CN106202636B - A kind of method and system of micro-capacitance sensor electro-magnetic transient real-time simulation - Google Patents
A kind of method and system of micro-capacitance sensor electro-magnetic transient real-time simulation Download PDFInfo
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Abstract
The invention discloses a kind of method and system of micro-capacitance sensor electro-magnetic transient real-time simulation, the precision and efficiency of the real-time simulation of micro-capacitance sensor electro-magnetic transient are realized using tile and hierarchy parallel mode, parallel mode includes the hierarchical solving of network blocks equivalence and sub-network；Network blocks equivalence includes piecemeal and equivalence, and piecemeal part determines elementary net network size and port input variable, etc. value parts determine the differencing state variable equation and external characteristics equation of elementary net network；The hierarchical solving of sub-network includes the merging of sub-network and retrodicting for port input quantity, sub-network is merged into high one layer of merging sub-network, it obtains merging the external characteristics equation of sub-network and retrodicts equation, the port input quantity for retrodicting its lower layer's sub-network by the port input quantity of merging sub-network again obtains the port input quantity of all elementary net networks and determines the state variable of elementary net network.
Description
Technical Field
The invention relates to the field of power systems, in particular to a method and a system for real-time simulation of electromagnetic transient of a micro-grid.
Background
The micro-grid is used as a distributed power supply to be connected into a power system, and becomes an effective means for adapting to new energy revolution and undertaking new mission of a power grid. In order to ensure the safe operation of the micro-grid, it is necessary to research the hardware-in-the-loop real-time simulation for testing and verifying the equipment such as the relay protection of the micro-grid, the control of the converter and the like.
The micro-grid comprises a large number of high-frequency power switches and nonlinear elements, the action frequency of the power switches is usually from thousands of hertz to hundreds of thousands of hertz, and in order to well simulate the electromagnetic transient process of the micro-grid, the simulation step length is as short as microsecond, preferably sub-microsecond; when a plurality of nonlinear elements such as power diodes, distributed power supplies and the like exist, the compensation method is used for solving the power system containing the nonlinear elements, the dimension of a nonlinear equation set is large, and the difficulty of real-time simulation of the microgrid is further increased.
In order to improve the speed of real-time simulation, an inverse matrix method can be adopted on the basis of linearization to avoid solving the power system, but because a micro-grid contains a lot of nonlinear elements, when the inverse matrix method is applied to the micro-grid real-time simulation, the pre-stored parameter data amount can easily reach the intolerable degree. The inverse matrix method is adopted and the L/C switch model is utilized to enable the inverse matrixes in different converter operation states to be the same, so that the problem of inverse matrix prestoring does not exist, but the simulation step length is greatly limited. The interface transformer method or the mixed difference method can divide the micro-grid into a plurality of independent subsystems, so that the dimension and the combination number of the pre-stored inverse matrix are greatly reduced, but the simulation precision is reduced to some extent, and even the problem of calculation stability can occur.
Compared with a large power grid, the micro-grid has complex composition and operation modes and frequent topological structure change, and the micro-grid contains a large number of high-frequency power switches and nonlinear elements, so that high requirements are provided for real-time simulation of the micro-grid, and the main problems to be solved are how to select a proper simulation step length, improve simulation precision and reduce the data volume of the inverse matrix prestore. Therefore, the research of the partitioning layered parallel method which not only ensures the simulation precision, but also reduces the pre-stored data volume of the inverse matrix is of great significance.
Disclosure of Invention
The invention aims to provide a method and a system for real-time simulation of electromagnetic transient state of a micro-grid, in particular to a partitioned layered parallel simulation method which not only ensures simulation precision, but also can reduce the data volume of an inverse matrix prestorage, and converts a sub-network simultaneous solving problem into a problem of partitioning equivalence and layered solving for a network.
In order to solve the above technical problem, the present invention provides a method for real-time simulation of electromagnetic transient of a microgrid, comprising:
calculating a differential state variable equation and an external characteristic equation of a basic sub-network of the micro-grid according to a coefficient matrix of the basic sub-network;
combining the basic sub-networks layer by layer, and sequentially calculating an external characteristic equation and a back-off equation of each combined sub-network from low to high;
according to the external characteristic equation and the backward-pushing equation of each merging sub-network, port input quantities of each merging sub-network are sequentially calculated from high to low to obtain port input quantities of all basic sub-networks;
and calculating the state variable of the basic sub-network according to the port input quantity of the basic sub-network.
Before calculating the differential state variable equation and the external characteristic equation of the basic sub-network according to the coefficient matrix of the basic sub-network of the micro-grid, the method further comprises the following steps:
and dividing the micro-grid according to the size of a preset basic sub-network, and determining port input variables of the divided basic sub-network and a pre-stored coefficient matrix of the basic sub-network.
The method for calculating the differential state variable equation and the external characteristic equation of the basic sub-network according to the coefficient matrix of the basic sub-network of the micro-grid comprises the following steps:
reading in independent current source, independent voltage source and converter bridge arm driving signals of the basic sub-network;
estimating the port input quantity of the basic sub-network by using a linear extrapolation method;
calculating the electrical quantity of the nonlinear element of the basic sub-network according to a nonlinear element electrical quantity equation, and determining the state of the nonlinear element by adopting an iteration method; changing and calculating a coefficient matrix of the electrical quantity of the nonlinear element according to the state of the nonlinear element, and judging whether the iteration times are reached;
and if the iteration times are reached, determining coefficient matrixes of the differential state variable equation and the external characteristic equation of the basic sub-network, and calculating equivalent injection sources of the differential state variable equation and the external characteristic equation of the basic sub-network to obtain the differential state variable equation and the external characteristic equation of the basic sub-network.
The method comprises the following steps of combining the basic sub-networks layer by layer, and sequentially calculating an external characteristic equation and a back-off equation of each combined sub-network from low to high, wherein the method comprises the following steps:
combining a predetermined number of sub-networks with adjacent relation into a combined sub-network of a higher layer, and establishing an external characteristic equation and a constraint equation of each sub-network of a lower layer of the combined sub-network from low to high; and simplifying by a Gaussian reduction elimination method to obtain an external characteristic equation and an inverse equation of the combined sub-network until the external characteristic equation and the constraint equation of each sub-network of the lower layer of the top layer network are connected.
According to the external characteristic equation and the inverse equation of each merging sub-network, port input quantities of each merging sub-network are calculated sequentially from high to low to obtain port input quantities of all basic sub-networks, and the method comprises the following steps:
establishing external characteristic equations and constraint equations of the sub-networks of the lower layer of the top layer network simultaneously to obtain port input quantities of the sub-networks of the lower layer of the top layer network;
and reversely deducing the port input quantity of the corresponding lower sub-network from the port input quantity of the merging sub-network from high to low according to the corresponding push equation to obtain the port input quantities of all the basic sub-networks.
Wherein calculating the state variables of the basic sub-network according to the port input quantity of the basic sub-network comprises:
and determining the state variable of the basic sub-network according to the differential state variable equation of the basic sub-network and the port input quantity of the basic sub-network.
The invention provides a micro-grid electromagnetic transient real-time simulation system, which comprises:
the equivalent module is used for calculating a differential state variable equation and an external characteristic equation of a basic sub-network of the micro-grid according to the coefficient matrix of the basic sub-network;
the sub-network merging module is used for merging the basic sub-networks layer by layer and sequentially calculating an external characteristic equation and a backward equation of each merged sub-network from low to high;
the port input quantity pushing module is used for sequentially calculating the port input quantities of the merging sub-networks from high to low according to the external characteristic equation and the backward-pushing equation of the merging sub-networks of each layer to obtain the port input quantities of all the basic sub-networks;
and the state variable calculation module is used for calculating the state variable of the basic sub-network according to the port input quantity of the basic sub-network.
Wherein, still include:
and the dividing module is used for dividing the micro-grid according to the size of a preset basic sub-network and determining port input variables of the divided basic sub-network and a pre-stored coefficient matrix of the basic sub-network.
Wherein the equivalence module comprises:
the signal acquisition unit is used for reading in independent current sources, independent voltage sources and converter bridge arm driving signals of the basic sub-network;
a port input amount calculation unit for estimating a port input amount of the basic sub-network by using a linear extrapolation method;
the iteration unit is used for calculating the nonlinear element electrical quantity of the basic sub-network according to a nonlinear element electrical quantity equation and determining the state of the nonlinear element by adopting an iteration method; changing and calculating a coefficient matrix of the electrical quantity of the nonlinear element according to the state of the nonlinear element, and judging whether the iteration times are reached;
and the equivalence unit is used for determining the coefficient matrixes of the differentiated state variable equation and the external characteristic equation of the basic sub-network if the iteration times are reached, and calculating the equivalent injection sources of the differentiated state variable equation and the external characteristic equation of the basic sub-network to obtain the differentiated state variable equation and the external characteristic equation of the basic sub-network.
The sub-network merging module is used for merging a predetermined number of sub-networks with adjacent relation into a merging sub-network of a higher layer, and simultaneously merging the external characteristic equation and the constraint equation of each sub-network of the lower layer of the sub-network from low to high; and the external characteristic equation and the backward-pushing equation of the merging sub-networks are obtained by utilizing the reduction of a Gaussian reduction elimination method until the external characteristic equation and the constraint equation of each sub-network of the lower layer of the top layer network are connected.
The invention provides a method for simulating the electromagnetic transient state of a microgrid in real time, which comprises the following steps: calculating a differential state variable equation and an external characteristic equation of a basic sub-network of the micro-grid according to a coefficient matrix of the basic sub-network; combining the basic sub-networks layer by layer, and sequentially calculating an external characteristic equation and a back-off equation of each combined sub-network from low to high; according to the external characteristic equation and the backward-pushing equation of each merging sub-network, port input quantities of each merging sub-network are sequentially calculated from high to low to obtain port input quantities of all basic sub-networks; calculating the state variable of the basic sub-network according to the port input quantity of the basic sub-network;
therefore, the method realizes the precision and the efficiency of the micro-grid electromagnetic transient real-time simulation by utilizing a block layered parallel mode, wherein the parallel mode comprises network block equivalence and layered solution of a sub-network; the network block equivalence comprises block and equivalence, wherein the block part determines the size of a basic sub-network and a port input variable, and the equivalence part determines a differencing state variable equation and an external characteristic equation of the basic sub-network; the hierarchical solution of the sub-networks comprises the merging of the sub-networks and the backward-pushing of the port input quantity, the sub-networks are merged into a merging sub-network of a higher layer to obtain an external characteristic equation and a backward-pushing equation of the merging sub-network, and then the port input quantity of the sub-network of the lower layer is backward-pushed by the port input quantity of the merging sub-network to obtain the port input quantities of all basic sub-networks and determine the state variables of the basic sub-networks; the invention also provides a system for the real-time simulation of the electromagnetic transient of the microgrid, which has the effects and is not repeated herein.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flowchart of a method for real-time simulation of electromagnetic transient of a microgrid according to an embodiment of the present invention;
fig. 2(a) is a schematic diagram of a layer combination of a microgrid 1 according to an embodiment of the present invention;
fig. 2(b) is a schematic diagram of a 2-layer integration of a microgrid provided in an embodiment of the present invention;
fig. 2(c) is a schematic diagram of a 3-layer integration of the microgrid provided in the embodiment of the present invention;
fig. 2(d) is a schematic diagram of a 4-layer integration of the microgrid provided in the embodiment of the present invention;
fig. 3(a) is an equivalent schematic diagram of a micro-grid multi-port network according to an embodiment of the present invention;
fig. 3(b) is an equivalent schematic diagram of a micro-grid multi-port passive resistance network according to an embodiment of the present invention;
fig. 4(a) is a schematic diagram of a parallel connection manner of the microgrid sub-networks according to an embodiment of the present invention;
fig. 4(b) is a schematic diagram of a series connection of the microgrid sub-networks according to an embodiment of the present invention;
fig. 4(c) is a schematic diagram of a hybrid connection of a microgrid sub-network according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a simulation flow of local iteration provided in an embodiment of the present invention;
FIG. 6 is a diagram illustrating an exemplary simulation algorithm for local iteration according to an embodiment of the present invention;
fig. 7 is a block diagram of a system for real-time simulation of electromagnetic transients in a microgrid according to an embodiment of the present invention.
Detailed Description
The core of the invention is to provide a method and a system for real-time simulation of the electromagnetic transient state of the microgrid, which are a block layered parallel simulation method capable of ensuring the simulation precision and reducing the data volume of the inverse matrix prestorage, and convert the simultaneous solving problem of the sub-networks into the problem of performing block equivalence on the network and performing layered solving.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, fig. 1 is a flowchart illustrating a method for real-time simulation of electromagnetic transient of a microgrid according to an embodiment of the present invention; the method can comprise the following steps:
s100, calculating a differential state variable equation and an external characteristic equation of a basic sub-network of the micro-grid according to a coefficient matrix of the basic sub-network;
before the step, basic sub-networks are required to be divided into the micro-grid, the micro-grid is divided according to the size of the preset basic sub-networks, and port input variables of the divided basic sub-networks and a pre-stored coefficient matrix of the basic sub-networks are determined. Therefore, the number of basic sub-networks is determined according to the actual situation of the microgrid. The number and size of the elementary subnetworks are not limited here.
The size of the predetermined basic sub-network may be determined by network partitioning based on network structure, the number of time controlled elements and non-linear elements, etc. Determination of port input variables of the basic subnetwork: for the current port, the current is an input variable, and the voltage is an output variable; for the voltage port, the voltage is an input variable, and the current is an output variable; preferably, the state variables, namely the inductive current and the capacitive voltage, are used as port input variables of the sub-networks, and then the port input variables are selected according to the connection mode of the sub-networks, when the sub-networks are connected in parallel, the voltage ports are adopted by the sub-networks, and when the sub-networks are connected in series, the current ports are adopted by the sub-networks.
The coefficient matrix here is a simulated initial value given according to the actual situation of each elementary sub-network. And when equivalence is carried out on the basic sub-network, an inductor, a capacitor, an independent current source and a voltage source in the basic sub-network are extracted, and the differential state variable equation and the external characteristic equation of the basic sub-network are obtained by carrying out implicit trapezoidal difference on the characteristic equations of the inductor and the capacitor according to the equivalent principle of the multi-port passive resistance network. The specific process can be as follows:
reading in independent current source, independent voltage source and converter bridge arm driving signals of the basic sub-network;
estimating the port input quantity of the basic sub-network by using a linear extrapolation method;
calculating the electrical quantity of the nonlinear element of the basic sub-network according to a nonlinear element electrical quantity equation, and determining the state of the nonlinear element by adopting an iteration method; changing and calculating a coefficient matrix of the electrical quantity of the nonlinear element according to the state of the nonlinear element, and judging whether the iteration times are reached;
and if the iteration times are reached, determining coefficient matrixes of the differential state variable equation and the external characteristic equation of the basic sub-network, and calculating equivalent injection sources of the differential state variable equation and the external characteristic equation of the basic sub-network to obtain the differential state variable equation and the external characteristic equation of the basic sub-network.
The input quantity of each basic sub-network port is estimated through a linear extrapolation method, the voltage and the current of a nonlinear element are calculated according to an electrical quantity equation of the nonlinear element, the state of the nonlinear element is judged by adopting an iteration method, coefficient matrixes of a differential state variable equation and an external characteristic equation of the basic sub-network are determined, and an equivalent injection source of the differential state variable equation and the external characteristic equation of the basic sub-network is calculated to obtain the differential state variable equation and the external characteristic equation of the basic sub-network.
The method comprises the following steps of (1) expressing nonlinear elements such as a photovoltaic power supply by using a piecewise linear equivalent model; for naturally commutated switching devices such as diodes, only two resistor branches (R) may be usedon、Roff) To describe which branch depends on the voltage across the switching device; for a converter bridge arm with a forced reversing switching device such as an IGBT and the like connected in parallel with a freewheeling diode, two resistance branches can be used for describing, and particularly, which branch needs to consider a driving signal gate of a control system. Reducing the inverse matrix data storage pressure caused by controlled switching by network blocks, extracting inductors, capacitors, independent current sources and voltage sources in each basic sub-network of the micro-grid, and carrying out implicit trapezoidal difference on characteristic equations of the inductors and the capacitors according to the equivalent principle of a multi-port passive resistance network to obtain a differential state variable equation and an external characteristic equation of the basic sub-network, wherein the differential state variable equation and the equivalent injection source R of the external characteristic equation of the basic sub-network arel(t) and SlAnd (t) the independent current source and the independent voltage source of the sub-network at the moment t are related, and the inductive current, the capacitive voltage, the independent current source, the independent voltage source and the port input quantity of the sub-network at the moment t-delta t are related, but the voltages and the currents of other sub-networks are not related.
S110, merging the basic sub-networks layer by layer, and sequentially calculating an external characteristic equation and a back-off equation of each merged sub-network from low to high;
the merging method of the basic sub-networks can be performed according to the actual requirements of users, and the merging method is only required to be the largest network which can merge the basic sub-networks into the final micro-grid layer by layer. Referring to fig. 2(a), 2(b), 2(c), and 2(d), several merging manners are shown as examples, wherein l represents the number of the basic sub-networks, and the basic sub-networks are hierarchically merged according to four merging schemes, as shown in fig. 2(a) to 2 (d). Scheme 1 directly merges all the basic sub-networks. Scheme 2 constructs two layers of merging subnetworks according to a minimization method. Scheme 3 the merging subnetworks (1, 2, 3, 4) and (8, 9, 10, 11) in scheme 2 are subdivided into three layers of merging subnetworks. Scheme 4 constitutes a three-tier merging subnetwork in accordance with the maximum independent set method. It can be seen from the four figures that the number of sub-networks including the sub-network of the lower layer in each sub-network in the merging process is not necessarily all the same, as long as the number of sub-networks is satisfied, and the number of basic sub-networks is at most, and finally only one complete micro-grid is provided.
Wherein, the specific process of the step can be as follows:
combining a predetermined number of sub-networks with adjacent relation into a combined sub-network of a higher layer, and establishing an external characteristic equation and a constraint equation of each sub-network of a lower layer of the combined sub-network from low to high; and simplifying by a Gaussian reduction elimination method to obtain an external characteristic equation and an inverse equation of the combined sub-network until the external characteristic equation and the constraint equation of each sub-network of the lower layer of the top layer network are connected.
S120, according to the external characteristic equation and the backward-pushing equation of each merging sub-network, port input quantities of each merging sub-network are sequentially calculated from high to low to obtain port input quantities of all basic sub-networks;
s130, calculating the state variable of the basic sub-network according to the port input quantity of the basic sub-network.
Wherein, the specific processes of the two steps can be as follows:
establishing external characteristic equations and constraint equations of the sub-networks of the lower layer of the top layer network simultaneously to obtain port input quantities of the sub-networks of the lower layer of the top layer network;
and reversely deducing the port input quantity of the corresponding lower sub-network from the port input quantity of the merging sub-network from high to low according to the corresponding push equation to obtain the port input quantities of all the basic sub-networks.
And determining the state variable of the basic sub-network according to the differential state variable equation of the basic sub-network and the port input quantity of the basic sub-network.
Based on the technical scheme, the method for simulating the electromagnetic transient state of the microgrid in real time converts a simultaneous solving problem of a sub-network into a problem of partitioning a multi-port network, equating the multi-port network and solving the multi-port network in a layered manner, and mainly comprises the steps of segmenting the multi-port network, determining the size and port input variables of a basic sub-network, estimating the port input quantity of each basic sub-network by adopting a linear extrapolation method, calculating the voltage or current of nonlinear elements of each basic sub-network according to an electric quantity equation of the nonlinear elements, determining the state of the nonlinear elements by adopting an iteration method, and determining a differential state variable equation and an external characteristic equation of the basic sub-network; the hierarchical solution comprises merging of sub-networks and backward-pushing of port input quantities, merging the sub-networks with adjacent relations, connecting the external characteristic equations and constraint equations of the sub-networks at the lower layer of the merging sub-networks from low to high, obtaining the external characteristic equations and backward-pushing equations of the merging sub-networks by adopting Gaussian reduction elimination reduction until connecting the external characteristic equations and constraint equations of the sub-networks at the lower layer of the top-layer network, obtaining the port input quantities of the sub-networks at the lower layer of the top-layer network, backward-pushing the port input quantities of the sub-networks at the lower layer of the merging sub-networks from high to low in sequence, finally obtaining the port input quantities of all basic sub-networks, and determining the state variables of the basic sub-networks according to the differential state variable equations of the basic sub-networks.
The operation steps of the scheme in the above embodiment are described in detail below with reference to fig. 3, fig. 4 and mathematical formulas, as described below:
the data storage pressure of the inverse matrix can be reduced by a network blocking method, and when the network comprises m controlled switches, 2 controlled switches need to be prestoredmIf the network is divided into n sub-networks and the number of controlled switches in each sub-network block is the same, only n.2 pre-storage is neededm/nAn inverse matrix.
FIG. 3(a) shows the second place in the microgridl blocks of sub-networks, having k current ports and m voltage ports. For current port, current iilIs an input variable, voltage uolIs an output variable; for voltage port, voltage uilIs an input variable, current iolIs an output variable. The inductor, the capacitor, the independent current source and the voltage source in the sub-network are extracted and sequentially usedLl、iLl、uCl、iCl、usl、Isl、Usl、islTo represent the voltage and current of these extraction ports, as shown in fig. 3 (b).
According to the equivalent principle of the multi-port passive resistance network, the following steps are carried out:
characteristic equation u for inductanceLl(t)＝-LldiLlCharacteristic equation i of (t)/dt and capacitanceCl(t)＝-ClduCl(t)/dt is subjected to an implicit trapezoidal difference to convert [ i [ ]Ll(t),uCl(t)]TIs marked as xl(t)，[uol(t),iol(t)]TIs marked as yl(t)，[iil(t),uil(t)]TIs denoted by vl(t)，[Isl(t),Usl(t)]TIs marked as Vl(t) combining the formulae (1) and (2) with
xl(t)＝Al1vl(t)+Al1vl(t-Δt)+Al2Vl(t)+Al2Vl(t-Δt)+Al3xl(t-Δt) (3)
yl(t)＝Bl1vl(t)+Bl2vl(t-Δt)+Bl3Vl(t)+Bl4Vl(t-Δt)+Bl5xl(t-Δt) (4)
Wherein A isl1～Al3、Bl1～Bl5Are coefficient matrices. The formulae (3) and (4) are abbreviated
xl(t)＝Al1vl(t)+Rl(t) (5)
yl(t)＝Bl1vl(t)+Sl(t) (6)
Equation (5) is a differentiated state variable equation of the sub-network, and equation (6) is an external characteristic equation of the sub-network. Rl(t) and SlAnd (t) the independent current source and the independent voltage source of the sub-network at the moment t are related, and the inductive current, the capacitive voltage, the independent current source, the independent voltage source and the port input quantity of the sub-network at the moment t-delta t are related, but the voltages and the currents of other sub-networks are not related.
The more sub-networks divided by the micro-grid, the more the number of constraint equations among the sub-networks, and the larger constraint equation set generally has the characteristic of sparsity. By utilizing the characteristic, a plurality of sub-networks are combined into a new sub-network, and the sub-network simultaneous solution problem is converted into a sub-network hierarchical combination problem.
Define (n, j) as the jth sub-network in the nth layer, where (1,1) represents the entire network. Defining p (n, j) as the set of lower subnets of the (n, j) subnets. Will be provided withThe (n, j) sub-networks of (a) are called basic sub-networks, and the other sub-networks are called merging sub-networks.
Let the port output variables and port input variables of the (n, j) subnetwork be denoted as y(n,j)(t) and v(n,j)(t) its external characteristic equation is expressed as
y(n,j)(t)＝B(n,j)v(n,j)(t)+S(n,j)(t) (7)
If (n, j) happens to be the basic subnetwork shown in FIG. 3(a), then there is B(n,j)＝Bl，S(n,j)(t)＝Sl(t)。
To obtain B merging subnetworks(n,j)、S(n,j)(t), let the external property equations for all sub-networks in p (n, j) be abbreviated
At y(n,j)(t)、v(n,j)(t)、Andwill not involve in the constraint equation ofThe constraint equations of (a) are denoted as class a constraint equations, and the other constraint equations are denoted as class B constraint equations. When y is(n,j)(t) has m(n,j)When the element is one, m is taken out of B(n,j)A is related to y(n,j)(t) or v(n,j)(t) and these equations are denoted as B2 type constraint equations, and the other B type constraint equations are denoted as B1 type constraint equations.
Listing the comprehensive equation of (n, j) according to the sequence of the external characteristic equation of p (n, j), the A type constraint equation of (n, j), the B1 type constraint equation of (n, j) and the B2 type constraint equation
Wherein,andis derived from Is composed ofAnd all elements have appeared in the class a constraint equations,is composed ofIn the other part of the above-mentioned patent document,are coefficient matrices.
Elimination of class B constraint equations using an external property equation for p (n, j) and a class A constraint equation for (n, j)Andto obtain
Wherein,the middle element is composed ofAndthe middle element is obtained by addition and subtraction operation;andthe middle element is composed ofThe medium elements are obtained by addition and subtraction.
Simplified equation (10) is reduced by Gauss jordan elimination method to obtain
The second equation of equation (11) is consistent with equation (7), i.e., it is the (n, j) external property equation for the merged subnetwork. Substituting the two equations of equation (11) into a class A constraint equation, have
Wherein,the middle element is composed ofAnd B(n,j)The middle element is obtained by addition and subtraction operation;the middle element is composed of S(n,j)(t) andthe medium elements are obtained by addition and subtraction.
The first equation of equation (11) and equation (12) are combined and described
Equation (13) is referred to as a backward-push equation for merging subnets, and is in the sense consistent with equation (5) for differencing state variables. In particular, when (n, j) ═ 1,
fig. 4 shows different connection modes of (n, j) sub-networks consisting of (n +1,1), (n +1,2) and (n +1,3) sub-networks, and table 1 shows the number of class a constraint equations of the (n, j) sub-networks under different (n +1,1), (n +1,2) and (n +1,3) sub-network port types.
TABLE 1 number of class A constraint equations
As can be seen from table 1, when the sub-networks are connected in parallel, the sub-networks should use voltage ports; when sub-networks are connected in series, the sub-networks employ current ports.
The block layered solution of the network can be divided into four steps:
1. a according to the basic sub-networkl1～Al3、Bl1～Bl5Parameters, calculating R of the differencing state variable equation and the extrinsic property equation of the basic subnetworkl(t) and Sl(t)；
2. According to the external characteristic equation and the constraint equation of the merging sub-networks, the parameters A of the external characteristic equation and the backward-pushing equation of each merging sub-network in each layer are calculated from low to high in sequence(n,j)、B(n,j)、R(n,j)(t) and S(n,j)(t)；
3. Calculating the port input quantity v of each layer from high to low in sequence according to the inverse equation of the merging sub-network(n，j)；
4. Port input quantity v according to basic sub-networklCalculating the state variable x inside the elementary subnetworkl。
A of a basic sub-network when it contains non-linear elementsl1～Al3、Bl1～Bl5Related to the current flowing through or the voltage across the nonlinear element. Calculating w for judging state of nonlinear elementl(t) and calculating yl(t) is similar, i.e.
wl(t)＝Dl1vl(t)+Dl2vl(t-Δt)+Dl3ul(t)+Dl4ul(t-Δt)+Dl5xl(t-Δt) (14)
Equation (14) is an electrical quantity equation of a nonlinear element, since Dl1～Dl5And also the state of the nonlinear element, an iterative method is used to determine the state of the nonlinear element. The calculation of equation (14) requires knowledge of vlAnd (t) the first 3 steps of block layered solution are involved, and the iterative computation amount is large. Port input quantity v when the basic sub-network containing non-linear elementsl(t) is exactly the current in the inductor or the voltage across the capacitor terminal vl(t) does not mutate, and v can be usedl(t-2Δt)、vl(t-. DELTA.t) vs. vl(t) estimating. Fig. 5 shows a simulation flow of such a local iteration.
In order to make the method of the present invention better understood by those skilled in the art, the present invention will be described in detail with reference to the accompanying drawings and examples, but the present invention is not limited thereto.
The test calculation example adopts a typical european union low-voltage microgrid system which is connected with 2 same photovoltaic power generation systems and 1 light-storage hybrid power generation system, as shown in fig. 6.
Under the conditions of 398K of temperature and 1000W/m2 of illumination intensity, the parameters of the segmented equivalent circuit of the photovoltaic cell are shown in the table 2:
TABLE 2 piecewise equivalent circuit parameters of photovoltaic cells
The storage battery adopts an equivalent circuit which takes the overpotential and the self-discharge behavior into account, wherein the battery capacitance is 5500F, the self-discharge resistance is 10k omega, the overpotential resistance is 0.001 omega, the overpotential capacitance is 1F, and the connection resistance and the battery internal resistance are both 0.02 omega. The capacitance of the photovoltaic cell Boost circuit is 0.5mF, and the inductance of the photovoltaic cell Boost circuit is 0.5 mH. The capacitance of the Buck/boost circuit of the storage battery is 1mF, and the inductance is 5 mH. The DC side capacitance of the DC/AC converter is 5 mF. The inductance of the LC filter circuit is 0.32mH, and the capacitance is 275 uF. The leakage reactance of the isolation transformer is 0.18mH, and the transformation ratio is 1.
To facilitate testing of the performance of the converter controllers and protection devices, various short-circuit faults and ground faults that may occur at the nodes 14, 16, 20, 22, 24 are described by a common fault model.
To ensure that the mimic eukaryote can accommodate all basic subnetworks Al1～Al3、Bl1～Bl5The node 3, 8, 26, 27, 31, 32, 35, 36 is taken as a division point to divide the microgrid system into 12 basic sub-networks, as shown in fig. 6. The hollow ports represent voltage ports, the solid ports represent current ports, and the determination of the ports needs to comprehensively consider whether the sub-networks contain nonlinear elements, the connection mode among the sub-networks and other factors.
These basic sub-networks are hierarchically merged according to four merging schemes, as shown in fig. 2(a) to 2(d), respectively. Scheme 1 directly merges all the basic sub-networks. Scheme 2 constructs two layers of merging subnetworks according to a minimization method. Scheme 3 the merging subnetworks (1, 2, 3, 4) and (8, 9, 10, 11) in scheme 2 are subdivided into three layers of merging subnetworks. Scheme 4 constitutes a three-tier merging subnetwork in accordance with the maximum independent set method. The state of the nonlinear element is determined by adopting 3 times of iteration, the eukaryon-simulated instruction stream is generated by utilizing a table scheduling algorithm, and the calculation amount and the serial degree of each combination scheme in the calculation step are shown in table 3.
Table 3 comparison of results for four pooling schemes
Analysis of table 3 shows that the hierarchy reduces the serialization of step ② but increases the serialization of step ③, and the minimization method can effectively reduce the computation amount, but the implementation of the minimization method cannot be guaranteed due to excessive parallelization, so that the computation amount is increased.
The embodiment of the invention provides a method for simulating the electromagnetic transient of a microgrid in real time, which is a block layered parallel simulation method capable of ensuring the simulation precision and reducing the data volume of an inverse matrix prestorage, and is used for transforming the simultaneous solving problem of sub-networks into the problem of performing block equivalence on the network and performing layered solving.
The system for real-time simulation of electromagnetic transient of a microgrid provided by the embodiment of the invention is introduced below, and the system for real-time simulation of electromagnetic transient of a microgrid described below and the method for real-time simulation of electromagnetic transient of a microgrid described above can be referred to correspondingly.
Referring to fig. 7, fig. 7 is a block diagram illustrating a system for real-time simulation of electromagnetic transient of a microgrid according to an embodiment of the present invention; the system may include:
the equivalence module 100 is configured to calculate a differential state variable equation and an external characteristic equation of a basic sub-network of the microgrid according to a coefficient matrix of the basic sub-network;
the sub-network merging module 200 is configured to merge the basic sub-networks layer by layer, and sequentially calculate an external characteristic equation and a back-off equation of each merged sub-network from low to high;
the port input quantity pushing module 300 is configured to calculate port input quantities of the merging sub-networks of each layer in sequence from high to low according to the external characteristic equation and the backward-pushing equation of the merging sub-networks of each layer, so as to obtain port input quantities of all the basic sub-networks;
a state variable calculating module 400, configured to calculate a state variable of the basic sub-network according to the port input amount of the basic sub-network.
Optionally, the system further comprises:
and the dividing module is used for dividing the micro-grid according to the size of a preset basic sub-network and determining port input variables of the divided basic sub-network and a pre-stored coefficient matrix of the basic sub-network.
Optionally, based on any of the above embodiments, the equivalence module 100 includes:
the signal acquisition unit is used for reading in independent current sources, independent voltage sources and converter bridge arm driving signals of the basic sub-network;
a port input amount calculation unit for estimating a port input amount of the basic sub-network by using a linear extrapolation method;
the iteration unit is used for calculating the nonlinear element electrical quantity of the basic sub-network according to a nonlinear element electrical quantity equation and determining the state of the nonlinear element by adopting an iteration method; changing and calculating a coefficient matrix of the electrical quantity of the nonlinear element according to the state of the nonlinear element, and judging whether the iteration times are reached;
and the equivalence unit is used for determining the coefficient matrixes of the differentiated state variable equation and the external characteristic equation of the basic sub-network if the iteration times are reached, and calculating the equivalent injection sources of the differentiated state variable equation and the external characteristic equation of the basic sub-network to obtain the differentiated state variable equation and the external characteristic equation of the basic sub-network.
Optionally based on any of the above embodiments, the sub-network merging module 200 is specifically configured to merge a predetermined number of sub-networks having an adjacent relationship into a merging sub-network of a higher layer, and associate an external characteristic equation and a constraint equation of each sub-network of a lower layer of the merging sub-network from low to high; and the external characteristic equation and the backward-pushing equation of the merging sub-networks are obtained by utilizing the reduction of a Gaussian reduction elimination method until the external characteristic equation and the constraint equation of each sub-network of the lower layer of the top layer network are connected.
Optionally based on any of the above embodiments, the port input quantity pushing module 300 specifically includes an external characteristic equation and a constraint equation of each sub-network of the lower layer of the simultaneous top-layer network, and obtains the port input quantity of each sub-network of the lower layer of the top-layer network; and the port input quantities of the corresponding lower sub-networks are inversely deduced from the port input quantities of the merging sub-networks from high to low according to the corresponding push equations to obtain the port input quantities of all the basic sub-networks.
Optionally, based on any of the above embodiments, the state variable calculating module 400 is specifically a module that determines the state variable of the basic sub-network from the port input quantity of the basic sub-network according to the differentiated state variable equation of the basic sub-network.
The embodiments are described in a progressive manner in the specification, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The method and the system for the real-time simulation of the electromagnetic transient of the microgrid provided by the invention are described in detail above. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
Claims (6)
1. A method for simulating electromagnetic transient of a microgrid in real time is characterized by comprising the following steps:
reading in an independent current source, an independent voltage source and a converter bridge arm driving signal of a basic sub-network;
estimating the port input quantity of the basic sub-network by using a linear extrapolation method;
calculating the electrical quantity of the nonlinear element of the basic sub-network according to a nonlinear element electrical quantity equation, and determining the state of the nonlinear element by adopting an iteration method; changing and calculating a coefficient matrix of the electrical quantity of the nonlinear element according to the state of the nonlinear element, and judging whether the iteration times are reached;
if the iteration times are reached, determining coefficient matrixes of the differential state variable equation and the external characteristic equation of the basic sub-network, and calculating equivalent injection sources of the differential state variable equation and the external characteristic equation of the basic sub-network to obtain the differential state variable equation and the external characteristic equation of the basic sub-network;
combining the basic sub-networks layer by layer, and sequentially calculating an external characteristic equation and a back-off equation of each combined sub-network from low to high;
according to the external characteristic equation and the backward-pushing equation of each merging sub-network, port input quantities of each merging sub-network are sequentially calculated from high to low to obtain port input quantities of all basic sub-networks;
calculating the state variable of the basic sub-network according to the port input quantity of the basic sub-network;
the method comprises the following steps of combining the basic sub-networks layer by layer, and sequentially calculating an external characteristic equation and a back-off equation of each combined sub-network from low to high, wherein the method comprises the following steps:
combining a predetermined number of sub-networks with adjacent relation into a combined sub-network of a higher layer, and establishing an external characteristic equation and a constraint equation of each sub-network of a lower layer of the combined sub-network from low to high; and simplifying by a Gaussian reduction elimination method to obtain an external characteristic equation and an inverse equation of the combined sub-network until the external characteristic equation and the constraint equation of each sub-network of the lower layer of the top layer network are connected.
2. The method for real-time simulation of electromagnetic transients in a microgrid according to claim 1, wherein before calculating the differencing state variable equations and external characteristic equations of the elementary sub-networks of the microgrid based on the coefficient matrices of the elementary sub-networks, further comprising:
and dividing the micro-grid according to the size of a preset basic sub-network, and determining port input variables of the divided basic sub-network and a pre-stored coefficient matrix of the basic sub-network.
3. The method for simulating electromagnetic transients in a microgrid in real time according to claim 1, wherein port input quantities of each merging sub-network are calculated sequentially from high to low according to an external characteristic equation and a back-off equation of each merging sub-network to obtain port input quantities of all basic sub-networks, and the method comprises the following steps:
establishing external characteristic equations and constraint equations of the sub-networks of the lower layer of the top layer network simultaneously to obtain port input quantities of the sub-networks of the lower layer of the top layer network;
and reversely deducing the port input quantities of the corresponding lower sub-networks according to the corresponding reverse push equation by the port input quantities of the merging sub-networks from high to low in sequence to obtain the port input quantities of all the basic sub-networks.
4. The method for real-time simulation of electromagnetic transients in a microgrid according to claim 3, wherein calculating state variables of said primary sub-networks from port inputs of said primary sub-networks comprises:
and determining the state variable of the basic sub-network according to the differential state variable equation of the basic sub-network and the port input quantity of the basic sub-network.
5. A system for real-time simulation of electromagnetic transients in a microgrid, comprising:
the equivalent module is used for calculating a differential state variable equation and an external characteristic equation of a basic sub-network of the micro-grid according to the coefficient matrix of the basic sub-network;
the sub-network merging module is used for merging the basic sub-networks layer by layer and sequentially calculating an external characteristic equation and a backward equation of each merged sub-network from low to high;
the port input quantity pushing module is used for sequentially calculating the port input quantities of the merging sub-networks from high to low according to the external characteristic equation and the backward-pushing equation of the merging sub-networks of each layer to obtain the port input quantities of all the basic sub-networks;
a state variable calculation module, configured to calculate a state variable of the basic sub-network according to the port input amount of the basic sub-network;
wherein the equivalence module comprises:
the signal acquisition unit is used for reading in independent current sources, independent voltage sources and converter bridge arm driving signals of the basic sub-network;
a port input amount calculation unit for estimating a port input amount of the basic sub-network by using a linear extrapolation method;
the iteration unit is used for calculating the nonlinear element electrical quantity of the basic sub-network according to a nonlinear element electrical quantity equation and determining the state of the nonlinear element by adopting an iteration method; changing and calculating a coefficient matrix of the electrical quantity of the nonlinear element according to the state of the nonlinear element, and judging whether the iteration times are reached;
the equivalent unit is used for determining the coefficient matrixes of the differencing state variable equation and the external characteristic equation of the basic sub-network if the iteration times are reached, and calculating the equivalent injection sources of the differencing state variable equation and the external characteristic equation of the basic sub-network to obtain the differencing state variable equation and the external characteristic equation of the basic sub-network;
the sub-network merging module is specifically used for merging a predetermined number of sub-networks with adjacent relation into a merging sub-network of a higher layer, and simultaneously merging the external characteristic equation and the constraint equation of each sub-network of the lower layer of the sub-networks from low to high; and the external characteristic equation and the backward-pushing equation of the merging sub-networks are obtained by utilizing the reduction of a Gaussian reduction elimination method until the external characteristic equation and the constraint equation of each sub-network of the lower layer of the top layer network are connected.
6. The system for real-time simulation of microgrid electromagnetic transients of claim 5, further comprising:
and the dividing module is used for dividing the micro-grid according to the size of a preset basic sub-network and determining port input variables of the divided basic sub-network and a pre-stored coefficient matrix of the basic sub-network.
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