CN105576667B - External network equivalent network boundary voltage power-less supports abundance computational methods - Google Patents

External network equivalent network boundary voltage power-less supports abundance computational methods Download PDF

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CN105576667B
CN105576667B CN201610131377.XA CN201610131377A CN105576667B CN 105576667 B CN105576667 B CN 105576667B CN 201610131377 A CN201610131377 A CN 201610131377A CN 105576667 B CN105576667 B CN 105576667B
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equivalent
boundary node
node
maxo
mino
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CN105576667A (en
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陈涛
张�林
代伟
周宁
史成钢
吴迎霞
余娟
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Chongqing University
State Grid Corp of China SGCC
State Grid Chongqing Electric Power Co Ltd
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Chongqing University
State Grid Corp of China SGCC
State Grid Chongqing Electric Power Co Ltd
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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
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

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  • Power Engineering (AREA)
  • Pharmaceuticals Containing Other Organic And Inorganic Compounds (AREA)
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Abstract

The invention discloses a kind of external network equivalent network boundary voltage power-less to support abundance computational methods, inputs at PMU measurement boundary nodes equivalent network parametric data under the method for operation of the voltage for needing section, power and minimax.Multiport external network equivalent method according to being measured based on PMU establishes model, solve external network equivalent parameter, then the idle work optimization of outer net is carried out, calculates external network equivalent network boundary voltage power-less enabling capabilities, then selects effective equivalence method according to reactive power enabling capabilities.The computational methods external network equivalent method comprehensive based on element is considered, calculate the voltage power-less enabling capabilities at the actual internal net boundary node of outer net, then judge whether the check-in such as extension in practical power systems node is correct, think that PV is equivalent and effective if there are sufficient voltage power-less enabling capabilities if outer net；Think only to consider that the comprehensive external network equivalent method of element is effective if the voltage power-less enabling capabilities that outer net does not possess abundance.

Description

Method for calculating reactive support abundance of boundary voltage of external network equivalent network
Technical Field
The invention belongs to the field of static equivalence methods of power systems, and particularly relates to a method for calculating the margin of reactive support of equivalent network boundary voltage of an external network of an interconnected power grid.
Background
With the increasing demand of electric energy, for the reasonable allocation of resources, modern electric power systems have been developed into large systems with tightly interconnected subnetworks, and the interaction and influence between the subnetworks are further enhanced. When each intranet makes a steady-state analysis decision, it is necessary to consider the influence of the adjacent subnets (extranets) closely connected to the intranet. In order to ensure the accuracy of the reactive power optimization calculation of the interconnected power grid, the influence of the outer network on the inner network is necessary to be considered. However, the data volume of the external network is huge, and online calculation and storage are not easy, so that the external network can be equivalent into an equivalent network with small scale, less data, easy maintenance and no secret involvement, and further, reactive power optimization calculation is performed. However, due to commercial confidentiality or technical problems, it is difficult to acquire real-time synchronization data of the whole network, and for this situation, a non-topological method of estimating equivalent parameters of the external network by using measurement information of the internal network can be adopted for equivalence, and the static analysis of the interconnected power network under different network structures and different operation modes has various characteristics.
In the existing actual static analysis of the interconnected power grid, external equivalence is directly used as a simple on-line equivalence machine in many cases, namely the external equivalence is used as a PV node or a PQ node at a boundary node. The PV nodes are the outer network and can provide sufficient voltage reactive support capability for the inner network, the PQ nodes are the outer network and can not provide any voltage reactive support capability for the inner network, and the existing method for calculating the voltage reactive support capability of the inner network by the outer network is not available. This method is very simple but may introduce significant errors and even errors. The main defects of the PV or PQ equivalent method are that the voltage reactive power supporting capability of an external network to an internal network cannot be correctly reflected, and errors and even errors are brought in static analysis of a power system.
Disclosure of Invention
The invention aims at providing a method for calculating the reactive support capability of an outer network to an inner network without a voltage reactive support capability calculation method of the outer network to the inner network, the calculation method is based on the outer network equivalence method considering the comprehensiveness of elements, the voltage reactive support capability of the actual outer network to inner network boundary nodes is calculated, then whether a hanging equivalent machine node in an actual power system is correct is judged, and if the outer network has sufficient voltage reactive support capability, PV equivalent is considered to be effective; and if the outer net does not have sufficient voltage reactive support capacity, only the equivalent method of the outer net considering the comprehensiveness of elements is considered to be effective.
The technical scheme for realizing the purpose of the invention is as follows: a method for calculating the margin of reactive support of the boundary voltage of an external network equivalent network utilizes a computer and a program to input the voltage and the power of a section required by a PMU measurement boundary node and the data of network parameters with equal values in the maximum and minimum operation modes. And then establishing a model according to a multi-port external network equivalence method based on PMU measurement, solving external network equivalence parameters, performing reactive power optimization on the external network according to the external network equivalence parameters, calculating the boundary voltage reactive power supporting capacity of the external network equivalence network, and then selecting an effective equivalence method according to the reactive power supporting capacity. The method comprises the following specific steps:
1) Determining the number of m time instants
And determining the PMU time number required for solving the equivalent network parameters according to the number of ports connected with the internal network and the external network.
2mn＞n 2 +6n (1)
In the formula, n is the number of ports connected with the internal network and the external network, and m is the number of PMU sampling moments to be solved.
2) Inputting measured data
Inputting voltage measurement values of PMUs at boundary nodes at m momentsAnd the equivalent current measurement value injected into the inner network by each boundary node at m momentsWherein i =1, 2.. The n, n is the number of ports connected with the internal and external networks, and t = t 1 ,t 2 ,...,t m T is the PMU sampling time, and m is the total PMU sampling time.Andthere are m measurements.
3) Establishing an equivalent network measurement equation
Establishing a measurement equation of an equivalent network according to the voltage measurement and equivalent measurement input in the step 2)And
and withRespectively representing the real part and the imaginary part of the measurement equation at the ith boundary node at the time t. x = [ E = i,Re ,E i,Im ,Z i,Re ,Z i,Im ,Z ij,Re ,Z ij,Im ,S Li,Re ,S Li,Im ,B i ] T I =1, 2., n, j =1, 2.,. N, j ≠ i, x is an equivalent network parameter matrix to be solved, i represents the ith boundary node, j represents the jth boundary node, and n is the number of ports connected with the internal network and the external network. Wherein E i,Re And E i,Im Respectively corresponding to the ith boundary node, namely the real part and the imaginary part of the voltage of the equivalent virtual generator node, Z i,Re And Z i,Im Respectively the resistance and reactance, Z, of the equivalent branch corresponding to the ith boundary node ij,Re And Z ij,Im Are respectively asResistance and reactance, S, of the equivalent branch between the ith and jth boundary nodes Li,Re And S Li,Im Real and imaginary parts of the equivalent current, B, respectively, corresponding to the load at the ith boundary node i Is the corresponding ground branch at the ith boundary node.Andthe real part and the imaginary part of the voltage of the ith boundary node, respectively, the above expression t represents the t-th time,andthe real part and the imaginary part of the voltage of the ith boundary node are respectively. I is i,Re And I i,Im Respectively a real part and an imaginary part of the sum of the load equivalent current at the ith boundary node and the equivalent current injected into the inner network by the boundary node. Alpha and beta respectively representThe real and imaginary parts of (eta) and (mu) respectively representReal and imaginary parts of, wherein Z ij Is the equivalent impedance between boundary node i and boundary node j, Z ik Is the equivalent impedance between boundary node i and boundary node k, k =1, 2.
The above parameters can be seen in detail in the attached figure 1.
4) Establishing an equivalent parameter constraint equation
Equation (4) represents the equivalent parameter vector x of the equivalent network in the maximum operation mode of the input maxo ：
x maxo ＝[E i,maxo ,R i,maxo ,X i,maxo ,R ij,maxo ,X ij,maxo ,P Li,maxo ,Q Li,maxo ,B i,maxo ] T (4)
Equation (5) is expressed as the equivalent parameter vector x of the equivalent network in the input minimum operation mode mino ：
x mino ＝[E i,mino ,R i,mino ,X i,mino ,R ij,mino ,X ij,mino ,P Li,mino ,Q Li,mino ,B i,mino ] T (5)
Establishing equivalent parameter constraint equations of formulas (6) - (13) according to the equivalent parameters of the maximum and minimum operation modes:
B i,mino ≤B i '≤B i,maxo (6)
R i,maxo ≤Z i,Re '≤R i,mino (7)
X i,maxo ≤Z i,Im '≤X i,mino (8)
R ij,maxo ≤Z ij,Re '≤R ij,mino (9)
X ij,maxo ≤Z ij,Im '≤X ij,mino (10)
P Li,mino ≤S Li,Re '≤P Li,maxo (11)
Q Li,mino ≤S Li,Im '≤Q Li,maxo (12)
wherein B is i,mino And B i,maxo The equivalent ground branch corresponding to the ith boundary node in the minimum operation mode and the maximum operation mode, B i ' is the corresponding ground branch at the ith boundary node to be solved. R is i,mino And R i,maxo The resistance Z of the equivalent branch corresponding to the ith boundary node in the minimum operation mode and the maximum operation mode respectively i,Re ' is the resistance of the corresponding equivalent branch at the ith boundary node to be solved currently. X i,mino And X i,maxo Are respectively minimumReactance, Z, of the equivalent branch corresponding to the ith boundary node in the maximum operating mode i,Im ' is the reactance of the corresponding equivalent branch at the ith boundary node to be solved currently. R ij,mino And R ij,maxo The resistances of the equivalent branches between the ith boundary node and the jth boundary node in the minimum operation mode and the maximum operation mode, Z ij,Re ' is the resistance of the equivalent branch between the ith boundary node and the jth boundary node to be solved currently. X ij,mino And X ij,maxo Reactance, Z, of the equivalent branch between the ith and jth boundary nodes in the minimum and maximum operating modes, respectively ij,Im ' is the reactance of the equivalent branch between the ith boundary node and the jth boundary node to be solved currently. E i,min And E i,max The node voltages E of the equivalent virtual generators corresponding to the ith boundary node in the minimum operation mode and the maximum operation mode respectively i,Re ' and E i,Im ' are the real part and the imaginary part of the equivalent virtual generator node voltage corresponding to the ith boundary node to be solved. P is Li,mino And P Li,maxo The load active power, Q, at the ith boundary node in the minimum operation mode and the maximum operation mode respectively Li,mino And Q Li,maxo Load reactive power, S, at the ith boundary node in the minimum and maximum operating modes, respectively Li,Re ' and S Li,Im ' are the active power and reactive power of the equivalent load corresponding to the load at the ith boundary node to be solved, respectively.
5) Optimization model for establishing equivalent network
Equation (14) is an objective function of the equivalent network optimization model, where m is the number of PMU sampling times, and n is the number of ports connected to the internal and external networks.Andrespectively representing the real part and the imaginary part of the measurement equation at the ith boundary node at the time t. The optimization model of the equivalent network is formed by equations (6) to (14).
6) Solving external network equivalent parameters
Equations (6) - (14) constitute a nonlinear optimization problem for solving the external network equivalent parameters. And directly obtaining the external network equivalent parameter x by an interior point method.
7) Reactive power optimization model of equivalent external network
And establishing a reactive power optimization model of the equivalent external network according to the external network equivalent parameters in the step 6).
Establishing an objective function with minimum external network reactive loss:
minf E (Q G ,Q b ) (15)
in the formula, Q G Is an equivalent generator reactive power vector, Q b Is an equivalent ground branch reactive power vector.
Establishing a power balance equation of a reactive power optimization model:
in the formula, a and b are equal external network nodes, a =1,2, \8230, N, b =1,2, \8230, N, N are the total number of all nodes of the equal external network, P a And Q a Respectively injecting active power and reactive power into the node a; u shape a 、δ a The voltage amplitude and phase angle, U, at node a b 、δ b The voltage amplitude and phase angle at node b, respectively, where δ a,b ＝δ a -δ b ；G a,b 、B a,b The real part and the imaginary part of the item element of the a-th row and the b-th column of the node admittance matrix are respectively, and sin and cos are respectively a sine function and a cosine function.
Establishing an inequality constraint equation of a reactive power optimization model:
in the formula (I), the compound is shown in the specification,for the reactive power generated by the equivalent generator at node e,e＝1,2,...,N B ，N B in order to equal the total number of generators,andthe upper limit and the lower limit of the reactive power generated by the equivalent generator at the node e are set; u shape f Is the voltage amplitude at node f, f =1, 2.., N is the total number of equal value outer net nodes,andthe upper and lower limits of the voltage amplitude at the node f; solving the nonlinear optimization problem by using an interior point method to obtain Q b Wherein Q is bi ∈Q b ；Q bi And the reactive power of the equivalent ground branch at the node is obtained.
(8) Calculating the upper and lower limits of reactive power
The upper and lower limits of the reactive power of the equivalent grounding branch can be obtained through the equivalent grounding branch in the maximum and minimum operation mode of the external network;
Q bi,min ＝U i 2 B i,mino (20)
Q bi,max ＝U i 2 B i,maxo (21)
in formulae (20) and (21), B i,maxo And B i,mino The equivalent ground branches under the maximum operation mode and the minimum operation mode at the ith boundary node are respectively; u shape i Is the voltage amplitude at the ith boundary node; q bi,max And Q bi,min And the upper limit and the lower limit of the reactive power of the equivalent earth branch of the ith boundary node are respectively.
9) Selection of equivalence methods
If Q bi ≤Q bi,max If the boundary nodes have sufficient voltage reactive power supporting capacity, the external network is equivalent by using a simple PV equivalent method; if Q bi ≥Q bi,max And the boundary nodes do not have sufficient voltage reactive support capability, and the external network only adopts an external network equivalent method considering the comprehensiveness of elements.
After the technical scheme is adopted, the invention mainly has the following effects:
the method can accurately reflect the voltage reactive power supporting capability of the boundary node of the external network, thereby ensuring the correctness of static analysis of the power system. The method can select an effective equivalence method by considering the voltage reactive power supporting capacity at the boundary, and adopts the PV equivalence method when the PV equivalence method can be adopted, so that the calculation scale is reduced on the premise of ensuring the precision.
Drawings
FIG. 1 is an outer net equivalent network considering the comprehensiveness of the components;
fig. 2 is a division diagram of IEEE39 intra-and inter-node networks.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and examples, but it should not be construed that the scope of the above-described subject matter is limited to the examples. Various substitutions and modifications can be made without departing from the technical idea of the invention and the scope of the invention according to the common technical knowledge and the conventional means in the field.
As shown in an IEEE39 node internal and external network division diagram in fig. 2, the method for calculating the margin of reactive support of the external network equivalent network boundary voltage specifically comprises the following steps:
1) Determining the number of m time instants
And determining the time number required for solving the equivalent network parameters according to the number of ports connected with the internal network and the external network.
2mn＞n 2 +6n (1)
In the formula, n =2 is the number of ports connected with the internal and external networks, and m is the number of PMU sampling moments to be solved. And (3) calculating the result: m is greater than 4. In order to reduce the calculation amount on the premise of ensuring the existence of a solution, taking m =5.
2) Inputting measured data
Inputting voltage measurement values of PMU (phasor measurement Unit) at boundary nodes at m =5 momentsAnd equivalent current measurement value injected into the internal network by each boundary nodeWhere i =1,2,n =2 is the number of ports connected to the internal and external networks, and t = (t =) 1 ,t 2 ,…,t 5 ) T is the PMU sampling time, and m =5 is the total number of PMU sampling times. Wherein:
andthere were 5 measurements.
3) Establishing equivalent network measurement equation
And (3) establishing a measurement equation of the equivalent network according to the voltage measurement and equivalent measurement input in the step 2).
And withRespectively representing the real part and the imaginary part of the measurement equation at the ith boundary node at the time t. x = [ E = i,Re ,E i,Im ,Z i,Re ,Z i,Im ,Z ij,Re ,Z ij,Im ,S Li,Re ,S Li,Im ,B i ] T I =1,2, \8230;, n, j ≠ i, n =2, i represents the ith boundary node, j represents the jth boundary node, and since the number of nodes is large, the calculation process is described by taking i =1, j = 2. x is the equivalent network parameter matrix to be solved, where E i,Re And E i,Im The voltage real part and imaginary part, Z, of the equivalent virtual generator node corresponding to the 1 st boundary node i,Re And Z i,Im Respectively the resistance and reactance, Z, of the equivalent branch corresponding to the 1 st boundary node ij,Re And Z ij,Im The resistance and reactance, S, of the equivalent branch between the 1 st and the 2 nd boundary nodes, respectively Li,Re And S Li,Im Real and imaginary parts of the equivalent current, B, respectively, corresponding to the load at the 1 st boundary node i The corresponding ground branch at the 1 st border node.Andthe real part and imaginary part of the voltage of the 1 st boundary node, respectively, and the above equation t represents the t-th time, for example: when t = t 1 When it is, then Andrespectively the real part and imaginary part of the voltage of the 2 nd boundary node, whereinI i,Re And I i,Im Respectively a real part and an imaginary part of the sum of the load equivalent current at the 1 st boundary node and the equivalent current injected into the inner network by the boundary node, I i,Re ＝3.0482，I i,Im = -2.1872. Alpha and beta respectively representThe real and imaginary parts of (eta) and (mu) respectively representReal and imaginary parts of (c). It is provided withMiddle Z ij Is the equivalent impedance between boundary node 1 and boundary node 2, Z ik For equal impedance between border node 1 and border node k, k = (1, 2), and since k ≠ i, j, i.e., k ≠ 1,2, η and μ do not exist in the 2-port case.
The above parameters can be seen in detail in the attached figure 1. The input values at 5 moments are respectively substituted into the measurement equations of 2 ports, and then 20 measurement equations can be obtained.
4) Establishing an equivalent parameter constraint equation
Equation (4) represents the equivalence parameter vector x of the equivalence network in the maximum operation mode of the input maxo ；
x maxo ＝[E i,maxo ,R i,maxo ,X i,maxo ,R ij,maxo ,X ij,maxo ,P Li,maxo ,Q Li,maxo ,B i,maxo ] T (4)
Equation (5) is expressed as the equivalent parameter vector x of the equivalent network in the input minimum operation mode mino ；
x mino ＝[E i,mino ,R i,mino ,X i,mino ,R ij,mino ,X ij,mino ,P Li,mino ,Q Li,mino ,B i,mino ] T (5)
Establishing equivalent parameter constraint equations of formulas (6) - (13) according to the maximum and minimum operation mode equivalent parameters;
B i,mino ≤B i '≤B i,maxo (6)
R i,maxo ≤Z i,Re '≤R i,mino (7)
X i,maxo ≤Z i,Im '≤X i,mino (8)
R ij,maxo ≤Z ij,Re '≤R ij,mino (9)
X ij,maxo ≤Z ij,Im '≤X ij,mino (10)
P Li,mino ≤S Li,Re '≤P Li,maxo (11)
Q Li,mino ≤S Li,Im '≤Q Li,maxo (12)
when i =1,j =2, the calculation process is explained. Wherein B is i,mino =0.7248 and B i,maxo =1.0871 equal-value ground branch corresponding to 1 st boundary node in minimum operation mode and maximum operation mode, respectively, B i ' is the corresponding ground branch at the currently pending 1 st border node. R is i,mino =0.0055 and R i,maxo =0.0018 resistance of equivalent branch corresponding to 1 st boundary node in minimum operation mode and maximum operation mode, Z i,Re ' is the resistance of the corresponding equivalent branch at the 1 st boundary node to be solved currently. X i,mino =0.0054 and X i,maxo =0.0016 reactance of equivalent branch corresponding to 1 st boundary node in minimum operation mode and maximum operation mode, Z i,Im ' is the reactance of the corresponding equal-value branch at the currently sought 1 st boundary node. R is ij,mino =0.0107 and R ij,maxo =0.0025 resistance of equivalent branch between 1 st and 2 nd boundary nodes in minimum and maximum operation mode, respectively, Z ij,Re ' is the resistance of the equal-value branch between the 1 st boundary node and the 2 nd boundary node to be solved currently. X ij,mino =0.1671 and X ij,maxo =0.0295 reactance of equivalent branch between 1 st and 2 nd boundary nodes in minimum and maximum operation modes, respectively, Z ij,Im ' is the reactance of the equivalent branch between the 1 st boundary node and the 2 nd boundary node to be solved currently. E i,min =1.0 and E i,max =1.1 equivalent generator node voltages, E, corresponding to 1 st boundary node in minimum and maximum operating modes, respectively i,Re ' and E i,Im ' are the real part and imaginary part of the equivalent virtual generator node voltage corresponding to the 1 st boundary node to be solved. P is Li,mino =394.35Mw and P Li,maxo =693.34Mw for minimum mode and maximum mode of operation, respectivelyLoad active power, Q, at the 1 st boundary node in row mode Li,mino = -1.95Mvar and Q Li,maxo =14.49Mvar load reactive power, S, at 1 st border node in minimum and maximum mode of operation, respectively Li,Re ' and S Li,Im ' the active power and the reactive power of the equivalent load corresponding to the load at the 1 st boundary node to be solved are respectively.
5) Optimization model for establishing equivalent network
Equation (14) is an objective function of the equivalent network optimization model, where m =5 is the number of PMU sampling times, and n =2 is the number of ports connected to the internal and external networks.Andrespectively representing the real part and the imaginary part of the measurement equation at the ith boundary node at the time t. The optimization model of the equivalent network is formed by equations (6) to (14).
6) Solving external network equivalent parameters
Equations (6) - (14) constitute a nonlinear optimization problem for solving the outer net equivalent parameters. And directly obtaining the external network equivalent parameter x by an interior point method.
And (3) calculating a result: e 1 ＝1.0529∠0.1811，E 2 ＝1.0472∠-0.8853，Z 1,Re ＝0.0036，Z 1,Im ＝0.0373，Z 2,Re ＝0.0035，Z 2,Im ＝0.0490，Z 12,Re ＝0.0066，Z 12,Im ＝0.0943，S LI,Re ＝2.1501，S LI,Im ＝-2.558，S L2,Re ＝2.3980，S L2,Im ＝0.7484，B 1 ＝0.9061，B 2 ＝0.8503。
7) Reactive power optimization model of equivalent external network
And (5) establishing a reactive power optimization model of the equivalent external network according to the external network equivalent parameters in the step 6).
Establishing an objective function with minimum external network reactive loss:
minf E (Q G ,Q b ) (15)
in the formula, Q G Is an equivalent generator reactive power vector, Q b Is an equivalent ground branch reactive power vector.
Establishing a power balance equation of a reactive power optimization model:
in the formula, a and b are equal external network nodes, a =1,2, \8230, N, b =1,2, \8230, N, N are the total number of all nodes of the equal external network, P a And Q a Respectively injecting active power and reactive power into the node a; u shape a 、δ a The voltage amplitude and phase angle, U, at node a b 、δ b The amplitude and phase angle of the voltage at node b, respectively, where δ a,b ＝δ a -δ b ；G a,b 、B a,b The real part and the imaginary part of the item element of the a-th row and the b-th column of the node admittance matrix are respectively, and sin and cos are respectively a sine function and a cosine function.
Establishing an inequality constraint equation of a reactive power optimization model:
in the formula (I), the compound is shown in the specification,for the reactive power generated by the equivalent generator at node e,e＝1,2,...,N B ，N B in order to equal the total number of generators,andthe upper limit and the lower limit of the reactive power generated by the equivalent generator at the node e are set; u shape f Is the voltage amplitude at node f, f =1, 2.., N is the total number of equal value outer net nodes,andthe upper and lower limits of the voltage amplitude at the node f; solving the nonlinear optimization problem by using an interior point method to obtain Q b Wherein Q is bi ∈Q b ；Q bi And the reactive power of the equivalent ground branch at the node is obtained.
And (3) calculating the result: q b1 ＝179.33Mvar，Q b2 ＝153.47Mvar。
8) Calculating the upper limit of reactive power
The upper and lower limits of the reactive power of the equivalent grounding branch can be obtained through the equivalent grounding branch in the maximum and minimum operation mode of the external network.
Q bi,min ＝U i 2 B i,mino (20)
Q bi,max ＝U i 2 B i,maxo (21)
In equations (20) and (21), assuming that i =1, the entire calculation process is described. Then B is i,maxo =1.0871 and B i,mino =0.7248 is the equivalent ground branch at the maximum minimum operating mode at node 1. U shape i = voltage amplitude at node 1. Q bi,max And Q bi,min Respectively is the upper limit and the lower limit of the equivalent ground branch reactive power at the node 1.
And (3) calculating the result: q b1,max ＝108.76Mvar，Q b2,max ＝102.00Mvar
9) Selection of equivalent methods
If Q is bi ≤Q bi,max Then the boundary nodes are considered to have sufficient voltage reactive support capability, and the outer net can be used as a simple PV equivalent method equivalent. If Q is bi ≥Q bi,max And the boundary nodes are considered to have insufficient voltage reactive support capability, and the external network can only adopt an external network equivalent method considering the element comprehensiveness.
And (3) calculating a result: q b1 ＝179.33Mvar，Q b1,max ＝108.76Mvar，Q b2 ＝153.47Mvar，Q b2,max =102.00Mvar, known as Q bi ≥Q bi,max And considering that the boundary nodes do not have sufficient voltage reactive support capability, and adopting an external network equivalent method only considering the comprehensiveness of elements for the external network.
Test effects
The method adopts an external network equivalence method considering the comprehensiveness of elements to calculate the boundary reactive voltage support abundance of the external network equivalence network, selects an effective equivalence method, and applies the equivalence method to the effectiveness of the reactive power optimization verification selection equivalence method. Specifically, reactive power optimization is calculated through an element comprehensive external network equivalence method, a PQ equivalence method and a PV equivalence method, then the reactive power optimization is compared with a total network calculated reactive power optimization result, a relative error and an absolute error are obtained, and experimental examples are that an IEEE39 node system (C1) and an IEEE39 system (C2) with sufficient voltage reactive power supporting capability are constructed through the external network. The table 1 shows the calculation results of the reactive voltage support of the outer network equivalent network boundary, and the table 2 shows the error results of the reactive power output of the generator in reactive power optimization by different equivalent methods under an IEEE39 node system. And the table 3 shows the reactive power output error results of the power generator with different equivalent methods and reactive power optimization after IEEE39 reconstruction.
TABLE 1 reactive power output results at boundary nodes under different systems
From Table 1, Q is found in the case of C1 bi ≥Q bi,max And the boundary nodes are considered to have insufficient voltage reactive support capability, and the external network can only adopt an external network equivalent method considering the element comprehensiveness.
TABLE 2 reactive power output error result of power generator with reactive power optimization by different equivalence methods of IEEE39 node system
The results in table 2 also illustrate that the outer net equivalent method considering the comprehensiveness of the components has the smallest error; in the case of C2, Q is known bi ≤Q bi,max The outer net can be used as a simple PV equivalence method equivalent.
TABLE 3 reactive power output error result of generator reactive power optimization by different equivalence methods of IEEE39 construction node system
It can also be seen from table 3 that the PV equivalent method has minimal error with the external grid equivalent method taking the element comprehensiveness into account, but the PV method is simpler and therefore the PV equivalent method is used. The correctness of the results is proved.
From the experimental results, it can be seen that:
the method can accurately reflect the voltage reactive power supporting capability of the boundary node of the external network, thereby ensuring the correctness of the static analysis of the power system. The method can select an effective equivalence method by considering the voltage reactive support capacity at the boundary, and adopt the PV equivalence method when the PV equivalence method can be adopted, thereby reducing the calculation scale on the premise of ensuring the precision.

Claims (1)

1. The method for calculating the margin of reactive power support of the boundary voltage of the external network equivalent network is characterized by comprising the following steps of: the method comprises the following specific steps;
1) Determining the number of m time instants
Determining PMU time number required for solving equivalent network parameters through a formula (1) according to the number of ports connected with an internal network and an external network;
2mn＞n 2 +6n (1)
in the formula, n is the number of ports connected with the internal network and the external network, and m is the number of PMU sampling moments to be solved;
2) Inputting measured data
Inputting voltage measurement values of PMUs at boundary nodes at m momentsAnd the equivalent current measurement value injected into the inner network by each boundary node at m momentsWherein i =1, 2.. Said, n, n is the number of ports connected to the internal and external networks, and t = t 1 ,t 2 ,...,t m T is PMU sampling time, and m is the total PMU sampling time number;
3) Establishing equivalent network measurement equation
Establishing a measurement equation of an equivalent network according to the voltage measurement and equivalent measurement input in the step 2)And
andrespectively representing the real part and the imaginary part of a measurement equation at the ith boundary node at the time t, and x = [ E = [ i,Re ,E i,Im ,Z i,Re ,Z i,Im ,Z ij,Re ,Z ij,Im ,S Li,Re ,S Li,Im ,B i ] T I =1, 2., n, j =1, 2.,. N, j ≠ i, x is an equivalent network parameter matrix to be solved, i represents the ith boundary node, j represents the jth boundary node, and n is the number of ports connected with the internal network and the external network; wherein E i,Re And E i,Im Respectively providing a real part and an imaginary part of the voltage of the equivalent virtual generator node corresponding to the ith boundary node; z is a linear or branched member i,Re And Z i,Im Respectively the resistance and reactance of the equivalent branch corresponding to the ith boundary node; z is a linear or branched member ij,Re And Z ij,Im Respectively setting the resistance and reactance of an equivalent branch between the ith boundary node and the jth boundary node; s Li,Re And S Li,Im The real part and the imaginary part of the equivalent current corresponding to the load at the ith boundary node respectively; b is i A corresponding ground branch at the ith boundary node;andthe voltage real part and the voltage imaginary part of the ith boundary node are respectively;andthe real part and the imaginary part of the voltage of the jth boundary node are respectively, and t represents the tth moment; I.C. A i,Re And I i,Im Respectively a real part and an imaginary part of the sum of the load equivalent current at the ith boundary node and the equivalent current injected into the inner network by the boundary node; alpha and beta respectively representThe real part and the imaginary part of (eta) and (mu) respectively representReal and imaginary parts of (1), wherein Z ij Is the equivalent impedance between boundary node i and boundary node j, Z ik Is the equivalent impedance between the boundary node i and the boundary node k, k =1, 2.. The n, k ≠ i, j;
4) Establishing an equivalent parameter constraint equation
Equation (4) represents the equivalent parameter vector x of the equivalent network in the maximum operation mode of the input maxo ；
x maxo ＝[E i,maxo ,R i,maxo ,X i,maxo ,R ij,maxo ,X ij,maxo ,P Li,maxo ,Q Li,maxo ,B i,maxo ] T (4)
Equation (5) represents the equivalent parameter vector x of the equivalent network in the minimum operation mode of input mino ；
x mino ＝[E i,mino ,R i,mino ,X i,mino ,R ij,mino ,X ij,mino ,P Li,mino ,Q Li,mino ,B i,mino ] T (5)
Establishing equivalent parameter constraint equations of formulas (6) - (13) according to the equivalent parameters of the maximum and minimum operation modes;
B i,mino ≤B i '≤B i,maxo (6)
R i,maxo ≤Z i,Re '≤R i,mino (7)
X i,maxo ≤Z i,Im '≤X i,mino (8)
R ij,maxo ≤Z ij,Re '≤R ij,mino (9)
X ij,maxo ≤Z ij,Im '≤X ij,mino (10)
P Li,mino ≤S Li,Re '≤P Li,maxo (11)
Q Li,mino ≤S Li,Im '≤Q Li,maxo (12)
wherein B is i,mino And B i,maxo Equivalent ground branches corresponding to the ith boundary node in the minimum operation mode and the maximum operation mode respectively; b is i ' is a corresponding ground branch at the ith boundary node to be solved currently; r is i,mino And R i,maxo The resistances of the equivalent branches corresponding to the ith boundary node in the minimum operation mode and the ith boundary node in the maximum operation mode respectively; z i,Re ' is the resistance of the corresponding equivalent branch at the ith boundary node to be solved; x i,mino And X i,maxo The reactance of the equivalent branch corresponding to the ith boundary node in the minimum operation mode and the reactance of the equivalent branch corresponding to the ith boundary node in the maximum operation mode are respectively obtained; z i,Im The reactance of a corresponding equivalent branch at the ith boundary node to be solved currently is' obtained; r is ij,mino And R ij,maxo The resistances of the equivalent branch circuits between the ith boundary node and the jth boundary node in the minimum operation mode and the maximum operation mode respectively; z ij,Re ' is the resistance of the equivalent branch between the ith boundary node and the jth boundary node to be solved currently; x ij,mino And X ij,maxo The reactance of an equivalent branch between the ith boundary node and the jth boundary node in the minimum operation mode and the maximum operation mode respectively; z ij,Im ' is the reactance of an equivalent branch between the ith boundary node and the jth boundary node to be solved currently; e i,min And E i,max The node voltages of equivalent virtual generators corresponding to the ith boundary node in the minimum operation mode and the ith boundary node in the maximum operation mode respectively; e i,Re ' and E i,Im The real part and the imaginary part of the equivalent virtual generator node voltage corresponding to the ith boundary node to be solved are respectively; p Li,mino And P Li,maxo Load active power at the ith boundary node in the minimum operation mode and the maximum operation mode respectively; q Li,mino And Q Li,maxo Load reactive power at the ith boundary node in the minimum operation mode and the maximum operation mode respectively; s Li,Re ' and S Li,Im Respectively obtaining the active power and the reactive power of equivalent load corresponding to the load at the ith boundary node to be solved;
5) Optimization model for establishing equivalent network
Establishing an objective function of the equivalent network optimization model by using a formula (14);
in the formula, m is the PMU sampling time number, and n is the number of ports connected with the internal network and the external network;andrespectively representing a real part and an imaginary part of a measurement equation at the ith boundary node at the time t;
6) Solving external network equivalent parameters
Directly obtaining an external network equivalent parameter x by an interior point method;
7) Reactive power optimization model of equivalent external network
Establishing a reactive power optimization model of the equivalent external network according to the external network equivalent parameters in the step 6);
establishing a target function with minimum external network reactive loss;
minf E (Q G ,Q b ) (15)
in the formula, Q G Is an equivalent generator reactive power vector, Q b Is an equivalent earth branch reactive power vector;
establishing a power balance equation of a reactive power optimization model;
in the formula, a and b are equivalent external network nodes, a =1, 2., N, b =1,2, \8230, N and N are the total number of the equivalent external network nodes, P a And Q a Respectively injecting active power and reactive power into the node a; u shape a 、δ a The voltage amplitude and phase angle, U, at node a b 、δ b The voltage amplitude and phase angle at node b, respectively, where δ a,b ＝δ a -δ b ；G a,b 、B a,b Respectively being the real part and the imaginary part of the item elements of the a-th row and the b-th column of the node admittance matrix, sin and cos being respectively a sine function and a cosine function;
establishing an inequality constraint equation of a reactive power optimization model;
in the formula (I), the compound is shown in the specification,for the equivalent reactive power generated by the generator at node e,e＝1,2,...,N B ，N B is the total number of the equivalent generators,andthe upper limit and the lower limit of the reactive power generated by the equivalent generator at the node e are set; u shape f Is the voltage magnitude at node f, f =1, 2., N is the total number of equal value outer net nodes,andthe upper and lower limits of the voltage amplitude at the node f; solving the nonlinear optimization problem by an interior point method to obtain Q b Wherein Q is bi ∈Q b ；Q bi The reactive power of the equivalent earth branch at the node is obtained;
8) Calculating the upper and lower limits of reactive power
The upper and lower limits of the reactive power of the equivalent grounding branch can be obtained through the equivalent grounding branch in the maximum and minimum operation mode of the external network;
Q bi,min ＝U i 2 B i,mino (20)
Q bi,max ＝U i 2 B i,maxo (21)
in formulae (20) and (21), B i,maxo And B i,mino Equivalent ground branches under the maximum and minimum operation modes at the ith boundary node respectively; u shape i Is the voltage amplitude at the ith boundary node; q bi,max And Q bi,min Respectively setting the upper limit and the lower limit of the reactive power of the equivalent ground branch of the ith boundary node;
9) Selection of equivalent methods
If Q is bi ＜Q bi,max If the boundary node has sufficient voltage reactive support capability, the external network is equivalent by using a simple PV equivalent method; if Q bi ＞Q bi,max And the boundary nodes do not have sufficient voltage reactive support capability, and the external grid can only adopt an external grid equivalent method considering the comprehensiveness of elements.
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