New energy power grid robust recovery model considering safety frequency convex envelope constraint

Abstract

The invention discloses a new energy power grid robust recovery method and system considering a dynamic frequency safety convex envelope constraint, and the method is characterized in that the new energy power grid robust recovery method based on two-stage optimization and the dynamic frequency safety convex envelope constraint comprises the following steps: S1, building the dynamic frequency safety constraint, a power grid robust recovery model is established on the basis; s2, performing linear substitution on the highly nonlinear dynamic frequency security constraint by using a McCormick convex envelope construction method, and then improving the linearization precision by using a boundary contraction algorithm; and S3, building the recovery model into a two-stage robust optimization form, and generating a main problem and a sub-problem by using a column sum constraint generation algorithm to carry out iterative solution. Compared with other methods, the new energy power grid robust recovery method and system provided by the invention have obvious advantages in the aspect of dealing with the dynamic frequency safety problem. In addition, the dynamic frequency convex envelope constraint can effectively reduce the impact of the random fluctuation of the new energy output on the dynamic frequency and recovery feasibility of the system, thereby ensuring the safety and stability of the power grid recovery process.

Description

Technical Field

[0001] The present invention relates to new energy power grid restoration, and in particular to a new energy power grid restoration method considering safety frequency convex envelope constraints. Background Art

[0002] Natural disasters, cyber attacks, equipment failures, and even staff operational errors may lead to serious power outages, causing incalculable social and economic losses. Therefore, rapid, safe and stable power grid restoration after an accident is of great practical significance for ensuring social power safety and reducing people’s property losses.

[0003] In addition, with the advancement of the "dual carbon" goal and the construction of new power systems, the proportion of new energy power generation represented by wind power connected to the grid has increased rapidly. However, new energy power generation systems are generally connected to the grid through power electronic equipment and cannot spontaneously provide inertia response, resulting in a reduction in the system's rotational inertia. In addition, most new energy units adopt a maximum power tracking strategy and cannot respond to frequency changes in the power system. Especially in the process of power grid restoration, due to insufficient frequency modulation power supply, under the power impact of unit, load grid connection and wind turbine output fluctuations, the dynamic frequency safety problem caused by low inertia and weak frequency modulation of new energy will be more prominent. Therefore, ensuring frequency safety during the restoration process has become the key and difficulty of stable power grid restoration. In addition, the random fluctuation characteristics of new energy output such as wind power not only pose severe challenges to the power grid restoration strategy, but also lead to the uncertainty of power impact in the restoration process, threatening the feasibility of frequency safety verification in the power grid restoration process. Therefore, it is urgent to consider the dynamic frequency safety constraints of new energy grid restoration strategies in uncertain environments to ensure the safety and reliability of the power grid restoration process.

[0004] At present, some studies have considered the dynamic frequency security constraints of the power grid in steady-state problems such as day-ahead dispatching of the power grid. However, the optimization and simulation iteration logic of the transient simulation-driven method is unclear, and it is difficult to ensure the optimality of the restoration decision. The frequency dynamic difference method will introduce a large number of differential equation constraints, greatly increase the dimension of the restoration model, and make it difficult to solve the model. The approximate analytical method will introduce a large number of integer variables, which will greatly increase the scale of the model.

[0005] Some studies have been conducted on the uncertainty of renewable energy output during the power grid restoration process. The main coping methods include stochastic optimization and robust optimization algorithms. However, the performance of stochastic optimization depends largely on the probability distribution function fitted based on historical data, so the actual operation effect is often worse than expected. Robust optimization does not require the true probability distribution of uncertain variables. It usually uses interval sets to describe the upper and lower bounds of uncertain variables, avoiding the generation of scenario trees, and is suitable for large-scale actual power systems. However, most of the current research focuses on coping with the disturbance of renewable energy random volatility to the power balance problem in the restoration process, and there is little research on methods to deal with the random fluctuation of power under frequency security constraints in the restoration process.

[0006] In summary, on the one hand, the existing methods cannot effectively deal with the dynamic frequency security issues in the restoration of new energy power grids, and on the other hand, there is a lack of joint response to the random fluctuations of new energy in steady-state power balance and frequency security verification. To this end, this paper proposes a robust restoration strategy for new energy power grids that considers dynamic frequency security constraints. Compared with existing research, the proposed method can avoid solving complex transient simulation models while ensuring the dynamic frequency security of the power grid, greatly reducing the scale and difficulty of solving the power grid restoration optimization model; it can avoid the massive integer variables introduced by piecewise linearization, greatly improving the solution efficiency; it can effectively reduce the impact of the random volatility of new energy output on the system dynamic frequency and restoration feasibility, which is of great significance to ensure the safety and stability of the power grid restoration process and reduce social property losses. Summary of the invention

[0007] Symbols and definitions:

[0008] A. Indices, Sets, and Matrices:

[0009]

[0010] B. Variables

[0011]

[0012] C. Constants

[0013]

[0014]

[0015] D.Abbreviation

[0016] CCG Column and constraint generation algorithms RoCoF Maximum frequency change rate

[0017] The purpose of the present invention is to provide a method for robust recovery of a new energy power grid that takes into account the convex envelope constraint of the safety frequency. The method proposes a new robust recovery method for a new energy power grid. According to the frequency response characteristics during the recovery process of the new energy power grid, the system dynamic frequency safety constraint is derived, and the McCormick convex envelope construction method based on boundary contraction is used for reasonable linearization. By analyzing and characterizing the power grid recovery process, a power grid recovery model that takes into account dynamic frequency safety is established, and a two-stage robust optimization method is used to deal with the uncertainty in the recovery process. This method is superior in resisting the random volatility of new energy / load demand and achieving rapid power grid recovery while ensuring frequency safety.

[0018] In order to achieve the above-mentioned object, the present invention discloses a method and system for robust restoration of a new energy power grid considering dynamic frequency safety convex envelope constraints, characterized in that the robust restoration method for a new energy power grid based on a two-stage robust optimization method and dynamic frequency safety convex envelope constraints comprises the following steps:

[0019] S1. Establish dynamic frequency security constraints and build a robust power grid recovery model based on them;

[0020] S2, use McCormick convex envelope construction method to linearly replace the highly nonlinear dynamic frequency safety constraints, and then use the boundary shrinkage algorithm to improve the accuracy of linearization;

[0021] S3. The recovery model is constructed in the form of a two-stage robust optimization, and the column and constraint generation algorithm is used to generate the main problem and sub-problems for mutual iterative solution.

[0022] Preferably, the safety frequency constraint and deterministic recovery model are established:

[0023] (1) Dynamic frequency safety constraint establishment

[0024] When a power step disturbance ΔP occurs during grid recovery due to load connection or other reasons, e =ΔP s / s, the frequency response of the system is shown in formula (1).

[0025]

[0026] in:

[0027]

[0028] Convert equation (2) into time domain form, as shown in equation (3).

[0029]

[0030] in:

[0031]

[0032] From formula (1), the steady-state frequency change of the system can be obtained as

[0033]

[0034] From formula (3), the frequency change rate and the maximum frequency change rate can be obtained as follows:

[0035]

[0036] When the frequency change rate of the system is 0, the frequency change of the system reaches the maximum value, and the corresponding time t can be obtained. nadir for

[0037]

[0038] Substituting equation (8) into equation (3) can obtain the frequency change when the system frequency is at the lowest point, as shown in equation (9).

[0039]

[0040] So far, the three system dynamic frequency security constraints during the power grid restoration process are obtained, as shown in formula (10).

[0041]

[0042] Where: RoCoF max Indicates the maximum limit of the frequency change rate; Δf max Indicates the maximum limit of the change in the lowest frequency point; Indicates the maximum limit of steady-state frequency change.

[0043] (2) Objective function

[0044] In order to speed up the load recovery efficiency while ensuring the safety of grid frequency, the cumulative amount of electric energy consumed by the restored load is taken as the objective function, and different loads are assigned different importance levels, which takes into account both the load size and the importance level, and meets the actual needs of grid restoration.

[0045]

[0046] Where: α l is the importance weight coefficient of load l; P l,t Indicates the amount of load l that has been restored at time t.

[0047] (3) Black start unit operation constraints

[0048]

[0049] Where: P gb,t Indicates the output of the black start unit gb; Indicates the upper limit of the climbing rate of the black start unit; and They respectively represent the rated output upper limit and minimum stable output of the black start unit.

[0050] (4) Non-black start unit operation constraints

[0051]

[0052] Where: P g,t Indicates the output of non-black unit g; u g,t is a Boolean variable representing the start / stop status of non-black units; Indicates the upper limit of the non-black unit climbing rate; and Indicates the minimum and maximum start time of non-black start units.

[0053] (5) Fan output constraints

[0054]

[0055] Where: P w,t Indicates the output of the wind farm; Indicates the output of a single fan; Indicates the installed capacity of a single wind turbine; Represents the predicted value of the fan output efficiency; x w,t Indicates the number of wind turbines connected to the wind farm; u w,t is a Boolean variable representing the access status of the wind farm.

[0056] (6) Load recovery constraints

[0057]

[0058] Where: P l,t is the connected load; P l,max and P l,min Indicates the upper and lower limits of the load; u l,t Boolean variable indicating the load restoration status.

[0059] (7) Network flow constraints

[0060]

[0061] Where: u ij,t is a Boolean variable representing the on / off state of branch ij at time t; Represents the maximum line capacity of branch ij.

[0062] (8) System backup constraints

[0063]

[0064] Where: l % and δ w % is the prediction error coefficient of load and fan.

[0065] (9) System recovery order constraints

[0066]

[0067] (10) Frequency disturbance analysis during recovery

[0068] In the problem of power grid restoration, since the system is in a relatively weak state, it is impossible to ensure the dynamic frequency safety of the system in large disturbance scenarios such as system N-1 failure. Therefore, in the restoration process, only the power disturbance caused by load grid connection and wind turbine output fluctuation at the steady-state operation level is considered.

[0069] a) Power disturbance of load connected to the grid

[0070]

[0071] Where: l Indicates the correction factor of cold load starting characteristics (ρ l >1); ΔP l,t Represents the access change of load l at time t.

[0072] b) Power disturbance caused by wind turbine output fluctuation

[0073]

[0074] Where: and Indicates the actual and predicted output values ​​of the wind power plant.

[0075] Preferably, a robust power grid restoration model considering the uncertainty of renewable energy is:

[0076] (1) Construction of wind turbine output uncertainty set

[0077] According to the distribution of historical data of wind turbine output, the uncertainty set of wind turbine output capacity coefficient can be established, as shown in formula (21).

[0078]

[0079] Where: and They represent the actual value and predicted value of the fan output capacity coefficient respectively.

[0080] For the Boolean variable in formula (23) By constraining the values, the conservatism of the two-stage robust model can be adjusted, as shown in formula (22).

[0081]

[0082] Where: B t is the conservative tuning parameter for the two-stage robust model.

[0083] (2) Construction of a two-stage robust recovery model

[0084] In the process of grid restoration with a high proportion of wind power penetration, there are a large number of wind power output uncertainty scenarios, which pose severe challenges to the dynamic frequency security of the system and the feasibility of the restoration strategy. Therefore, a two-stage robust algorithm is adopted to reconstruct the grid restoration model to ensure the safety and reliability of the restoration strategy. The reconstructed two-stage robust restoration model is shown in Equation (25).

[0085]

[0086] Where: and is the constant positive slack variable of the node power flow balance constraint; ε is the safety threshold of the slack variable; F is the penalty coefficient. By adding slack variables and using them as the feasibility verification standard and penalty function of the power grid restoration strategy, the feasibility of the optimization solution obtained by the model is verified.

[0087] For ease of expression, all variables are divided into four types and expressed in vector form, as shown in Equation (26). The reformulated model is shown in Equation (24).

[0088]

[0089] Where: G1-G4, D1-D5, A, I, b, c, d, g, t, v represent the relevant parameter matrices in the robust model. Preferably, the McCormick convex envelope linearization method and CCG algorithm are used to solve the robust model:

[0090] (1) McCormick convex envelope construction method

[0091] The dynamic frequency safety constraint (10) has a large number of nonlinear parts, which will cause great difficulties in solving. It is necessary to perform McCormick linearization construction preprocessing on these frequencies and convert them into linear constraints. Before constructing the McCormick convex envelope, it is necessary to mathematically convert it into In order to simplify the frequency minimum point constraint where the nonlinear term coupling is the most complex, it is assumed that when the damping is small, the response of the primary frequency modulation process can be approximated as the power disturbance. Therefore, before the frequency reaches the minimum point, the primary frequency modulation process can be simplified to a slope of ΔP e / t nadir is a linear function of time t. Based on this approximation, the time domain expression (3) of the system frequency can be approximately derived as equation (26).

[0092]

[0093] Substituting the expression of the lowest frequency point time into the equation, we can obtain the simplified lowest frequency point Δf nadir The approximate expression of (27).

[0094]

[0095] make The inverse trigonometric function y in equation (27) is -1 (x) The McCormick envelope construction idea is used to convert it into a convex envelope form composed of multiple linear functions, as shown in formula (28).

[0096]

[0097] in:

[0098]

[0099] From formula (28), we can get the lowest frequency constraint of McCormick convex envelope, as shown in formula (30).

[0100]

[0101] Will Substituting into (31), we can get formula (31).

[0102]

[0103] At this point, the frequency dynamic safety constraints have been converted to The function form can be approximated by using the convex envelope construction idea. z=x·y、z=x / y and The convex envelopes of are shown in (32), (33) and (34) respectively.

[0104]

[0105] (2) Boundary shrinkage algorithm

[0106] The convex envelope construction method based on McCormick is actually a convex relaxation of highly nonlinear functions, and its accuracy depends on the boundary values ​​of the frequency variables. and A smaller variable range can improve the approximation of the original function, thereby improving the accuracy of the method. Therefore, a boundary shrinkage algorithm is proposed to improve the accuracy of the convex envelope substitution, as shown in Table (1):

[0107] Table (1) Boundary shrinkage algorithm

[0108]

[0109]

[0110] (3) Solving the main problem model

[0111] By continuously adding scenarios and variables obtained from sub-problems to the main problem, it gradually approaches the optimal solution to the original problem, thereby effectively reducing the difficulty of solving and the number of iterations.

[0112]

[0113] (4) Solving the sub-problem model

[0114] The sub-problem verifies the feasibility of the recovery strategy optimized by the main problem in massive uncertain scenarios through the added slack variables, and substitutes the scenarios that do not meet the feasibility verification back to the main problem.

[0115]

[0116] The subproblem model is a complex min-max two-layer optimization model. It is necessary to use the duality theory to transform the inner max problem into a min problem. The subproblem after the dual transformation is shown in formula (39).

[0117]

[0118] Where: μ1 and μ2 represent the dual variables corresponding to the constraints.

[0119] (5) Column and Constraint Generation Algorithm

[0120] The modified column and constraint generation algorithm is used to solve the two-stage robust optimization model, and equation (25) is decomposed into the main problem and sub-problems for iterative solution, as shown in Table (2):

[0121] Table 2 Column and Constraint Generation Algorithm (CCG)

[0122] BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 The principle diagram of the boundary shrinkage method

[0124] Figure 2 is a diagram of an IEEE 24-node power transmission system adopted in an embodiment of the present invention;

[0125] Figure 3 It is a short-term prediction curve and fluctuation range diagram of wind power output adopted in the embodiment of the present invention;

[0126] Figure 4 is a diagram of optimization results of load recovery amount in each time period obtained by each recovery model in the embodiment of the present invention;

[0127] Figure 5 is a load recovery process diagram obtained by each recovery model in the embodiment of the present invention;

[0128] Figure 6 is a graph of steady-state frequency variation obtained by each recovery model in the embodiment of the present invention;

[0129] Figure 7 is a graph of the lowest point frequency variation obtained by each restoration model in the embodiment of the present invention;

[0130] Figure 8 is a graph of maximum frequency change rates obtained by each restoration model in the embodiment of the present invention;

[0131] Fig. 9 is a graph showing a change in the frequency error at the lowest point of the boundary shrinkage algorithm used in the embodiment of the present invention;

[0132] Fig.10 is a load recovery progress diagram obtained by each recovery model in the embodiment of the present invention;

[0133] Fig.11 is a graph of the lowest point frequency variation obtained by each recovery model in a severe scenario according to an embodiment of the present invention;

[0134] Fig.12 is a graph of maximum frequency change rates obtained by various recovery models in a severe scenario according to an embodiment of the present invention;

[0135] Fig.13 is a graph of the lowest point frequency variation obtained by each recovery model in a more severe scenario according to an embodiment of the present invention;

[0136] Fig.14 is a graph of maximum frequency change rates obtained by various recovery models in a more severe scenario according to an embodiment of the present invention;

[0137] Fig.15 is a load recovery process diagram obtained by each recovery model in an embodiment of the present invention on a 118-node power transmission system;

[0138] Fig.16 It is a graph of the lowest point frequency variation obtained by each restoration model in the embodiment of the present invention on the 118-node power transmission system. DETAILED DESCRIPTION

[0139] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0140] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0141] The purpose of the present invention is to provide a robust evaluation method for the new energy absorption capacity of distribution networks considering active network management. The method proposes a new method for evaluating the new energy absorption capacity of distribution networks. According to the frequency response characteristics of the new energy power grid recovery process, the system dynamic frequency security constraints are derived, and the McCormick convex envelope construction method based on boundary contraction is used for reasonable linearization. By analyzing and characterizing the power grid recovery process, a power grid recovery model considering dynamic frequency security is established, and a two-stage robust optimization method is used to deal with the uncertainty in the recovery process.

[0142] In the embodiment study, a case study was conducted on the IEEE 24-bus transmission system. Figure 2 As shown, the effectiveness of the proposed model is verified.

[0143] A. Test system and parameter settings

[0144] In the tested distribution system, at the initial moment, the two black start synchronous units at node 2 and node 15 have completed the restoration and grid connection, the remaining units and loads have not yet been connected to the grid, and the main grid lines of the system have not yet been fully restored. The total amount of load to be restored in the system is 2910MW, the load prediction error coefficient is 2%, and the load parameters of each node are shown in Table A3. The system recovery decision is expressed in the form of time periods, each time period represents 2.5 minutes, where time period 0 represents the initial moment of system recovery, and the process ends when the system recovery is completed.

[0145] (1) In order to verify the superiority of dynamic frequency security constraints in power grid restoration problems, three different frequency-constrained power grid restoration models are used for analysis and comparison:

[0146] Model 1: Grid restoration model without considering frequency security;

[0147] Model 2: Grid restoration model considering only steady-state frequency security constraints;

[0148] Model 3: Grid restoration model considering the proposed dynamic frequency security constraints.

[0149] (2) In order to verify the effectiveness and accuracy of linear substitution, an equivalent model simulating the dynamic frequency response process of the power system under different power disturbances was built using simulation tools. The simulation model consists of a thermal power unit with a rated capacity of 1560MW and a wind farm with a rated capacity of 1400MW.

[0150] (3) In order to verify the effectiveness and superiority of the proposed two-stage robust optimization-based power grid restoration method, three groups of control restoration models were set up for analysis and comparison. t Set to 5, and set the uncertainty interval of wind power output to ±20% of the predicted value. Figure 3 It is the short-term prediction curve and fluctuation range of wind power output.

[0151] Model 1: Deterministic grid restoration model based on short-term forecast of wind turbine output;

[0152] Model 2: Power grid restoration model considering stochastic optimization method;

[0153] Model 3: Consider the proposed two-stage robust optimization grid restoration model.

[0154] (4) In order to further verify the universality of the proposed method for power systems of different sizes, the proposed grid restoration strategy is further analyzed and verified on the IEEE 118-node system. Three grid restoration models with different frequency constraints are also analyzed and compared:

[0155] Model 1: Grid restoration model without considering frequency security;

[0156] Model 2: Grid restoration model considering only steady-state frequency security constraints;

[0157] Model 3: Grid restoration model considering the proposed dynamic frequency security constraints.

[0158] B. Feasibility analysis of power grid restoration scheme considering dynamic frequency safety

[0159] The feasibility of the proposed grid restoration method under dynamic frequency security constraints is verified, and the restoration plans of nodes, transmission lines and units after solving the restoration model are shown in Table (3).

[0160] Table (3) Grid restoration optimization results

[0161]

[0162] As can be seen from the table, at time t1, the black start units G4 and G5 are connected to the grid and the system nodes and transmission lines are restored in an orderly manner starting from nodes i2 and i5 according to the predetermined restoration order constraints. 10The power transmission network was fully restored in an instant, effectively ensuring the rapid recovery of subsequent user loads.

[0163] And the units can be connected to the grid in an orderly manner according to the grid recovery requirements. In the early stage of grid recovery, due to the poor system inertia level and frequency regulation capability, in order to ensure the stability of the system frequency, the synchronous units G1, G2 and G3 are connected to the grid at t3 and t5 respectively after their nodes are restored, providing frequency support and restoring output for the grid. After the system's transmission grid is roughly restored and the frequency support capacity is improved, in order to meet the load recovery requirements, the wind turbines are connected from t 11 During the entire restoration process, the order of nodes, lines, and units being connected to the grid was reasonable, and the normal operation of the power transmission network was guaranteed, which verified the rationality and feasibility of the restoration strategy.

[0164] After the load node is connected to the grid, the generator set can supply power to the load, so that the grid load is gradually restored. The optimization results of the load recovery amount in each period are as follows: Figure 4 shown.

[0165] from Figure 4 It can be seen from the table that in the initial period of system recovery, t1-t5, since the transmission network is in the early stage of construction, most of the unit output needs to be used for the restoration of the transmission network, and most of the load nodes and units have not yet been connected to the grid, so the load recovery amount is at a low level and unstable. After t5, the transmission line has basically completed the restoration, and all synchronous units have been connected to the grid, so the load recovery amount begins to increase and stabilize. Combining Table (3) and Figure 2 It can be seen that as the load recovery amount increases, the output of the synchronous unit cannot meet the load recovery demand, so at t9-t 10 The load recovery amount decreased slightly during the period. 11 After time t, the wind turbines start to connect to the grid and participate in load recovery. However, as the wind turbine output ratio increases, the wind turbine output is uncontrollable and difficult to dispatch. 21 After the time, the system load recovery rate decreases until all loads are connected to the grid and restored.

[0166] The entire system recovery process takes into account both load recovery efficiency and dynamic frequency safety. The grid connection order of transmission lines, units, and load nodes is reasonable, which fully reflects the feasibility and safety of the recovery strategy.

[0167] C. Necessity verification of dynamic frequency safety constraints

[0168] (1) Comparison of power grid restoration effects

[0169] The load recovery process under the three models is as follows: Figure 5As shown, due to the heavy load on a single node, the entire recovery process requires multiple periods.

[0170] As can be seen from the figure, model 1 requires 9 time periods totaling 23 minutes to complete the grid restoration, model 2 requires 15 time periods totaling 40 minutes to complete the restoration, and model 3 requires 35 time periods totaling 85.5 minutes to complete the entire grid restoration process. Models 1 and 2 do not consider the dynamic frequency safety of the system or consider it insufficiently, which increases the amount of power disturbance that the system can withstand and speeds up the load recovery rate, but in the actual restoration process, it is very likely to cause frequency limit accidents in the power grid. Model 3, which takes into account the proposed dynamic frequency safety constraints, strictly guarantees the dynamic frequency safety during the system restoration process, and the recovery time is relatively long, but it still maintains a reasonable recovery efficiency and meets the efficiency requirements of grid restoration.

[0171] (2) Comparison of system frequency changes

[0172] According to the grid restoration strategies obtained under the three restoration models, the frequency changes during the restoration process are calculated according to the calculation method of the dynamic frequency security index. The steady-state frequency change, the lowest frequency change and the maximum frequency change rate under different models are shown as follows: Figure 6 , Figure 7 and Figure 8 shown.

[0173] from Figure 6 It can be seen that Model 2 with steady-state frequency constraints and Model 3 with dynamic frequency safety constraints can ensure that the steady-state frequency remains within the safety threshold during the entire recovery process. 11 The steady-state frequency change index during the time period is always near the safety threshold of 0.15Hz, indicating that the steady-state frequency constraint is the main constraint limiting its load recovery efficiency, ensuring the steady-state frequency safety during the recovery process.

[0174] Since model three takes into account the proposed dynamic frequency safety constraints, its steady-state frequency can retain more safety margins; finally, for model one, since it does not take into account the frequency safety constraints, its overly fast grid recovery efficiency causes its steady-state frequency change to significantly exceed the safety threshold of 0.15Hz during the time period t2-t9, which does not meet the safety requirements of grid recovery.

[0175] from Figure 7 and Figure 8 It can be seen that although the steady-state frequency constraint of model 2 can ensure that its steady-state frequency change is within the safety threshold, 15 During the period, the frequency change at the lowest point and the maximum frequency change rate exceeded the safety range allowed by the system, which may easily lead to the failure of the relatively weak power grid in the early stage of recovery, posing a safety hazard.

[0176] Since the proposed dynamic frequency safety index constraint is adopted in model 3, the frequency change of the lowest point of the system in each recovery period Δf nadir The maximum frequency change rate RoCoF can be well maintained within the safety range, effectively ensuring the frequency safety during the power grid restoration process and meeting the safety requirements of the power grid.

[0177] It can be seen from this that the power grid restoration method considering dynamic frequency safety proposed in the present invention can well balance system frequency safety and restoration efficiency, which fully demonstrates the effectiveness and superiority of the method.

[0178] D. Validity analysis of McCormick convex envelope construction based on boundary shrinkage algorithm

[0179] By conducting simulation experiments under different power disturbances, the dynamic frequency safety index of the system after the disturbance is obtained and compared with the frequency safety index calculated by the proposed McCormick convex envelope construction and boundary shrinkage method. The feasibility of the linearization method is verified by comparing the errors between the two. The comparison results are shown in Table (4).

[0180] Table (4) Comparison of frequency safety index results under different methods

[0181]

[0182] It can be seen from Table (4) that under different power disturbance scenarios, the lowest frequency change Δf after the disturbance obtained by the simulation experiment is nadir The maximum deviation of the lowest frequency change calculated by the proposed method is 0.526%, the maximum deviation of the maximum frequency change rate RoCoF is 0.168%, and the quasi-steady-state frequency Δf ss The maximum deviation value is 0.685%, which is within the error range allowed by power grid restoration. It can be seen that the dynamic frequency index value obtained by the proposed McCormick envelope construction method based on the boundary contraction algorithm is close to the actual simulation result, which can meet the accuracy requirements of system dynamic frequency security in power grid restoration decision-making, proving its effectiveness and feasibility.

[0183] Fig. 9 The most critical dynamic frequency safety indicator in the power grid recovery process—the frequency change at the lowest point Δf nadirThe error value changes with the number of iterations of the boundary shrinkage algorithm. As can be seen from the figure, when the boundary shrinkage algorithm is not used, the error between the lowest point frequency change obtained by the McCormick convex envelope construction method and the actual value is 68.57%, and after 25 boundary shrinkage iterations, the error is reduced to 0.526%, which fully demonstrates the effectiveness of the boundary shrinkage algorithm in improving the McCormick convex envelope linearization method.

[0184] E. Verification and analysis of robust recovery method considering wind turbine uncertainty

[0185] Fig.10 It represents the recovery process of the loads of the three models. Since Model 2 and Model 3 are 17 The output of synchronous units is large during the period, so the load recovery speed is faster than that of deterministic model 1; and t 18 After the proportion of wind turbine output increases, the load recovery speed of Model 2 and Model 3 begins to slow down due to the need to consider the feasibility of recovery strategies for typical scenarios / multiple scenarios and dynamic frequency safety, but still maintains a higher recovery efficiency than the deterministic model.

[0186] Fig.11 and Fig.12 The following are the lowest frequency change and maximum frequency change rate diagrams of the three groups of models in the severe scenario. Model 1 does not consider the random fluctuation of wind turbine output, so its recovery rate is faster, but it also has a more serious frequency limit phenomenon. As shown in the figure, at t 11 After the wind turbine is connected to the grid, due to the deviation between the actual output value and the predicted value of the wind turbine, the lowest frequency change Δf of the model is determined. nadir It immediately exceeded the safety threshold of 0.2Hz. 16 After the time, due to the increase in the proportion of wind turbine output, its maximum frequency change rate RoCoF also began to exceed the limit, and the over-limit amount of the two frequency safety indicators continued to increase with the increase in the proportion of wind turbine output. It can be seen that if the impact of wind turbine uncertainty is not considered in the recovery strategy, it will have a serious impact on the dynamic frequency safety of the power grid.

[0187] The random optimization model 2 and the two-stage robust optimization model 3 are used. Since the influence of the wind turbine output prediction deviation is reasonably handled, its recovery strategy can ensure that the dynamic frequency safety index remains within the safe range during the entire recovery period. 14 -t 19 Compared with the dynamic frequency safety index of model 2, model 3 can retain more safety margins during the period and can ensure the feasibility of the recovery strategy in more severe scenarios.

[0188] Fig.13 and Fig.14 They respectively represent the minimum frequency change and maximum frequency change rate of the three groups of models under the more severe scenario 2. As can be seen from the figure, under the more severe wind turbine output scenario, t 13 and t 17 After time t, the minimum frequency change and maximum frequency change rate of model 2 also exceeded the limit to varying degrees. This shows that although the random optimization method can ensure the frequency security of the power grid in most scenarios, the frequency index will still exceed the limit in extreme scenarios.

[0189] Model 3, which uses robust optimization, can keep the dynamic frequency safety index within a safe range in different severe scenarios during the entire recovery process because the proportion of wind turbine output is always maintained at a reasonable level. This ensures that the optimized recovery strategy has good robustness and meets the safety requirements of power grid restoration, fully demonstrating the superiority of the two-stage robust optimization adopted.

[0190] F. 118-node system effectiveness analysis

[0191] In the above case analysis, the IEEE 24-bus system was used to verify the proposed power grid restoration method and dynamic frequency security constraints, effectively demonstrating its effectiveness and superiority.

[0192] from Fig.15 and Fig.16 It can be seen that the proposed method can still well ensure that the power grid is restored within a reasonable time range on the 118-node power system, maintaining a high recovery efficiency. And compared with other methods, the proposed method can well ensure that the system frequency is always kept within a safe range during the entire recovery process, which fully demonstrates the applicability of this method to different power grid environments.

Claims

1. A robust restoration method for a new energy power grid considering dynamic frequency security convex envelope constraints, characterized in that: The robust restoration method of renewable energy power grid based on two-stage robust optimization method and dynamic frequency security convex envelope constraint is as follows: S1. Establish dynamic frequency security constraints and build a robust power grid recovery model based on them; S2, use McCormick convex envelope construction method to linearly replace the highly nonlinear dynamic frequency safety constraints, and then use the boundary shrinkage algorithm to improve the accuracy of linearization; S3. The recovery model is constructed in the form of a two-stage robust optimization, and the column and constraint generation algorithm is used to generate the main problem and sub-problems for mutual iterative solution.

2. According to a method and system for robustly evaluating the new energy consumption capacity of a distribution network considering active network management according to claim 1, it is characterized in that: Dynamic frequency safety constraint indicators: (1) Dynamic frequency safety constraint establishment When a power step disturbance ΔP occurs during grid recovery due to load connection or other reasons, e =ΔP s / s, the frequency response of the system is shown in formula (1). in: Convert equation (2) into time domain form, as shown in equation (3). in: From formula (1), the steady-state frequency change of the system can be obtained as From formula (3), we can get the frequency change rate and the maximum frequency change rate as follows: When the frequency change rate of the system is 0, the frequency change of the system reaches the maximum value, and the corresponding time t can be obtained. nadir for Substituting equation (8) into equation (3) can obtain the frequency change when the system frequency is at the lowest point, as shown in equation (9). So far, the three system dynamic frequency security constraints during the power grid restoration process are obtained, as shown in formula (10). Where: RoCoF max Indicates the maximum limit of the frequency change rate; Δf max Indicates the maximum limit of the change in the lowest frequency point; Indicates the maximum limit of steady-state frequency change.

3. According to a method and system for robustly evaluating the new energy consumption capacity of a distribution network considering active network management according to claim 1, it is characterized in that: Considering the deterministic recovery model of dynamic frequency safety: (1) Objective function In order to speed up the load recovery efficiency while ensuring the safety of grid frequency, the cumulative amount of electric energy consumed by the restored load is taken as the objective function, and different loads are assigned different importance levels, which takes into account both the load size and the importance level, and meets the actual needs of grid restoration. Where: α l is the importance weight coefficient of load l; P l,t Indicates the amount of load l that has been restored at time t. (2) Black start unit operation constraints Where: P gb,t Indicates the output of the black start unit gb; Indicates the upper limit of the climbing rate of the black start unit; and They respectively represent the rated output upper limit and minimum stable output of the black start unit. (3) Non-black start unit operation constraints Where: P g,t Indicates the output of non-black unit g; u g,t is a Boolean variable representing the start / stop status of non-black units; Indicates the upper limit of the non-black unit climbing rate; and Indicates the minimum and maximum start time of non-black start units. (4) Fan output constraints Where: P w,t Indicates the output of the wind farm; Indicates the output of a single fan; Indicates the installed capacity of a single wind turbine; Represents the predicted value of the fan output efficiency; x w,t Indicates the number of wind turbines connected to the wind farm; u w,t is a Boolean variable representing the access status of the wind farm. (5) Load recovery constraints Where: P l,t is the connected load; P l,max and P l,min Indicates the upper and lower limits of the load; u l,t Boolean variable indicating the load restoration status. (6) Network flow constraints Where: u ij,t is a Boolean variable representing the on / off state of branch ij at time t; Represents the maximum line capacity of branch ij. (7) System backup constraints Where: l % and δ w % is the prediction error coefficient of load and fan. (8) System recovery order constraints (9) Frequency disturbance analysis during recovery In the problem of power grid restoration, since the system is in a relatively weak state, it is impossible to ensure the dynamic frequency safety of the system in large disturbance scenarios such as system N-1 failure. Therefore, in the restoration process, only the power disturbance caused by load grid connection and wind turbine output fluctuation at the steady-state operation level is considered. a) Power disturbance of load connected to the grid Where: l Indicates the correction factor of cold load starting characteristics (ρ l >1); ΔP l,t Represents the access change of load l at time t. b) Power disturbance caused by wind turbine output fluctuation Where: and Indicates the actual and predicted output values ​​of the wind power plant.

4. According to a method and system for robustly evaluating the new energy consumption capacity of a distribution network considering active network management according to claim 1, it is characterized in that: Robust power grid restoration model considering uncertainty of renewable energy: (1) Construction of wind turbine output uncertainty set According to the distribution of historical data of wind turbine output, the uncertainty set of wind turbine output capacity coefficient can be established, as shown in formula (21). Where: and They represent the actual value and predicted value of the fan output capacity coefficient respectively. For the Boolean variable in formula (21) By constraining the values, the conservatism of the two-stage robust model can be adjusted, as shown in formula (22). Where: B t is the conservative adjustment parameter of the two-stage robust model. (2) Construction of a two-stage robust recovery model In the process of grid restoration with a high proportion of wind power penetration, there are a large number of wind power output uncertainty scenarios, which pose severe challenges to the dynamic frequency security of the system and the feasibility of the restoration strategy. Therefore, a two-stage robust algorithm is adopted to reconstruct the grid restoration model to ensure the safety and reliability of the restoration strategy. The reconstructed two-stage robust restoration model is shown in Equation (23). Where: and is the constant positive slack variable of the node power flow balance constraint; ε is the safety threshold of the slack variable; F is the penalty coefficient. By adding slack variables and using them as the feasibility verification standard and penalty function of the power grid restoration strategy, the feasibility of the optimization solution obtained by the model is verified. For ease of expression, all variables are divided into four types and expressed in vector form, as shown in formula (24). The reformulated model is shown in formula (25). Where: G1-G4, D1-D5, A, I, b, c, d, g, t, v represent the relevant parameter matrices in the robust model respectively.

5. According to a method and system for robustly evaluating the new energy consumption capacity of a distribution network considering active network management according to claim 1, it is characterized in that: Linearization of safe frequency constraints: (1) McCormick convex envelope construction method The dynamic frequency safety constraint (10) has a large number of nonlinear parts, which will cause great difficulties in solving. It is necessary to perform McCormick linearization construction preprocessing on these frequencies and convert them into linear constraints. Before constructing the McCormick convex envelope, it is necessary to mathematically convert it into In order to simplify the frequency minimum point constraint where the nonlinear term coupling is the most complex, it is assumed that when the damping is small, the response of the primary frequency modulation process can be approximated as the power disturbance. Therefore, before the frequency reaches the minimum point, the primary frequency modulation process can be simplified to a slope of ΔP e / t nadir is a linear function of time t. Based on this approximation, the time domain expression (3) of the system frequency can be approximately derived as equation (26). Substituting the expression of the lowest frequency point time into the equation, we can obtain the simplified lowest frequency point Δf nadir The approximate expression of (27). make The inverse trigonometric function y in equation (27) is -1 (x) The McCormick envelope construction idea is used to convert it into a convex envelope form composed of multiple linear functions, as shown in formula (28). in: From formula (28), we can get the lowest frequency constraint of McCormick convex envelope, as shown in formula (30). Will Substituting into (31), we can get formula (31). At this point, the frequency dynamic safety constraints have been converted to The function form can be approximated by using the convex envelope construction idea. z=x·y、z=x / y and The convex envelopes of are shown in (32), (33) and (34) respectively. (2) Boundary shrinkage algorithm The convex envelope construction method based on McCormick is actually a convex relaxation of highly nonlinear functions, and its accuracy depends on the boundary values ​​of the frequency variables. and A smaller variable range can improve the approximation of the original function, thereby improving the accuracy of the method. Therefore, a boundary shrinkage algorithm is proposed to improve the accuracy of the convex envelope substitution, as shown in Table (1): Table (1) Boundary shrinkage algorithm 6. According to a method and system for robustly evaluating the new energy consumption capacity of a distribution network considering active network management according to claim 1, it is characterized in that: CCG algorithm: (1) Solving the main problem model By continuously adding scenarios and variables obtained from sub-problems to the main problem, it gradually approaches the optimal solution to the original problem, thereby effectively reducing the difficulty of solving and the number of iterations. (2) Solving the sub-problem model The sub-problem verifies the feasibility of the recovery strategy optimized by the main problem in massive uncertain scenarios through the added slack variables, and substitutes the scenarios that do not meet the feasibility verification back to the main problem. The subproblem model is a complex min-max two-layer optimization model. It is necessary to use the duality theory to transform the inner max problem into a min problem. The subproblem after the dual transformation is shown in formula (39). Where: μ1 and μ2 represent the dual variables corresponding to the constraints. (3) Column and Constraint Generation Algorithm The modified column and constraint generation algorithm is used to solve the two-stage robust optimization model, and equation (25) is decomposed into the main problem and sub-problems for iterative solution, as shown in Table (2): Table 2 Column and Constraint Generation Algorithm (CCG)

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