactive power loss of the line between nodes (i, j) connected during period s; Indicates the state of the line between connection nodes (i, j) during time period s. A value of 1 indicates that the node has been restored. A value of 0 indicates that the node has not been restored; Denote the voltage amplitude of the node i connected during the time period s; Denote the voltage amplitude of the node j connected at the time period s; Indicate With The phase angle of.

5. The novel power system grid restoration method based on second-order cone transformation according to claim 1, wherein, The step of using the second-order cone relaxation technique to simplify the AC power flow constraints includes: Performing variable substitution on the voltage phase angle cross terms of the AC power flow constraints of the system restoration two-stage robust optimization model to obtain the AC power flow constraints after variable substitution; Adding second-order cone relaxation constraints to the AC power flow constraints after variable substitution to obtain the simplified AC power flow constraints.

6. The novel power system grid restoration method based on second-order cone transformation according to claim 5, wherein, The simplified AC power flow constraint is expressed as: Among them, Denote the voltage magnitude of the node i connected during the time period s; Denote the voltage amplitude of the connection node j during the time period s; Indicate With phase angle; Indicate square of, Indicate square of; G ij represents the conductance value of the line connecting nodes (i, j), B ij represents the susceptance value of the line connecting nodes (i, j); Indicates the active power flowing through the line between connection nodes (i, j) during time period s; Denotes the reactive power flowing through the line between connecting nodes (i, j) during time period s; Indicates the active power flowing through the line connecting nodes (j, i) during time period s; Denote the reactive power flowing through the line between connection nodes (j, i) during time period s; Indicates the active power loss of the line between nodes (i, j) connected during period s; represents the reactive power loss of the line connecting nodes (i, j) in time period s.

7. The novel power system grid restoration method based on second-order cone transformation according to claim 1, wherein The step of solving the master problem and the sub-problem to obtain an optimization result includes: Adopting a solution acceleration strategy, eliminating the line transmission power constraints and unit output ramp constraints of the mixed-integer second-order cone two-stage robust optimization model, solving the master problem without the line transmission power constraints and the unit output ramp constraints, obtaining a solution result, and transmitting the solution result to the sub-problem; Comparing the solution result with the line transmission power constraints and the unit output ramp constraints, and checking the problematic conventional units that violate the line transmission power constraints or the unit output ramp constraints; For the problematic conventional units, adding the transmission power constraints and the unit output ramp constraints to the constraints of the sub-problem to form added constraints, and solving the master problem and the sub-problem based on the added constraints to obtain an optimization result.

8. The novel power system grid restoration method based on second-order cone transformation according to claim 7, wherein, The step of solving the master problem and the sub-problem based on the added constraints to obtain an optimization result includes: Solve the master problem based on the added constraints to obtain the optimal solution of the master problem and the corresponding first objective function value; Update the iterative lower bound of the two-stage robust optimization model of the mixed-integer second-order cone based on the first objective function value; Solve the sub-problem based on the optimal solution of the master problem to obtain the optimal solution of the sub-problem and the corresponding second objective function value, as well as the set of worst-case energy fluctuation scenarios; Update the iterative upper bound of the two-stage robust optimization model of the mixed-integer second-order cone based on the second objective function value; Calculate the ratio of the difference between the updated iterative lower bound and the updated iterative upper bound to the updated iterative lower bound. In response to the ratio being greater than a preset threshold, update the second objective function value and update the set of worst-case energy fluctuation scenarios; Update the added constraints based on the updated second objective function value and the updated set of worst-case energy fluctuation scenarios; Go back to solving the master problem based on the updated added constraints and continue the iterative solution until the ratio is less than or equal to the preset threshold, then stop the iteration to obtain the optimization result.

9. The novel power system grid restoration method based on second-order cone transformation according to any one of claims 1 to 8, wherein, The objective function f of the main problem MP is expressed as: The objective function f of the sub-problem SP is expressed as: The added constraints for the sub-problems include: where α is an auxiliary variable; Rm i represents the ramp rate of the i-th conventional unit; Denote the upper limit of the active power output of the i-th conventional unit in period s; Denote the lower limit of the active power output of the i-th conventional unit in period s; Denote the upper limit of the reactive power output of the i-th conventional unit in period s; Indicates the lower limit of the reactive power output of the i-th conventional unit in period s; Denote the reactive power of the $i$-th load node at time period $s$; Denote the reactive power of the \(i\)-th load node after adjustment in the rescheduling stage at time period \(s\); denotes the upper limit of the reactive power output of the \(i\)-th load node at time period \(s\); \(N\) T denotes the number of time periods in the restoration process of the new power system. The time length of each time period is \(\Delta T\), and the total restoration time is \(N\) S , and it is assumed that the black-start unit and the node where it is located are restored at time \(0\); Indicates the state of the i-th bus node at time period s, A value of 1 indicates that the i-th bus node has been restored. A value of 0 indicates that the i-th bus node has not been restored; Indicates the status of the i-th load node at time period s, A value of 1 indicates that the i-th load node has been restored. A value of 0 indicates that the i-th load node has not been restored; Indicates the state of the i-th unit node at time period s, A value of 1 indicates that the i-th unit node has been restored. A value of 0 indicates that the i-th unit node has not been restored; Indicates whether the line connecting nodes (i, j) is restored during time period s. A value of 1 indicates that the node has been restored, A value of 0 indicates that the node has not been restored; Denote the active power output of the $i$-th conventional unit in period $s$ under the expected scenario; Denote the reactive power output of the i-th conventional unit in period s under the expected scenario; Denote the r-th new energy unit in period s Actual active power output; Denote the predicted value of the active power output of the r-th new energy unit in the s-th time period under the expected scenario; Indicates the amount of load restored by the i-th load node at time period s, W i,d Indicates the load weight coefficient of the i-th load node; Denote the active power output of the i-th conventional unit after adjustment in the rescheduling stage at time period s; Denote the reactive power output of the i-th conventional unit after adjustment in the rescheduling stage at time period s; Indicates the actual active power output of the r-th new energy unit after adjustment in the rescheduling stage at time period s; Denote the restored load of the \(i\)-th load node after adjustment in the rescheduling stage at time period \(s\); \(N\) BUS Denote the total number of all bus nodes; Is the outer optimization variable of the second-stage objective function.

10. A power grid restoration device for a power system based on second-order cone transformation, comprising: A data acquisition module configured to acquire power data of a new power system; A model establishment module configured to construct a two-stage robust optimization model of the new power system based on a multi-state uncertainty set, which is mixed-integer nonlinear, considering the uncertainty of the output of new energy units, wherein the mixed-integer nonlinear two-stage robust optimization model includes AC power flow constraints; A first calculation module configured to simplify the AC power flow constraints by using second-order cone relaxation technology and transform the mixed-integer nonlinear two-stage robust optimization model into a two-stage robust optimization model of a mixed-integer second-order cone; A second calculation module configured to decompose the two-stage robust optimization model of the mixed-integer second-order cone into a master problem and a sub-problem, solve the master problem and the sub-problem to obtain an optimization result; A solution generation module configured to generate a power grid restoration solution for the new power system based on the optimization result.

Images