CN107681682B - Alternating current-direct current system equivalence method based on WARD equivalence - Google Patents

Alternating current-direct current system equivalence method based on WARD equivalence Download PDF

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CN107681682B
CN107681682B CN201711009021.XA CN201711009021A CN107681682B CN 107681682 B CN107681682 B CN 107681682B CN 201711009021 A CN201711009021 A CN 201711009021A CN 107681682 B CN107681682 B CN 107681682B
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node
equivalent
representing
direct current
line
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CN107681682A (en
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郭贤珊
赖清平
马为民
薛英林
吴方劼
石岩
杨一鸣
张涛
胡志坚
罗福玲
付颖
杜晓磊
郝致远
李达
季一鸣
程炜
赵峥
常云辉
勇智
韩旭杉
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State Grid Corp of China SGCC
Wuhan University WHU
State Grid Gansu Electric Power Co Ltd
State Grid Economic and Technological Research Institute
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State Grid Corp of China SGCC
Wuhan University WHU
State Grid Gansu Electric Power Co Ltd
State Grid Economic and Technological Research Institute
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention relates to an alternating current-direct current system equivalence method based on WARD equivalence, which comprises the following steps: establishing each basic element model, acquiring nodes of the whole network as basic data, and determining a data format; carrying out load flow calculation on the whole network to obtain a load flow solution of the whole network; dividing nodes into an internal node set, a boundary node set and an external node set, wherein elements in each set are arranged from small to large according to node numbers; forming a node admittance matrix of the whole network, and forming a block node admittance matrix for equivalent calculation according to the divided node set; calculating equivalent matrix, boundary equivalent capacitance and boundary equivalent injection power; forming a new structure data body, storing the equivalent basic data of the system, and defining the data as Rempc; and carrying out load flow calculation on the system after equivalence, comparing load flow results of the reserved branches and nodes before and after equivalence, and selectively outputting the load flow results. The method can effectively ensure that the tidal current error of the retention system before and after equivalence is very small, and can be applied to an ultrahigh-voltage direct-current layered system in an expanded way.

Description

Alternating current-direct current system equivalence method based on WARD equivalence
Technical Field
The invention relates to the field of extra-high voltage alternating current and direct current equivalence calculation of an electric power system, in particular to an alternating current and direct current system equivalence method based on WARD equivalence.
Background
Along with the construction of extra-high voltage direct current engineering, the direct current transmission capacity is continuously increased, direct current drop points are more and more concentrated, the existing direct current single-layer access mode is not beneficial to tidal current evacuation of a receiving end system, and a series of problems can be caused in the aspects of the receiving capacity, the voltage support and the like of the receiving end of the system. Under the mode of extra-high voltage direct current layered access, the topological structure of a direct current system is more complex, and the interaction influence between an alternating current system and a direct current system and between two layers of receiving terminals also becomes a research problem needing attention. In order to accurately simulate the transient characteristics of a large alternating current-direct current power grid with layered access in an asymmetric fault period or design an alternating current filter with layered access to a direct current project, the large-scale power grid generally needs to be simplified and equalized to provide calculation speed and simulation efficiency. The layered connection of the alternating current and the extra-high voltage direct current brings many benefits to people, and inevitably brings new problems and challenges. The power transmission advantage of an extra-high voltage direct current layered access alternating current system is exerted, and the key technical problem in the voltage class is solved. The method has important significance for further improving the power transmission capacity, realizing large-power long-distance power transmission and long-distance power system interconnection and further realizing large-area power grid interconnection.
Disclosure of Invention
Aiming at the problems, the invention aims to provide an alternating current and direct current system equivalence method based on WARD equivalence, which can provide a basis for the design of extra-high voltage alternating current and direct current transmission engineering.
In order to achieve the purpose, the invention adopts the following technical scheme: a WARD equivalence-based alternating current and direct current system equivalence method is characterized by comprising the following steps: 1) establishing each basic element model in the WARD equivalent model, acquiring the nodes of the whole network from each basic element model as basic data, and determining that the data format is MatpowerThe standard data format is the BPA data format, and if the standard data format is the BPA data format, the BPA data format is converted into the Matpower standard format for calculation; 2) carrying out load flow calculation on the whole network to obtain a load flow solution of the whole network, and defining a load flow result in a structural body named result, wherein the format of the load flow result is similar to that of a data structural body; 3) dividing nodes into an internal node set I, a boundary node set B and an external node set E, wherein elements in each set are arranged from small to large according to node numbers; 4) calling a node admittance subfunction makeYbus to form a node admittance matrix of the whole network, and forming a block node admittance matrix for equivalent calculation according to the divided node set; 5) calculating the matrix YEQObtaining the equivalent boundary equivalent branch parameters from the boundary equivalent capacitor C, and calculating the boundary equivalent injection power SEQ＝Pi EQ+jQi EQ(ii) a 6) Forming a new structure data body, storing the equivalent basic data of the system, defining the basic data as Rempc, and adding the step 5) into the new structure data body; 7) and carrying out load flow calculation on the system after equivalence, comparing load flow results of the reserved branches and nodes before and after equivalence, and selectively outputting the load flow results.
Further, in the step 1), the basic element model comprises a line model, a generator and load model, a parallel element model, an asymmetric line model, a transformer branch and a boundary capacitor.
Further, in the step 2), the load flow calculation for the whole network includes a node power equation, a converter basic equation, a direct current network equation and a control equation.
Further, the node power equation:
Figure BDA0001445087040000021
wherein i ═ na+k，k＝1,2,…,ncIn the formula, a positive sign represents an inverter, and a negative sign represents a rectifier. Compared with the network equation of the alternating current system, V is increaseddk，IdkAnd
Figure BDA0001445087040000022
and three variables respectively representing the direct-current node voltage, the injected current and the included angle between the voltage and the current, namely the power factor angle of the converter. Delta PiRepresenting a given active unbalance amount; delta QiRepresenting a given reactive unbalance; pisRepresenting a given active power; qisRepresenting a given reactive power; viRepresents the voltage of node i; vjRepresents the voltage at node j; thetaijRepresenting the phase angle difference between node i and node j; gijRepresenting the real part of the admittance matrix; b isijRepresenting the imaginary part of the admittance matrix.
Further, the basic converter equation has the following equation for the converter k:
Figure BDA0001445087040000023
Figure BDA0001445087040000024
wherein, Δ d1k、Δd2kRepresenting the amount of DC voltage unbalance; vdkWhich represents the dc voltage of the inverter,
Figure BDA0001445087040000025
expressing the voltage per unit value of the AC side line of the converter transformer, IdkRepresenting the direct current of the converter; xckRepresenting the equivalent impedance, k, of a converter transformer kTkRepresenting the transformation ratio, k, of the converter transformerγIs a constant close to 1, thetadkThe control angle of the inverter k is shown,
Figure BDA0001445087040000026
representing the power factor angle of the converter.
Further, the standard form of the dc network equation:
Figure BDA0001445087040000027
wherein, Δ d3kRepresenting the amount of unbalance of the DC current output by the converter, IdkRepresents the direct current of the converter k; vdjIndicating the DC voltage of the jth DC node, gdkjAnd the node conductance matrix elements of the direct current network after the communication nodes are eliminated are shown, wherein voltage and current all represent the voltage and current of a direct current 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:
Figure BDA0001445087040000031
in the formula, R represents the resistance of a direct current line; i isd1Representing the current of a direct current node at the 1 end; i isd2Represents the current of a 2-terminal direct-current node; if the resistance of the DC line is sufficiently small, V can be considered approximatelyd1＝Vd2，Id1＝Id2。
Further, the governing equation:
Δd4k＝d4k(Idk,Vdk,cosθdk,kTk)＝0(k＝1,2,…,nc)
Δd5k＝d5k(Idk,Vdk,cosθdk,kTk)＝0(k＝1,2,…,nc)
in the formula (d)4kRepresenting the function of the converter transformation ratio and the current unbalance, Δ d4kRepresenting the amount of unbalance of the rectifier control variable, d5kFunction representing the inverter transformation ratio and the amount of control angle unbalance, Δ d5kRepresenting the unbalance of the inverter control variable, IdkRepresents the direct current of the converter k; vdkRepresents the inverter k dc voltage; thetadkRepresenting the converter k control angle; k is a radical ofTkRepresenting the transformation ratio of the converter transformer; since all the variables related to the control angle in the formula are observed to be in cos thetadkAll appear in cos θ to improve the linearity of the equationdkIs a direct demand.
Further, in the step 3), two fault tolerance capabilities need to be provided: first, it is determined that there is no intersection between sets I, B and E, and the number of union sets I, B and E is equal to the total number of nodes; and secondly, detecting whether the set I contains a balance node, if not, forcibly retaining the balance node as a boundary node, entering the next step, and if so, directly entering the next step.
Further, in the step 5), the boundary equivalent capacitance C is:
the pure line calculation method comprises the following steps:
C(k)＝C(k)+ykj
wherein k is belonged to i;
the method comprises the following steps of calculating a transformer line, wherein a boundary node is a first node:
Figure BDA0001445087040000032
the transformer line calculation method is characterized in that boundary nodes are tail nodes:
Figure BDA0001445087040000033
wherein, Yij(i ≠ j) represents the negative value of the line admittance of the branch formed by the node i and the node j, and the relevant parameters of the branch are expressed as: line admittance yijLine total to ground admittance bijTransformer transformation ratio tauijPhase shift θij。
Further, in the step 6), the node definition principle is that the nodes are arranged according to the sequence of the internal node set and the boundary node set, the generator data and the branch data in the system are reserved, and the new generator data and the new branch data need to be changed correspondingly according to the rearranged node numbers; the added equivalent virtual branch and boundary capacitance data is then added to the branch and node data, respectively, for the new data.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. the invention takes the difference between the WARD equivalence method and the improved WARD equivalence method into consideration, namely the packageThe method has the characteristics of simplicity and practicability of the conventional WARD equivalence method, and also has the advantage of equivalence of various improved WARD methods. 2. The method carries out detailed analysis on a static equivalent basic model and the detail problem in the equivalent process, including the processing of boundary capacitance and the selection of an equivalent branch model. Node clustering is proposed, i.e. the forced reservation of a balanced node as a border node when it is not inside the reservation system. 3. The invention develops an equivalent tool of a large power grid alternating current-direct current hybrid system based on a conventional WARD equivalent method, gives an example analysis of the application of the equivalent tool to different alternating current and direct current systems, and shows that the tidal current error of a reserved system before and after equivalence is very small. 4. According to the invention, a network equation of the whole system is established according to node classification, wherein a Y matrix is a node admittance matrix of the whole network, and the Y matrix is rearranged according to a node division result to form a corresponding block node admittance matrix. After equivalence, an equivalence admittance matrix Y formed by external nodes and boundary nodes is introduced into the admittance matrixEQWhile the other changed part is only the injection current I of the boundary node of the original systemBThe internal nodes are unchanged. For a linear system, this process will be a strictly equivalent one, as long as the injection current I of the external network is such thatEIf no change occurs, the flow of the equivalent system should be consistent with the original network in any operation mode. 5. When a model of a direct current line is added in the system, a corresponding direct current network equation needs to be added when calculating the power flow timing of the alternating current-direct current hybrid system. The structure of the direct current system is greatly different from that of the alternating current system, so that the alternating current-direct current hybrid system cannot be directly calculated by using a method for calculating the load flow of the alternating current system. The analysis is carried out from a model of a direct-current line, and a network equation of an alternating-current and direct-current hybrid system is correspondingly modified mainly from four aspects: a node power equation, a converter fundamental equation, a direct current network equation and a control equation. 6. The traditional static equivalence method of the power grid aims at an alternating current system, and the essence of equivalence is to simplify a network equation and eliminate the influence of external nodes. However, for an ac/dc hybrid system, the network equation of the system is greatly changed due to the dc, a uniform node admittance matrix cannot be formed, and the conventional war equivalentThe method of (3) is also not applicable. Therefore, the equivalent branch method and the equivalent power method are adopted to process the direct current line, the direct current line is converted into a model which can be processed by the equivalent of the alternating current system, and then the equivalent calculation is carried out. 7. On the basis of a static equivalence method of an alternating current system, a direct current power transmission system model is researched, an alternating current and direct current equivalent model is established according to alternating current and direct current power flow calculation results, and equivalence research is carried out on the alternating current and direct current system.
Drawings
FIG. 1 is a schematic view of the WARD equivalent flow of the present invention;
FIG. 2 is a schematic diagram of a transformer line model employed in the present invention;
FIG. 3 is a schematic diagram of an asymmetric line model employed by the present invention;
FIG. 4 is a schematic diagram of an asymmetric line post-processing model employed in the present invention;
FIG. 5 is a schematic diagram of a pi-type equivalent branch of a transformer employed in the present invention;
FIG. 6 is a schematic diagram of an equivalent model of a compensation capacitor used in the present invention;
FIG. 7 is a diagram of the clustering process of the reservation balancing node of the present invention;
FIG. 8 is a schematic diagram of the DC power transmission basic principle employed in the present invention;
FIG. 9 is an equivalent pi-type circuit diagram of the equivalent branch method employed by the present invention;
FIG. 10 is a diagram of an equivalent symmetric pi-shaped line by the equivalent branch method employed in the present invention;
FIG. 11 is a schematic diagram of the DC line equivalent power method of the present invention;
FIG. 12a is a flow error graph before equivalence of the IEEE30 node system;
FIG. 12b is a flow error graph after the present invention is applied to the equivalence of IEEE30 node systems;
FIG. 13a is a graph of the prior equivalent reactive error and the prior equivalent reactive error after the invention is applied to the IEEE30 node system to change the operation mode;
FIG. 13b is a graph of the equivalent reactive and reactive errors after the present invention is applied to the IEEE30 node system to change the operation mode;
FIG. 14 is a diagram of a CEPRI-36 system topology in an example of the invention;
FIG. 15a is a graph of active power flow error comparison of the present invention applying the equivalent leg method to the CEPRI-36 system;
FIG. 15b is a comparison chart of the reactive power flow error of the present invention applying the equivalent bypass method to the CEPRI-36 system;
FIG. 16a is a graph showing the comparison 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 graph of the reactive power flow error of the present invention applying the equivalent power source method to the CEPRI-36 system.
Detailed Description
The invention is described in detail below with reference to the figures and examples. It is to be understood, however, that the drawings are provided solely for the purposes of promoting an understanding of the invention and that they are not to be construed as limiting the invention.
As shown in fig. 1, the present invention provides a method for equating an ac/dc system based on the war equivalence, which comprises the following steps:
1) establishing each basic element model in the WARD equivalent model, acquiring the nodes of the whole network from each basic element model as basic data, determining whether the data format is a Matpower standard data format or a BPA data format, and if the data format is the BPA data format, converting the data format into the Matpower standard format for calculation. Defining the basic data into a structural body mpc; the master node comprises a master node, a slave node, a master node, a slave node and a master node, wherein the master node, the slave node, the master node, the slave node and the master node respectively represent node data, branch;
each basic element model comprises a line model, a generator and load model, a parallel element model, an asymmetric line model, a transformer branch and a boundary capacitor; a dc model introduced by the ac-dc hybrid system is also included.
When static equivalence analysis is carried out, an accurate element model is a key factor for ensuring that accurate and reliable load flow calculation results are obtained. In the process of researching the WARD equivalent model, various typical basic element models are referred, and the basic element models established by the invention are as follows:
1.1) establishing a line model:
as shown in FIG. 2, in practical engineering, the line models all adopt standard pi-shaped lines, and the line admittance ys＝1/(rs+jxs) Wherein r issRepresenting the line resistance, xsRepresents the line reactance; total charge capacity bcThe standard line model is connected with a transformer in series, namely the line model containing the transformer, and the excitation impedance of the transformer is ignored. The transformer is positioned at the head end of each line, the nonstandard transformation ratio is represented by tau, and the phase shift angle of the transformer is thetashift，ifAnd itRespectively representing the current at the head and tail ends of the line, vfAnd vtRespectively, the voltage at the head and tail ends of the line, and the positive direction of the current is the same as the direction of the arrow in fig. 2. From the line model shown in fig. 2, the node voltage equation for the line can be obtained as follows:
Figure BDA0001445087040000061
wherein:
Figure BDA0001445087040000062
1.2) establishing a generator and load model:
because the static equivalence process does not involve the transient state and optimal power flow process, the generator and the load model can be set simply and are both regarded as complex power injection of a certain preset node. For generator nodes, injecting power
Figure BDA0001445087040000063
Can be expressed as:
Figure BDA0001445087040000064
in the formula (I), the compound is shown in the specification,
Figure BDA0001445087040000065
indicating that the generator node is injecting active power.
Figure BDA0001445087040000066
Indicating that the generator node injects reactive power and i indicates the node number (same below).
Load power for node i
Figure BDA0001445087040000067
Comprises the following steps:
Figure BDA0001445087040000068
in the formula (I), the compound is shown in the specification,
Figure BDA0001445087040000069
representing the active power of the load;
Figure BDA00014450870400000610
representing the reactive power of the load.
1.3) establishing a parallel element model:
usually, some reactive compensation of capacitive or inductive elements are required on the high voltage lines, which are referred to as parallel elements. The parallel 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 parallel element admittance of a node is defined as:
Figure BDA0001445087040000071
in the formula (I), the compound is shown in the specification,
Figure BDA0001445087040000072
represents the parallel element admittance;
Figure BDA0001445087040000073
represents the parallel element conductance;
Figure BDA0001445087040000074
representing the parallel element susceptance.
The shunt capacitance injects capacitive idle work into the system, and plays a role in maintaining the node voltage to be constant. The parallel inductor injects inductive reactive power into the system to inhibit the node voltage from being too high, so the data of the parallel element is usually written in the form of power. And the change of the node voltage can change the injected reactive power of the parallel elements, so that the data of the part is written into a data file in the form of the power injected into the system by the parallel elements when the per unit value of the corresponding node voltage is 1.0, and the corresponding units are MW and MVAR. And the actual injection of reactive power is changed correspondingly according to the actual voltage value.
1.4) processing of asymmetric line models
Typically, a model of an asymmetric line is shown in FIG. 3. Wherein C is1And C2Representing capacitors connected in parallel on the left and right sides of the line, typically C1And C2Has a value of two equal positive numbers or one positive one negative when C1Or C2A negative value indicates that an inductor is connected in parallel.
For two equal positive values, the two positive values are treated as pi-type lines, and the treatment method is the same as that of a common line. For a positive-negative case, the processing method adopted by the invention is to convert the line into two parts, namely a symmetrical pi-type line and a parallel inductor, so that the asymmetrical line is added into the line parameter and the node parameter respectively. The transformed model is shown in fig. 4, where,
Figure BDA0001445087040000075
Figure BDA0001445087040000076
and
Figure BDA0001445087040000077
respectively representing the capacitive reactance of the left side and the right side of the asymmetric line; xLRepresenting the equivalent parallel reactance of the asymmetric line.
1.5) Transformer Branch treatment
The accurate equivalent branch of the transformer is a T-shaped equivalent branch which can accurately reflect the real running condition of the transformer, but the T-shaped equivalent branch has a series-parallel connection mode and is very inconvenient for analyzing an electric power system. Considering that the excitation impedance is relatively large when the transformer normally operates, the excitation impedance branch is usually advanced, so that the excitation impedance branch becomes a type equivalent branch. The establishment of the transformer model is very important, and particularly has great influence on the reactive accuracy of the system. And (3) carrying out pi-type conversion on the branch of the transformer as shown in figure 5, thus neglecting the influence of the nonstandard transformation ratio of the transformer, and modifying the branch of the transformer into Matpower basic data by using a method for processing an asymmetric line. The problem of the transformation ratio direction does not need to be considered after the pi-type equivalent circuit is adopted.
1.6) processing of boundary capacitances
As shown in fig. 6, the dummy lines are treated as pure impedance lines, and then the parallel compensation capacitance is calculated at each boundary node. The boundary nodes are represented by a set B, and the number of the boundary nodes is nb; the internal nodes are represented by set I and the number of internal nodes is represented by ni. Y isij(i ≠ j) represents the negative value of the line admittance of the branch formed by the node i and the node j, and the relevant parameters of the branch are expressed as: line admittance yijLine total to ground admittance bijTransformer transformation ratio tauijPhase shift θij. The array c (i) (1, 2 … nb) is defined to store the border node capacitance. The specific calculation formula is as follows:
the pure line calculation method comprises the following steps:
C(k)＝C(k)+ykj
wherein k is belonged to i;
the method comprises the following steps of calculating a transformer line, wherein a boundary node is a first node:
Figure BDA0001445087040000081
the transformer line calculation method is characterized in that boundary nodes are tail nodes:
Figure BDA0001445087040000082
1.7) DC line model
A simple dc power transmission system is shown in fig. 8, and when a model of a dc line is added to the system, a corresponding dc network equation is required to be added in calculating the power flow timing of the ac/dc hybrid system. The structure of the direct current system is greatly different from that of the alternating current system, so that the alternating current-direct current hybrid system cannot be directly calculated by using a method for calculating the load flow of the alternating current system. The analysis is carried out from a model of a direct-current line, and a network equation of an alternating-current and direct-current hybrid system is correspondingly modified mainly from four aspects: a node power equation, a converter fundamental equation, a direct current network equation and a control equation.
2) And carrying out load flow calculation on the whole network to obtain a whole network load flow solution. Defining the trend result in a structure named result, wherein the format is similar to that of a data structure, and the trend result is convenient to call;
assuming that the number of nodes of the AC/DC hybrid system is n, and the number of the DC nodes is ncIf the number of the AC nodes is na＝n-nc. The nodes are sequentially ordered in the order of alternating current and direct current.
2.1) node power equation:
Figure BDA0001445087040000083
wherein i ═ na+k，k＝1,2,…,ncIn the formula, a positive sign represents an inverter, and a negative sign represents a rectifier. Compared with the network equation of the alternating current system, V is increaseddk，IdkAnd
Figure BDA0001445087040000084
and three variables respectively representing the direct-current node voltage, the injected current and the included angle between the voltage and the current, namely the power factor angle of the converter. Delta PiRepresenting a given active unbalance amount; delta QiRepresenting a given reactive unbalance; pisRepresenting a given active power; qisRepresenting a given reactive power; viRepresents the voltage of node i; vjRepresents the voltage at node j; thetaijRepresenting the phase angle difference between node i and node j; gijRepresenting the real part of the admittance matrix; b isijRepresenting the imaginary part of the admittance matrix. Since the equations increase the number of unknowns, other equations are needed as supplements.
2.2) fundamental equation of converter
For inverter k, the following equation is:
Figure BDA0001445087040000091
Figure BDA0001445087040000092
wherein, Δ d1k、Δd2kRepresenting the amount of DC voltage unbalance; vdkWhich represents the dc voltage of the inverter,
Figure BDA0001445087040000093
expressing the voltage per unit value of the AC side line of the converter transformer, IdkRepresenting the direct current of the converter; xckRepresenting the equivalent impedance, k, of a converter transformer kTkRepresenting the transformation ratio, k, of the converter transformerγIs a constant close to 1, thetadkThe control angle of the inverter k is shown,
Figure BDA0001445087040000094
representing the power factor angle of the converter.
2.3) direct current network equation
The equations used to describe the dc power transmission model, called the dc network equations, generally have the following standard form:
Figure BDA0001445087040000095
wherein, Δ d3kRepresenting the amount of unbalance of the DC current output by the converter, IdkRepresents the direct current of the converter k; vdjIndicating the DC voltage of the jth DC node, gdkjRepresenting the elements of the conductance matrix of the nodes of the DC network after the elimination of the tie nodes, in which the voltage and current are equalShowing the voltage and current of the dc line. For a simple two-terminal dc transmission system, the dc network equation is simplified as follows:
Figure BDA0001445087040000096
in the formula, R represents the resistance of a direct current line; i isd1Representing the current of a direct current node at the 1 end; i isd2Represents the current of a 2-terminal direct-current node; if the resistance of the DC line is sufficiently small, V can be considered approximatelyd1＝Vd2，Id1＝Id2。
2.4) equation of control
Because two new variables are introduced into the basic equation and the direct current network equation of the converter, two more equations must be added to ensure that the equations have unique solutions, the control equations of the converter and the inverter are usually used as supplementary equations, and the variables of the two equations have independence.
The following generally exists for the control of converters:
① fixed control angle control cos thetad-cosθds＝0；θdRepresenting converter control angle, thetadsRepresenting a given control angle;
② constant ratio control kT-kTs＝0；kTRepresenting the transformer ratio, k, of the converterTsRepresenting a given transformation ratio;
③ constant current controld-Ids＝0；IdIndicating the output DC of the inverter, IdsRepresenting a given dc constant value;
④ constant voltage control Vd-Vds＝0；VdIndicating the output DC voltage, V, of the inverterdsRepresenting a given dc voltage value;
⑤ constant power controldId-Pds＝0，PdsRepresenting the inverter output power set point.
Generally, the inverter adopts a control mode of a fixed control angle and a fixed transformation ratio; the rectifier usually adopts a constant current and constant transformation ratio control mode. To make the equations generic, the governing equation is generally defined as follows:
Δd4k＝d4k(Idk,Vdk,cosθdk,kTk)＝0(k＝1,2,…,nc)
Δd5k＝d5k(Idk,Vdk,cosθdk,kTk)＝0(k＝1,2,…,nc)
in the formula (d)4kRepresenting the function of the converter transformation ratio and the current unbalance, Δ d4kRepresenting the amount of unbalance of the rectifier control variable, d5kFunction representing the inverter transformation ratio and the amount of control angle unbalance, Δ d5kRepresenting the unbalance of the inverter control variable, IdkRepresents the direct current of the converter k; vdkRepresents the inverter k dc voltage; thetadkRepresenting the converter k control angle; k is a radical ofTkRepresenting the transformation ratio of the converter transformer; since all the variables related to the control angle in the formula are observed to be in cos thetadkAll appear in cos θ to improve the linearity of the equationdkIs a direct demand.
The node power equation, the converter basic equation, the direct current network equation and the control equation jointly form a power flow calculation equation of the alternating current-direct current hybrid system. The method requires to solve the load flow of the AC-DC hybrid system, needs to calculate the voltage amplitude and phase angle of all nodes, and also needs to calculate ncThe direct current voltage, the direct current, the converter transformer transformation ratio, the converter control angle and the converter power factor angle of each direct current node are five to-be-solved quantities. For each additional converter, five additional equations will be added.
3) According to the use requirement, the nodes are divided into an internal node set I, a boundary node set B and an external node set E, and elements in each set are arranged from small to large according to the node numbers.
The method has two fault-tolerant capabilities: firstly, it can be judged that there is no intersection between the set I, B and E, and the number of the union of the set I, B and E is equal to the total number of nodes; secondly, whether the set I contains the balance nodes is detected, if not, the balance nodes are taken as boundary nodes to be forcibly reserved, and the next step is carried out; if yes, directly entering the next step.
The first step of static equivalence is to distinguish nodes, find out internal nodes and proper boundary nodes to be reserved according to research needs, and eliminate all other nodes. After the relevant parameters of the equivalent network are calculated, load flow calculation needs to be carried out on the system after the equivalent, and the accuracy of the equivalent result is verified by comparing the load flow result of the reserved network. The reservation system has no balance node, the system automatically reserves the balance node, the reservation system is treated as a group, the balance node is used as another group, and the balance node and the reservation system have direct contact by establishing a virtual branch between the two groups.
As shown in fig. 7, the cluster processing structure treats the balance node as a reservation node. Although there is no direct connection between the balance node and the internal system, the matrix Y is known by operationEQIs a highly dense matrix such that off-diagonal elements associated with the balanced nodes are treated as impedance values for the virtual branches, creating virtual branches between the balanced nodes and the boundary nodes. By this method, the balance node has direct connection with the reservation system.
4) Calling a node admittance subfunction makeYbus to form a node admittance matrix of the whole network, and forming a block node admittance matrix Y for equivalent calculation according to the divided node setEE、YEB、YBBAnd YBE；
Establishing a network equation of the whole system according to node classification, wherein a Y matrix is a node admittance matrix of the whole network, and rearranging the Y matrix according to a node division result to form a corresponding block node admittance matrix:
Figure BDA0001445087040000111
the following three equations are developed:
Figure BDA0001445087040000112
Figure BDA0001445087040000113
Figure BDA0001445087040000114
wherein:
Figure BDA0001445087040000115
Figure BDA0001445087040000116
in the formula, the equivalent former network parameters: y isEERepresenting the admittance matrix between external nodes, YEBRepresenting the admittance matrix between the external node and the boundary node, YBERepresenting the admittance matrix between the boundary node and the external node, YBBRepresenting the admittance matrix between the boundary nodes, YBIRepresenting the admittance matrix, Y, between the boundary node and the internal nodeIBRepresenting the admittance matrix between internal and boundary nodes, YIIRepresenting the admittance matrix, V, between internal nodesERepresenting the external node voltage, VBRepresenting the boundary node voltage, VIRepresenting the internal node voltage, IIRepresents the internal node injection current, IBRepresents the boundary node injection current, IERepresents the external node injection current; equivalent network parameters: y isEQAn equivalent admittance matrix representing the external nodes and the boundary nodes,
Figure BDA0001445087040000117
and expressing the current of the equivalent injection boundary node of the external network, wherein the parameters of the boundary node before and after the equivalence are the same as those of the internal node.
The block admittance matrix is a node network equation after equivalent calculation, and it can be seen that the network equation of the system does not have VEThat is to say eliminateThe influence of the external network is removed. The admittance matrix is added with YEQWhile the other part of the variation is only YBBAnd injection current I of boundary nodeBThe internal nodes are unchanged. For a linear system, the equivalent calculation process is a strictly equivalent process, as long as the injection current I of the external network is equalEIf no change occurs, the flow of the equivalent system should be consistent with the original network in any operation mode.
5) Calculating the matrix YEQAnd a boundary equivalent capacitor C is obtained, the process of obtaining the boundary equivalent capacitor C is given by the step 1.6), the boundary equivalent branch parameters after equivalence are finally obtained, and the boundary equivalent injection power S is calculatedEQ＝Pi EQ+jQi E(ii) a Wherein, Pi EQRepresenting equivalent injection active power of a node i;
Figure BDA0001445087040000121
indicating node i equal injected reactive power.
Since in practical systems, the injected current data is usually not available, and the line power and node voltage values are usually known, the injected current of all nodes can be expressed in the following form:
Figure BDA0001445087040000122
in the formula (I), the compound is shown in the specification,
Figure BDA0001445087040000123
which represents the current injected by the node,
Figure BDA0001445087040000124
which is representative of the voltage at the node,
Figure BDA0001445087040000125
representing the node injected power.
After the current is expressed by the power, the original linear equation becomes a nonlinear equation, namely:
Figure BDA0001445087040000126
defining:
Figure BDA0001445087040000127
the above equation can be expressed as:
Figure BDA0001445087040000128
in the formula (I), the compound is shown in the specification,
Figure BDA0001445087040000129
indicating that the external node is injecting power,
Figure BDA00014450870400001210
it is shown that the boundary nodes inject power,
Figure BDA00014450870400001211
representing the internal node injected power.
Under the condition of knowing the load flow results of the internal network and the boundary nodes under the basic condition, calculating the equivalent injection power of the boundary nodes according to the following formula:
Figure BDA00014450870400001212
wherein, Pi EQRepresenting equivalent injection active power of a node i;
Figure BDA00014450870400001213
representing the equivalent injection reactive power of a node i; vi 0And
Figure BDA00014450870400001214
respectively representing the voltage modulus values of the bus at the node i and the node j under the basic condition; thetaiAnd thetajRespectively represent the bus voltages of the node i and the node j in the basic conditionPhase angle, θij＝θi-θjRepresenting the phase difference between node i and node j; gij+jbijRepresenting the admittance to ground value of the branch connected to node i; gi0+jbi0Representing the admittance of the branch connected to node i to the ground path on side i.
The method for calculating the injection power of the boundary node is very simple and convenient, and only the load flow data of the boundary node and the network topology structure connected with the boundary node need to be known. For a large system, the trend data of the external network may not be timely and accurately obtained, and the related data of the boundary node may be timely obtained through the state estimator, so that the calculation method shown in the above formula is more suitable for online application.
6) And forming a new structural data body, and storing the equivalent basic data of the system, which is defined as Rempc. The principle of node definition is that the generator data and the branch data in the system are reserved according to the sequence arrangement of an internal node set and a boundary node set, and the new generator data and the new branch data need to be changed correspondingly according to the rearranged node numbers. Then, adding the equivalent branch parameters and the boundary injection power obtained in the step 5) into the branch and node data of the new data respectively;
7) and (3) carrying out load flow calculation on the system after equivalence, and comparing with the load flow calculation result in the step 2), namely comparing the load flow results of the reserved branches and nodes before and after equivalence, and selectively outputting the load flow results.
In the above steps, the method for processing the direct current line in the alternating current and direct current hybrid system is as follows:
the traditional static equivalence method of the power grid aims at an alternating current system, and the essence of equivalence is to simplify a network equation and eliminate the influence of external nodes. However, for an ac/dc hybrid system, the network equation of the system is greatly changed due to the dc, so that a uniform node admittance matrix cannot be formed, and the conventional method equivalent to the WARD cannot be applied. Therefore, the equivalent branch method and the equivalent power method are adopted to process the direct current line, convert the direct current line into a model which can be processed by the equivalent of the alternating current system, and then perform equivalent calculation.
(1) Equivalent branch method
According to the tidal current result, the direct current circuit is equivalent to a pi-type circuit, V as shown in FIG. 91And theta1Representing the voltage amplitude and phase angle, V, of the AC node of the rectifier-side transformer2And theta2Representing the amplitude and phase angle, P, of the voltage at the AC node of the inverter-side transformer1And Q1Respectively representing the active and reactive power, P, transmitted from the AC system at the rectifying side to the DC system2And Q2Respectively showing active power and reactive power transmitted from an inverter side alternating current system to a direct current system, wherein the positive direction is the same as the arrow direction in the figure, and direct current is equivalent to admittance parameters of a pi-shaped circuit: g and b are the series conductance and susceptance of the equivalent branch, b1And b2The equivalent branch circuit is the parallel susceptance to ground on the left and right sides, and the quantities are the quantities to be solved.
Node voltage of AC system
Figure BDA0001445087040000131
And admittance matrix element YijCan be expressed as:
Figure BDA0001445087040000132
Yij＝Gij+jBij
in the formula, ei＝Vicosθi，fi＝Visinθi，ViAnd thetaiRespectively representing the voltage amplitude and the phase of the node i; gijAnd BijRespectively representing conductance and susceptance of branch ij
The general form of the power flow equation for an n-node power system is:
Figure BDA0001445087040000141
in the formula, PiAnd QiRespectively indicating that the node i injects active power and reactive power.
The power flow equation corresponding to fig. 9 can thus be obtained:
Figure BDA0001445087040000142
Figure BDA0001445087040000143
wherein, theta12＝θ1-θ2(ii) a The other parameters correspond to the parameters in fig. 9. The line transmission power, the node voltage and the phase angle can be obtained through load flow calculation, and finally, the parameters of the direct current line equivalent to the alternating current line in fig. 9 are obtained through calculation as follows:
Figure BDA0001445087040000144
Figure BDA0001445087040000145
Figure BDA0001445087040000146
Figure BDA0001445087040000147
the parameters of the equivalent branch can be calculated by the four formulas, but b is usually present1≠b2That is to say, the equivalent pi-type line is asymmetric, and it needs to be converted into a symmetric pi-type line for participating in calculation, and the processing method is the same as the method for processing an asymmetric line, and the equivalent branch is converted into a symmetric pi-type line and a reactance or an inductance connected in parallel at one end of the line. The equivalent diagram is shown in FIG. 10, b1-2And the difference value of the parallel admittance of the left side and the right side of the equivalent circuit to the ground is shown. All direct current lines in the system can be processed into alternating current lines in such a processing mode, so that an alternating current and direct current hybrid system is changed into a pure alternating current system, and then the equivalent method of the alternating current system is applied to the pure alternating current systemAnd (4) calculating.
(2) Equivalent power method
When the alternating current system equation is solved by using the alternating iteration method, the direct current system is equivalent to loads with known active power and reactive power connected to corresponding nodes. Therefore, the equivalent power method is to make the power transmitted by the dc part equivalent to the generator connected to the ac nodes on both sides according to the result of the load flow calculation, and the two ac nodes are defined as PQ nodes. The equivalent process is shown in FIG. 11, in which
Figure BDA0001445087040000151
And
Figure BDA0001445087040000152
respectively, the power transmitted by the first node and the last node of the direct current line.
The equivalent power method is to directly equivalent the power transmitted by the direct current line into two equivalent machines, and the premise is that the power transmitted by the direct current is assumed to be unchanged. Therefore, corresponding conversion can be carried out only according to the tidal current result of the converter transformer line.
Example (b): the static equivalence of the system to which the invention is applied is detailed below by means of specific embodiments. Example 1: IEEE30 node standard system; example 2: 36 nodal alternating current-direct current hybrid system of China's electric academy of sciences. The calculation process and results of the specific embodiment are as follows:
example 1:
(1) IEEE30 node standard system
Table 1 gives detailed results of IEEE-30 node partitioning.
TABLE 1 IEEE-30 node partitioning
Figure BDA0001445087040000153
An equivalence program is applied to perform equivalence calculation on the standard 30-node calculation example, a boundary equivalence machine (as PQ node processing) is performed, the boundary node virtual branch impedance value and boundary parallel compensation data are shown in tables 2, 3 and 4.
TABLE 2 boundary equivalentment machine (Unit: MW/MVAR)
Figure BDA0001445087040000154
Table 3 boundary node virtual branch impedance value (pu.)
Figure BDA0001445087040000155
Table 4 boundary parallel compensation value (pu.)
Figure BDA0001445087040000161
In order to verify the accuracy of the equivalence result, the power flows of the system before equivalence and the system after equivalence need to be compared. Load flow calculation was performed on the system after the peer-to-peer operation in the same manner, and the results are shown in table 5.
TABLE 5 internal network tidal current error (Unit: MW/MVAR)
Figure BDA0001445087040000162
It can be seen from table 5 that the tidal current result of the equivalent system is substantially consistent with that of the original system under the condition that the operation mode is not changed. The comparison result of the power flow error is shown in the equivalent front-back power flow error diagram of FIG. 11, and it can be seen from FIG. 11 that the order of magnitude of the line active error is 10-8The order of magnitude of the reactive error is 10-7. So the equivalent result is quite accurate in the case of the ground state of the system.
(2) Changes in the operating mode of IEEE30 systems
When the operation mode of the system changes, particularly when the system needs reactive increment, certain errors exist in the equivalent WARD. The equivalent simulation analysis is carried out on the system under the condition that the branch 4-6 of the IEEE30 system has a disconnection fault. Since node 11 is a PV node, the node is first repartitioned as a cancel node, and the repartitioned node is shown in table 6.
TABLE 6 node partitioning
Figure BDA0001445087040000171
And considering that the branch circuits 4-6 are short-circuited, calculating the steady-state load flow of the system after short circuit, performing equivalence calculation on the system, and calculating the steady-state load flow of the system after short circuit. And comparing the steady-state power flow before equivalence with the steady-state power flow after equivalence. As shown in fig. 12a and 12b, the active and reactive power flow errors of the system before and after equivalence under the condition of considering the change of the operation mode. It can be seen that in the event of a short circuit on lines 4-6, the error value increases but remains within the engineering acceptable range compared to the condition where the operating regime is not changed. The active power flow error is basically kept within 5 percent, and the maximum error is 7 percent. The reactive error is basically kept within 10 percent, and the maximum error is 15 percent. It can be seen that the reactive error is slightly larger than the active error, which is also a drawback inherent in the war equivalent, because when the internal operation mode of the system changes, the injection power of the external system changes to some extent, especially the reactive power. The boundary injection power of the equivalent system is still calculated according to the situation of the ground state, so the error is increased. But in summary, after the system operation mode is changed, the WARD equivalence still has good equivalence effect.
Example 2: 36 nodal alternating current-direct current hybrid system of China's electric academy of sciences.
Taking a 36-node alternating current and direct current hybrid system of China electric academy of sciences as an example, an equivalent branch method and an equivalent power method are respectively provided by adopting the report, and equivalence analysis is carried out on the alternating current and direct current hybrid system.
(1) Equivalent branch method
The power flow of the test system is first calculated. The ac node load flow results (pu) on both sides of the dc lines are shown in table 7, where the positive direction is defined as in fig. 13a, 13 b.
TABLE 7 tidal flow results
Figure BDA0001445087040000181
In Table 7, P33And Q33Respectively representing the active and reactive power injected at node 33, P34And Q34Indicating that node 34 injects active and reactive power, respectively; v33And
Figure BDA0001445087040000182
respectively representing the magnitude and phase angle, V, of the voltage at node 3334And
Figure BDA0001445087040000183
representing the node 34 voltage magnitude and phase angle, respectively.
Substituting the known quantity in table 7 into an equation, calculating the parameters of the equivalent branch as follows: g-0.5820, b-7.3541, b1＝0.05117，b20.61253. Processing related data according to an equivalent branch processing method, removing direct current line parameters between buses 33 and 34, adding an alternating current line 33-34, wherein the impedance parameter is 0.0107+ j0.1351, and connecting a total capacitor b in parallelc0.1023, the bus 34 parallel capacitance injection power B56.14 MAVR, and the MATLAB basic data is modified according to the calculation result.
The CEPRI-36 is node partitioned. For convenience, the report retains several important generator nodes including the balance node, all the rest nodes are eliminated, and the node division result is shown in table 8.
TABLE 8 CEPRI-36 node partitioning results
Figure BDA0001445087040000184
And (4) applying an equivalence program to perform equivalence calculation on the test system. Fig. 13 shows the comparison results of the active power flow and the reactive power flow of the original system, the processed system and the system reserved branch after equivalence.
(2) Equivalent power method
According to the trend result, modifying the basic data of CEPRI-36, removing the DC branches 33-34, and adding load data (per unit value, rated power of 100MW) P at the nodes 33 and 3433+Q333.0015+ j0.4270, an additional load P is added at node 3434+Q34＝-2.9057+j0.1174。
The node classification is the same as in the CEPRI-36 node partition results in Table 8. And (4) applying an equivalence program to perform equivalence calculation on the test system. As shown in fig. 15a to 16b, the comparison results of the power flow of the original system, the processed system and the equivalent system are shown.
According to the above two simulation results, the following conclusion can be obtained:
(1) an equivalent power supply method and an equivalent branch method are adopted, and the results of the front tide and the rear tide are highly consistent under the condition that the operation mode of the system is not changed;
(2) the results obtained by the two processing methods are basically the same, and the network tide results before and after equivalence are highly consistent and have small errors. Therefore, the equivalence results are very accurate.
The above embodiments are only used for illustrating the present invention, and the implementation steps of the method and the like can be changed, and all equivalent changes and modifications based on the technical scheme of the present invention should not be excluded from the protection scope of the present invention.

Claims (8)

1. A WARD equivalence-based alternating current and direct current system equivalence method is used for accurately simulating transient characteristics of a large alternating current and direct current power grid with layered access in an asymmetric fault period or network equivalence of alternating current filter design for performing layered access direct current engineering, and is characterized by comprising the following steps of:
1) establishing each basic element model in the WARD equivalent model, acquiring a whole network node from each basic element model as basic data, determining whether the data format is a Matpower standard data format or a BPA data format, and converting the data format into the Matpower standard format for calculation if the data format is the BPA data format;
2) carrying out load flow calculation on the whole network to obtain a load flow solution of the whole network, and defining a load flow result in a structural body named result, wherein the format of the load flow result is similar to that of a data structural body;
3) dividing nodes into an internal node set I, a boundary node set B and an external node set E, wherein elements in each set are arranged from small to large according to node numbers;
two types of fault tolerance are required: first, it is determined that there is no intersection between sets I, B and E, and the number of union sets I, B and E is equal to the total number of nodes; secondly, detecting whether the set I contains a balance node, if not, forcibly reserving the balance node as a boundary node, entering the next step, and if so, directly entering the next step;
4) calling a node admittance subfunction makeYbus to form a node admittance matrix of the whole network, and forming a block node admittance matrix for equivalent calculation according to the divided node set;
5) calculating the matrix YEQObtaining the equivalent boundary equivalent branch parameters from the boundary equivalent capacitor C, and calculating the boundary equivalent injection power SEQ＝Pi EQ+jQi EQ(ii) a Wherein, Pi EQRepresenting equivalent injection active power of a node i; qi EQRepresenting the equivalent injection reactive power of a node i;
6) forming a new structure data body, storing the equivalent basic data of the system, defining the basic data as Rempc, and adding the step 5) into the new structure data body;
the principle of node definition is that the generator data and the branch data in the system are reserved according to the sequence arrangement of an internal node set and a boundary node set, and the new generator data and the new branch data need to be changed correspondingly according to the rearranged node numbers; then, adding the added equivalent virtual branch and boundary capacitance data into the branch and node data of new data respectively;
7) carrying out load flow calculation on the system after equivalence, comparing load flow results of reserved branches and nodes before and after equivalence, and selectively outputting the load flow results;
processing the direct current line by adopting an equivalent branch method and an equivalent power supply method, converting the direct current line into a model which can be processed by the equivalent of an alternating current system, and then performing equivalent calculation:
(1) equivalent branch method
The direct current circuit is equivalent to a pi-type circuit, and the parameters of the pi-type circuit are as follows:
Figure FDA0002607219930000021
Figure FDA0002607219930000022
Figure FDA0002607219930000023
Figure FDA0002607219930000024
wherein g and b are the series conductance and susceptance of the equivalent branch; b1And b2The equivalent branch circuit is connected with susceptances in parallel to the ground on the left and the right sides; v1And theta1Representing the voltage amplitude and phase angle, V, of the AC node of the rectifier-side transformer2And theta2Representing the amplitude and phase angle, P, of the voltage at the AC node of the inverter-side transformer1And Q1Respectively representing the active and reactive power, P, transmitted from the AC system at the rectifying side to the DC system2And Q2Respectively representing active power and reactive power transmitted from an alternating current system at an inversion side to a direct current system; theta12＝θ1-θ2；
Due to the presence of b1≠b2The equivalent pi-shaped line is asymmetric, and needs to be converted into a symmetric pi-shaped line to participate in calculation, the processing method is the same as that for processing the asymmetric line, and the equivalent branch is converted into a symmetric pi-shaped line and a reactance or an inductance which is connected in parallel at one end of the line; all direct current lines in the system are processed into alternating current lines in the processing mode, so that an alternating current-direct current hybrid system is changed into a pure alternating current system, and then an equivalent method of the alternating current system is applied to calculation;
(2) equivalent power method
And according to the result of the load flow calculation, the power transmitted by the direct current part is equivalent to a generator connected with alternating current nodes on two sides on the premise that the power transmitted by the direct current is not changed.
2. The method of claim 1, wherein the method comprises the steps of: in the step 1), the basic element model comprises a line model, a generator and load model, a parallel element model, an asymmetric line model, a transformer branch and a boundary capacitor.
3. The method of claim 1, wherein the method comprises the steps of: in the step 2), the load flow calculation of the whole network comprises a node power equation, a converter basic equation, a direct current network equation and a control equation.
4. The method of claim 3, wherein the method comprises the steps of: the node power equation:
Figure FDA0002607219930000025
wherein i ═ na+k，k＝1,2,…,ncIn the formula, a positive sign represents an inverter, a negative sign represents a rectifier, and V is added in comparison with an alternating current system network equationdk，IdkAnd
Figure FDA0002607219930000035
three variables representing the DC node voltage, the included angle between the injected current and the voltage current, i.e. the power factor angle of the converter, Δ PiRepresenting a given active unbalance amount; delta QiRepresenting a given reactive unbalance; pisRepresenting a given active power; qisRepresenting a given reactive power; viRepresents the voltage of node i; vjRepresents the voltage at node j; thetaijRepresenting the phase angle difference between node i and node j; gijRepresenting the real part of the admittance matrix; b isijRepresenting the imaginary part of the admittance matrix.
5. The method of claim 3, wherein the method comprises the steps of: the basic equation of the converter is as follows for the converter k:
Figure FDA0002607219930000031
Figure FDA0002607219930000032
wherein, Δ d1k、Δd2kRepresenting the amount of DC voltage unbalance; vdkWhich represents the dc voltage of the inverter,
Figure FDA0002607219930000037
expressing the voltage per unit value of the AC side line of the converter transformer, IdkRepresenting the direct current of the converter; xckRepresenting the equivalent impedance, k, of a converter transformer kTkRepresenting the transformation ratio, k, of the converter transformerγIs a constant close to 1, thetadkThe control angle of the inverter k is shown,
Figure FDA0002607219930000036
representing the power factor angle of the converter.
6. The method of claim 3, wherein the method comprises the steps of: the standard form of the dc network equation:
Figure FDA0002607219930000033
wherein, Δ d3kRepresenting the amount of unbalance of the DC current output by the converter, IdkRepresents the direct current of the converter k; vdjIndicating the DC voltage of the jth DC node, gdkjRepresenting the elements of the conductance matrix of the nodes of the DC network after the elimination of the tie nodes, in which the voltage and current are both representative of the electricity of the DC linesVoltage and current, for a simple two-terminal dc transmission system, the dc network equation is simplified as follows:
Figure FDA0002607219930000034
in the formula, R represents the resistance of a direct current line; i isd1Representing the current of a direct current node at the 1 end; i isd2Represents the current of a 2-terminal direct-current node; if the resistance of the DC line is sufficiently small, V is considered approximatelyd1＝Vd2，Id1＝Id2。
7. The method of claim 3, wherein the method comprises the steps of: the control equation:
Δd4k＝d4k(Idk,Vdk,cosθdk,kTk)＝0(k＝1,2,…,nc)
Δd5k＝d5k(Idk,Vdk,cosθdk,kTk)＝0(k＝1,2,…,nc)
in the formula (d)4kRepresenting the function of the converter transformation ratio and the current unbalance, Δ d4kRepresenting the amount of unbalance of the rectifier control variable, d5kFunction representing the inverter transformation ratio and the amount of control angle unbalance, Δ d5kRepresenting the unbalance of the inverter control variable, IdkRepresents the direct current of the converter k; vdkRepresents the inverter k dc voltage; thetadkRepresenting the converter k control angle; k is a radical ofTkRepresenting the transformation ratio of the converter transformer; since all the variables related to the control angle in the formula are observed to be in cos thetadkAll appear in cos θ to improve the linearity of the equationdkIs a direct demand.
8. The method of claim 1, wherein the method comprises the steps of: in the step 5), the boundary equivalent capacitance C is:
the pure line calculation method comprises the following steps:
C＝C(k)+ykj
wherein k is belonged to i;
the method comprises the following steps of calculating a transformer line, wherein a boundary node is a first node:
Figure FDA0002607219930000041
the transformer line calculation method is characterized in that boundary nodes are tail nodes:
Figure FDA0002607219930000042
wherein, Yij(i ≠ j) represents the negative value of the line admittance of the branch formed by the node i and the node j, and the relevant parameters of the branch are expressed as: line admittance yijLine total to ground admittance bijTransformer transformation ratio tauijPhase shift θij。
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