Power Network Restoration Decision-Making Method Considering the Coupling Characteristics of Power-Gas Networks

Abstract

The present invention relates to a power network restoration decision-making method considering the coupling characteristics of the power-gas network, including: establishing a power network restoration model based on the coupling characteristics of the power-gas network; establishing a power network restoration decision-making model based on the augmented Lagrangian function; solving the power network restoration decision-making model based on the ADMM distributed algorithm; obtaining a power network restoration decision-making scheme, including a load restoration scheme, a power source and gas source output plan scheme, and the power flow of lines or pipelines. Compared with the prior art, the present invention has the advantages of high decision-making efficiency and fast power network restoration.

Description

Technical Field

[0001] The present invention relates to the technical field of power network restoration, and in particular to a power network restoration decision-making method considering the coupling characteristics of power-gas networks. Background Art

[0002] Traditional power system restoration means that after a partial power outage or a large-scale power outage in the system, gas turbine units, hydroelectric units and other units with black start capabilities in the system or external power sources provide start-up power for other units in the system that do not have self-starting capabilities, gradually restoring the main backbone network and load of the system, and safely and effectively restoring the system to a new normal operating state.

[0003] However, the traditional method has the following defects: ① Taking the restoration of the transmission network as the core, it less considers the self-restoration ability of the distribution network. The distribution network needs to be restored after the main units are connected to the grid and the main transmission network is restored, which affects the continuous power supply of important loads; ② After a large-scale energy supply interruption accident occurs, there is a close interdependence between the restoration of power and gas energy networks. The traditional power network black start method fails to consider the impact of the coupling characteristics of power-gas networks on power network restoration.

[0004] In the prior art, the decision-making process for power network restoration methods mostly adopts a centralized decision-making method, making decisions based on a large amount of collected data and model data. Most of the time in the restoration process is spent on the decision-making process, resulting in a slow power network restoration time and low efficiency. Summary of the Invention

[0005] The purpose of the present invention is to provide a power network restoration decision-making method considering the coupling characteristics of power-gas networks, which has high decision-making efficiency and fast power network restoration, so as to overcome the defects existing in the above-mentioned prior art.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A power network restoration decision-making method considering the coupling characteristics of power-gas networks, the decision-making method includes:

[0008] Step 1: Establish a power network restoration model based on the coupling characteristics of power-gas networks;

[0009] Step 2: Establish a power network restoration decision model based on the augmented Lagrangian function;

[0010] Step 3: Solve the power network restoration decision model based on the ADMM distributed algorithm;

[0011] Step 4: Obtain a power network restoration decision plan, including a load restoration plan, a power source and gas source output plan, and the power flow of lines or pipelines.

[0012] Preferably, step 1 is specifically as follows:

[0013] Step 1-1: Establish a basic restoration model for the power network;

[0014] Specifically:

[0015] Assume that an energy supply interruption accident occurs at time t0. Starting from time t k moment, the restoration of electricity and gas loads at the transmission-gas transmission system level begins, and at the same time, the large-scale restoration of loads in the distribution-gas distribution system officially starts;

[0016] The hierarchical collaborative restoration of the electricity-gas interconnected system starts from time t k moment, that is, the restoration preparation stage has been completed, and each power source and gas source within the transmission-gas transmission system start, and transmission lines, gas transmission channels, distribution network substations, and gas distribution network pressure regulating stations have been put into operation;

[0017] Based on the electricity-gas interconnected system at this time, establish a hierarchical collaborative restoration model for the electricity-gas interconnected system;

[0018] Maximizing the weighted supply of electricity loads and gas loads within the transmission-gas transmission system and the distribution-gas distribution system is the objective function of the model, specifically:

[0019]

[0020] Among them, the superscript T of each variable represents the transmission grid or gas transmission network, and the superscript D represents the distribution grid or gas distribution network; the subscript E represents the power system, and the subscript G represents the natural gas system; the superscript L represents the load; the subscript t represents each restoration moment, and T R represents the set of each restoration moment; the subscript m represents the transmission grid node number, the subscript n represents the gas transmission network node number, the subscript i represents the distribution grid node number, and the subscript j represents the gas distribution network node number; and respectively represent the sets of all nodes of the transmission grid, gas transmission network, distribution grid, and gas distribution network respectively; and respectively represent the weight coefficients of each node of the corresponding system; are the load amounts restored by each system at each moment respectively;

[0021] The basic power grid restoration model has transmission - gas system restoration constraints and distribution - gas system restoration constraints; the transmission - gas system restoration constraints include power grid flow constraints and security constraints, gas network flow constraints and security constraints, and transmission - gas system load restoration constraints; the distribution - gas system restoration constraints include distribution network flow constraints and security constraints, gas distribution network flow constraints and security constraints, and distribution - gas system load restoration constraints.

[0022] Step 1 - 2: Add transmission - gas system coupling constraints, distribution - gas system coupling constraints, and boundary connection constraints between the transmission - gas system and the distribution - gas system to the basic power grid restoration model.

[0023] Step 1 - 3: Set the boundary connection variables of the transmission - gas system and the distribution - gas system during the restoration process.

[0024] Step 1 - 4: Obtain the power grid restoration model.

[0025] More preferably, the transmission - gas system coupling constraints and the distribution - gas system coupling constraints are specifically as follows:

[0026] The transmission - gas system coupling constraints and the distribution - gas system coupling constraints include:

[0027] Energy conversion relationship constraints of gas turbines:

[0028]

[0029] Among them, is the natural gas consumption of the gas turbine connected between distribution network node i and gas distribution network node j at time t; is the active power output of the gas turbine; is the power generation efficiency; G is the lower heating value of natural gas;

[0030] Energy conversion relationship constraints of gas turbines connected to the power grid and the gas network;

[0031] Energy conversion relationship constraints of P2G facilities:

[0032]

[0033] Among them, is the active power consumed by the P2G facility as an electrical load; is the corresponding natural gas flow rate, is the gas production efficiency;

[0034] Relationship constraints between the natural gas flow rate transmitted by the power - driven pressure regulating station in the gas network and the consumed electrical power:

[0035]

[0036] Among them, is the natural gas flow rate flowing through the power-driven pressure regulating station between the gas transmission network node n and the gas distribution network node j; is the electric power consumed by the power-driven pressure regulating station as an electrical load; β reg,T is the energy consumption coefficient;

[0037] The boundary connection constraints of the said power transmission-gas transmission system and power distribution-gas distribution system are specifically as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Among them, V t D,m,sub,sqr represents the square of the voltage amplitude of the substation connected to the power transmission network node m; and are the boundary connection constraints of the gas transmission-gas distribution system, represents the gas pressure on the boosting side of the gas distribution pressure regulating station connected to the gas transmission network node n, represents the gas pressure on the reducing side, Γ c is the boosting ratio.

[0044] More preferably, the said boundary connection variables include P t sub,D,m , V t D,m,sub,sqr , and

[0045] Preferably, the said step 2 is specifically as follows:

[0046] Step 2-1: Formalize the power network restoration model;

[0047] Step 2-2: Define the augmented Lagrangian function with respect to the boundary connection variables;

[0048] Step 2-3: Relax the boundary connection constraints;

[0049] Step 2-4: Establish the power network restoration decision model.

[0050] More preferably, the specific steps of step 2-1 are as follows:

[0051]

[0052]

[0053] and respectively represent the vectors composed of the boundary connection variables of the power transmission - gas transmission system and the power distribution - gas distribution system, that is:

[0054]

[0055]

[0056] and respectively represent the vectors composed of other decision variables in the power transmission - gas transmission system and the power distribution - gas distribution system except the boundary connection variables. f T and f D,m(n) respectively represent the negative forms of the function expressions related to the power transmission - gas transmission system and the power distribution - gas distribution system in the original objective function; h and g respectively represent the sets of corresponding equality and inequality constraints; the constraints h T and g T represent the power transmission - gas transmission system constraints, and h D,m(n) and g D,m(n) represent the power distribution - gas distribution system constraints. is the boundary connection constraint.

[0057] More preferably, the specific steps of step 2-2 are as follows:

[0058]

[0059] where ρ is the penalty coefficient when using the ADMM distributed algorithm to solve, and it is a positive constant; represents the vector composed of the boundary connection variables related to the power distribution system m and the gas distribution system n in the power transmission - gas transmission system restoration sub - problem, that is are the corresponding Lagrange multipliers; the < > operator represents the inner product operation between two vectors.

[0060] More preferably, the specific steps of step 2-4 are as follows:

[0061] The power network restoration model is:

[0062]

[0063]

[0064] The decision-making model includes the decision-making model for the transmission-gas system restoration sub-problem and the decision-making model for the distribution-gas system restoration sub-problem;

[0065] The decision-making model for the transmission-gas system restoration sub-problem is specifically as follows:

[0066]

[0067]

[0068] The decision-making model for the distribution-gas system restoration sub-problem is specifically as follows:

[0069]

[0070]

[0071] Preferably, step 3 is specifically as follows:

[0072] Step 3-1: Obtain the system parameters of the electricity-gas interconnected system, the power source and gas source parameters, the load parameters, and the power network restoration model parameters;

[0073] Step 3-2: Determine whether the convergence criterion is zero. If so, execute the steps; otherwise, execute the steps.

[0074] Step 3-3: Solve the decision-making model for the transmission-gas system restoration sub-problem and update the variable value, and then execute step 3-4;

[0075] Step 3-4: Solve the decision-making model for the distribution-gas system restoration sub-problem and update the variables and values, and then execute step 3-5;

[0076] Step 3-5: Update the Lagrange multiplier variable and then return to step 3-2;

[0077] Step 3-6: End the iteration and output the load restoration plan, the power source and gas source output plan, and the power flow of the line or pipeline.

[0078] More preferably, the convergence criterion is specifically as follows:

[0079] Take the primary residual and the dual residual as the convergence criterion, and the calculation method is:

[0080]

[0081]

[0082] If The optimal solutions of the sub-problems obtained by solving will finally converge to the optimal solution of the original problem.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] High decision-making efficiency and fast power network restoration: The power network restoration decision method in the present invention is based on the hierarchical collaborative restoration mechanism of the electric-gas interconnected system of the ADMM distributed algorithm. The transmission-gas system restoration sub-problem and the distribution-gas system restoration sub-problem can be independently solved separately only through the information interaction of limited boundary connection variables. Compared with the centralized restoration system of the electric-gas interconnected system in which the power system and the natural gas system are tightly coupled, on the basis of fully considering the characteristics of the hierarchical operation of the transmission and distribution of the electric and gas energy systems and the topological connection characteristics, this mechanism decouples the original problem into the transmission-gas system restoration sub-problem and the distribution-gas system restoration sub-problem, overcoming the disadvantages of low efficiency, difficult convergence, and possible non-global optimality in the process of solving the original problem, and effectively improving the solution efficiency of the large-scale electric-gas interconnected system restoration problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a schematic flow chart of the power network restoration decision method in the present invention;

[0086] Figure 2 is a schematic flow chart when using the ADMM distributed algorithm to solve the power network restoration decision model in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0087] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0088] A power network restoration decision method considering the coupling characteristics of the power-natural gas network, the process of which is as Figure 1 shown, includes:

[0089] Step 1: Establish a power network restoration model based on the coupling characteristics of the power-natural gas network;

[0090] Step 2: Establish a power network restoration decision model based on the augmented Lagrangian function;

[0091] Step 3: Solve the power network restoration decision model based on the ADMM distributed algorithm;

[0092] Step 4: Obtain the power network restoration decision-making scheme, including the load restoration scheme, the power generation and gas supply output plan scheme of power sources and gas sources, and the power flow of lines or pipelines.

[0093] The above steps are described in detail as follows:

[0094] I. Establish a power network restoration model based on the coupling characteristics of the power-gas network

[0095] Step 1-1: Establish a basic power network restoration model;

[0096] Specifically:

[0097] Assume that an energy supply interruption accident occurs at time t0. Starting from time t k moment, the electricity and gas loads at the transmission-gas transmission system level are restored, and at the same time, the loads of the distribution-gas distribution system officially start to be massively restored;

[0098] The hierarchical collaborative restoration of the electricity-gas interconnected system starts from time t k moment, that is, the restoration preparation stage has been completed, and each power source and gas source inside the transmission-gas transmission system starts, and the transmission lines, gas transmission channels, distribution network substations, and gas distribution network pressure regulating stations have been put into operation;

[0099] Based on the electricity-gas interconnected system at this time, establish a hierarchical collaborative restoration model of the electricity-gas interconnected system;

[0100] Maximize the weighted supply of electricity loads and gas loads in the transmission-gas transmission system and the distribution-gas distribution system as the objective function of the model. Specifically:

[0101]

[0102] Among them, the superscript T of each variable represents the transmission grid or gas transmission network, and the superscript D represents the distribution grid or gas distribution network; the subscript E represents the power system, and the subscript G represents the natural gas system; the superscript L represents the load; the subscript t represents each restoration moment, and T R represents the set of each restoration moment; the subscript m represents the node number of the transmission grid, the subscript n represents the node number of the gas transmission network, the subscript i represents the node number of the distribution grid, and the subscript j represents the node number of the gas distribution network; and respectively represent the sets of all nodes of the transmission grid, gas transmission network, distribution grid, and gas distribution network; and respectively represent the weight coefficients of each node of the corresponding system; are the load amounts restored by each system at each moment;

[0103] The basic power network restoration model is provided with transmission - gas system restoration constraints and distribution - gas system restoration constraints; the transmission - gas system restoration constraints include transmission network power flow constraints and security constraints, gas network power flow constraints and security constraints, and transmission - gas system load restoration constraints; the distribution - gas system restoration constraints include distribution network power flow constraints and security constraints, gas distribution network power flow constraints and security constraints, and distribution - gas system load restoration constraints;

[0104] 1. Transmission - gas system restoration constraints

[0105] (1) Transmission network power flow constraints and security constraints

[0106] For the power system restoration problem, reactive power and voltage problems need to be considered, so an AC power flow model of the transmission system needs to be established. The duration of the electromechanical transient process of the power system is on the order of seconds, and the duration of the electromagnetic transient process is on the order of milliseconds or even microseconds. The focus of this embodiment is on the restoration process of the power system and the natural gas system, and the time interval for its restoration optimization and control is 15 minutes. Therefore, it can be assumed that the transient process of the power system has been completed within the time interval between adjacent restoration moments. Thus, the transient process of the power system during the restoration process is not considered in this embodiment. The transmission network power flow constraints can be established based on the steady - state power system algebraic power flow equation.

[0107] Active and reactive power balance constraints for transmission system nodes:

[0108]

[0109]

[0110] Among them, the superscript G of each variable represents the power source. m′ is the node adjacent to m, and K T is the set of transmission lines connected to node m. are respectively the active power injection of node m and the active power flowing through line mm′; are respectively the reactive power injection, reactive power load of node m and the reactive power flowing through line mm′. The and on the right - hand side of the equation respectively represent the total active and reactive power losses on the transmission lines connected to node m.

[0111] Active and reactive power balance constraints for transmission system lines:

[0112]

[0113]

[0114] Among them, are respectively the conductance and susceptance of line mm′; are the voltage magnitudes of nodes m and m′ respectively; is the phase angle difference of the voltages at both ends of line mm′. Among them, the voltage magnitude and the cosine term and the sine term for the cross-product terms are processed using the quadratic relaxation technique, and the squared voltage magnitude term is processed using the improved piecewise linearization method, thus obtaining a convexified expression form of the line power flow constraint and realizing the convex relaxation of the constraint.

[0115] Transmission network restoration security constraints:

[0116] Include voltage magnitude constraints, upper and lower limits constraints and ramp constraints for the active and reactive power outputs of power sources, which are respectively:

[0117]

[0118]

[0119]

[0120]

[0121] Among them, and are respectively the upper and lower limits of the active power output of the power source; and are respectively the upper and lower limits of the reactive power output of the power source, is the upper limit of the ramp capacity of the power source within adjacent restoration periods.

[0122] Meanwhile, to ensure the frequency stability of the transmission system during the restoration process, the change in the total active load restoration amount between adjacent restoration moments should be lower than the maximum total active load restoration amount:

[0123]

[0124] (2) Gas network power flow constraints and security constraints

[0125] This embodiment mainly studies the physical processes and mechanism models of information interaction and mutual support between the transmission-gas system and the distribution-gas system during the restoration process. For the power flow constraint modeling of the gas network and the distribution network, the steady-state Weymouth power flow equation that ignores the dynamic characteristics is adopted.

[0126] Gas flow balance constraint for node n in the gas network system:

[0127]

[0128] Among them, and The natural gas flow rate injected by the gas source at node n and the natural gas flow rate consumed by the gas load at time t, respectively. Is the natural gas flow rate flowing through the gas transmission pipeline nn'.

[0129] Constraint on the relationship between the gas flow rate of the gas transmission pipeline and the pressure difference at both ends of the pipeline:

[0130]

[0131] Among them, Are the gas pressures at nodes n and n' respectively, Is the Weymouth constant of the pipeline nn'.

[0132] Among them, the expression of the sign function regarding the pressure difference at both ends of the pipeline is:

[0133]

[0134] For the non-linear terms in the above constraints, an improved piecewise linearization method is adopted for processing.

[0135] Safety constraint for the restoration of the gas transmission network:

[0136] Including the upper and lower limits of the pipeline gas flow, the upper and lower limits of the node gas pressure, the upper and lower limits of the gas source output, and the ramp constraint, which are respectively:

[0137]

[0138]

[0139]

[0140]

[0141] (3) Load restoration constraints for the power transmission - gas transmission system

[0142] Including the active load restoration constraint, the reactive load restoration constraint, the upper limit constraint of the power transmission network load, and the gas source safe operation constraint of the gas transmission system, which are respectively:

[0143]

[0144]

[0145] Among them, And Are the maximum active and reactive loads to be restored at node m respectively. The restoration of the active load of the power transmission network should be limited by the maximum load of its nodes, and at the same time, the reactive load should be restored proportionally to the active load according to a specific power factor.

[0146] Since it is assumed in this embodiment that the load nodes of the transmission network are the substation nodes of the distribution network, the upper limit of the transmission network load is the capacity of the distribution network substation:

[0147]

[0148] Similar to the transmission system, the safety operation constraints of the gas source in the gas transmission system are:

[0149]

[0150]

[0151] 2. Restoration Constraints of the Distribution-Gas Transmission System

[0152] (1) Power Flow Constraints and Safety Constraints of the Distribution Network

[0153] In this embodiment, the impact of unbalanced three-phase loads in the distribution network on restoration is ignored, and it is assumed that the distribution network is a three-phase balanced system. The power flow constraints of the distribution network are modeled using the single-phase closed-form branch flow model. For the mth distribution network (the number of the distribution network is the same as the load node number of the transmission network, and the superscript m of the distribution network number is omitted here for simplicity), the mathematical expression of the power flow constraints is as follows:

[0154] Active and Reactive Power Balance Constraints at Node i in the mth Distribution Network at Time t:

[0155]

[0156]

[0157] Where, and are the active power flow and reactive power flow through line ii' connected to node i, respectively; is the square of the current amplitude flowing through line ii'. It should be noted that since the current amplitude only appears in the form of a square term in the power flow constraints of the distribution network, is regarded as an independent variable rather than a quadratic variable. and are the active power and reactive power injected at node i, respectively, and are the actually restored active load and reactive load at node i, respectively.

[0158] Relationship Constraint between the Squares of the Voltage Magnitudes between Node i and Node i':

[0159]

[0160] Where, rii′ and x ii′ are the resistance and reactance of line ii′, respectively; is the square of the line impedance modulus. Similarly, since the voltage amplitude only appears in the form of a square term, it is regarded as an independent variable.

[0161] Relationship constraints between the node voltage amplitude and the corresponding line current amplitude, active and reactive power flow values:

[0162]

[0163] This constraint is a non-convex constraint. For the cross-product term the McCormick convex relaxation method is used, and for the variable square term the piecewise linearization method is used.

[0164] Distribution network security constraints:

[0165] Include voltage assignment page numbers, upper and lower limit constraints on the active and reactive power outputs of power sources, and ramp constraints, specifically:

[0166]

[0167]

[0168]

[0169]

[0170] (2) Gas distribution network power flow constraints and security constraints

[0171] The mathematical expression forms of the power flow constraints and security constraints of the gas distribution network are the same as those of the gas transmission network.

[0172] (3) Load restoration constraints

[0173] The load restoration constraints of the distribution network are similar to those of the transmission network:

[0174]

[0175]

[0176] To ensure the restoration effect, the restoration of the terminal electricity load should be continuous, that is, the load restored at subsequent moments should not be less than that at the previous moment:

[0177]

[0178] In addition, the active / reactive power received by the distribution substation should not exceed the power flowing out of the node of the transmission network to which it is connected:

[0179]

[0180]

[0181] Similarly, the constraints for the recovery of the end - use gas load in the gas distribution network are as follows:

[0182]

[0183]

[0184] The natural gas flow received by the gas distribution and pressure - regulating station should also satisfy the following constraints:

[0185]

[0186] Step 1 - 2: Add the coupling constraints between the power transmission - gas transmission system, the power distribution - gas distribution system, and the boundary connection constraints between the power transmission - gas transmission system and the power distribution - gas distribution system to the basic power network restoration model;

[0187] The coupling constraints between the power transmission - gas transmission system and the power distribution - gas distribution system include:

[0188] The energy conversion relationship constraints of gas - fired units:

[0189]

[0190] Among them, is the natural gas consumption of the gas - fired unit connected between the power distribution network node i and the gas distribution network node j at time t; is the active power output of the gas - fired unit; is the power generation efficiency; G is the lower calorific value of natural gas;

[0191] The energy conversion relationship constraints of gas - fired units connected to the power transmission network and the gas transmission network;

[0192] The energy conversion relationship constraints of P2G facilities:

[0193]

[0194] Among them, is the active power consumed by the P2G facility as an electricity load; is the corresponding natural gas flow, is the gas production efficiency;

[0195] The relationship constraints between the natural gas flow transmitted by the power - driven pressure - regulating station in the gas transmission network and the consumed electric power:

[0196]

[0197] Among them, is the natural gas flow rate of the electric-driven pressure regulating station flowing between the transmission network node n and the distribution network node j; is the electric power consumed by the electric-driven pressure regulating station as an electric load; β reg,T is the energy consumption coefficient;

[0198] The boundary connection constraints of the transmission-gas transmission system and the distribution-gas distribution system are specifically as follows:

[0199]

[0200]

[0201]

[0202]

[0203]

[0204] Among them, V t D,m,sub,sqr represents the square of the voltage amplitude of the substation connected to the transmission network node m; and are the boundary connection constraints of the gas transmission-distribution system, represents the gas pressure on the boosting side of the gas pressure regulating station connected to the gas transmission network node n, represents the gas pressure on the reducing side, Γ c is the boosting ratio;

[0205] Steps 1-3: Set the boundary connection variables of the transmission-gas transmission system and the distribution-gas distribution system during the restoration process, including P t sub,D,m , V t D,m,sub,sqr , and

[0206] Step 1-4: Obtain the power network restoration model.

[0207] II. Establish a power network restoration decision model based on the augmented Lagrangian function

[0208] Step 2-1: Formalize the power network restoration model;

[0209] Step 2-1 is specifically as follows:

[0210]

[0211]

[0212] and represent the vectors composed of the boundary connection variables of the power transmission - gas transmission system and the power distribution - gas distribution system respectively, that is:

[0213]

[0214]

[0215] and represent the vectors composed of other decision variables in the power transmission - gas transmission system and the power distribution - gas distribution system except the boundary connection variables, f T and f D,m(n) represent the negative - form of the function expressions related to the power transmission - gas transmission system and the power distribution - gas distribution system in the original objective function respectively; h and g represent the sets of corresponding equality and inequality constraints; the constraints h T and g T represent the power transmission - gas transmission system constraints, h D,m(n) and g D,m(n) represent the power distribution - gas distribution system constraints, is the boundary connection constraint;

[0216] Step 2 - 2: Define the augmented Lagrangian function for the boundary connection variables;

[0217] Specifically:

[0218]

[0219] where ρ is the penalty coefficient when using the ADMM distributed algorithm to solve, and it is a positive constant; represents the vector composed of the boundary connection variables associated with the power distribution system m and the gas distribution system n in the power transmission - gas transmission system restoration sub - problem, that is is the corresponding Lagrange multiplier; the < > operator represents the inner - product operation between two vectors;

[0220] Step 2 - 3: Relax the boundary connection constraints;

[0221] Step 2 - 4: Establish the power network restoration decision model;

[0222] The power network restoration model is:

[0223]

[0224]

[0225] In view of the problems existing in the centralized restoration optimization of large-scale electric-gas interconnected systems, such as difficulties in data acquisition of each subsystem, inconvenient information interaction, and high solution complexity, this embodiment uses the ADMM distributed algorithm to decompose the centralized restoration optimization problem of large-scale electric-gas interconnected systems into the transmission-gas system restoration sub-problem and the distribution-gas system restoration sub-problem, and realizes the solution through a finite number of iterations.

[0226] The ADMM algorithm is a typical decomposition and coordination algorithm. By establishing mutually coordinated superior and subordinate institutions, the original large-scale system optimization problem can be decomposed into internal subsystem problems and solved distributively. The ADMM algorithm combines the advantages of the Lagrange multiplier method and dual decomposition, and has advantages such as a simple derivation form, good global convergence, and strong solution robustness. The ADMM algorithm usually uses the augmented Lagrangian relaxation method to handle the consistency constraint, that is, the boundary connection constraint established in this embodiment, and calculates the divided sub-problems in an alternating iteration form.

[0227] This embodiment uses the ADMM distributed algorithm to solve the above optimization problem based on the augmented Lagrangian function. By solving the transmission-gas system restoration sub-problem and the distribution-gas system restoration sub-problem through a finite number of iterations and performing information interaction, the decomposition and dimension reduction of the problem and efficient solution can be achieved. The ADMM distributed algorithm needs to calculate in each iteration:

[0228]

[0229]

[0230]

[0231] where k represents the iteration number.

[0232] In the solution process of the (k + 1)-th iteration, the transmission-gas system restoration sub-problem is solved based on the and obtained in the k-th step to solve the values of and and update them to and All distribution-gas system restoration sub-problems are solved based on the obtained in the k-th step to solve and and update them to and After that, solve and update it to

[0233] It should be noted that in each iterative solution process, the variables participating in the iterative update are all taken from the results obtained in the previous iterative step, rather than the results obtained in the previous iterative steps, to ensure better convergence of the iterative solution. In addition, the decision variables and are also calculated and participate in information interaction.

[0234] So far, the power network restoration model can be sorted out into a decision-making model for the transmission-gas system restoration sub-problem and a decision-making model for the distribution-gas system restoration sub-problem.

[0235] The decision-making model for the transmission-gas system restoration sub-problem is specifically as follows:

[0236]

[0237]

[0238] In each iteration, the transmission-gas system restoration sub-problem only takes the boundary connection variables and obtained by solving the distribution-gas system restoration sub-problem in the previous iteration, that is, only limited information interaction is carried out.

[0239] The decision-making model for the distribution-gas system restoration sub-problem is specifically as follows:

[0240]

[0241]

[0242] In each iteration process, based on the boundary connection variables obtained by solving the transmission-gas system restoration sub-problem in the previous step, each distribution-gas system restoration sub-problem is solved in parallel to update the corresponding Lagrange multipliers and and pass them to the solution of the next transmission-gas system restoration sub-problem.

[0243] III. Solving the power network restoration decision model based on the ADMM distributed algorithm

[0244] The solution process is as Figure 2 shown and includes:

[0245] Step 3-1: Obtain the system parameters of the electricity-gas interconnected system, the parameters of power sources and gas sources, the load parameters, and the parameters of the power network restoration model;

[0246] Step 3-2: Judge whether the convergence criterion is zero. If so, execute the steps, otherwise, execute the steps;

[0247] Step 3-3: Solve the transmission-gas pipeline system restoration sub-problem and update the values of the variables, then execute Step 3-4; and then execute Step 3-4;

[0248] Step 3-4: Solve the distribution-gas pipeline system restoration sub-problem and update the values of the variables and and then execute Step 3-5;

[0249] Step 3-5: Update the Lagrange multiplier variables and then return to Step 3-2;

[0250] Step 3-6: End the iteration, and output the load restoration plan, the power generation and gas supply plans of the power sources and gas sources, and the power flows of the lines or pipelines.

[0251] During the iteration process of each step, the primary residual and the dual residual can be used as the convergence criteria. Their values are solved respectively through the following two formulas to determine whether the convergence requirements are met:

[0252]

[0253]

[0254] It can be proved that if then the optimal solutions of the sub-problems obtained by iterative solution using the ADMM distributed algorithm will finally converge to the optimal solution of the original problem.

[0255] As described above, it is only the specific implementation manners of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A power network restoration decision-making method considering the coupling characteristics of the power-gas network, characterized in that The described decision-making method includes: Step 1: Establish a power network restoration model based on the coupling characteristics of the power-gas network; Step 2: Establish a power network restoration decision model based on the augmented Lagrangian function; Step 3: Solve the power network restoration decision model based on the ADMM distributed algorithm; Step 4: Obtain the power network restoration decision plan, including the load restoration plan, the power generation and gas supply output plan of power sources and gas sources, and the power flow of lines or pipelines; The specific content of Step 1 is as follows: Step 1-1: Establish a basic power network restoration model; Specifically: Suppose an energy supply interruption accident occurs at time t0, and starting from time t k , the electricity and gas loads at the transmission and gas transmission system levels begin to be restored, and at the same time, the loads of the distribution and gas distribution systems officially begin to be restored on a large scale; The hierarchical collaborative restoration of the electric-gas interconnected system starts from time t k That is, the preparation stage of restoration has been completed, and all power sources and gas sources within the power transmission-gas transmission system start, and the power transmission lines, gas transmission channels, distribution network substations, and gas distribution network pressure regulating stations have been put into operation; Based on the power-gas interconnected system at this time, establish a hierarchical collaborative restoration model for the power-gas interconnected system; Maximize the weighted supply of electrical loads and gas loads in the transmission-gas transmission system and the distribution-gas distribution system as the objective function of the model. Specifically: Among them, the superscript T of each variable represents the transmission power grid or gas transmission network, and the superscript D represents the distribution power grid or gas distribution network; the subscript E represents the power system, and the subscript G represents the natural gas system; the superscript L represents the load; the subscript t represents each restoration time, and T R represents the set of each restoration time; the subscript m represents the node number of the transmission power grid, the subscript n represents the node number of the gas transmission network, the subscript i represents the node number of the distribution power grid, and the subscript j represents the node number of the gas distribution network; and respectively represent the sets of all nodes of the transmission power grid, gas transmission network, distribution power grid, and gas distribution network; and respectively represent the weight coefficients of each node of the corresponding system; are respectively the load amounts restored by each system at each time; The basic power network restoration model is provided with transmission-gas transmission system restoration constraints and distribution-gas distribution system restoration constraints; the transmission-gas transmission system restoration constraints include transmission network power flow constraints and security constraints, gas transmission network power flow constraints and security constraints, and transmission-gas transmission system load restoration constraints; the distribution-gas distribution system restoration constraints include distribution network power flow constraints and security constraints, gas distribution network power flow constraints and security constraints, and distribution-gas distribution system load restoration constraints; Step 1-2: Add transmission-gas transmission system coupling constraints, distribution-gas distribution system coupling constraints, and boundary connection constraints between the transmission-gas transmission system and the distribution-gas distribution system to the basic power network restoration model; Step 1-3: Set the boundary connection variables of the transmission-gas transmission system and the distribution-gas distribution system during the restoration process; Step 1-4: Obtain the power network restoration model; The specific content of Step 2 is as follows: Step 2-1: Formalize the power network restoration model; Step 2-2: Define the augmented Lagrangian function regarding the boundary connection variables; Step 2-3: Relax the boundary connection constraints; Step 2-4: Establish the power network restoration decision model; The specific content of Step 2-1 is as follows: and respectively represent the vectors composed of the boundary connection variables of the power transmission - gas transmission system and the power distribution - gas distribution system, that is: and respectively represent the vectors composed of other decision variables except the boundary connection variables in the power transmission - gas transmission system and the power distribution - gas distribution system, f T and f D,m(n) respectively represent the negative - form of the function expressions related to the power transmission - gas transmission system and the power distribution - gas distribution system in the original objective function; h and g respectively represent the sets of corresponding equality and inequality constraints; the constraints h T and g T represent the power transmission - gas transmission system constraints, h D,m(n) and g D,m(n) represent the power distribution - gas distribution system constraints, is the boundary connection constraint; The specific content of Step 2-2 is as follows: where ρ is the penalty coefficient when solving using the ADMM distributed algorithm and is a positive constant; denotes the vector composed of the boundary connection variables associated with the distribution system m and the gas distribution system n in the power - to - gas system restoration sub - problem, that is is the corresponding Lagrange multiplier; the <> operator represents the inner product operation between two vectors; The specific content of Step 2-4 is as follows: The power network restoration model is: The decision model includes a transmission-gas transmission system restoration sub-problem decision model and a distribution-gas distribution system restoration sub-problem decision model; The transmission-gas transmission system restoration sub-problem decision model is specifically: The distribution-gas distribution system restoration sub-problem decision model is specifically: The specific content of Step 3 is as follows: Step 3-1: Obtain the system parameters of the power-gas interconnected system, the parameters of power sources and gas sources, the load parameters, and the parameters of the power network restoration model; Step 3-2: Judge whether the convergence criterion is zero. If so, execute the steps, otherwise, execute the steps; Step 3-3: Solve the decision-making model for the power-gas system restoration sub-problem and update the variables values, and then execute Step 3-4; Step 3-4: Solve the decision-making model for the distribution-gas system restoration sub-problem and update the variables and the values of, and then execute Step 3-5; Step 3-5: Update the Lagrange multiplier variable Then return to Step 3-2; Step 3-6: End the iteration and output the load restoration plan, the power generation and gas supply output plan of power sources and gas sources, and the power flow of lines or pipelines.

2. A power network restoration decision-making method considering the coupling characteristics of the power-gas network according to claim 1, characterized in that The specific content of the transmission-gas transmission system coupling constraints and the distribution-gas distribution system coupling constraints is as follows: The transmission-gas transmission system coupling constraints and the distribution-gas distribution system coupling constraints include: Energy conversion relationship constraints of gas turbines: Among them, is the natural gas consumption of the gas turbine connected between the distribution network node i and the gas distribution network node j at time t; is the active power output of the gas turbine; is the power generation efficiency; G is the low calorific value of natural gas; Energy conversion relationship constraints of gas turbines connected to the transmission network and the gas transmission network; Energy conversion relationship constraints of P2G facilities: Among them, is the active power consumed by the P2G facility as an electrical load; is the corresponding natural gas flow rate, is the gas production efficiency; Constraint on the relationship between the gas flow rate transmitted by the power-driven pressure regulating station in the gas transmission network and the consumed electric power: wherein, is the natural gas flow rate of the electric-driven pressure regulating station flowing between the gas transmission network node n and the gas distribution network node j; is the electric power consumed by the electric-driven pressure regulating station as an electric load; β reg,T is the energy consumption coefficient; The boundary connection constraint of the power transmission-gas transmission system and the power distribution-gas distribution system is specifically as follows: Among them, V t D,m,sub,sqr represents the square of the voltage amplitude of the substation connected to the transmission network node m; and are the boundary connection constraints of the gas transmission - distribution system, represents the gas pressure on the step - up side of the gas distribution regulating station connected to the gas transmission network node n, represents the gas pressure on the step - down side, Γ c is the step - up ratio, P t sub,D,m represents the active power received by the distribution transformer substation, represents the reactive power received by the distribution transformer substation, represents the reactive power load of node m, represents the voltage amplitude of node m.

3. A power grid restoration decision-making method considering the coupling characteristics of the power-gas network according to claim 2, characterized in that, The boundary connection variables include P t sub,D,m , V t D ,m,sub,sqr , and 4. A power network restoration decision-making method considering the coupling characteristics of the power-gas network according to claim 1, characterized in that, The convergence criterion is specifically as follows: Take the primary residual and the dual residual as the convergence criterion, and the calculation method is as follows: If then the optimal solutions of the sub-problems obtained by solving finally converge to the optimal solution of the original problem.

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