CN112084674B

CN112084674B - Electromagnetic transient parallel simulation method and system based on semi-implicit relaxation

Info

Publication number: CN112084674B
Application number: CN202010981230.6A
Authority: CN
Inventors: 姚蜀军; 庞博涵; 姚逸凡
Original assignee: North China Electric Power University
Current assignee: North China Electric Power University
Priority date: 2020-09-17
Filing date: 2020-09-17
Publication date: 2024-02-27
Anticipated expiration: 2040-09-17
Also published as: CN112084674A

Abstract

The invention provides an electromagnetic transient parallel simulation method based on semi-implicit relaxation, which comprises the following steps: dividing an alternating current-direct current system into a plurality of first subnetworks by taking a grounding capacitor as a boundary; simulating a first sub-network meeting a single branch form or a coupling branch form in a plurality of first sub-networks by using a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result; constructing a first sub-network which does not meet the single branch form or the coupling branch form in the plurality of first sub-networks into a space distribution network; and simulating the spatial distribution network by using a node voltage method to obtain a spatial distribution simulation result. Starting from the state equation integration format, a semi-implicit differential equation is provided by analyzing time delay characteristics among variables of different integration formats, and an efficient parallel computing method of an alternating-current/direct-current system based on a semi-implicit relaxation method is constructed, so that the speed of electromagnetic transient simulation degree is improved.

Description

Electromagnetic transient parallel simulation method and system based on semi-implicit relaxation

Technical Field

The invention relates to the technical field of electromagnetic transient simulation, in particular to an electromagnetic transient parallel simulation method and system based on semi-implicit relaxation.

Background

With the development of high-voltage direct current transmission (high-voltage direct current, HVDC), flexible alternating current transmission (flexible AC transmission system, FACTS) and large-scale new energy sources, a large number of power electronic devices are connected into a power grid, so that the power system of the present day shows a trend of power electronics. The power electronic device has the characteristics of high action frequency and fast transient process, and the system containing a large amount of power electronic equipment has high equation order, and small step simulation is needed to ensure the numerical stability, so that the traditional electromagnetic transient simulation and the existing commercial product simulation are slow in speed and low in efficiency. Multi-rate simulation can increase the simulation speed, but when the system is large in scale, the problem of solving the ultra-high order linear algebraic equation set still faces. The parallel computing is adopted to divide the large-scale AC/DC power grid into a plurality of small-scale subnets with the same speed or different speeds, so that the dimension reduction of the large power grid can be realized, the computing amount is reduced, and the simulation efficiency can be improved by means of a parallel computing technology.

The traditional electromagnetic transient parallel simulation method has a plurality of methods, and the specific situations are as follows:

(1) When the simulation step length is smaller than the transmission time of electromagnetic waves in the line, the electromagnetic connection at the two ends of the long transmission line is only reacted by the electric quantity at the previous moment, and the two ends are not directly in topological connection, so that natural decoupling is realized. However, the method requires that network segmentation is performed on a long-distance power transmission line adopting distributed parameters, and has the defects of lack of flexibility, different sub-block specifications obtained by segmentation, and incapability of meeting the synchronism requirement of parallel computing, so that the parallel computing efficiency is reduced.

(2) The multi-area Thevenin Equivalent Method (MATE) divides the whole network into a plurality of sub-networks based on node tearing or branch dividing, and each sub-network is replaced by multi-port Thevenin Equivalent and forms a related network with tearing nodes or dividing branches after scale reduction. The number of sub-networks and the scale of the associated network and the solution method are important factors affecting the simulation efficiency. In the calculation, the associated network needs to be solved in series, and the calculation efficiency is lower than that of the natural network separation of the transmission line.

(3) The waveform relaxation method (waveform relaxation, WR) is used for dividing the whole network into a plurality of sub-networks by artificially introducing 'relaxation' among variables, and each sub-network uses the previous iteration waveform as an estimated value of an associated sub-system in each simulation step length, so that the state variable waveforms of the sub-systems are independently and parallelly solved, and the waveforms are used as information of interaction among the sub-systems and criteria of iteration convergence. Techniques and methods for multi-window, overlapping partition, multi-split, step-wise, etc. are presented for improving convergence of iterations. The waveform relaxation method has no associated network among subnetworks, and is easy to parallelize. However, the introduced iterative process sometimes causes multiple increase of the calculated amount, and loses the advantage of improving the calculation efficiency by the network splitting dimension reduction.

(4) Delay insertion (latency insert method, LIM) adds and couples a small ground capacitance to the non-capacitive ground node by adding a small inductance to the non-inductive leg in the system, so that all legs of the overall system become inductive legs and all nodes are grounded through the parallel capacitance. Through the processing, and by introducing delay in a differential equation of the inductance branch and the capacitance branch, the solutions of the current and the node voltage of each branch are mutually decoupled, and fine-grained parallelism of the branch level can be realized.

(5) The parallel network dividing method based on the forward Euler method is characterized in that the forward Euler method is applied to the inductance and the capacitance in the system, a network connected in parallel with the capacitance or connected in series with the inductance can be divided into a plurality of sub-networks, the ports are equivalent by using a voltage source or a current source, natural decoupling among the sub-networks can be realized without a transmission line, but the application of the forward Euler method is limited by lower calculation precision and non-A numerical stability.

In addition, with the development of hardware technology, the computing capacity of the GPU is greatly superior to that of the CPU, and a low-cost high-performance method is provided for parallel simulation. Generally, GPUs are more suitable for "fine-granularity" computations, while linear system of equations solutions in simulation processes pertain to "coarse-granularity" computations. In GPU-based electromagnetic transient simulation, even with sparse techniques, the computation links associated with the matrix take up approximately 60% of the computation time.

Under the background of an alternating current/direct current power grid containing high-proportion power electronic equipment, the equipment characteristics are complex, the system time scale is enlarged, the power grid scale is large, the traditional electromagnetic transient simulation needs to solve the formed ultra-high-order equation set in a short time, the simulation step size is small, the speed is low, and the requirement of rapidness cannot be met.

The invention starts from the state equation integration format, proposes a semi-implicit differential equation by analyzing the time delay characteristics among variables adopting different integration formats, and builds a high-efficiency parallel computing method of an alternating-current/direct-current system based on a semi-implicit relaxation method to solve the problems.

Disclosure of Invention

The invention aims to provide an electromagnetic transient parallel simulation method and system based on semi-implicit relaxation, so as to improve the speed of electromagnetic transient simulation.

In order to achieve the above object, the present invention provides the following solutions:

an electromagnetic transient parallel simulation method based on semi-implicit relaxation, the simulation method comprising the following steps:

dividing an alternating current-direct current system into a plurality of first subnetworks by taking a grounding capacitor as a boundary;

simulating a first sub-network meeting a single branch form or a coupling branch form in a plurality of first sub-networks by using a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result;

Constructing a first sub-network which does not meet the single branch form or the coupling branch form in the plurality of first sub-networks into a space distribution network;

simulating the spatial distribution network by using a node voltage method to obtain a spatial distribution simulation result;

and increasing the value of the simulation time length t by deltat and increasing the simulation times n by 1, returning to the step of simulating the first subnetwork meeting the single branch form or the coupling branch form in the plurality of first subnetworks by using a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result, and performing the next step of simulation.

Optionally, the simulation of the first subnetwork satisfying the single branch form in the plurality of first subnetworks by using a semi-implicit relaxation method specifically includes:

the time step of the advance is half, that is,at time of day, use the formula +.>Updating the voltage of each node of the first subnetwork;

advancing by one time step, i.e. at time t+Δt, using the formulaUpdating the current of each branch of the first subnetwork;

wherein,for the voltage of node i after the n-th simulation update,/->For the n-th simulation of the voltage of node i before updating,/->For the branch voltage of node j after the nth simulation update, +.>C is the value of the current source of the node i at the starting time of the nth simulation _i For the capacitance value of node i, G _i For the conductance value of node i, M _i The number of branches connected with the node of the ith branch; />Representing the pre-update current of the kth leg connected to node i; l (L) _ij Represents the inductance value between node i and node j, R _ij Representing the resistance value between node i and node j; />A voltage source between a time node i and a node j representing a half time step after the start time of the nth simulation; />And->The current between the node i and the node j before and after the nth simulation update is respectively represented, and Δt represents the time interval of one time step.

Optionally, the simulation of the first subnetwork satisfying the coupling branch form in the plurality of first subnetworks by using a semi-implicit relaxation method specifically includes:

wherein α is a first intermediate amount, and β is a second intermediate amount;

a, B are the system matrix and input matrix of AC/DC system respectively;

wherein 1,2 … N represents the label of the branch, L represents the self inductance of the line, M represents the mutual inductance between the lines, and R represents the resistance on the branch.

Optionally, the simulating the spatial distribution network by using a node voltage method to obtain a spatial distribution simulation result specifically includes:

a plurality of nodes are selected as split points in the spatial distribution network,

splitting the spatial distribution network into a plurality of mutually independent second sub-networks according to the splitting points;

the time step of the advance is half, that is,at time of day, use the formula +.>Updating the voltage of each splitting point of the sub-network;

based on the current source of each second sub-network and the voltage of each split point, the formula is usedCalculating the voltage of the node inside each second sub-network;

wherein Y is ₁ Representing a node admittance matrix of the spatially distributed network,Y ₁₁ 、Y ₂₂ and Y _KK Respectively representing node admittances of the 1 st, 2 nd and K th second subnetworks; />Node voltage column vector representing the spatial distribution network after the nth simulation update, +.> And->Respectively representing node voltages of the 1 st, 2 nd and K th second subnetworks after the nth simulation update; />Equivalent historical current source column vector representing the spatial distribution network before the nth simulation update, ++> And->Respectively representing equivalent historical current sources of the 1 st, 2 nd and K th subnetworks before the nth simulation update; / >Representation->Injecting current column vector into nodes of time space distribution network> And->Respectively indicate->Injecting current into the nodes of the 1 st, 2 nd and K th second subnetworks at the moment; y is Y ₂ Admittance vector, Y, representing the splitting point of a spatially distributed network ₂ ＝[Y _1t Y _2t … Y _tt ]，Y _1t 、Y _2t And Y _1t Admittances of the 1 st, 2 nd and t th split points, respectively; />Voltage column vector representing division point after nth simulation update, +.> And->Respectively representing node voltages of the 1 st, 2 nd and t th split points after the nth simulation update;

advancing by one time step, i.e. at time t+Δt, using the formulaOr formula->Calculating the current source of each second subnetwork k>

Wherein,current source representing inductance element of second subnetwork k after the nth simulation update, +.>Current source representing current element of second subnetwork k after the nth simulation update,/>For the current flowing to node m at time t, node k, +.>And->Respectively->The voltages at the time point k and the node m are L, which is the inductance value of the inductance element, and C, which is the capacitance value of the capacitance element.

selecting a plurality of branches from the space distribution network as cutting branches;

Dividing the spatial distribution network into a plurality of mutually independent second sub-networks according to the cutting branches;

the time step of the advance is half, that is,at time of day, use the formula +.>Updating the voltage of the internal node of the second subnet;

advancing by one time step, i.e. at time t+Δt, using the formulaUpdating the second subnet cutting branch current;

utilization of formulas utilizing formulasOr formula (la)Calculating the current source of each second subnetwork k>

Wherein,node voltage column vector representing the spatial distribution network after the nth simulation update, +.>Injecting current column vectors into nodes of the spatial distribution network representing time t, < >>Representing the current matrix on the cut branch before the nth simulation update, < >> And->Representing the current on the 1 st, 2 nd and K th split branches before the nth simulation update, respectively; m represents a node-branch correlation matrix M= [ M ] ₁ M ₂ … M _K ]，M ₁ 、M ₂ And M _K The submatrices corresponding to the 1 st, 2 nd and K th divided branches in the section-branch correlation matrix are respectively.

An electromagnetic transient parallel simulation system based on semi-implicit relaxation, the simulation system comprising the steps of:

the network dividing module is used for dividing the AC/DC system into a plurality of first sub-networks by taking the grounding capacitance as a boundary;

the semi-implicit relaxation simulation module is used for simulating a first sub-network meeting a single branch form or a coupling branch form in a plurality of first sub-networks by utilizing a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result;

The space distribution network construction module is used for constructing a space distribution network from a plurality of first sub-networks which do not meet the single branch form or the coupling branch form;

the node voltage method simulation module is used for simulating the spatial distribution network by using a node voltage method to obtain a spatial distribution simulation result;

and the return module is used for increasing the value of the simulation time t by deltat and increasing the simulation times n by 1, and returning to the step of simulating the first subnetwork meeting the single branch form or the coupling branch form in the plurality of first subnetworks by using the semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result and performing the next step of simulation.

Optionally, the semi-implicit relaxation simulation module specifically includes:

the first node voltage update sub-module, for advancing half a time step, i.e.,at time of day, the formula is usedUpdating the voltage of each node of the first subnetwork;

a first branch current updating sub-module for advancing a time step, namely, at the time t+delta t, by using a formulaUpdating the current of each branch of the first subnetwork;

wherein,for the voltage of node i after the n-th simulation update,/->For the n-th simulation of the voltage of node i before updating,/- >For the branch voltage of node j after the nth simulation update, +.>C is the value of the current source of the node i at the starting time of the nth simulation _i For the capacitance value of node i, G _i For the conductance value of node i, M _i The number of branches connected with the node of the ith branch; />Representing the pre-update current of the kth leg connected to node i; l (L) _ij Represents the inductance value between node i and node j, R _ij Representing the resistance value between node i and node j; />A voltage source between a time node i and a node j representing a half time step after the start time of the nth simulation; />And->The current between the node i and the node j before and after the nth simulation update is respectively represented, and Δt represents the time interval of one time step.

a second node voltage update sub-module for advancing half a time step, i.e.,at time of day, the formula is usedUpdating the voltage of each node of the first subnetwork;

a second branch current updating sub-module for advancing a time step, namely, at the time of t+delta t, by using a formulaUpdating the current of each branch of the first subnetwork;

a, B are the system matrix and input matrix of AC/DC system respectively;

Optionally, the node voltage method simulation module specifically includes:

a split point selecting sub-module for selecting a plurality of nodes in the spatial distribution network as split points,

a network splitting sub-module, configured to split the spatial distribution network into a plurality of mutually independent second sub-networks according to the splitting point;

the split point voltage update sub-module is used to advance half a time step, that is,at time of day, the formula is usedUpdating the voltage of each splitting point of the sub-network;

a node voltage update sub-module for using a formula according to the current source of each second sub-network and the voltage of each split pointCalculating the voltage of the node inside each second sub-network;

wherein Y is ₁ Representing a node admittance matrix of the spatially distributed network,Y ₁₁ 、Y ₂₂ and Y _KK Respectively representing node admittances of the 1 st, 2 nd and K th second subnetworks; />Node voltage column vector representing the spatial distribution network after the nth simulation update, +.> And->Respectively representing node voltages of the 1 st, 2 nd and K th second subnetworks after the nth simulation update; / >Equivalent historical current source column vector representing the spatial distribution network before the nth simulation update, ++> And->Respectively representing equivalent historical current sources of the 1 st, 2 nd and K th subnetworks before the nth simulation update; />Representation->Injecting current column vector into nodes of time space distribution network> And->Respectively indicate->Injecting current into the nodes of the 1 st, 2 nd and K th second subnetworks at the moment; y is Y ₂ Admittance vector, Y, representing the splitting point of a spatially distributed network ₂ ＝[Y _1t Y _2t … Y _tt ]，Y _1t 、Y _2t And Y _1t Admittances of the 1 st, 2 nd and t th split points, respectively; />Voltage column vector representing division point after nth simulation update, +.> And->Respectively representing node voltages of the 1 st, 2 nd and t th split points after the nth simulation update;

a first current source updating sub-module for using a formulaOr formula (la)Calculating the current source of each second subnetwork k>

Wherein,current source representing inductance element of second subnetwork k after the nth simulation update, +.>Current element representing second subnet k after nth simulation updateCurrent source of->The current flowing to node m for node k at time t,and->Respectively->The voltages at the time point k and the node m are L, which is the inductance value of the inductance element, and C, which is the capacitance value of the capacitance element.

Optionally, the node voltage method simulation module specifically includes:

the cutting branch selecting submodule is used for selecting a plurality of branches from the space distribution network to serve as cutting branches;

the network segmentation sub-module is used for segmenting the space distribution network into a plurality of mutually independent second sub-networks according to the cutting branch;

the second subnetwork internal node voltage update sub-module, for advancing half a time step, i.e.,at time of day, use the formula +.>Updating the voltage of the internal node of the second subnet;

a cutting branch current updating sub-module for advancing a time step, namely, at the time of t+delta t, by using a formulaUpdating the second subnet cutting branch current;

a second current source updating sub-module for utilizing the formula to utilize the formulaOr formula->Calculating the current source of each second subnetwork k>

According to the specific embodiment provided by the invention, the invention discloses the following technical effects:

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a schematic circuit diagram of a general branch circuit according to the present invention;

FIG. 2 is a schematic circuit diagram of a general node according to the present invention;

FIG. 3 is a schematic circuit diagram of a branch stage parallel system according to the present invention;

FIG. 4 is a schematic diagram of a semi-implicit relaxation time axis provided by the present invention;

fig. 5 is a schematic circuit diagram of a T-type subnetwork parallel system provided by the present invention;

FIG. 6 is a schematic circuit diagram of a pi-type network division parallel system provided by the invention;

fig. 7 is an equivalent circuit diagram of an inductance element circuit provided by the present invention; fig. 7 (a) is a circuit diagram of an inductance element, and fig. 7 (b) is an equivalent circuit diagram of the inductance element;

fig. 8 is an equivalent circuit diagram of a capacitive element circuit provided by the present invention; fig. 8 (a) is a circuit diagram of a capacitive element, and fig. 8 (b) is an equivalent circuit diagram of the capacitive element;

FIG. 9 is a schematic diagram of a semi-implicit relax parallel simulation method provided by the present invention;

fig. 10 is a flowchart of an electromagnetic transient parallel simulation method based on semi-implicit relaxation.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.

The invention provides a semi-implicit relaxation electromagnetic transient parallel simulation method, which realizes natural decoupling, has simple interface strategy and can consider the stability and the parallel performance of simulation numerical characteristics.

1. Establishment of semi-implicit differential equation

The parallel computing method of the alternating current-direct current system based on the semi-implicit relaxation method is constructed by analyzing the time delay characteristics among variables with different integral formats.

The semi-implicit differential equation is established as follows:

step 1: state equation of column writing system

Assuming that a certain system state quantity is divided into N groups, the state equation of the i (i e 1,2 … N) th group state quantity is:

wherein, the state variable X (t) epsilon RN, the constant matrix A, B epsilon RN multiplied by N and the input function u (t) epsilon RN.

Step 2: differentiating the equation of state of formula (3) in step 1

During the (n, n+1) time:

step 3: the implicit trapezoidal method is adopted for the two integral terms (1) and (2) at the right end of the equation of the formula (4) in the step 2:

step 4: for the formula (5) in the step 3, partial state quantity X is reserved in a difference format of front and back step sizes; for other state quantities and input quantities or disturbance quantities u, a central integration format is adopted:

step 5: simplifying the term of the formula (6) in the step 4 to obtain a semi-implicit differential equation represented by the formula (7):

wherein the method comprises the steps of

2. Semi-implicit relaxed parallel algorithm principle

The invention firstly provides the concepts of the universal branch and the universal node, and provides a form that a semi-implicit differential equation is specifically applied to electromagnetic transient simulation.

2.1 general purpose branch

As shown in fig. 1, the general branch is composed of a voltage source, a resistor and an inductor which are connected in series. The voltages to ground at the two points i and j are respectively V _i And V _j Branch current I _ij Let i flow to j.

The general branch iterative form derivation based on the semi-implicit differential equation comprises the following steps:

step 1: applying KVL to the arm shown in FIG. 1, we get the arm equation (9)

Step 2: differentiating the formula (9) obtained in the step 1 by using an implicit trapezoidal method

Step 3: using different integration formats for different variables in equation (10)

For voltage, a central integration format is adopted; for current, the implicit trapezoidal differential format relationship is preserved. From the center integral, wherein the area of the trapezoidal integral at times n to n+1 is equal to the rectangular area at times n+1/2, equation (11) is obtained

Step 4: performing item reduction on the equation (11) obtained in the step 3 to obtain an equation (12)

Equation (12) is an iterative equation for the generic branch, and at each time step, equation (12) is applied to the generic branch to update the current value of the generic branch.

2.2 general node

Fig. 2 is a general node schematic. General node V _i The parallel combination of conductance and capacitance is grounded via a current source.

The general node iterative form derivation based on the semi-implicit differential equation comprises the following steps:

Step 1: applying KCL to node i in fig. 2, yields the node equation:

where Mi is the number of branches connected to node i (excluding the ground branch), i=1, 2,.. _n 。

Step 2: similar to the previous processing of the general branch, the differential differentiation is performed at the time of n-1/2 to n+1/2 in the formula (13), and the area equivalent is performed on the input quantity by using the center integral, thereby obtaining

Step 3: simplifying (14)

Equation (15) is an iterative equation for a generic node. At each time step, equation (15) is applied to the generic node in the system to update the voltage value of the current generic node.

From equation (12), the calculation of the RL series leg must be known to the voltage V across the first half-step leg _i And V _j According to equation (15), the voltage across the branch is obtained by calculating the RC parallel branch by the previous step, so the voltage across the RL branch must be known relative to the reference point, and the voltage across the RL branch is known to include two cases, one being directly connected to the voltage source at node i or j, and the other being connected to the capacitance to ground branch at node i or j at the first half of the step. The semi-implicit relaxation method requires a grounded capacitance or voltage source as the boundary between the subnetworks. According to the network dividing condition, the whole system is divided into two partsDividing the sub-network into 4 parallel computing methods (1, branch stage parallel, 2, coupling branch stage parallel, 3, T-type sub-network parallel and 4, pi-type sub-network parallel) according to different dividing sub-network types, wherein each type of sub-network is simulated by adopting different methods.

2.2.1 Branch stage parallelism

If all branches and nodes in a system meet the requirements of the general branches and general nodes, as shown in fig. 3, that is, each branch in the system contains an inductor, and each node is grounded through a capacitor, the whole system can realize branch stage parallelism.

With time, in the branch stage parallel network, the branch current I _ij And node voltage V _i Alternately and with half a time step, as shown in fig. 4.

The pseudo code of the branch level parallel sub-network calculation step is represented as follows:

wherein Nt time nodes number; nb is the branch number; nn is the number of nodes.

2.2.2 coupling tributary stage parallelism

If the subnetwork comprises coupled branches (e.g. transformers), the branch current column vectors I are similar to the solving process in the form of a single branch _ij And node voltage column vector V _i Alternately solved and differing by half a time step. The KVL equation is written to the coupling branch column to obtain a semi-implicit differential equation (16) for the coupling branch current.

In (16)

Wherein a, B are a system matrix and an input matrix.

The parallel computing steps of the coupling branch stages are as follows:

For branch＝1:Nb

updating the coupling branch current according to the calculation formula (16);

Next branch；

when the semi-implicit relaxation method is applied, if the network does not meet the parallel condition of the branch level or the coupling branch level, the whole large-scale system is divided into a plurality of sub-networks, each sub-network is solved by adopting a proper method, and then data exchange among the sub-networks is carried out through the voltage or the current of the sub-network boundary.

The semi-implicit relaxation method requires a grounded capacitance or voltage source as the boundary between the subnetworks. After the system is divided into a plurality of subnets by a grounding capacitor or a voltage source according to a network dividing condition, for the subnets which do not meet the single branch form and the coupling branch form, the partial networks can be regarded as a whole, a state space method or a node voltage method is used for simulation, and the partial networks are divided into a T-type network dividing parallel type subnets and a pi-type network dividing parallel type subnets according to the difference of the connecting line forms, and the specific method is as follows:

2.2.3T network division parallel

Step 1: for a given power network, the network equation described by the admittance matrix is

Wherein Y is an N multiplied by N order node admittance matrix;the voltage column vector is N-dimensional node voltage column vector; />Is an N-dimensional node current column vector.

Step 2: selecting some nodes in the network and tearing the nodes apart, the original network can be broken down into several smaller independent sub-networks, which are called split points. With these split points arranged at the back, and the nodes of each sub-network together, the network equations can be written in block diagonal form:

in the formula, the original network is divided into K sub-networks, and each sub-network is independent and is respectively associated with a splitting point. The set of split points is denoted by the subscript t.

Step 3: solving for the internal node voltages of the subnetworks.

If the split point in (19) is at a voltage to groundAs is known, the node voltage for each subnetwork can be found by:

FIG. 5 is a schematic diagram of a T-type split network parallel system, in which node tearing is applied to achieve that the capacitance to ground on the interconnection line between subnetworks corresponds to the split point, i.e., V _t ＝V _C ，V _C From the first half, the node voltages within each sub-network are determined using equation (20) for known values.

2.2.4 pi-type network division parallel

Step 1: a portion of the branches in a given power network are selected and cut apart, and these branches are referred to as cut branches if the original network can now become several sub-networks independent of each other. If these branches are replaced with current sources, the network equations can be described in the form:

wherein i is _L The current on the L cutting branches is L multiplied by 1-dimensional column vectors; m is the corresponding cutting branch in the node-branch association matrixA sub-matrix; y is Y _d The node admittance matrix formed by the subnetworks after the cutting branch is removed is a block diagonal matrix.

Step 2: the potential difference between the current on the cutting line and the node voltage at the two ends of the cutting line has the following relationship:

wherein y is _L To cut the branch admittance matrix.

Step 3: combining the formula (21) and the formula (22) together to write into a block matrix form

Step 4: if the network is divided into K sub-networks after the branch is taken off, the detailed expression of equation (23) is

Equation (24) has the same diagonal structure of the bordered block as equation (19) and can be solved in the same manner.

Step 5: if the string current i is known _L The node voltage of each subsystem can be obtained by the method (25)

Fig. 6 is a pi-type network parallel system, two systems are connected by an RL series branch, which is equivalent to a cutting line, and the end points of two ends of the cutting line are nodes containing capacitance to ground.

Cutting line current i _L From the first half time step, the node voltage in each sub-network can be obtained by the equation (25) as the known value, and the sub-networks can be solved in parallel.

3. Semi-implicit relaxed parallel algorithm calculation step

As shown in fig. 7:

step 1: the system is divided into a plurality of sub-networks with ground capacitance as a boundary.

Step 2: reading data, initializing a system network, including calculating system equivalent historical current sources and conductance matrixes of nodes of all subnetworks

Step 3: if a switching action or fault occurs, the node conductance matrix and the equivalent historical current source are modified.

The switch adopts a two-value resistance model, the on resistance is 0.01 omega, and the off resistance is 106 omega.

The historical current source calculation formula is as follows:

inductive element history current source:

wherein i is _k,m For the current flowing through the inductance u _k And u _m Is the voltage at two ends of the inductor; the equivalent circuit of the inductive element is shown in fig. 8.

Capacitive element history current source:

wherein i is _k,m For the current flowing through the capacitor u _k And u _m Is the voltage across the capacitor. The equivalent circuit of the capacitive element is shown in fig. 9.

Step 4: according to different dividing sub-network types (1, branch stage parallel system; 2, coupling branch stage parallel system; 3, T-type sub-network; 4, pi-type sub-network), respectively adopting different methods to simulate: if the sub-network is the branch-level parallel sub-network, jumping to the step 5; if the coupling branch level parallel sub-network exists, the step 6 is skipped; if the T-shaped sub-network exists, jumping to the step 7; if pi-type network division is performed, jumping to the step 8;

step 5: for a branch level parallel system, the calculation method is summarized by the following pseudo code:

/>

step 6: for a coupled branch level parallel system, the current of the coupled branch is updated by equation (16) at each time step, similar to the calculation method for the branch level parallel system.

Step 7: if the voltage is T-shaped sub-network, the voltage of the split point to the ground is obtained by the first half time step, and the node voltage in each sub-network is calculated by a formula (20);

Step 8: if pi-type network division is adopted, the cutting line current is obtained from the first half time step, and the node voltage in each sub-network can be obtained by using the formula (25).

Step 9: updating the network equation history current source.

Step 10: advance to the next time step.

Step 11: and repeating the steps 3 to 10 until the simulation is finished.

The flow chart of the simulation algorithm is shown in fig. 7. The branch stage parallel system and the coupling branch stage parallel system are simply called local relaxation network; a system that does not satisfy branch level parallelism and coupled branch level parallelism is simply referred to as an EMT subnetwork.

As shown in fig. 10, the invention provides an electromagnetic transient parallel simulation method based on semi-implicit relaxation, which comprises the following steps:

step 101, dividing the ac/dc system into a plurality of first sub-networks with the ground capacitor as a boundary.

Step 102, simulating a first sub-network meeting a single branch form or a coupling branch form in a plurality of first sub-networks by using a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result.

As a preferred embodiment, but not limited to this embodiment, the first subnetwork satisfying the single branch form, the simulation of the first subnetwork satisfying the single branch form in the plurality of first subnetworks by using the semi-implicit relaxation method specifically includes: the method can be used for advancing the time step by half, That is to say,at time of day, use the formula +.>Updating the voltage of each node of the first subnetwork; advancing by one time step, i.e. at time t+Δt, using the formula +.>Updating the current of each branch of the first subnetwork; wherein (1)>For the voltage of node i after the n-th simulation update,/->For the n-th simulation of the voltage of node i before updating,/->For the branch voltage of node j after the nth simulation update, +.>C is the value of the current source of the node i at the starting time of the nth simulation _i For the capacitance value of node i, G _i For the conductance value of node i, M _i The number of branches connected with the node of the ith branch; />Representing the pre-update current of the kth leg connected to node i; l (L) _ij Represents the inductance value between node i and node j, R _ij Representing the resistance value between node i and node j; />A voltage source between a time node i and a node j representing a half time step after the start time of the nth simulation; />And->Representing the current between node i and node j before and after the nth simulation update, respectively.

As a preferred embodiment, but not limited to this embodiment, the first subnetwork satisfying the coupling branch form, and the simulation of the first subnetwork satisfying the coupling branch form in the plurality of first subnetworks by using the semi-implicit relaxation method specifically includes: the time step of the advance is half, that is, At time of day, use the formula +.>Updating the voltage of each node of the first subnetwork;

advancing by one time step, i.e. at time t+Δt, using the formulaUpdating the current of each branch of the first subnetwork; wherein α is a first intermediate amount, and β is a second intermediate amount; />A, B are the system matrix and input matrix of AC/DC system respectively;

Step 103, constructing a first subnetwork which does not meet the single branch form or the coupling branch form in a plurality of first subnetworks into a space distribution network;

and 104, simulating the spatial distribution network by using a node voltage method to obtain a spatial distribution simulation result.

As a preferred embodiment, but not limited to this embodiment, the simulating the spatial distribution network by using the node voltage method in step 104 obtains a spatial distribution simulation result, which specifically includes: selecting a plurality of nodes in the spatial distribution network as splitting points; splitting the spatial distribution network into a plurality of mutually independent second sub-networks according to the splitting points; the time step of the advance is half, that is, At time of day, use the formula +.>Updating the voltage of each splitting point of the sub-network;

wherein Y is ₁ Representing a node admittance matrix of the spatially distributed network,Y ₁₁ 、Y ₂₂ and Y _KK Respectively representing node admittances of the 1 st, 2 nd and K th second subnetworks; />Node voltage column vector representing the spatial distribution network after the nth simulation update, +.> And->Respectively representing node voltages of the 1 st, 2 nd and K th second subnetworks after the nth simulation update; />Equivalent historical current source column vector representing the spatial distribution network before the nth simulation update, ++> And->Respectively representing equivalent historical current sources of the 1 st, 2 nd and K th subnetworks before the nth simulation update; />Representation->Injecting current column vector into nodes of time space distribution network> And->Respectively indicate->Time 1 stInjecting current into the nodes of the 2 nd and the K th second sub-networks; y is Y ₂ Admittance vector, Y, representing the splitting point of a spatially distributed network ₂ ＝[Y _1t Y _2t … Y _tt ]，Y _1t 、Y _2t And Y _1t Admittances of the 1 st, 2 nd and t th split points, respectively; />Voltage column vector representing division point after nth simulation update, +. > And->Respectively representing node voltages of the 1 st, 2 nd and t th split points after the nth simulation update;

As a preferred embodiment, but not limited to this embodiment, the simulating the spatial distribution network by using the node voltage method in step 104 obtains a spatial distribution simulation result, which specifically includes:

and selecting a plurality of branches from the space distribution network as cutting branches.

Dividing the spatial distribution network into a plurality of mutually independent second sub-networks according to the cutting branches.

The time step of the advance is half, that is,at time of day, use the formula +.>Updating the voltage of the internal node of the second subnetwork.

Advancing by one time step, i.e. at time t+Δt, using the formula Updating the second subnet cut branch current. />

Utilization of formulas utilizing formulasOr formula->Calculating the current source of each second subnetwork k>

Step 105, increasing the value of the simulation time t by Δt, increasing the simulation times n by 1, and returning to the step of simulating the first subnetwork meeting the single branch form or the coupling branch form in the plurality of first subnetworks by using the semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result, and performing the next step of simulation.

The invention also provides an electromagnetic transient parallel simulation system based on semi-implicit relaxation, which comprises:

the network dividing module is used for dividing the alternating current-direct current system into a plurality of first subnetworks by taking the grounding capacitance as a boundary.

And the semi-implicit relaxation simulation module is used for simulating the first subnetworks meeting the single branch form or the coupling branch form in the plurality of first subnetworks by utilizing a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result.

As a preferred embodiment, but not limited to this embodiment, the semi-implicit relaxation simulation module specifically includes: the first node voltage update sub-module, for advancing half a time step, i.e.,at time of day, the formula is usedUpdating the voltage of each node of the first subnetwork; a first branch current updating sub-module for advancing a time step, i.e. at the time t+Δt, using the formula +.>Updating the current of each branch of the first subnetwork; wherein (1)>For the voltage of node i after the n-th simulation update,/->For the n-th simulation of the voltage of node i before updating,/->For the branch voltage of node j after the nth simulation update, +.>C is the value of the current source of the node i at the starting time of the nth simulation _i For the capacitance value of node i, G _i For the conductance value of node i, M _i The number of branches connected with the node of the ith branch; />Representing the pre-update current of the kth leg connected to node i; l (L) _ij Represents the inductance value between node i and node j, R _ij Representing the resistance value between node i and node j; />A voltage source between a time node i and a node j representing a half time step after the start time of the nth simulation; />And->Representing the current between node i and node j before and after the nth simulation update, respectively.

As a preferred embodiment, but not limited to this embodiment, the semi-implicit slack simulation module further comprises: a second node voltage update sub-module for advancing half a time step, i.e.,at time of day, use the formula +.>Updating the voltage of each node of the first subnetwork; a second branch current updating sub-module for advancing a time step, i.e. at the time t+Δt, using the formula +.>Updating the current of each branch of the first subnetwork; wherein α is a first intermediate amount, and β is a second intermediate amount; />A, B are the system matrix and input matrix of AC/DC system respectively; /> Wherein 1,2 … N represents the label of the branch, L represents the self inductance of the line, M represents the mutual inductance between the lines, and R represents the resistance on the branch.

And the node voltage method simulation module is used for simulating the spatial distribution network by using a node voltage method to obtain a spatial distribution simulation result.

As a preferred embodiment, but not limited to this embodiment, the node voltage method simulation module specifically includes: the splitting point selecting submodule is used for selecting a plurality of nodes in the spatial distribution network as splitting points; a network splitting sub-module, configured to split the spatial distribution network into a plurality of mutually independent second sub-networks according to the splitting point; the split point voltage update sub-module is used to advance half a time step, that is,at time of day, use the formula +.>Updating the voltage of each splitting point of the sub-network; a node voltage update sub-module for using the formula +.>Calculating the voltage of the node inside each second sub-network; wherein Y is ₁ Node admittance matrix representing a spatially distributed network, < ->Y ₁₁ 、Y ₂₂ And Y _KK Respectively representing node admittances of the 1 st, 2 nd and K th second subnetworks; />Node voltage column vector representing the spatial distribution network after the nth simulation update, +.> And->Respectively representing node voltages of the 1 st, 2 nd and K th second subnetworks after the nth simulation update; / >Equivalent historical current source column vector representing the spatial distribution network before the nth simulation update, ++> And->Respectively representing equivalent historical current sources of the 1 st, 2 nd and K th subnetworks before the nth simulation update; />Representation->Node injection current column vector of time-of-day spatial distribution network And->Respectively indicate->Injecting current into the nodes of the 1 st, 2 nd and K th second subnetworks at the moment; y is Y ₂ Admittance vector, Y, representing the splitting point of a spatially distributed network ₂ ＝[Y _1t Y _2t … Y _tt ]，Y _1t 、Y _2t And Y _1t Admittances of the 1 st, 2 nd and t th split points, respectively; />A voltage column vector representing the splitting point after the nth simulation update, and->Respectively representing node voltages of the 1 st, 2 nd and t th split points after the nth simulation update; a first current source updating sub-module for updating the sub-module with the formula +.>Or formula->Calculating the current source of each second subnetwork k>Wherein (1)>Current source representing inductance element of second subnetwork k after the nth simulation update, +.>Current source representing current element of second subnetwork k after the nth simulation update,/>For the current flowing to node m at time t, node k, +.>And->Respectively isThe voltages at the time point k and the node m are L, which is the inductance value of the inductance element, and C, which is the capacitance value of the capacitance element.

As a preferred embodiment, but not limited to this embodiment, the node voltage method simulation module further includes: the cutting branch selecting submodule is used for selecting a plurality of branches from the space distribution network to serve as cutting branches; the network segmentation sub-module is used for segmenting the space distribution network into a plurality of mutually independent second sub-networks according to the cutting branch; the second subnetwork internal node voltage update sub-module, for advancing half a time step, i.e.,at time of day, the formula is usedUpdating the voltage of the internal node of the second subnet; a cutting branch current updating sub-module for advancing a time step, namely, at the time of t+delta t, by using the formula +.>Updating the second subnet cutting branch current; a second current source updating sub-module for using formula +.>Or formula->Calculating the current source of each second subnetwork k>Wherein (1)>Node voltage column vector representing the spatial distribution network after the nth simulation update, +.>Injecting current column vectors into nodes of the spatial distribution network representing time t, < >>Representing the current matrix on the cut branch before the nth simulation update, < >> And->Representing the current on the 1 st, 2 nd and K th split branches before the nth simulation update, respectively; m represents a node-branch correlation matrix M= [ M ] ₁ M ₂ … M _K ]，M ₁ 、M ₂ And M _K The submatrices corresponding to the 1 st, 2 nd and K th divided branches in the section-branch correlation matrix are respectively.

according to the equivalent geometric meaning of the trapezoidal integral and the central integral, the invention provides a semi-implicit differential equation combining the implicit trapezoidal integral and the explicit central integral to obtain a simulation calculation format with relatively stable numerical characteristics and parallelism. And decoupling between variables/variable groups is realized by utilizing the time delay characteristic of the semi-implicit differential equation, so that an electromagnetic transient simulation iterative solving format is constructed. And a natural network division and parallel calculation strategy based on a semi-implicit differential equation is established. Has the following advantages:

1. flexibility in network separation

The network division of the semi-implicit relaxation method is positioned at the grounding capacitor of the system network, the network division is not needed to be carried out on a long-distance power transmission line adopting distributed parameters, the natural decoupling among the subnetworks can be realized without the help of the transmission line, and the network division is more flexible.

2. High simulation precision

Table 1 combination of implicit and explicit integration formats

The integration format combinations for the two items (1) and (2) at the right end of equation (4) are shown in table 1.

The right-end two terms of the semi-implicit differential equation adopt an implicit trapezoidal integral format, and meanwhile, the characteristic that the trapezoidal integral is equivalent to the central integral area is utilized to construct a time delay characteristic, so that the precision is the same as that of the implicit trapezoidal integral, and the simulation precision is higher than that of a parallel algorithm based on a forward Euler method or a backward Euler method.

3. Good numerical stability

When the sub-network which does not meet the single branch form and the coupling branch form is processed by the semi-implicit relaxation method, the sub-network is regarded as a whole, and data interaction is carried out between the sub-network and the adjacent sub-network, so that small inductance and small capacitance are not needed to be additionally introduced like LIM, and the stability condition is more allowance. Meanwhile, the implicit trapezoidal integration format is superior to the explicit integration format in terms of numerical stability.

4. High parallel efficiency

In the semi-implicit differential equation, an implicit integral format is applied to a part of variables, an explicit integral format is applied to other variables, and the iterative format is made to be an explicit format while the numerical stability of the implicit format is better, so that simultaneous equations are not needed, and independent parallel solving can be achieved among variable groups. In addition, in the semi-implicit relaxation method, the subnets do not need to be equivalent, and the associated networks among the subnets do not need to be formed and solved, so that the parallel efficiency is further improved.

In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.

The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims

1. The electromagnetic transient parallel simulation method based on semi-implicit relaxation is characterized by comprising the following steps of:

increasing the value of the simulation time length t by deltat and increasing the simulation times n by 1, returning to the step of simulating a first subnet meeting a single branch form or a coupling branch form in a plurality of first subnets by using a semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result, and performing next-step simulation;

simulating a first subnet meeting a single branch form in a plurality of first subnets by using a semi-implicit relaxation method, wherein the simulation method specifically comprises the following steps of:

wherein V is _i ^n+1/2 For the voltage of node i after the n-th simulation update, V _i ^n-1/2 For the voltage of node i before the nth simulation update,for the branch voltage of node j after the nth simulation update, +.>C is the value of the current source of the node i at the starting time of the nth simulation _i For the capacitance value of the node i,G _i for the conductance value of node i, M _i The number of branches connected with the node of the ith branch; / >Representing the pre-update current of the kth leg connected to node i; l (L) _ij Represents the inductance value between node i and node j, R _ij Representing the resistance value between node i and node j; />A voltage source between a time node i and a node j representing a half time step after the start time of the nth simulation; />And->Respectively representing current between a node i and a node j before and after the nth simulation update, wherein Δt represents a time interval of one time step;

simulating a first subnet meeting the coupling branch form in a plurality of first subnets by using a semi-implicit relaxation method, wherein the simulation method specifically comprises the following steps of:

a, B are the system matrix and input matrix of AC/DC system respectively;

2. The electromagnetic transient parallel simulation method based on semi-implicit relaxation according to claim 1, wherein the simulating the spatial distribution network by using a node voltage method obtains a spatial distribution simulation result, and specifically comprises:

wherein Y is ₁ Representing a node admittance matrix of the spatially distributed network,Y ₁₁ 、Y ₂₂ and Y _KK Respectively representing node admittances of the 1 st, 2 nd and K th second subnetworks; />Node voltage column vector representing the spatial distribution network after the nth simulation update, +.>And->Respectively representing node voltages of the 1 st, 2 nd and K th second subnetworks after the nth simulation update; />Equivalent historical current source column vector representing the spatial distribution network before the nth simulation update, ++>And->Respectively representing equivalent historical current sources of the 1 st, 2 nd and K th subnetworks before the nth simulation update; />Representation->Empty of timeNode injection current column vector for inter-distributed networkAnd->Respectively indicate->Injecting current into the nodes of the 1 st, 2 nd and K th second subnetworks at the moment; y is Y ₂ Admittance vector, Y, representing the splitting point of a spatially distributed network ₂ ＝[Y _1t Y _2t …Y _tt ]，Y _1t 、Y _2t And Y _1t Admittances of the 1 st, 2 nd and t th split points, respectively; />Voltage column vector representing division point after nth simulation update, +.>V ₁ ^n+1/2 、/>And V _t ^n+1/2 Respectively representing node voltages of the 1 st, 2 nd and t th split points after the nth simulation update;

advancing by one time step, i.e. at time t+Δt, using the formulaOr formula (la)Calculating the current source of each second subnetwork k>

Wherein,current source representing inductance element of second subnetwork k after the nth simulation update, +.>Current source representing current element of second subnetwork k after the nth simulation update,/>For the current flowing to node m at time t, node k, +.>Andrespectively->The voltages at the time point k and the node m are L, which is the inductance value of the inductance element, and C, which is the capacitance value of the capacitance element.

3. The electromagnetic transient parallel simulation method based on semi-implicit relaxation according to claim 2, wherein the simulating the spatial distribution network by using a node voltage method obtains a spatial distribution simulation result, and specifically comprises:

using the formulaOr formula->Calculating the current source of each second subnetwork k>

Wherein,node voltage column vector representing the spatial distribution network after the nth simulation update, +.>Injecting current column vectors into nodes of the spatial distribution network representing time t, < >>Representing the current matrix on the cut leg prior to the nth simulation update,and->Respectively represent the 1 st, 2 nd and K th components before the nth simulation updateCurrent on the cut branch; m represents a node-branch correlation matrix M= [ M ] ₁ M ₂ …M _K ]，M ₁ 、M ₂ And M _K The submatrices corresponding to the 1 st, 2 nd and K th divided branches in the section-branch correlation matrix are respectively.

4. An electromagnetic transient parallel simulation system based on semi-implicit relaxation, which is characterized by comprising the following steps:

the return module is used for increasing the value of the simulation time t by deltat and increasing the simulation times n by 1, and returning to the step of simulating the first subnetwork meeting the single branch form or the coupling branch form in the plurality of first subnetworks by using the semi-implicit relaxation method to obtain a semi-implicit relaxation simulation result and performing the next step of simulation;

the semi-implicit relaxation simulation module specifically comprises:

the first node voltage update sub-module, for advancing half a time step, i.e.,at time of day, the formula is usedUpdating the electricity of each node of the first subnetworkPressing;

wherein V is _i ^n+1/2 For the voltage of node i after the n-th simulation update, V _i ^n-1/2 For the voltage of node i before the nth simulation update, For the branch voltage of node j after the nth simulation update, +.>C is the value of the current source of the node i at the starting time of the nth simulation _i For the capacitance value of node i, G _i For the conductance value of node i, M _i The number of branches connected with the node of the ith branch; />Representing the pre-update current of the kth leg connected to node i; l (L) _ij Represents the inductance value between node i and node j, R _ij Representing the resistance value between node i and node j; />A voltage source between a time node i and a node j representing a half time step after the start time of the nth simulation; />And->Represents the current between node i and node j before and after the nth simulation update, respectively, Δt represents oneTime intervals of the time steps;

the semi-implicit relaxation simulation module specifically comprises:

a, B are the system matrix and input matrix of AC/DC system respectively;

5. The electromagnetic transient parallel simulation system based on semi-implicit relaxation according to claim 4, wherein said node voltage method simulation module specifically comprises:

the splitting point selecting submodule is used for selecting a plurality of nodes in the spatial distribution network as splitting points;

wherein Y is ₁ Representing a node admittance matrix of the spatially distributed network,Y ₁₁ 、Y ₂₂ and Y _KK Respectively representing node admittances of the 1 st, 2 nd and K th second subnetworks; />Node voltage column vector representing the spatial distribution network after the nth simulation update, +.>And->Respectively represent Simulating the node voltages of the 1 st, 2 nd and K th second subnetworks after updating for the nth time; />Equivalent historical current source column vector representing the spatial distribution network before the nth simulation update, ++>And->Respectively representing equivalent historical current sources of the 1 st, 2 nd and K th subnetworks before the nth simulation update; />Representation->Node injection current column vector of time-of-day spatial distribution networkAnd->Respectively indicate->Injecting current into the nodes of the 1 st, 2 nd and K th second subnetworks at the moment; y is Y ₂ Admittance vector, Y, representing the splitting point of a spatially distributed network ₂ ＝[Y _1t Y _2t …Y _tt ]，Y _1t 、Y _2t And Y _1t Admittances of the 1 st, 2 nd and t th split points, respectively; />Representing the splitting point after the nth simulation updateVoltage column vector>V ₁ ^n+1/2 、/>And V _t ^n+1/2 Respectively representing node voltages of the 1 st, 2 nd and t th split points after the nth simulation update;

Wherein,current source representing inductance element of second subnetwork k after the nth simulation update, +.>Current source representing current element of second subnetwork k after the nth simulation update,/>For the current flowing to node m at time t, node k, +.>Andrespectively- >The voltages at the time point k and the node m are L, which is the inductance value of the inductance element, and C, which is the capacitance value of the capacitance element.

6. The electromagnetic transient parallel simulation system based on semi-implicit relaxation according to claim 5, wherein said node voltage method simulation module specifically comprises:

the second subnetwork internal node voltage update sub-module, for advancing half a time step, i.e.,at time of day, the formula is usedUpdating the voltage of the internal node of the second subnet;

Wherein,node voltage column vector representing the spatial distribution network after the nth simulation update, +.>Injecting current column vectors into nodes of the spatial distribution network representing time t, < > >Representing the current matrix on the cut leg prior to the nth simulation update,and->Representing the current on the 1 st, 2 nd and K th split branches before the nth simulation update, respectively; m represents a node-branch correlation matrix M= [ M ] ₁ M ₂ …M _K ]，M ₁ 、M ₂ And M _K The submatrices corresponding to the 1 st, 2 nd and K th divided branches in the section-branch correlation matrix are respectively.