CN107681682A - A kind of ac and dc systemses equivalence method equivalent based on WARD - Google Patents

Abstract

The invention relates to an equivalent method for AC and DC systems based on WARD equivalents, the steps of which are: establishing models of basic components, obtaining nodes of the entire network as basic data, and determining the data format; performing power flow calculations on the entire network, and obtaining power flows of the entire network Solution; divide the nodes into internal node sets, boundary node sets and external node sets, and arrange the elements in each set according to the node numbers from small to large; form the node admittance matrix of the entire network, and form equivalent calculations according to the divided node sets The block node admittance matrix used; calculate the equivalent matrix and boundary equivalent capacitance and boundary equivalent injection power; form a new structure data body, and save the basic data of the equivalent system, defined as Rempc; equivalent value Afterwards, the system performs power flow calculation, compares the power flow results of reserved branches and nodes before and after the equivalence, and selectively outputs the power flow results. The invention can effectively ensure that the power flow error of the reserved system before and after equivalence is very small, and can be extended and applied to UHV DC layered systems.

Description

An Equivalence Method for AC and DC Systems Based on WARD Equivalence

technical field

The invention relates to the field of calculation of UHV AC/DC equivalents in power systems, in particular to an AC/DC system equivalent method based on WARD equivalents.

Background technique

With the construction of the UHV DC project, the DC transmission capacity continues to increase, and the DC landing point is becoming more and more concentrated. The existing DC single-layer access method will not be conducive to the power flow evacuation of the receiving end system. There will be a series of problems in terms of support and so on. Due to the layered connection of UHV DC, the topology of the DC system is more complex, and the interaction between the AC and DC systems and between the two layers of receivers has also become a research issue that needs to be paid attention to. In order to accurately simulate the transient characteristics of large-scale AC and DC power grids with hierarchical access during asymmetric faults, or to design AC filters for DC projects with hierarchical access, it is generally necessary to simplify the equivalent value of ultra-large-scale power grids to provide Computational speed and simulation efficiency. Therefore, while AC layered access to UHVDC brings us many benefits, it inevitably brings new problems and challenges. Give full play to the power transmission advantages of UHV DC layered access to AC system, and solve the key technical problems faced at this voltage level. This is of great significance for further improving power transmission capacity, realizing high-power long-distance power transmission, long-distance power system interconnection, and then realizing large-scale regional power grid interconnection.

Contents of the invention

In view of the above problems, the object of the present invention is to provide an equivalent method of AC and DC systems based on WARD equivalent, which can provide a basis for the design of UHV AC and DC transmission projects.

In order to achieve the above object, the present invention adopts the following technical scheme: a kind of AC/DC system equivalent method based on WARD equivalent, it is characterized in that comprising the following steps: 1) establish each basic element model in the WARD equivalent model, from each basic element In the model, the nodes of the whole network are obtained as the basic data, and the data format is determined to be Matpower standard data format or BPA data format. If it is BPA data format, it is converted to Matpower standard format for calculation; 2) For the power flow calculation of the whole network, Obtain the power flow solution of the whole network, define the power flow result in a structure named result, the format is similar to the data structure; 3) divide the nodes into internal node set I, boundary node set B and external node set E, each The elements in the set are arranged according to the node number from small to large; 4) Call the node admittance sub-function makeYbus to form the node admittance matrix of the entire network, and form the block node admittance matrix for equivalent calculation according to the divided node set; 5 ) Calculate the matrix Y ^EQ and the boundary equivalent capacitance C to obtain the boundary equivalent branch parameters after equivalent value, thus calculate the boundary equivalent injection power S ^EQ =P _i ^EQ +jQ _i ^EQ ; 6) form a new structure data body , and save the basic data of the equivalent system, defined as Rempc, add step 5) to the new structure data body; 7) perform power flow calculation on the equivalent system, and compare the power flow results of the reserved branches and nodes before and after the equivalent , to selectively output the power flow results.

Further, in the step 1), the basic component model includes a line model, a generator and load model, a parallel component model, an asymmetrical line model, a transformer branch and boundary capacitance.

Further, in the step 2), the power flow calculation for the whole network includes node power equations, basic converter equations, DC network equations and control equations.

Further, the node power equation:

_Wherein , i=n _a +k, k=1, 2, . Compared with the AC system network equation, V _dk , I _dk and Three variables, which respectively represent the DC node voltage, the angle between the injected current and the voltage and current, that is, the power factor angle of the converter. ΔP _i represents the given active unbalance; ΔQ _i represents the given reactive unbalance; P _is represents the given active power; Q _is represents the given reactive power; V _i represents the voltage of node i; V _j represents The voltage of node j; θ _ij represents the phase angle difference between node i and node j; G _ij represents the real part of the admittance matrix; B _ij represents the imaginary part of the admittance matrix.

Further, the basic equation of the converter, for the converter k, has the following equation:

Among them, Δd _1k and Δd _2k represent the DC voltage unbalance; V _dk represents the DC voltage of the converter, Indicates the per-unit value of the AC side line voltage of the converter transformer, I _dk indicates the DC current of the converter; X _ck indicates the equivalent impedance of the converter transformer k, k _Tk indicates the transformation ratio of the converter transformer, k _γ is a constant close to 1 , θ _dk represents the converter k control angle, Indicates the power factor angle of the converter.

Further, the standard form of the DC network equation:

Among them, Δd _3k represents the unbalanced output DC current of the converter, I _dk represents the DC current of the converter k; V _dj represents the DC voltage of the jth DC node, and g _dkj represents the node of the DC network after the contact node is eliminated Conductance matrix elements, where the voltage and current represent the voltage and current of the DC line. For a simple two-terminal DC transmission system, the DC network equation is simplified as follows:

For a simple two-terminal DC transmission system, the DC network equation is simplified as follows:

In the formula, R represents the resistance of the DC line; I _d1 represents the current of the DC node at terminal 1; I _d2 represents the current of the DC node at 2 terminals; if the resistance of the DC line is small enough, it can be approximately considered that V _d1 = V _d2 , I _d1 =I _d2 .

Further, the governing equation:

Δd _4k =d _4k (I _dk ,V _dk ,cosθ _dk ,k _Tk )=0(k=1,2,...,n _c )

Δd _5k =d _5k (I _dk ,V _dk ,cosθ _dk ,k _Tk )=0(k=1,2,...,n _c )

In the formula, d _4k represents the function of rectifier transformation ratio and current unbalance, Δd _4k represents the unbalance of rectifier control variable, d _5k represents the function of inverter transformation ratio and control angle unbalance, Δd _5k represents the inverter control variable , I _dk represents the DC current of converter k; V _dk represents the DC voltage of converter k; θ _dk represents the control angle of converter k; k _Tk represents the conversion ratio of the converter transformer; The variables related to the control angle all appear in the form of _cosθdk . In order to improve the linearity of the equation, _cosθdk is used as the direct quantity to be sought.

Further, in the step 3), it is necessary to have two kinds of fault-tolerant capabilities: firstly, it is determined that there is no intersection between the sets I, B, and E, and the number of the union of sets I, B, and E is equal to the total number of nodes; secondly, the detection set Is whether balance nodes are included in I, if not, the balance nodes are forcibly reserved as boundary nodes, and enter the next step, if included, directly enter the next step.

Further, in the step 5), the boundary equivalent capacitance C is:

Pure line calculation method:

C(k)=C(k)+y _kj

In the formula, k∈i;

Transformer line calculation method, and the boundary node is the first node:

Transformer line calculation method, and the boundary node is the end node:

Among them, Y _ij (i≠j) represents the negative value of the line admittance of the branch formed by node i and node j, and the relevant parameters of the branch are expressed as: line admittance y _ij , total line-to-ground admittance b _ij , Transformer transformation ratio τ _ij , phase displacement θ _ij .

Further, in the step 6), the principle of node definition is to arrange according to the order of the internal node set and the boundary node set, keep the generator data and branch data in the system, and the new generator data and branch data need to be rearranged according to Make corresponding changes to the node numbers; then, add the added equivalent virtual branch and boundary capacitance data to the branch and node data of the new data respectively.

The present invention has the following advantages due to the adoption of the above technical scheme: 1. The present invention takes into account the difference between the WARD equivalent method and the improved WARD equivalent method, and not only includes the simple and practical features of the conventional WARD equivalent method, but also takes into account The merits of each improved WARD method for equivalence are shown. 2. The present invention analyzes in detail the basic model of static equivalence and the details of the equivalence process, including the processing of boundary capacitance and the selection of equivalence branch models. A node grouping is proposed, that is, when the balance node is not inside the reservation system, the balance node is forced to be reserved as a boundary node. 3. The present invention is based on the conventional WARD equivalent method to develop an equivalent tool for the AC/DC hybrid system of a large power grid, and gives an example analysis of the application of the equivalent tool in different AC and DC systems, and shows that the power flow error of the reserved system before and after the equivalent is very small. small. 4. The present invention establishes the network equation of the entire system according to the node classification, wherein the Y matrix is the node admittance matrix of the entire network, and rearranges the Y matrix according to the node division results to form a corresponding block node admittance matrix. After equivalence, the equivalent admittance matrix Y _EQ formed by external nodes and boundary nodes is introduced into the admittance matrix, and the other changes are only the injection current I _B of the original system boundary nodes, and the internal nodes remain unchanged. For a linear system, this process will be strictly equivalent. As long as the injection current I _E of the external network does not change, the power flow of the equivalent system should be consistent with the original network in any operating mode. 5. When the model of the DC line is added to the system, the present invention needs to add the corresponding DC network equation when calculating the power flow timing of the AC-DC hybrid system. The structure of the DC system is very different from that of the AC system, so it is impossible to directly calculate the AC-DC hybrid system using the method of calculating the power flow of the AC system. From the analysis of the model of the DC line, the network equations of the AC-DC hybrid system are mainly modified from four aspects: node power equations, converter basic equations, DC network equations and control equations. 6. The traditional grid static equivalence methods are all aimed at AC systems. The essence of equivalence is to simplify the network equations and eliminate the influence of external nodes. However, for the AC-DC hybrid system, the network equation of the system has changed greatly due to the inclusion of DC, and a unified node admittance matrix cannot be formed, and the conventional WARD equivalent method cannot be applied. Therefore, the present invention adopts the equivalent branch method and the equivalent power source method to process the DC line, convert it into a model that can handle the equivalent value of the AC system, and then perform the equivalent calculation. 7. On the basis of the static equivalence method of the AC system, the present invention studies the DC transmission system model, establishes the AC-DC equivalent model according to the calculation results of the AC-DC power flow, and conducts equivalent research on the AC-DC system. The content of the present invention proposes The AC-DC equivalent model can be extended and applied to the UHV DC layered system.

Description of drawings

Fig. 1 is the WARD equivalent flow diagram of the present invention;

Fig. 2 is the transformer line model schematic diagram that the present invention adopts;

Fig. 3 is the schematic diagram of the asymmetric line model that the present invention adopts;

Fig. 4 is the schematic diagram of the model after the processing of the asymmetric circuit adopted in the present invention;

Fig. 5 is the transformer π type equivalent branch schematic diagram that the present invention adopts;

Fig. 6 is a schematic diagram of a compensation capacitance equivalent model adopted in the present invention;

Fig. 7 is a grouping processing structural diagram of reserved balance nodes in the present invention;

Fig. 8 is the wiring diagram of the basic principle of direct current transmission adopted by the present invention;

Fig. 9 is the equivalent π-type circuit diagram of the equivalent branch method adopted in the present invention;

Fig. 10 is the equivalent symmetrical π-type circuit diagram of the equivalent branch method adopted in the present invention;

Fig. 11 is a schematic diagram of the DC line equivalent power supply method of the present invention;

Fig. 12a is the power flow error graph before the present invention is applied to the IEEE 30-node system equivalent;

Fig. 12b is the power flow error diagram after the present invention is applied to the IEEE 30-node system equivalent;

Fig. 13a is a diagram of active and reactive power errors before the equivalent value after the present invention is applied to the IEEE 30-node system after changing the operation mode;

Fig. 13b is a diagram of active and reactive power errors after equivalent value after the present invention is applied to the IEEE 30-node system after changing the operation mode;

Fig. 14 is the CEPRI-36 system topology structure diagram in the example of the present invention;

Fig. 15a is a comparison diagram of the active power flow error of the present invention applying the equivalent branch method to the CEPRI-36 system;

Figure 15b is a comparison diagram of the reactive power flow error of the present invention applying the equivalent branch method to the CEPRI-36 system;

Fig. 16a is a comparison diagram of the active power flow error of the present invention applying the equivalent power source method to the CEPRI-36 system;

Fig. 16b is a comparison diagram of reactive power flow error of the present invention applying the equivalent power source method to the CEPRI-36 system.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments. However, it should be understood that the accompanying drawings are provided only for better understanding of the present invention, and they should not be construed as limiting the present invention.

As shown in Figure 1, the present invention provides a kind of AC/DC system equivalence method based on WARD equivalence, and it comprises the following steps:

1) Establish each basic component model in the WARD equivalent model, obtain the entire network node as the basic data from each basic component model, and determine whether the data format is Matpower standard data format or BPA data format, if it is BPA data format, then convert it to Convert to Matpower standard format for calculation. Define the basic data as the structure mpc; where mpc.bus, mpc.branch, mpc.gen and mpc.baseMVA respectively represent node data, branch data, generator data and reference power;

Each basic component model includes line model, generator and load model, parallel component model, asymmetrical line model, transformer branch and boundary capacitance; also includes the DC model introduced by the AC-DC hybrid system.

When performing static equivalent analysis, an accurate component model is a key factor to ensure accurate and reliable power flow calculation results. In the process of researching the WARD equivalent model, with reference to various typical basic element models, each basic element model that the present invention sets up is as follows:

1.1) Establish a line model:

As shown in Figure 2, in actual engineering, the line models all adopt standard π-type lines, and the line admittance y _s = 1/( _rs + jx _s ), where _rs represents line resistance and x _s represents line reactance; The total charging capacitance is represented by b _c . Connecting a standard line model in series with a transformer is a line model with a transformer, and the excitation impedance of the transformer is ignored. The position of the transformer is at the head end of each line, the non-standard transformation ratio is represented by τ, the phase shift angle of the transformer is θ _shift , if _f and it represent the current at the head end of the line respectively, and v _f and v _t represent the current at the head end of the line respectively _. The voltage at the end, the positive direction of the current is the same as that of the arrow in Figure 2. According to the line model shown in Figure 2, the node voltage equation of the line can be obtained as follows:

in:

1.2) Establish generator and load model:

Since the static equivalent process does not involve the process of transient state and optimal power flow, the generator and load models can be set relatively simply, and both are regarded as complex power injection of a preset node. For generator nodes, the injected power It can be expressed as:

In the formula, Indicates the active power injected by the generator node. Indicates the reactive power injected by the generator node, and i indicates the node number (the same below).

Load power for node i for:

In the formula, Indicates the load active power; Indicates the load reactive power.

1.3) Establish a parallel component model:

Generally, capacitors or inductance elements for reactive power compensation are required on high-voltage lines, and these capacitors or inductors are called parallel elements. The shunt element model is defined as a constant impedance model connected in parallel on the node side, and is given in the form of admittance. The shunt element admittance of a node is defined as:

In the formula, Indicates the admittance of the parallel element; Indicates the conductance of the parallel element; Indicates the susceptance of the parallel element.

Parallel capacitors inject capacitive reactive power into the system to maintain a constant node voltage. Parallel inductors inject inductive reactive power into the system, which can suppress excessive node voltage, so the data of parallel components is usually written in the form of power. The change of the node voltage will change the injected reactive power of the parallel element, so the data of this part is written into the data file in the form of the power injected into the system by the parallel element when the per unit value of the corresponding node voltage is 1.0, and the corresponding unit is MW and MVAR. The actual injected reactive power changes accordingly according to the actual voltage value.

1.4) Processing of asymmetric line models

Typically, the model of an asymmetrical line is shown in Figure 3. Among them, C ₁ and C ₂ represent the capacitors connected in parallel on the left and right sides of the line. Generally, the values of C ₁ and C ₂ are two equal positive numbers or one positive and one negative. When C ₁ or C ₂ is negative, it means that they are connected in parallel inductance.

For two equal positive values, it is treated as a π-type circuit in the same way as a general circuit. For the case of one positive and one negative, the processing method adopted by the present invention is to convert it into two parts for consideration, that is, a symmetrical π-type line and a parallel inductance, so that the asymmetrical line is added to the line parameters and node parameters respectively. The transformed model is shown in Figure 4, where, with Respectively represent the capacitive reactance of the left and right sides of the asymmetrical line; X _L represents the equivalent parallel reactance of the asymmetrical line.

1.5) Transformer branch processing

The exact equivalent branch of the transformer is a T-shaped equivalent branch, which can accurately reflect the real situation of the transformer operation, but the T-shaped equivalent branch contains a series-parallel form, which is very inconvenient when analyzing the power system . Considering that the excitation impedance of the transformer is relatively large during normal operation, the excitation impedance branch is usually advanced, so it becomes a Γ-type equivalent branch. The establishment of the transformer model is very important, especially it has a great influence on the reactive power accuracy of the system. Transform the transformer branch into π-type, as shown in Figure 5, so that the influence of the non-standard transformation ratio of the transformer is ignored, and then it is modified into the basic data of Matpower by the method of dealing with asymmetrical lines. After adopting the π-type equivalent circuit, there is no need to consider the problem of the transformation ratio direction.

1.6) Processing of boundary capacitance

As shown in Figure 6, the virtual line is treated as a pure impedance line, and then the parallel compensation capacitance at each boundary node is calculated. Boundary nodes are represented by set B, and the number of boundary nodes is nb; internal nodes are represented by set I, and the number of internal nodes is represented by ni. Y _ij (i≠ _j ) represents the negative value of the line admittance of the branch formed by node i and node _j , and the relevant parameters of the branch are expressed as: than τ _ij , the phase shift θ _ij . An array C(i) (i=1, 2...nb) is defined to store boundary node capacitances. The specific calculation formula is as follows:

Pure line calculation method:

C(k)=C(k)+y _kj

In the formula, k∈i;

Transformer line calculation method, and the boundary node is the first node:

Transformer line calculation method, and the boundary node is the end node:

1.7) DC line model

A simple DC transmission system is shown in Figure 8. When the DC line model is added to the system, the corresponding DC network equation needs to be added when calculating the power flow timing of the AC-DC hybrid system. The structure of the DC system is very different from that of the AC system, so it is impossible to directly calculate the AC-DC hybrid system using the method of calculating the power flow of the AC system. From the analysis of the model of the DC line, the network equations of the AC-DC hybrid system are mainly modified from four aspects: node power equations, converter basic equations, DC network equations and control equations.

2) Carry out power flow calculation on the whole network to obtain the power flow solution of the whole network. Define the power flow result in a structure named result, the format is similar to the data structure, and it is convenient to call;

Assuming that the number of nodes in the AC/DC hybrid system is n and the number of DC nodes is n _c , then the number of AC nodes is n _a =nn _c . Sort the nodes sequentially in the order of AC and DC.

2.1) Node power equation:

_Wherein , i=n _a +k, k=1, 2, . Compared with the AC system network equation, V _dk , I _dk and Three variables, which respectively represent the DC node voltage, the angle between the injected current and the voltage and current, that is, the power factor angle of the converter. ΔP _i represents the given active unbalance; ΔQ _i represents the given reactive unbalance; P _is represents the given active power; Q _is represents the given reactive power; V _i represents the voltage of node i; V _j represents The voltage of node j; θ _ij represents the phase angle difference between node i and node j; G _ij represents the real part of the admittance matrix; B _ij represents the imaginary part of the admittance matrix. Since the equation increases the number of unknowns, other equations are needed to complement it.

2.2) Basic equation of converter

For the converter k, there are the following equations:

Among them, Δd _1k and Δd _2k represent the DC voltage unbalance; V _dk represents the DC voltage of the converter, Indicates the per-unit value of the AC side line voltage of the converter transformer, I _dk indicates the DC current of the converter; X _ck indicates the equivalent impedance of the converter transformer k, k _Tk indicates the transformation ratio of the converter transformer, k _γ is a constant close to 1 , θ _dk represents the converter k control angle, Indicates the power factor angle of the converter.

2.3) DC network equation

The equations used to describe the DC transmission model are called DC network equations, and generally have the following standard form:

Among them, Δd _3k represents the unbalanced output DC current of the converter, I _dk represents the DC current of the converter k; V _dj represents the DC voltage of the jth DC node, and g _dkj represents the node of the DC network after the contact node is eliminated Conductance matrix elements, where the voltage and current represent the voltage and current of the DC line. For a simple two-terminal DC transmission system, the DC network equation is simplified as follows:

In the formula, R represents the resistance of the DC line; I _d1 represents the current of the DC node at terminal 1; I _d2 represents the current of the DC node at 2 terminals; if the resistance of the DC line is small enough, it can be approximately considered that V _d1 = V _d2 , I _d1 =I _d2 .

2.4) Governing equation

Since two new variables are introduced into the basic equation of the converter and the DC network equation, two more equations must be added to ensure that the equation has a unique solution, and the control equations of the converter and inverter are usually used as supplementary equations , and the variables of these two equations are independent.

There are generally the following methods for the control of the converter:

①Constant control angle control: cosθ _d -cosθ _ds = 0; θ _d represents the control angle of the converter, and θ _ds represents the given control angle;

②Constant transformation ratio control: k _T -k _Ts = 0; k _T represents the transformation ratio of the converter transformer, and k _Ts represents the given transformation ratio;

③Constant current control: I _d -I _ds = 0; I _d represents the output DC of the converter, and I _ds represents the given DC fixed value;

④Constant voltage control: V _d -V _ds = 0; V _d represents the output DC voltage of the converter, and V _ds represents the given DC voltage value;

⑤ Constant power control: V _d I _d -P _ds = 0, P _ds represents the given value of the output power of the converter.

Usually the inverter adopts the control method of constant control angle and constant transformation ratio; the rectifier usually adopts the control method of constant current and constant transformation ratio. In order to make the equations universal, the governing equations are generally defined as follows:

Δd _4k =d _4k (I _dk ,V _dk ,cosθ _dk ,k _Tk )=0(k=1,2,...,n _c )

Δd _5k =d _5k (I _dk ,V _dk ,cosθ _dk ,k _Tk )=0(k=1,2,...,n _c )

In the formula, d _4k represents the function of rectifier transformation ratio and current unbalance, Δd _4k represents the unbalance of rectifier control variable, d _5k represents the function of inverter transformation ratio and control angle unbalance, Δd _5k represents the inverter control variable , I _dk represents the DC current of converter k; V _dk represents the DC voltage of converter k; θ _dk represents the control angle of converter k; k _Tk represents the conversion ratio of the converter transformer; The variables related to the control angle all appear in the form of _cosθdk . In order to improve the linearity of the equation, _cosθdk is used as the direct quantity to be sought.

The node power equation, the basic equation of the converter, the DC network equation and the control equation together constitute the power flow calculation equation of the AC/DC hybrid system. To solve the power flow of the AC/DC hybrid system, it is necessary to calculate the voltage amplitude and phase angle of all nodes. In addition, it also needs to calculate the DC voltage, DC current, converter transformer ratio, and converter control angle of n _c DC nodes. and converter power factor angle five demanded quantities. For each additional converter, five supplementary equations will be added.

3) According to the needs of use, the nodes are divided into internal node set I, boundary node set B and external node set E, and the elements in each set are arranged according to the node number from small to large.

It has two fault-tolerant capabilities: first, it can judge that there is no intersection among sets I, B, and E, and the number of unions of sets I, B, and E is equal to the total number of nodes; secondly, it is necessary to detect whether set I contains balanced nodes, If it is not included, the balance node will be reserved as a boundary node forcibly and enter the next step; if it is included, it will directly enter the next step.

The first step of static equivalence is to distinguish the nodes, find out the internal nodes and appropriate boundary nodes to be retained according to the research needs, and eliminate all other nodes. After calculating the relevant parameters of the equivalent network, it is necessary to perform power flow calculation on the equivalent system, and verify the accuracy of the equivalent result by comparing the results of the power flow of the reserved network. If there is no balance node in the reservation system, the system will automatically reserve the balance node. The reservation system is treated as a group, and the balance node is another group. By establishing a virtual branch between the two groups, there is a direct connection between the balance node and the reservation system. contact.

In the grouping processing structure diagram shown in FIG. 7 , the balance node is treated as a reserved node. Although there is no direct connection between the balance node and the internal system, it can be known through calculation that the matrix Y _EQ is a highly dense matrix, so that the off-diagonal elements related to the balance node can be regarded as the impedance value of the virtual branch, Establish virtual branches between balance nodes and border nodes. Through this method, there is a direct connection between the balance node and the reservation system.

4) Call the node admittance sub-function makeYbus to form the node admittance matrix of the entire network, and form block node admittance matrices Y _EE , Y _EB , Y _BB and Y _BE for equivalent calculations according to the divided node sets;

According to the node classification, the network equation of the entire system is established, where the Y matrix is the node admittance matrix of the entire network, and the Y matrix is rearranged according to the node division results to form the corresponding block node admittance matrix:

Expanded into the following three equations:

in:

In the formula, the original network parameters before the equivalent: Y _EE represents the admittance matrix between external nodes, Y _EB represents the admittance matrix between external nodes and boundary nodes, Y _BE represents the admittance matrix between boundary nodes and external nodes, Y _BB Represents the admittance matrix between boundary nodes, Y _BI represents the admittance matrix between boundary nodes and internal nodes, Y _IB represents the admittance matrix between internal nodes and boundary nodes, Y _II represents the admittance matrix between internal nodes, V _E Represents the external node voltage, V _B represents the boundary node voltage, V _I represents the internal node voltage, I _I represents the injection current of the internal node, I _B represents the injection current of the boundary node, I _E represents the injection current of the external node; after equivalent network parameters: Y _EQ represents the equivalent admittance matrix of external nodes and boundary nodes, Indicates the equivalent injection current of the boundary node in the external network, and the parameters of the boundary node and the internal node before and after the equivalence are the same.

The block admittance matrix above is the node network equation after equivalent calculation. It can be seen that V _E is no longer in the network equation of the system, that is to say, the influence of the external network is eliminated. Y _EQ is added to the admittance matrix, while the other changed parts are only Y _BB and the injection current I _B of the boundary nodes, and the internal nodes remain unchanged. For a linear system, the above equivalent calculation process is a strict equivalent process. As long as the injection current I _E of the external network does not change, the power flow of the equivalent system should be consistent with the original network in any operating mode.

5) Calculate the matrix Y ^EQ and the boundary equivalent capacitance C, the calculation process of the boundary equivalent capacitance C is given by step 1.6), and finally obtain the boundary equivalent branch parameters after the equivalent value, and calculate the boundary equivalent injection power S ^EQ ＝P _i ^EQ +jQ _i ^E ; where, P _i ^EQ represents the equivalent injected active power of node i; Indicates that the reactive power injected into node i is equivalent.

Since in the actual system, the data of the injected current is usually unavailable, and the line power and node voltage values are usually known, therefore, the injected current of all nodes can be expressed as the following form:

In the formula, represents the node injection current, represents the node voltage, Indicates the node injected power.

After the current is expressed by the above power, the original linear equation becomes a nonlinear equation, namely:

definition:

Then the above formula can be expressed as:

In the formula, Indicates the external node injected power, Indicates the injected power of the boundary node, Indicates the injected power of internal nodes.

In the case of knowing the power flow results of the internal network and boundary nodes in the basic case, the equivalent injected power of the boundary nodes is calculated according to the following formula:

Among them, P _i ^EQ represents the equivalent injected active power of node i; Indicates the equivalent injected reactive power of node i; V _i ⁰ and respectively _represent the bus voltage _modulus of node _i and _{node j} in the basic situation; g _ij +jb _ij represents the ground admittance value of the branch connected to node i; g _i0 +jb _i0 represents the ground branch admittance of the branch connected to node i on side i.

Using the above formula to calculate the injected power of the boundary node is very simple, only need to know the power flow data of the boundary node and the network topology connected to the boundary node. For a large system, the power flow data of the external network may not be obtained timely and accurately, and the relevant data of the boundary nodes can be obtained in time through the state estimator. Therefore, the calculation method shown in the above formula is more suitable for online applications.

6) Form a new structural data body and save the basic data of the equivalent system, which is defined as Rempc. The principle of node definition is to arrange in the order of the internal node set and boundary node set, and retain the generator data and branch data in the system. The new generator data and branch data need to be changed according to the rearranged node numbers. Then, the equivalent branch parameters obtained in step 5) and the boundary injection power are added to the branch and node data of the new data respectively;

7) Perform power flow calculation on the system after equivalence, and compare with the power flow calculation results in step 2), that is, compare the power flow results of reserved branches and nodes before and after equivalence, and selectively output the power flow results.

In the above steps, the processing method for the DC line in the AC-DC hybrid system is as follows:

The traditional grid static equivalence methods are all aimed at AC systems, and the essence of equivalence is to simplify the network equations and eliminate the influence of external nodes. However, for the AC-DC hybrid system, the network equation of the system has changed greatly due to the inclusion of DC, and a unified node admittance matrix cannot be formed, and the conventional WARD equivalent method cannot be applied. Therefore, the DC line is processed by the equivalent branch method and the equivalent power source method, and converted into a model that can be handled by the equivalent value of the AC system, and then the equivalent calculation is performed.

(1) Equivalent branch method

According to the power flow results, the DC line is equivalent to a π-type line as shown in Figure 9, V ₁ and θ ₁ represent the voltage amplitude and phase angle of the AC node of the rectifier side transformer, and V ₂ and θ ₂ represent the AC voltage of the inverter side transformer The voltage amplitude and phase angle _of the node, P1 and Q1 respectively represent the active power and reactive power transmitted from the AC system _on the rectification side to the DC system, and P2 and _Q2 respectively represent the active power transmitted from the AC system _on the inverter side to the DC system Power and reactive power, the positive direction is the same as the direction of the arrow in the figure, and the DC is equivalent to the admittance parameters of the π-type circuit: g and b are the series conductance and susceptance of the equivalent branch, b ₁ and b ₂ are the equivalent The parallel susceptance to ground on the left and right sides of the branch is the quantity to be demanded.

AC system node voltage and admittance matrix elements Y _ij can be expressed as:

Y _ij =G _ij +jB _ij

In the formula, e _i =V _i cosθ _i , f _i =V _i sinθ _i , V _i and θ _i represent the voltage amplitude and phase of node i respectively; G _ij and B _ij represent the conductance and susceptance of branch ij respectively

The general form of the power flow equation for an n-node power system is:

In the formula, P _i and Q _i represent the active power and reactive power injected by node i, respectively.

Therefore, the power flow equation corresponding to Figure 9 can be obtained:

Wherein, θ ₁₂ =θ ₁ -θ ₂ ; other parameters correspond to those in FIG. 9 . Through the power flow calculation, the transmission power of the line, as well as the node voltage and phase angle can be obtained, and the parameters of the DC line equivalent to the AC line in Figure 9 are finally calculated as follows:

The parameters of the equivalent branch can be calculated by the above four formulas, but there is usually b ₁ ≠ b ₂ , that is to say, the equivalent π-type circuit is asymmetrical and needs to be converted into a symmetrical π-type circuit In order to participate in the calculation, the processing method is the same as that of the asymmetrical line, converting the equivalent branch into a symmetrical π-type line and a reactance or inductance connected in parallel at one end of the line. The equivalent diagram is shown in Figure 10, and b _1-2 represents the difference between the left and right sides of the equivalent line and the ground parallel admittance. Through this processing method, all DC lines in the system can be processed into AC lines, so an AC-DC hybrid system becomes a pure AC system, and then the equivalent method of the AC system is used for calculation.

(2) Equivalent power supply method

When using the alternate iteration method to solve the AC system equations, the DC system is equivalent to a load connected to the corresponding node whose active and reactive power is known. Therefore, the equivalent power supply method is based on the results of power flow calculations, and the power transmitted by the DC part is equivalent to the generators connected to the AC nodes on both sides. These two AC nodes are defined as PQ nodes. The equivalent process is shown in Figure 11, where with Respectively represent the power transmitted by the first and last nodes of the DC line.

The equivalent power supply method is to directly equate the power transmitted by the DC line into two equivalent machines, on the premise that the power transmitted by the DC is assumed to be unchanged. Therefore, the corresponding conversion can be done only according to the power flow result of the converter transformer line.

Embodiment: The static equivalent of the system applying the present invention will be described in detail below through specific embodiments. Embodiment 1: IEEE 30-node standard system; Embodiment 2: 36-node AC/DC hybrid system of China Electric Power Research Institute. Concrete embodiment calculation process and result are as follows:

Example 1:

(1) IEEE 30-node standard system

Table 1 presents the detailed results of IEEE-30 node division.

Table 1 IEEE-30 node division

Apply the equivalent program to the standard 30-node example for equivalent calculation, the boundary equivalent machine (treated as a PQ node), the boundary node virtual branch impedance value, and boundary parallel compensation data are shown in Table 2, Table 3, and Table 4.

Table 2 Boundary equivalent machine (unit: MW/MVAR)

Table 3 Boundary node virtual branch impedance value (pu.)

Table 4 Boundary parallel compensation value (pu.)

In order to verify the accuracy of the equivalent results, it is necessary to compare the power flows of the pre-equivalent system and the post-equivalent system. In the same operation mode, the power flow calculation is performed on the equivalent system, and the results are shown in Table 5.

Table 5 Internal network power flow error (unit: MW/MVAR)

It can be seen from Table 5 that the power flow results of the equivalent system are basically consistent with the original system when the operation mode does not change. Figure 11 shows the comparison results of power flow errors before and after the equivalence. It can be seen from Figure 11 that the order of magnitude of line active error is 10 ^-8 , and that of reactive power error is 10 ^-7 . Therefore, when the system is in the ground state, the equivalent results are very accurate.

(2) The operation mode of IEEE30 system changes

When the system operation mode changes, especially when the system requires reactive power increment, there is a certain error in the WARD equivalent. Now, in the case of disconnection faults in branches 4-6 of the IEEE30 system, the equivalent simulation analysis of the system is carried out. Since node 11 is a PV node, the node is re-divided first, and this node is used as the eliminated node. The re-divided nodes are shown in Table 6.

Table 6 Node division

Consider the short-circuit of branch 4-6, calculate the steady-state power flow of the system after the short-circuit, and then carry out the equivalent calculation of the system to calculate the steady-state power flow of the equivalent system after the short-circuit. Compare the steady-state power flow before and after equivalence. As shown in Figure 12a and Figure 12b, under the condition of considering the change of operation mode, the active and reactive power flow errors of the system before and after the equivalence. It can be seen that in the case of a short circuit on line 4-6, compared with the condition that the operation mode remains unchanged, the error value has increased, but it is still within the acceptable range of the project. The active power flow error is basically kept within 5%, and the maximum error is 7%. The reactive power error is basically kept within 10%, and the maximum error is 15%. It can be seen that the reactive power error is slightly larger than the active power error, which is also an inherent defect of the WARD equivalent itself, because when the internal operation mode of the system changes, the injected power of the external system will change to a certain extent, especially the reactive power. However, the boundary injection power of the equivalent system is still calculated according to the ground state, so the error will increase. But on the whole, after the system operation mode has changed, the WARD equivalent value still has a good equivalent effect.

Example 2: 36-node AC-DC hybrid system of China Electric Power Research Institute.

Taking the 36-node AC-DC hybrid system of China Electric Power Research Institute as an example, the equivalent branch method and the equivalent power source method proposed in this report are used to conduct equivalent analysis on the AC-DC hybrid system.

(1) Equivalent branch method

First calculate the power flow for the test system. The AC node power flow results (pu.) on both sides of the DC line are shown in Table 7, where the positive direction is the same as defined in Figure 13a and Figure 13b.

Table 7 Power flow results

In Table 7, P ₃₃ and Q ₃₃ represent the active power and reactive power injected by node 33 respectively, and P ₃₄ and Q ₃₄ represent the active power and reactive power injected by node 34 respectively; V ₃₃ and respectively represent the voltage amplitude and phase angle of node 33, V ₃₄ and represent the node 34 voltage amplitude and phase angle, respectively.

Substituting the known quantities in Table 7 into the formula, the calculated parameters of the equivalent branches are: g=0.5820, b=-7.3541, b ₁ =0.05117, b ₂ =0.61253. Process the relevant data according to the method of equivalent branch processing, remove the DC line parameters between the busbars 33 and 34, add the AC line 33-34, the impedance parameter is 0.0107+j0.1351, the total parallel capacitance _bc =0.1023, and the busbar 34 Parallel capacitor injection power B = 56.14MAVR, according to the calculation results to modify the basic data of MATLAB.

Carry out node division for CEPRI-36. For convenience, this report retains several important generator nodes including the balance node, and all other nodes are eliminated. The node division results are shown in Table 8.

Table 8 CEPRI-36 node division results

Equivalence calculations are performed on the test system using the equivalence program. Figure 13 shows the comparison results of active power and reactive power flow of the original system, the treated system and the reserved branch of the equivalent system.

(2) Equivalent power supply method

According to the power flow results, modify the CEPRI-36 basic data, remove the DC branches 33-34, add load data (per unit value, rated power is 100MW) at nodes 33 and 34 P ₃₃ +Q ₃₃ =3.0015+j0.4270, in The added load of node 34 is P ₃₄ +Q ₃₄ =-2.9057+j0.1174.

The node classification is the same as in the CEPRI-36 node division results in Table 8. Equivalence calculations are performed on the test system using the equivalence program. As shown in Figure 15a to Figure 16b, the power flow comparison results of the original system, the processed system and the equivalent system are given.

According to the above two simulation results, the following conclusions can be drawn:

(1) Using the equivalent power source method and the equivalent branch method, the power flow results before and after processing are highly consistent under the condition that the system operation mode remains unchanged;

(2) The results obtained by the two processing methods are basically the same, and the network power flow results before and after the equivalence are highly consistent, and the error is very small. Therefore, the equivalent result is very accurate.

The above-mentioned embodiments are only used to illustrate the present invention, and the various implementation steps of the method etc. all can be changed to some extent, and all equivalent transformations and improvements carried out on the basis of the technical solution of the present invention should not be excluded from the scope of the present invention. outside the scope of protection.

Claims (10)

1. a kind of AC/DC system equivalent method based on WARD equivalent, it is characterized in that comprising the following steps: 1) Establish each basic component model in the WARD equivalent model, obtain the entire network node as the basic data from each basic component model, and determine whether the data format is Matpower standard data format or BPA data format, if it is BPA data format, then convert it to Convert to Matpower standard format for calculation; 2) Carry out power flow calculation on the whole network, obtain the power flow solution of the whole network, define the power flow result in a structure named result, and the format is similar to the data structure; 3) Divide the nodes into internal node set I, boundary node set B and external node set E, and the elements in each set are arranged according to the node numbers from small to large; 4) Call the node admittance sub-function makeYbus to form the node admittance matrix of the entire network, and form the block node admittance matrix for equivalent calculation according to the divided node set; 5) Calculate the matrix Y ^EQ and the boundary equivalent capacitance C to obtain the boundary equivalent branch parameters after equivalent value, and thus calculate the boundary equivalent injection power S ^EQ =P _i ^EQ +jQ _i ^EQ ; 6) Form a new structural data body, and save the basic data of the equivalent system, which is defined as Rempc, and add step 5) to the new structural data body; 7) Carry out power flow calculation for the system after equivalence, compare the power flow results of reserved branches and nodes before and after equivalence, and selectively output the power flow results. 2. A kind of AC/DC system equivalence method based on WARD equivalence as claimed in claim 1, is characterized in that: in described step 1), basic element model comprises line model, generator and load model, parallel element model , asymmetrical line model, transformer branch and boundary capacitance. 3. A kind of AC-DC system equivalent method based on WARD equivalent as claimed in claim 1, is characterized in that: in described step 2), carrying out power flow calculation to the whole network includes node power equation, converter basic equation , DC network equations and governing equations. 4. a kind of AC/DC system equivalent method based on WARD equivalent as claimed in claim 3, is characterized in that: described node power equation: _Wherein , i=n _a +k, k=1, 2, . Compared with the AC system network equation, V _dk , I _dk and Three variables, which respectively represent the DC node voltage, the angle between the injected current and the voltage and current, that is, the power factor angle of the converter. ΔP _i represents the given active unbalance; ΔQ _i represents the given reactive unbalance; P _is represents the given active power; Q _is represents the given reactive power; V _i represents the voltage of node i; V _j represents The voltage of node j; θ _ij represents the phase angle difference between node i and node j; G _ij represents the real part of the admittance matrix; B _ij represents the imaginary part of the admittance matrix. 5. A kind of AC/DC system equivalent method based on WARD equivalent as claimed in claim 3, is characterized in that: described converter basic equation, for converter k, has following equation: <mrow><msub><mi>&amp;Delta;d</mi><mrow><mn>1</mn><mi>k</mi></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow><mi>d</mi><mi>k</mi></mrow></msub><mo>-</mo><msub><mi>k</mi><mrow><mi>T</mi><mi>k</mi></mrow></msub><msub><mi>V</mi><mrow><msub><mi>n</mi><mi>a</mi></msub><mo>+</mo><mi>k</mi></mrow></msub><msub><mi>cos&amp;theta;</mi><mrow><mi>d</mi><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>X</mi><mrow><mi>c</mi><mi>k</mi></mrow></msub><msub><mi>I</mi><mrow><mi>d</mi><mi>k</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo><mrow><mo>(</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><msub><mi>n</mi><mi>c</mi></msub><mo>)</mo></mrow></mrow> Among them, Δd _1k and Δd _2k represent the DC voltage unbalance; V _dk represents the DC voltage of the converter, Indicates the per-unit value of the AC side line voltage of the converter transformer, I _dk indicates the DC current of the converter; X _ck indicates the equivalent impedance of the converter transformer k, k _Tk indicates the transformation ratio of the converter transformer, k _γ is a constant close to 1 , θ _dk represents the converter k control angle, Indicates the power factor angle of the converter. 6. a kind of AC/DC system equivalent method based on WARD equivalent as claimed in claim 3, is characterized in that: the standard form of described DC network equation: <mrow><msub><mi>&amp;Delta;d</mi><mrow><mn>3</mn><mi>k</mi></mrow></msub><mo>=</mo><mo>&amp;PlusMinus;</mo><msub><mi>I</mi><mrow><mi>d</mi><mi>k</mi></mrow></msub><mo>-</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>g</mi><mrow><mi>d</mi><mi>k</mi><mi>j</mi></mrow></msub><msub><mi>V</mi><mrow><mi>d</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo>mo><msub><mi>n</mi><mi>c</mi></msub><mo>)</mo></mrow></mrow> Among them, Δd _3k represents the unbalanced output DC current of the converter, I _dk represents the DC current of the converter k; V _dj represents the DC voltage of the jth DC node, and g _dkj represents the node of the DC network after the contact node is eliminated Conductance matrix elements, where the voltage and current represent the voltage and current of the DC line. For a simple two-terminal DC transmission system, the DC network equation is simplified as follows: For a simple two-terminal DC transmission system, the DC network equation is simplified as follows: <mrow><mfenced open = "[" close = "]"><mtable><mtr><mtd><msub><mi>I</mi><mrow><mi>d</mi><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mrow><mo>-</mo><msub><mi>I</mi><mrow><mi>d</mi><mn>2</mn></mrow></msub></mrow></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mrow><mn>1</mn><mo>/</mo><mi>R</mi></mrow></mtd><mtd><mrow><mo>-</mo><mn>1</mn><mo>/</mo><mi>R</mi></mrow></mtd></mtr><mtr><mtd><mrow><mo>-</mo><mn>1</mn><mo>/</mo><mi>R</mi></mrow></mtd><mtd><mrow><mn>1</mn><mo>/</mo><mi>R</mi></mrow></mtd></mtr></mtable></mfenced><mfenced open = "[" close = "]"><mtable><mtr><mtd><msub><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>V</mi><mrow><mi>d</mi><mn>2</mn></mrow></msub></mtd></mtr></mtable></mfenced></mrow> In the formula, R represents the resistance of the DC line; I _d1 represents the current of the DC node at terminal 1; I _d2 represents the current of the DC node at 2 terminals; if the resistance of the DC line is small enough, it can be approximately considered that V _d1 = V _d2 , I _d1 =I _d2 . 7. a kind of AC/DC system equivalent method based on WARD equivalent as claimed in claim 3, is characterized in that: described control equation: Δd _4k =d _4k (I _dk ,V _dk ,cosθ _dk ,k _Tk )=0(k=1,2,...,n _c ) Δd _5k =d _5k (I _dk ,V _dk ,cosθ _dk ,k _Tk )=0(k=1,2,...,n _c ) In the formula, d _4k represents the function of rectifier transformation ratio and current unbalance, Δd _4k represents the unbalance of rectifier control variable, d _5k represents the function of inverter transformation ratio and control angle unbalance, Δd _5k represents the inverter control variable , I _dk represents the DC current of converter k; V _dk represents the DC voltage of converter k; θ _dk represents the control angle of converter k; k _Tk represents the conversion ratio of the converter transformer; The variables related to the control angle all appear in the form of _cosθdk . In order to improve the linearity of the equation, _cosθdk is used as the direct quantity to be sought. 8. A kind of AC-DC system equivalence method based on WARD equivalence as claimed in claim 1, is characterized in that: in described step 3), need possess two kinds of fault-tolerant capabilities: at first determine the set I, B and E There is no intersection among them, and the number of the union of sets I, B, and E is equal to the total number of nodes; secondly, check whether the set I contains balanced nodes, if not, then forcefully retain the balanced nodes as boundary nodes, and enter the next step, If included, go directly to the next step. 9. A kind of AC/DC system equivalent method based on WARD equivalent as claimed in claim 1, is characterized in that: in described step 5), boundary equivalent capacitance C is: Pure line calculation method: C(k)=C(k)+y _kj In the formula, k∈i; Transformer line calculation method, and the boundary node is the first node: <mrow><mi>C</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mi>C</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>y</mi><mrow><mi>k</mi><mi>j</mi></mrow></msub><mo>/</mo><mi>&amp;tau;</mi><mo>&amp;times;</mo><msup><mi>e</mi><msub><mi>&amp;theta;</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></msup><mo>-</mo><mn>0.5</mn><mi>i</mi><mo>&amp;times;</mo><msub><mi>b</mi><mrow><mi>k</mi><mi>j</mi></mrow></msub><mo>/</mo><msup><mi>&amp;tau;</mi><mn>2</mn></msup></mrow> Transformer line calculation method, and the boundary node is the end node: <mrow><mi>C</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mi>C</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>y</mi><mrow><mi>k</mi><mi>j</mi></mrow></msub><mo>&amp;times;</mo><msub><mi>&amp;tau;</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>&amp;times;</mo><msup><mi>e</mi><msub><mi>&amp;theta;</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></msup><mo>-</mo><mn>0.5</mn><mi>i</mi><mo>&amp;times;</mo><msub><mi>b</mi><mrow><mi>k</mi><mi>j</mi></mrow></msub></mrow> Among them, Y _ij (i≠j) represents the negative value of the line admittance of the branch formed by node i and node j, and the relevant parameters of the branch are expressed as: line admittance y _ij , total line-to-ground admittance b _ij , Transformer transformation ratio τ _ij , phase displacement θ _ij . 10. A kind of AC-DC system equivalence method based on WARD equivalence as claimed in claim 1, is characterized in that: in described step 6), the principle of node definition is to arrange according to internal node set and boundary node set order, Keep the generator data and branch data in the system, and the new generator data and branch data need to be changed according to the rearranged node numbers; then, add the added equivalent virtual branch and boundary capacitance data respectively into the branch and node data of the new data.