Black start method of power network considering coupling characteristics of power-gas network

Abstract

The present invention relates to a method for black start of an electric power network taking into account the coupling characteristics of an electric power-gas network, comprising: establishing a hierarchical collaborative recovery model of an electric-gas interconnected system based on the coupling characteristics of an electric-gas network; establishing a decision model of the hierarchical collaborative recovery model of an electric-gas interconnected system; solving the decision model to obtain a black start plan for the electric power network. Compared with the prior art, the present invention has the advantages of fast black start speed and high efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of power network restoration, and in particular to a power network black start method taking into account the coupling characteristics of power-natural gas networks. Background Art

[0002] Traditional power system recovery means that after a partial or large-scale power outage, gas units, hydropower units and other units with black start capabilities within the system or external power supplies are used to provide starting power for other units in the system that do not have self-starting capabilities, gradually restore the system backbone grid and load, and restore the system safely and effectively to a new normal operating state.

[0003] However, the traditional method has the following defects: ① The core is the restoration of the transmission network, and the recovery capacity of the distribution network itself is rarely considered. The distribution network needs to be restored after the main units are connected to the grid and the trunk transmission network is restored, which affects the continuous power supply of important loads; ② After a large-scale energy supply interruption accident, the restoration of the power and natural gas energy networks is closely interdependent. The traditional power network black start method fails to consider the impact of the coupling characteristics of the power-natural gas network on the restoration of the power network.

[0004] After a large-scale energy supply interruption accident, the restoration of the electricity and gas energy networks is closely interdependent. For the restoration of the power network, the transmission network relies on gas units to provide reliable system restoration power; the distribution network relies on micro gas turbines and other distributed power sources to maintain the power supply of important loads. For the restoration of the natural gas network, after the electric-driven pressure regulating station loses power supply, the natural gas-driven pressure regulating stations that are generally available can maintain the basic operation of the network, but the unavailability of the electric-driven pressure regulating station seriously reduces the transmission capacity of the natural gas network. The recovery capacity of the natural gas network load depends on the power supply of the electric-driven pressure regulating station to the electric-driven pressure regulating station. Therefore, it is necessary to study the coordinated restoration of the electricity and gas networks. Comprehensive consideration of the restoration of the electricity and natural gas networks can improve the recovery efficiency of the electricity-gas interconnection network. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a black start method for an electric power network with fast black start speed and high efficiency taking into account the coupling characteristics of the electric power-natural gas network.

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

[0007] A black start method for an electric power network taking into account the coupling characteristics of an electric power-natural gas network, the black start method for an electric power network comprising:

[0008] Step 1: Establish a hierarchical collaborative restoration model for the electricity-gas interconnection system based on the coupling characteristics of the electricity-gas network;

[0009] Step 2: Establish a decision model for the hierarchical collaborative restoration model of the electricity-gas interconnection system;

[0010] Step 3: Solve the decision model and obtain the black start plan for the power network.

[0011] Preferably, the method for establishing the hierarchical collaborative restoration model of the electric-gas interconnected system in step 1 is:

[0012] Assume that the energy supply interruption accident occurs at time t0. k From that moment on, the electricity and gas loads at the transmission and gas transmission system level will be restored, and at the same time, the loads of the distribution and gas distribution system will be restored on a large scale;

[0013] Hierarchical coordinated recovery of electricity-gas interconnection system k At the beginning of the moment, the recovery preparation phase has been completed, the power supply and gas source in the power transmission and gas transmission system have been started, and the power transmission lines, gas transmission channels, distribution network substations and gas distribution network pressure regulating stations have been put into operation;

[0014] Based on the current electricity-gas interconnection system, a hierarchical collaborative recovery model of the electricity-gas interconnection system is established.

[0015] Preferably, the hierarchical collaborative recovery model of the electricity-gas interconnection system is specifically:

[0016] The objective function of the model is to maximize the weighted supply of electricity load and gas load in the transmission-gas transmission system and the distribution-gas distribution system, specifically:

[0017]

[0018] Among them, the superscript T of each variable represents the transmission network or gas transmission network, the superscript D represents the distribution network or gas distribution network; the subscript E represents the power system, the subscript G represents the natural gas system; the superscript L represents the load; the subscript t represents the restoration time, T R represents the set of restoration moments; subscript m represents the node number of the transmission network, subscript n represents the node number of the gas transmission network, subscript i represents the node number of the distribution network, and subscript j represents the node number of the gas distribution network; and They represent the sets of all nodes of the transmission network, gas transmission network, distribution network and gas distribution network respectively; and Respectively represent the weight coefficients of each node of the corresponding system; are the load restored by each system at each moment.

[0019] Preferably, the hierarchical collaborative recovery model of the electricity-gas interconnection system is provided with a power transmission-gas transmission system recovery constraint and a distribution-gas distribution system recovery constraint; the power transmission-gas transmission system recovery constraint includes a power transmission network flow constraint and a safety constraint, a gas transmission network flow constraint and a safety constraint, and a power transmission-gas transmission system load recovery constraint; the distribution-gas distribution system recovery constraint includes a power distribution network flow constraint and a safety constraint, a gas distribution network flow constraint and a safety constraint, and a distribution-gas distribution system load recovery constraint.

[0020] Preferably, the hierarchical collaborative restoration model of the electricity-gas interconnection system is also provided with coupling constraints of the power transmission-gas transmission system, coupling constraints of the power distribution-gas distribution system, and boundary connection constraints of the power transmission-gas transmission system and the power distribution-gas distribution system.

[0021] More preferably, the power transmission-gas transmission system coupling constraints and the power distribution-gas distribution system coupling constraints include:

[0022] Energy conversion relationship constraints of gas units:

[0023]

[0024] in, is the natural gas consumption of the gas generating unit connected between the distribution network node i and the gas distribution network node j at time t; Provide active power for gas-fired units; is the power generation efficiency; G is the lower calorific value of natural gas;

[0025] Energy conversion relationship constraints of gas-fired units connected to the transmission grid and gas grid;

[0026] P2G facility energy conversion relationship constraints:

[0027]

[0028] in, The active power consumed by the P2G facility as an electrical load; is the corresponding natural gas flow rate, is the gas production efficiency;

[0029] Constraints on the relationship between the natural gas flow rate and the electric power consumed by the electric-driven pressure regulating station of the gas transmission network:

[0030]

[0031] in, is the natural gas flow rate of the power-driven pressure regulating station flowing through the gas transmission network node n and the gas distribution network node j; The electric power consumed by the electric drive voltage regulating station as an electric load; β reg,Tis the energy consumption coefficient.

[0032] More preferably, the boundary connection constraints of the power transmission-gas transmission system and the power distribution-gas distribution system are specifically:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] 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 is the boundary connection constraint of the gas transmission-distribution system, It represents the gas pressure on the boost side of the gas distribution and pressure regulating station connected to the gas transmission network node n. represents the pressure on the step-down side, Γ c is the step-up ratio.

[0039] More preferably, the hierarchical collaborative restoration model of the power-gas interconnection system is provided with boundary connection variables in the power transmission-gas transmission system and the power distribution-gas distribution system during the restoration process, including and

[0040] Preferably, the step 2 is specifically:

[0041] Based on the augmented Lagrangian function, the hierarchical coordinated restoration model of the electricity-gas interconnection system is decomposed into the restoration sub-problem of the power transmission-gas transmission system and the sub-problem of the power distribution-gas distribution system.

[0042] According to the power transmission-gas transmission system restoration subproblem and the power distribution-gas distribution system restoration subproblem, the power transmission-gas transmission system restoration decision model and the power distribution-gas distribution system restoration decision model are established respectively.

[0043] More preferably, the step 3 is specifically as follows:

[0044] The power transmission-gas transmission system restoration decision model and the power distribution-gas distribution system restoration decision model are solved based on the ADMM distributed algorithm.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] Fast black start speed and high efficiency: The power network black start method in the present invention can independently solve the transmission-gas transmission system recovery subproblem and the distribution-gas distribution system recovery subproblem only through the information interaction of limited boundary connection variables. Compared with the centralized recovery system of the electric-gas interconnected system in which the power system and the natural gas system are tightly coupled, the present invention decouples the original problem into the transmission-gas transmission system recovery subproblem and the distribution-gas distribution system recovery subproblem on the basis of fully considering the transmission-distribution layered operation characteristics and topological connection characteristics of the electricity and gas energy systems. It overcomes the shortcomings of the original problem in the solution process, such as low efficiency, difficulty in convergence, and possible non-global optimal results, effectively improves the solution efficiency of large-scale electric-gas interconnected system recovery problems, and improves the black start speed of the power network. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the black start method of the power network in the present invention;

[0048] Figure 2 A schematic diagram of the interaction between the power system and the natural gas system in an embodiment of the present invention;

[0049] Figure 3 The figure is a schematic diagram of the energy conversion and information interaction relationship between the power transmission-gas transmission system and the power distribution-gas distribution system during the coordinated restoration process in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0051] A black start method for an electric power network taking into account the coupling characteristics of an electric power-natural gas network, comprising:

[0052] Step 1: Establish a hierarchical collaborative restoration model for the electricity-gas interconnection system based on the coupling characteristics of the electricity-gas network;

[0053] Step 2: Establish a decision model for the hierarchical collaborative restoration model of the electricity-gas interconnection system;

[0054] Step 3: Solve the decision model and obtain the black start plan for the power network.

[0055] The following is a detailed description of each step:

[0056] 1. Establishing a hierarchical collaborative restoration model for the electricity-gas interconnection system

[0057] The method for establishing a hierarchical collaborative restoration model for the electricity-gas interconnection system is as follows:

[0058] Assume that the energy supply interruption accident occurs at time t0. k From that moment on, the electricity and gas loads at the transmission and gas transmission system level will be restored, and at the same time, the loads of the distribution and gas distribution system will be restored on a large scale;

[0059] Hierarchical coordinated recovery of electricity-gas interconnection system k At the beginning of the moment, the recovery preparation phase has been completed, the power supply and gas source in the power transmission and gas transmission system have been started, and the power transmission lines, gas transmission channels, distribution network substations and gas distribution network pressure regulating stations have been put into operation;

[0060] Based on the current electricity-gas interconnection system, a hierarchical collaborative recovery model of the electricity-gas interconnection system is established.

[0061] The objective function is defined as maximizing the weighted supply of electricity load and gas load in the transmission-gas transmission system and the distribution-gas distribution system:

[0062]

[0063] Among them, the superscript T of each variable represents the transmission network or gas transmission network (transmission level), the superscript D represents the distribution network or gas distribution network (distribution level); the subscript E represents the power system, the subscript G represents the natural gas system; the superscript L represents the load. The subscript t represents the restoration time, T R represents the set of restoration moments; subscript m represents the node number of the transmission network, subscript n represents the node number of the gas transmission network, subscript i represents the node number of the distribution network, and subscript j represents the node number of the gas distribution network. This embodiment assumes that each load node of the transmission network is connected to the distribution network and is not connected to the terminal power load, and the same is true for the gas transmission network. and They represent the sets of all nodes of the transmission network, gas transmission network, distribution network and gas distribution network respectively; and Respectively represent the weight coefficients of each node of the corresponding system. are the load restored by each system at each moment.

[0064] It should be noted that the electric load and natural gas load in the above objective function are normalized, that is, in the objective function, the restored electric load and natural gas load are the percentage of the restored load to the original total load. For the convenience of expression, the objective function is still written in the above form in this embodiment.

[0065] The hierarchical collaborative restoration model of the power-gas interconnection system also includes power flow constraints and security constraints of the transmission network and restoration constraints of the power-gas distribution system, which are described below:

[0066] 1. Restoration constraints of power and gas transmission systems

[0067] (1) Transmission network power flow constraints and safety constraints

[0068] The restoration of the power system needs to consider reactive power and voltage issues, so it is necessary to establish an AC power flow model for the transmission system. The duration of the electromechanical transient process of the power system is in seconds, and the duration of the electromagnetic transient process is in milliseconds or even microseconds. This embodiment focuses on the restoration process of the power system and the natural gas system. The time interval for 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. Therefore, this embodiment does not consider the transient process of the power system during the restoration process. The power flow constraints of the transmission network can be established based on the algebraic power flow equation of the steady-state power system.

[0069] Active and reactive balance constraints at transmission system nodes:

[0070]

[0071]

[0072] The superscript G of each variable represents the power source. m′ is the node adjacent to m, K T is the set of transmission lines connected to node m. are the active power injected into node m and the active power flowing through line mm′ respectively; are the reactive power injection of node m, reactive load and reactive power flowing through line mm′ respectively. and They represent the total active and reactive losses on the transmission line connected to node m respectively.

[0073] Active and reactive balance constraints of transmission system lines:

[0074]

[0075]

[0076] in, are the conductance and susceptance of line mm′ respectively; are the voltage amplitudes of nodes m and m′ respectively; is the phase difference of the voltage at both ends of line mm′. Among them, the voltage amplitude and cosine term And the sine term The cross product term is processed by quadratic relaxation technique, and the voltage amplitude square term An improved piecewise linearization method is used to obtain a convex expression of the line power flow constraints and achieve convex relaxation of the constraints.

[0077] Transmission grid restoration security constraints:

[0078] Including voltage amplitude constraints, upper and lower limits of active and reactive power output of power supply and climbing constraints, which are:

[0079]

[0080]

[0081]

[0082]

[0083] in, and They are the upper and lower limits of the active output of the power supply respectively; and are the upper and lower limits of the reactive power output of the power supply, It is the upper limit of the power supply's ramping capacity during adjacent recovery periods.

[0084] At the same time, in order to ensure the frequency stability of the transmission system during the restoration process, the change in the total amount of system active load restoration between adjacent restoration moments should be lower than the maximum active load restoration amount:

[0085]

[0086] (2) Gas transmission network flow constraints and safety constraints

[0087] This embodiment mainly studies the physical process and mechanism model of information interaction and mutual support between the power transmission-gas transmission system and the power distribution-gas distribution system during the recovery process. The steady-state Weymouth flow equation ignoring dynamic characteristics is used for the flow constraint modeling of the gas transmission network and the gas distribution network.

[0088] The airflow balance constraint at node n in the gas transmission network system is:

[0089]

[0090] in, and are the natural gas flow rate injected by the gas source and the natural gas flow rate consumed by the gas load at time t at node n, is the natural gas flow rate flowing through the gas pipeline nn′.

[0091] Constraints on the relationship between gas flow rate in a gas pipeline and the pressure difference at both ends of the pipeline:

[0092]

[0093] in, are the air pressures at nodes n and n′, respectively, is the Weymouth constant of the pipeline nn′.

[0094] Among them, the expression of the sign function of the pressure difference between the two ends of the pipeline is:

[0095]

[0096] For the nonlinear terms in the above constraints, an improved piecewise linearization method is used.

[0097] Gas grid restoration safety constraints:

[0098] Including pipeline airflow upper and lower limit constraints, node pressure upper and lower limit constraints, gas source output upper and lower limit constraints and climbing constraints, which are:

[0099]

[0100]

[0101]

[0102]

[0103] (3) Load recovery constraints of power and gas transmission systems

[0104] It includes active load recovery constraints, reactive load recovery constraints, transmission network load upper limit constraints, and gas source safe operation constraints of the gas transmission system, which are:

[0105]

[0106]

[0107] in, and are the maximum active and reactive loads to be restored at node m, respectively. The restoration of the active load of the transmission network should be capped at the maximum load of its node, and the reactive load should be restored in proportion to the active load according to a specific power factor.

[0108] Since this embodiment assumes that the transmission network load node is the distribution network substation node, the transmission network load upper limit is the distribution network substation capacity:

[0109]

[0110] Similar to the power transmission system, the gas source safety operation constraints of the gas transmission system are:

[0111]

[0112]

[0113] 2. Restoration constraints of power distribution and gas distribution system

[0114] (1) Distribution network power flow constraints and safety constraints

[0115] This embodiment ignores the impact of the three-phase unbalanced load of the distribution network on the recovery, and assumes that the distribution network is a three-phase balanced system. The single-phase closed-form branch flow model is used to model the power flow constraints of the distribution network. For the mth distribution network (the number of the distribution network is 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 constraint is as follows:

[0116] The active and reactive power balance constraints of node i in the mth distribution network at time t are:

[0117]

[0118]

[0119] in, and are respectively the active power flow and reactive power flow flowing through line ii′ connected to node i; is the square of the current amplitude flowing through line ii′. It is worth noting that since the current amplitude only appears in the form of square terms in the power flow constraints of the distribution network, Treated as an independent variable rather than a secondary variable. and are the active power and reactive power injected into node i, respectively. and are the active load and reactive load actually restored at node i, respectively.

[0120] The relationship constraint of the square of the voltage amplitude between node i and node i′ is:

[0121]

[0122] Among them, r ii′ and x ii′ are the resistance and reactance of line ii′ respectively; is the square of the line impedance modulus. Similarly, the voltage amplitude only appears in the form of a square term, so it is considered as an independent variable.

[0123] The relationship constraints between the node voltage amplitude and the corresponding line current amplitude, active and reactive power flow values ​​are:

[0124]

[0125] This constraint is a non-convex constraint. For the cross product term McCormick convex relaxation method is used to deal with the square term of the variable The piecewise linearization method is used.

[0126] Distribution network security constraints:

[0127] Including the voltage assignment page number, the upper and lower limit constraints of the active and reactive output of the power supply, and the climbing constraints, specifically:

[0128]

[0129]

[0130]

[0131]

[0132] (2) Gas distribution network flow constraints and safety constraints

[0133] The mathematical expressions of the flow constraints and safety constraints of the gas distribution network are the same as those of the gas transmission network.

[0134] (3) Load recovery constraints

[0135] The load restoration constraints of the distribution network are similar to those of the transmission network:

[0136]

[0137]

[0138] To ensure the recovery effect, the recovery of the terminal power load should be continuous, that is, the load restored at the subsequent moment should not be less than the previous moment:

[0139]

[0140] In addition, the active / reactive power received by the distribution substation should not exceed the power flowing out of the transmission grid node to which it is connected:

[0141]

[0142]

[0143] Similarly, the terminal gas load recovery constraints of the gas distribution network are as follows:

[0144]

[0145]

[0146] The natural gas flow rate received by the gas distribution and pressure regulating station should also meet the following constraints:

[0147]

[0148] 3. Transmission-gas transmission system coupling constraints and distribution-gas distribution system coupling constraints

[0149] Figure 2 The diagram is a diagram of the interaction between the power system and the natural gas system. It can be seen that the operation of the power system requires the natural gas system to supply fuel to the gas units and micro gas turbines; the pipeline transmission of natural gas in the natural gas system requires the power system to supply electricity to the electric-driven pressure regulating station. Therefore, the gas units in the power transmission system and the electric-driven pressure regulating station in the gas transmission system are the main coupling points of the power transmission-gas transmission system, and the micro gas turbines, power-to-gas facilities and gas distribution system step-down and pressure regulating stations included in the distribution system are the main coupling points of the power distribution-gas distribution system.

[0150] The following constraints are included:

[0151] Energy conversion relationship constraints of gas units:

[0152]

[0153] in, is the natural gas consumption of the gas generating unit connected between the distribution network node i and the gas distribution network node j at time t; Provide active power for gas-fired units; is the power generation efficiency; G is the lower calorific value of natural gas, which is 35590 kJ / m 3 .

[0154] The energy conversion relationship constraint of the gas-fired unit connected to the transmission grid and the gas transmission grid is the same as the expression of the energy conversion relationship constraint of the gas-fired unit, except for the variable symbols and superscripts, which are omitted here.

[0155] P2G facility energy conversion relationship constraints:

[0156]

[0157] in, The active power consumed by the P2G facility as an electrical load; is the corresponding natural gas flow rate, is the gas production efficiency;

[0158] After an extreme event, if the electric-driven pressure regulating station loses power supply, the remaining available natural gas-driven pressure regulating stations can maintain the basic operation of the network, but the transmission capacity of the gas transmission network will be seriously affected. Therefore, the goal of restoring the gas transmission network is to restore the network's transmission capacity as soon as possible and restore the supply capacity to the gas distribution network.

[0159] Constraints on the relationship between the natural gas flow rate and the electric power consumed by the electric-driven pressure regulating station of the gas transmission network:

[0160]

[0161] in, is the natural gas flow rate of the power-driven pressure regulating station flowing through the gas transmission network node n and the gas distribution network node j; The electric power consumed by the electric drive voltage regulating station as an electric load; β reg,T is the energy consumption coefficient.

[0162] 4. Boundary connection constraints between power transmission-gas transmission system and power distribution-gas distribution system

[0163] Substations and gas distribution and pressure regulating stations are key hubs connecting the power transmission system and the power distribution system, and the gas transmission system and the gas distribution system, respectively. Substations can be regarded as loads for the transmission network and as power sources for the distribution network, and the same is true for gas distribution and pressure regulating stations. The boundary connection constraints of the power transmission-gas transmission system and the power distribution-gas distribution system are defined as follows:

[0164]

[0165]

[0166]

[0167] The above constraints represent the power and voltage relationship between the power transmission system and the gas transmission system at the substation, where V t D,m,sub,sqr represents the square of the voltage amplitude of the substation connected to the transmission network node m; it should be noted that, in this embodiment, all voltage values ​​are normalized values.

[0168] At the same time, considering that the boost ratio of the gas distribution and pressure regulating station is fixed and the natural gas flow on both sides is the same, the boundary connection constraints of the gas transmission-distribution system can be obtained:

[0169]

[0170]

[0171] and is the boundary connection constraint of the gas transmission-distribution system, It represents the gas pressure on the boost side of the gas distribution and pressure regulating station connected to the gas transmission network node n. represents the pressure on the step-down side, Γ c is the step-up ratio.

[0172] In this embodiment, P t sub,D,m , V t D,m,sub,sqr , and Set as the boundary connection variable of the transmission-gas transmission system and the distribution-gas distribution system during the restoration process.

[0173] At this point, the energy conversion and information interaction relationship between the power transmission-gas transmission system and the power distribution-gas distribution system in the coordinated restoration process can be summarized as follows: Figure 3 shown.

[0174] 2. Establishing a decision-making model for the hierarchical collaborative restoration model of the electricity-gas interconnection system

[0175] The centralized electricity-gas interconnection system recovery model established in this embodiment can be written in the following abstract form:

[0176]

[0177]

[0178] and Represent the vectors composed of boundary connection variables of power transmission-gas transmission system and power distribution-gas distribution system, namely:

[0179]

[0180]

[0181] and represents the vectors of decision variables other than boundary connection variables in the power transmission-gas transmission system and the power distribution-gas distribution system, respectively, T and f D,m(n) They represent the opposite forms of the functions related to the power transmission-gas transmission system and the power distribution-gas distribution system in the original objective function. h and g represent the sets of corresponding equality and inequality constraints, respectively. It is worth noting that in this abstract expression, the constraint h T and g T It only represents the constraints related to the power transmission and gas transmission system, h D,m(n) and g D,m(n) It only represents the constraints related to the power distribution and gas distribution system. In other words, this abstract expression formally separates the power transmission-gas transmission system restoration subproblem and the power distribution-gas distribution system subproblem, and the two problems are only coupled through the boundary connection constraint.

[0182] In order to decompose the original problem into the power transmission-gas transmission system restoration subproblem and the power distribution-gas distribution system restoration subproblem, the augmented Lagrangian function with respect to the boundary connection variables is defined as follows.

[0183]

[0184] Among them, ρ is the penalty coefficient when using the ADMM distributed algorithm to solve the problem, which is a positive constant. represents the vector of boundary connection variables associated with the power distribution system m and the gas distribution system n in the power transmission-gas transmission system restoration subproblem, that is, is the corresponding Lagrange multiplier. The < > operator represents the inner product operation between two vectors.

[0185] At the same time, the boundary connection constraints are relaxed. At this point, the original problem can be expressed as a decomposable optimization problem based on the augmented Lagrangian function, and the restoration problem of the electricity-gas interconnection system can achieve hierarchical collaborative restoration at the transmission-gas transmission system level and the distribution-gas distribution system level:

[0186]

[0187]

[0188] In view of the problems existing in the centralized restoration optimization problem of large-scale electricity-gas interconnected systems, such as difficulty in data collection of each subsystem, inconvenience in information exchange, and high complexity of solution, this embodiment adopts the ADMM distributed algorithm to decompose the centralized restoration optimization problem of large-scale electricity-gas interconnected systems into the power transmission-gas transmission system restoration subproblem and the power distribution-gas distribution system restoration subproblem, and solves it through a finite number of iterations.

[0189] The ADMM algorithm is a typical decomposition and coordination algorithm. By setting up mutually coordinated superior and subordinate organizations, the original large-scale system optimization problem can be decomposed into internal subsystem problems and solved in a distributed manner. The ADMM algorithm combines the advantages of the Lagrange multiplier method and the dual decomposition, and has the advantages of simple derivation form, good global convergence, and strong solution robustness. The ADMM algorithm usually uses the augmented Lagrangian relaxation method to deal with consistency constraints, that is, the boundary connection constraints established in this embodiment, and calculates the divided sub-problems in the form of alternating iterations.

[0190] This embodiment uses the ADMM distributed algorithm to solve the above-mentioned optimization problem based on the augmented Lagrangian function. The power transmission-gas transmission system recovery subproblem and the power distribution-gas distribution system recovery subproblem are solved through finite iterations, and information exchange is performed, so as to achieve the decomposition, dimensionality reduction and efficient solution of the problem. The ADMM distributed algorithm needs to calculate in each iteration:

[0191]

[0192]

[0193]

[0194] Here, k represents the number of iterations.

[0195] In the k+1th iteration, the power transmission-gas transmission system restoration subproblem is solved based on the kth step solution. and Solution and and update it to and All the distribution-gas system recovery sub-problems are based on the k-th step solution Solution and And updated to and Afterwards, solve And updated to

[0196] It is worth pointing out that in each step of the iterative solution process, the variables involved in the iterative update are taken from the results of the previous iteration, rather than the results of the previous iteration step, to ensure that the iterative solution has better convergence. In addition, the decision variables and The value of is also calculated and participates in information interaction.

[0197] In each iteration, the main residual and the dual residual As the convergence criterion, the following two equations are used to solve their values ​​to determine whether the convergence requirements are met:

[0198]

[0199]

[0200] It can be proved that if The optimal solutions of each sub-problem obtained by iteratively solving the ADMM distributed algorithm eventually converge to the optimal solution of the original problem.

[0201] At this point, we can further write out the augmented Lagrangian function expression of the power transmission-gas transmission system recovery subproblem and the power distribution-gas distribution system recovery subproblem in each iteration process:

[0202] (1) Power and gas transmission system restoration sub-problem

[0203]

[0204]

[0205] In each iteration, the power transmission-gas transmission system restoration subproblem only takes the boundary connection variables obtained by solving the power distribution-gas distribution system restoration subproblem in the previous iteration. and , that is, only limited information interaction is performed.

[0206] (2) Power distribution and gas distribution system recovery sub-problem

[0207]

[0208]

[0209] In each iteration, the boundary connection variables obtained by solving the power transmission and gas transmission system restoration subproblem in the previous step are , solve each power distribution-gas distribution system recovery subproblem in parallel, and update the corresponding Lagrange multiplier and The value of is taken and passed to the next step of solving the power transmission-gas transmission system restoration sub-problem.

[0210] The above-mentioned power transmission-gas transmission system restoration sub-problem and power distribution-gas distribution system restoration sub-problem are two decision models.

[0211] 3. Solve the decision model and obtain the black start plan for the power network

[0212] The ADMM distributed algorithm is used to solve the two decision models of the power transmission-gas transmission system restoration subproblem and the power distribution-gas distribution system restoration subproblem. The solution process is as follows:

[0213]

[0214] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for black starting a power network taking into account the coupling characteristics of power and natural gas networks, characterized in that: The power network black start method comprises: Step 1: Establish a hierarchical collaborative restoration model for the electricity-gas interconnection system based on the coupling characteristics of the electricity-gas network; Step 2: Establish a decision model for the hierarchical collaborative restoration model of the electricity-gas interconnection system; Step 3: Solve the decision model to obtain the black start plan of the power network; The method for establishing the hierarchical collaborative restoration model of the electric-gas interconnected system in step 1 is: Assume that the energy supply interruption accident occurs at time t0. k From that moment on, the electricity and gas loads at the transmission and gas transmission system level will be restored, and at the same time, the loads of the distribution and gas distribution system will be restored on a large scale; Hierarchical coordinated recovery of electricity-gas interconnection system k At the beginning of the moment, the recovery preparation phase has been completed, the power supply and gas source in the power transmission and gas transmission system have been started, 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 current electricity-gas interconnection system, a hierarchical collaborative recovery model of the electricity-gas interconnection system is established; The hierarchical collaborative recovery model of the electricity-gas interconnection system is specifically as follows: The objective function of the model is to maximize the weighted supply of electricity load and gas load in the transmission-gas transmission system and the distribution-gas distribution system, specifically: Among them, the superscript T of each variable represents the transmission network or gas transmission network, the superscript D represents the distribution network or gas distribution network; the subscript E represents the power system, the subscript G represents the natural gas system; the superscript L represents the load; the subscript t represents the restoration time, T R represents the set of restoration moments; subscript m represents the node number of the transmission network, subscript n represents the node number of the gas transmission network, subscript i represents the node number of the distribution network, and subscript j represents the node number of the gas distribution network; and They represent the sets of all nodes of the transmission network, gas transmission network, distribution network and gas distribution network respectively; and Respectively represent the weight coefficients of each node of the corresponding system; are the loads restored by each system at each moment; The step 2 is specifically as follows: Based on the augmented Lagrangian function, the hierarchical coordinated restoration model of the electricity-gas interconnection system is decomposed into the restoration sub-problem of the power transmission-gas transmission system and the sub-problem of the power distribution-gas distribution system. According to the sub-problems of power transmission-gas transmission system restoration and distribution-gas distribution system restoration, a power transmission-gas transmission system restoration decision model and a distribution-gas distribution system restoration decision model are established respectively; The step 3 is specifically as follows: The power transmission-gas transmission system restoration decision model and the power distribution-gas distribution system restoration decision model are solved based on the ADMM distributed algorithm.

2. A method for black starting a power network taking into account the coupling characteristics of the power and natural gas networks according to claim 1, characterized in that: The hierarchical collaborative restoration model of the electricity-gas interconnection system is provided with a transmission-gas transmission system restoration constraint and a distribution-gas distribution system restoration constraint; the transmission-gas transmission system restoration constraint includes a transmission network flow constraint and a safety constraint, a gas transmission network flow constraint and a safety constraint, and a transmission-gas transmission system load restoration constraint; the distribution-gas distribution system restoration constraint includes a distribution network flow constraint and a safety constraint, a gas distribution network flow constraint and a safety constraint, and a distribution-gas distribution system load restoration constraint.

3. A method for black starting a power network taking into account the coupling characteristics of the power and natural gas networks according to claim 1, characterized in that: The hierarchical collaborative restoration model of the electricity-gas interconnected system is also provided with coupling constraints of the power transmission-gas transmission system, coupling constraints of the power distribution-gas distribution system, and boundary connection constraints of the power transmission-gas transmission system and the power distribution-gas distribution system.

4. A method for black starting a power network taking into account the coupling characteristics of the power and natural gas networks according to claim 3, characterized in that: The power transmission-gas transmission system coupling constraints and the power distribution-gas distribution system coupling constraints include: Energy conversion relationship constraints of gas units: in, is the natural gas consumption of the gas generating unit connected between the distribution network node i and the gas distribution network node j at time t; Provide active power for gas-fired units; is the power generation efficiency; G is the lower calorific value of natural gas; Energy conversion relationship constraints of gas-fired units connected to the transmission grid and gas grid; P2G facility energy conversion relationship constraints: in, The active power consumed by the P2G facility as an electrical load; is the corresponding natural gas flow rate, is the gas production efficiency; Constraints on the relationship between the natural gas flow rate and the electric power consumed by the electric-driven pressure regulating station of the gas transmission network: in, is the natural gas flow rate of the power-driven pressure regulating station flowing through the gas transmission network node n and the gas distribution network node j; The electric power consumed by the electric drive voltage regulating station as an electric load; β reg,T is the energy consumption coefficient.

5. The method for black starting a power network taking into account the coupling characteristics of the power and natural gas networks according to claim 3, characterized in that: The boundary connection constraints of the power transmission-gas transmission system and the power distribution-gas distribution system are specifically: in, represents the square of the voltage amplitude of the substation connected to the transmission network node m; and is the boundary connection constraint of the gas transmission-distribution system, It represents the gas pressure on the boost side of the gas distribution and pressure regulating station connected to the gas transmission network node n. represents the pressure on the step-down side, Γ c is the step-up ratio.

6. A method for black starting a power network taking into account the coupling characteristics of the power and natural gas networks according to claim 5, characterized in that: The hierarchical collaborative restoration model of the power-gas interconnection system is provided with boundary connection variables in the power transmission-gas transmission system and the power distribution-gas distribution system during the restoration process, including and

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