CN111900736B - Power distribution network load flow calculation method based on improved forward-backward substitution method - Google Patents
Power distribution network load flow calculation method based on improved forward-backward substitution method Download PDFInfo
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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
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- H—ELECTRICITY
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
Abstract
A power flow calculation method of a power distribution network by a forward-backward substitution method is improved, and belongs to the field of power distribution. Firstly, generating a corresponding power distribution network related parameter table, fully automatically numbering each node of a power distribution network, and generating a matrix A and a matrix B by adopting iterative node scale simplification processing so as to realize special processing on PV nodes; the node injection power is replaced by the node injection current to avoid calculating branch power losses at each iteration of the calculation. The power distribution network can be changed into a simple single-line diagram, so that the system scale is reduced; the node injection power in the regeneration process is replaced by the node injection current, so that the time for calculating the branch loss can be saved; the power distribution network containing the PV nodes is effectively processed through the reactive power correction equation of the PV nodes, and the problem that the PV nodes in the power distribution network system cannot be processed in the prior art is solved; under the condition of calculating the same configuration network, the method has the advantages of smaller error, better accuracy and higher calculation speed. The method can be widely applied to the field of planning and management of the power distribution network.
Description
Technical Field
The invention belongs to the field of power distribution, and particularly relates to a power flow calculation method for a power distribution network.
Background
With the rapid development of the electric power industry in China, the structure of an electric power system is more and more complex, but the development of a power distribution network is at a relatively lagged level, so that the automatic construction of the power distribution network becomes one of the important subjects of the current electric power system research. The load flow calculation, one of the most basic calculations for power system research, can not only provide running state information for scheduling, but also determine the performance of all other high-level application software depending on the calculation result.
The current power distribution network load flow calculation method mainly comprises the following steps: an improved Newton-Raphson method, an improved PQ decoupling method, a loop impedance method, a forward-backward substitution method and the like.
The Newton-Raphson method and the improved PQ decoupling method have the advantages that due to the fact that the principle of the Newton-Raphson method and the improved PQ decoupling method is definite, when the Newton-Raphson method and the improved PQ decoupling method are directly applied to power flow calculation of a power distribution network, the convergence is poor, and the calculation error is large; the loop impedance method is mainly applied to processing a ring network structure, has good convergence, but has complex node and branch numbering processing and large calculation amount; and aiming at the characteristics of the radial structure of the power distribution network, the forward-backward substitution method is one of the optimal algorithms for power flow calculation of the power distribution network, and has good convergence and calculation speed.
The traditional forward-backward substitution method needs to number nodes and branches of a network before calculation, and has the possibility of errors in a complex power distribution network, so that an automatic numbering method is proposed in the documents of 'a forward-backward substitution method applicable to multi-power distribution network power flow calculation' (Lexingan et al. & electric power system and automation bulletin thereof 2017,29(12): 121-plus 125.) and 'a forward-backward substitution method applicable to low-voltage distribution network power flow calculation' (Zhang Xiaomin et al. & hydro-electric energy science 2016,34(09): 183-plus 186+70.), but the method does not consider the influence of increasingly increased distributed power sources on the power distribution network; the document indicates that the difference between the reactive value and the actual value of the conventional forward-backward substitution method is often large, which increases the final calculation error and affects the iteration result, so that the PV nodes need to be converted into PQ nodes, and then the reactive and voltage equations are processed, however, the convergence of the power flow calculation is poor when all the PV nodes are converted into PQ nodes.
Disclosure of Invention
The invention aims to provide a power distribution network load flow calculation method with an improved forward-backward substitution method. Aiming at the defects of a push-back substitution method before the current power distribution network load flow calculation, an automatic node numbering method is provided, forward traversal and reverse traversal of nodes are realized, the calculation speed is improved, and the occupied computer memory is reduced; aiming at a special structure of a power distribution network, iterative node scale simplification processing is adopted, the load of the low-voltage side of a transformer is converted into the load of the high-voltage side for iterative calculation, nearly half of nodes and branches can be eliminated, and the calculation efficiency of an algorithm is greatly improved; and judging whether the PV node can be calculated as the PQ node or not on the basis of distinguishing the PQ node, the PV node and the balance node by adopting a node automatic numbering method, and further carrying out special processing on the PV node.
The technical scheme of the invention is as follows: the method for calculating the power flow of the power distribution network comprises the following steps of performing power flow calculation of the power distribution network by adopting a forward-backward substitution method, and is characterized in that the method is performed according to the following modes when the power flow calculation of the power distribution network is performed:
1) firstly, drawing a system node structure diagram of a power distribution network, and generating a corresponding power distribution network related parameter table by looking up impedance parameters of related lines, impedance of each branch and load of each node;
2) the node numbering processing rules are adopted to carry out full-automatic numbering on each node of the power distribution network, the node type is determined, and PV nodes are automatically identified;
3) generating a matrix A and a matrix B by adopting iterative node scale simplification processing according to a related parameter table of the power distribution network, and performing load flow calculation by utilizing the matrix A and the matrix B in cooperation with a traditional forward-backward substitution method;
4) converting the low-voltage side load of the transformer into a high-voltage side load for iterative computation by adopting a practical processing mode of simplifying the scale of iterative nodes through simple equivalent operation, so that the nodes participating in the iterative computation only contain all the high-voltage side nodes of the transformer branch and do not contain the low-voltage side nodes of the transformer branch, and further special processing on the PV nodes is realized;
5) in the algorithm back-substitution process, the node injection power is replaced by the node injection current, so that the branch power loss is prevented from being calculated during each iterative calculation, and the calculation speed is increased;
the power distribution network load flow calculation method can change a power distribution network into a simple single line diagram, thereby reducing the system scale; the node injection power in the regeneration process is replaced by the node injection current, so that the time for calculating the branch loss can be saved; the power distribution network containing the PV nodes is effectively processed through the reactive power correction equation of the PV nodes, and the problem that the PV nodes in the power distribution network system cannot be processed in the prior art is solved; under the condition of calculating the same configuration network, the method has the advantages of smaller error, better accuracy and higher calculation speed.
Wherein, the node numbering process comprises: naming nodes, starting from a root node along the direction of a radiation feeder, wherein the nodes connected with the root node through branches are child nodes of the root node, the root node is a father node of the node, and if one node is connected with different nodes through different branches, the nodes are brother nodes; and forming a node data table through node traversal, wherein the table needs to record the load, the node voltage and the node type of a father node, and also needs to record the load, the node voltage, the node type information of a child node and relevant parameters of a branch between two points.
Specifically, the node types include PQ nodes and PV nodes; the relevant parameters of the branch between the two points at least comprise branch impedance, branch current or power.
Specifically, when the load flow calculation is performed, an n × 2 matrix is generated in the calculation process, n is the number of network nodes, after a certain node is calculated, a corresponding second column in the matrix is automatically marked with 1, and the node marked with 1 skips the calculation, so as to avoid calculation errors caused by repeated calculation of the same node.
Furthermore, the matrix A is an a x b matrix, a is the number of the terminal nodes of the network, b is the number of the network nodes, and the number behind the leaf node in the matrix represents the number of the node passing through the shortest path from the leaf node to the root node; the matrix B is a matrix of c multiplied by d, c is the number of nodes in the network, and d is the number of nodes with the most child nodes in a father node in the network.
Further, when the iterative computation is performed, the iterative computation is performed according to the following conversion formula:
wherein, P1、Q1Active and reactive power, P, for the high-voltage side of the transformer2、Q2Active and reactive power, Δ P, for the low-voltage side of the transformer0、ΔPkRated no-load loss and rated short-circuit loss in a transformer nameplate parameter table, I0％、Us% is the percent of no-load current and the percent of short circuit voltage; u shape1、UNAnd SNThe voltage, the rated voltage and the rated capacity of the high-voltage side of the transformer are respectively; u shapes％、Ur% is the resistance and reactance when the current value in the transformer is exactly equal to the nominal current valuePercentage of voltage drop over.
Further, the special processing on the PV nodes includes reactive power modification of the PV nodes, and the reactive power modification of the PV nodes includes the following specific steps:
1) setting the initial value of reactive power output of the PV node power supply to be 0, and converting the initial value of the reactive power output into a PQ node;
2) calculating the calculated voltage of the upper-layer parent node connected with the PV node through load flow calculation;
3) and (3) solving the correction quantity of the reactive power output of the PV node accessed to the power supply by the calculated voltage of the parent node of the PV node, the impedance of the branch circuit connecting the PV node and the parent node thereof, and the constant voltage and the active power of the PV node:
wherein, λ is the calculation step length, -1<λ<1, generally taking the value of 0.1; q2、P2Calculating reactive power and active power for the PV node; qdReactive power for all branches and nodes connected to the PV node; u shaper1、Ur2The total node voltage component of the PV node and the father node thereof; u shape2An input voltage at the PV node; r, X is the impedance on the branch between the PV node and its parent node;
4) if the forward pushing is carried out for load flow calculation convergence, the convergence reactive power of the PV node can be obtained; otherwise, correcting the reactive power output of the PV node accessed power supply according to the formula, and turning to the step 2) to continue the next iterative calculation.
According to the technical scheme, all nodes of the power distribution network are numbered fully automatically through the power distribution network related parameter table, the matrix A and the matrix B, forward traversal and reverse traversal of the nodes are achieved, the calculation speed can be increased when power distribution network load flow calculation with more nodes is processed, matrix operation is not needed when a complex power distribution network is met, and meanwhile PV nodes can be identified automatically.
According to the technical scheme, the low-voltage side load of the transformer is converted into the high-voltage side load of the transformer for iterative computation by simplifying a practical processing mode of iterative node scale, so that a power distribution network is changed into a simple single line diagram, and the system scale is reduced; the occupied space of the computer memory is small, the trouble of nodes at the low-voltage side of the iterative transformer can be saved, the number of iterative nodes is greatly reduced, and the calculation speed is favorably accelerated;
according to the technical scheme, in the algorithm back-substitution process, the node injection power is replaced by the node injection current, so that the branch power loss is prevented from being calculated during each iterative calculation, and the calculation speed is convenient to increase.
Compared with the prior art, the invention has the advantages that:
1. the technical scheme of the invention provides a new method for automatically numbering nodes, which can realize forward traversal and reverse traversal of the nodes, save numbering time by generating three special matrixes, improve calculation speed and reduce the memory occupied by a computer;
2. the technical scheme provides an iterative node scale simplification method aiming at a special structure of a power distribution network, nearly half of nodes and branches are eliminated through pretreatment, the calculated amount is reduced, and the calculation efficiency is improved;
3. by adopting the technical scheme, on the basis that the PQ nodes, the PV nodes and the balance nodes can be distinguished by the automatic node numbering method, the PV node processing method is provided, and distribution network load flow calculation including the PV nodes is realized;
4. in a 10kV system, the PV nodes can be processed to control the error to be about +/-3%, and the error is much smaller than that of the traditional forward-backward substitution method.
Drawings
FIG. 1 is a schematic diagram of a 10kV power distribution system;
FIG. 2 is a simplified schematic diagram of a 10kV power distribution system;
FIG. 3 is a schematic diagram of reactive iterative computation of PV nodes;
fig. 4 is a schematic diagram of an IEEE33 node system.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Transmission and distribution networks also have the function of transmitting electricity, but their voltage levels and parameters are very different. The voltage class of the power transmission network is generally 110kV or above, and the power transmission network plays a role in long-distance power transmission; the distribution network is connected with a step-down transformer, electric energy is distributed to users after voltage reduction, the voltage level of the users is below 110kV, the users generally adopt closed-loop design and open-loop operation, the structure is generally a radiation network, the branch ratio is large, the number of branch lines is large, and the R/X ratio is large.
Therefore, the traditional gaussian-zehnder iteration method and the newton iteration method for calculating the power flow of the power transmission system have the serious problems of incapability of convergence and the like, and cannot be applied to complex power distribution networks.
The existing power distribution network load flow algorithm is mainly divided into two types, the first type is a bus type algorithm, the algorithm uses the injection amount of a bus as an independent variable, so that a load flow equation can be written, such as a Zbus algorithm and a Ybus algorithm, wherein the Zbus method has strong capacity of processing branch and ring networks of a power distribution network, the convergence speed of the Zbus method is close to that of a Newton method, but the method has weak capacity of processing PV nodes of the power distribution network, ignores the three-phase asymmetry problem of balance nodes, and has larger calculated amount. The second type is a branch method, and the algorithm is formed by taking data such as branch impedance of a power distribution system as a research target, and has the characteristics of simple and convenient programming, high convergence rate, strong numerical stability, small error and the like. Such methods include loop methods and push-back methods, wherein the push-back method is advantageous in processing power distribution networks with low complexity, because other algorithms integrate the entire power distribution system and form an admittance matrix, which can effectively process branches in the network, but this results in reduced computation speed and large memory space.
In the following, the power flow algorithm of each distribution network is analyzed from different aspects.
(1) Convergence rate of algorithm:
as an algorithm, the convergence rate of the algorithm is the most important one of the evaluation indexes, and the importance degree thereof is self-evident. The improved Newton-Raphson method has the principle that a nonlinear equation is converted into repeated solution of a corresponding linear equation through certain transformation, and is a second-order algorithm, so that the method has the characteristic of square convergence, an infinite approximation and accurate value can be quickly found in iteration of a unit number, and other algorithms are first-order algorithms and cannot achieve second-order convergence speed.
(2) Stability:
in a power distribution network, the influence of the network structure of the power system, line parameters and various disturbance factors on the output result of the algorithm is the stability. Since the newton-raphson algorithm is a second-order algorithm, it will be greatly affected, which is one of the main reasons that the power distribution network algorithm first excludes the traditional newton-raphson algorithm. The Newton Raphson method is also influenced by the high R/X ratio of the power distribution network, so that a calculation result close to the reality cannot be output, the influence of other algorithms is much smaller, and the influence of the forward-backward substitution method is the minimum.
(3) Complexity of the algorithm:
the algorithm using the simple principle is often most reliable, the forward-backward substitution method does not need to calculate the node admittance matrix during programming, the formula is simple, and the calculation efficiency is high.
In conclusion, the principle of the push-back method is closer to the structure of an actual power distribution network, the capability of the push-back method in processing the ring network structure is weaker, but the power distribution network is mainly characterized in that the power distribution network is radial in operation, and therefore the power distribution network is not greatly influenced. In addition, the method has small calculation error, is simple and direct, has short calculation time, can still ensure that an effective result is input when the system is abnormal, has convergence performance not influenced by the high R/X value of the power distribution network, and is widely used as a main algorithm for calculating the power flow of the power distribution network at present.
In addition, when carrying out load flow calculation of the distribution network, the concept of PQ nodes, PV nodes and buffer nodes is usually involved:
the PQ node is a node where the known node injects active power P and reactive power Q. The unknowns to be solved are the node voltage value U and the phase angle δ. Generally, a substation bus without power generation equipment and a power plant bus with fixed output can be used as a PQ node. Such nodes are a large part of the power system.
The PV node is the node where the known node injects the active power P and the voltage value U. The unknowns to be solved are the node injection reactive Q and the phase angle δ of the voltage. Such nodes are typically power plant buses with sufficient reactive reserve and substation buses with a certain reactive power supply.
The buffer node is a node in the balance node and is a node with a known phase angle delta of the voltage value U. What is required is the injected power (including active power P and reactive power Q) of the node. Generally, only one balancing node is arranged, and the balancing node is generally selected to be a power plant bus which plays a role of frequency regulation.
The principle of the technical solution of the present invention will be described below by taking the 10kV power distribution system shown in fig. 1 as an example.
The technical scheme is improved to a certain extent aiming at the defects of the common forward-backward substitution method, and mainly comprises three parts, namely node numbering processing, iterative node scale simplification processing and PV node special processing.
In fig. 1, there is a PV node 7 in the distribution network, assuming that its active power P is 126.25kW and its voltage V is 10.418 kV. The reference voltage of the head end of the power supply network is 10.5kV, and the reference value of three-phase power is 10 MVA.
By looking up the impedance parameters of the relevant lines, the impedance of each branch and the load of each node are shown in table 1.
Table 110kV distribution network related parameter
1. And (3) processing node numbers:
the nodes are named, starting from the root node along the direction of the radiation feeder, the nodes connected with the root node through the branches are child nodes of the root node, the root node is a father node of the node, and if one node is connected with different nodes through different branches, the nodes are brother nodes.
Through node traversal, a data table can be formed, and the table needs to record not only the load, node voltage and node type (such as PQ node and PV node) of a parent node, but also the load, node voltage, node type and other information of a child node (set) and related parameters (branch impedance, branch current or power) of a branch between two points.
As is known, the calculation can be started only by numbering nodes before calculation by a forward-backward substitution method, and the technical scheme can realize full-automatic numbering of each node of a power distribution network and forward traversal and reverse traversal of the nodes by the method, so that the calculation speed can be accelerated when the power distribution network load flow calculation with more nodes is processed, matrix calculation is not needed when a complex power distribution network is encountered, and meanwhile PV nodes can be automatically identified.
In fact, there is also a method that does not require the advance numbering of the distribution network, illustrated in the present solution in simplified form in fig. 1-fig. 2.
First, matrix a and matrix B are generated according to table 1. The matrix a is an a × b matrix, a is the number of the endmost child nodes (leaf nodes) of the network, in this example, four nodes, i.e., nodes 5, 8, 9, and 10, a is 4, b is the number of network nodes, and the number after the leaf node in the matrix represents the number of nodes that pass through from the leaf node to the root node via the shortest path. The resulting matrix is shown in table 2:
TABLE 2 matrix A
Matrix B is a c × d matrix, c is the number of nodes in the network, d is the number of nodes whose parent node has the most child nodes in the network, where d is 2, and the formed B matrix is shown in table 3:
TABLE 3 matrix B
The specific process comprises the following steps: matrix a and matrix B are generated in sequence from the network parameter map of table 1. Since the calculation is performed by a computer, a programming statement for generating the two matrices must be designed.
The specific generation method of the matrix A and the matrix B comprises the following steps: for the matrix a, firstly, the node numbers only appearing in the third column but not appearing in the second column in table 2 are found and are coded in the first column of the matrix a, so as to find the endmost node in the network system, then, a node search is performed on the node found in the previous step, for example, 5 nodes are found in the third column of table 3, the parent node 4 of 5 nodes is recorded, then, the parent node 3 of 4 nodes is found according to the method, and so on, the finally obtained line 5 → 4 → 3 → 2 → 1 → 0 returning to the following node 0 along the shortest path from 5 nodes is completed, and other lines can generate the matrix a according to the method; for the matrix B, the first column is numbered according to the node numbers 0-10, the child nodes of the matrix B are sequentially found, for example, the node 2 appears twice in the second column of the table 2, and therefore the third columns 3 and 6 of the two rows are recorded behind the node 2 of the matrix B, and the matrix B can be generated by analogy.
Then, load flow calculation is carried out by utilizing the matrixes to match with a traditional forward-backward substitution method, an n multiplied by 2 matrix is generated in the calculation process, n is the number of network nodes, a corresponding second column in the matrix is automatically marked as 1 after a certain node is calculated, and the node marked with 1 skips the calculation, so that the calculation error caused by repeated calculation of the same node can be avoided.
In conclusion, the technical scheme can improve the calculation speed by changing the principle of the algorithm and numbering or naming the nodes by means of computer programming, and meanwhile, relevant parameters such as matrixes and the like used in the method do not occupy too high computer memory.
2. Simplifying the size of the iteration nodes:
aiming at a two-winding transformer commonly used by a power distribution network, the topological structure of the two-winding transformer can be equivalent to a line, and in addition, in order to be matched with the existing line loss calculation program, the technical scheme only contains all high-voltage side nodes of a transformer branch circuit and does not contain low-voltage side nodes in consideration of nodes participating in iteration in practical processing. Therefore, compared with the existing calculation method, nearly half of calculation nodes and calculation branches can be reduced, and the calculation efficiency of the algorithm can be greatly improved.
Therefore, in the technical scheme, before calculation, the load on the low-voltage side of the transformer needs to be converted into the load on the high-voltage side for iterative calculation.
The specific conversion formula is as follows:
wherein, P1、Q1Active and reactive power, P, for the high-voltage side of the transformer2、Q2Active power and reactive power at the low-voltage side of the transformer; delta P0、ΔPkRated no-load loss and rated short-circuit loss in a transformer nameplate parameter table; i is0％、Us% is the percent of no-load current and the percent of short circuit voltage; u shape1、UNAnd SNThe voltage, the rated voltage and the rated capacity of the high-voltage side of the transformer are respectively; u shapes％、Ur% is the percentage of the voltage drop across the resistance and reactance when the current value in the transformer is exactly equal to the nominal current value.
The practical processing mode for simplifying the iterative node scale converts the load of the low-voltage side to the high-voltage side through simple equivalent operation, the occupied space of a computer memory is small, the trouble of iterating the low-voltage side node can be saved, the number of iterated nodes is greatly reduced, and the calculation speed is accelerated.
In addition, in the algorithm back-substitution process, the node injection power is replaced by the node injection current, the power loss of a branch circuit can be prevented from being calculated during each iterative calculation, and the calculation speed is increased.
3. The special processing method of the PV node comprises the following steps:
with the rapid development of Distributed Generation (DG) technology, a conventional power distribution system has only one power source and is radially Distributed, and the access of the Distributed power source has a certain influence on the conventional power distribution system.
In order to solve the problem, the current main processing method is to regard the distributed power supply as a PV node, and then simplify and equate the PV node and a parallel capacitor to a PQ node, so as to achieve the purpose of rapidly calculating the trend.
Aiming at the technical scheme that the automatic node numbering method can record the attributes of the nodes, so that PQ nodes, PV nodes and balance nodes can be distinguished.
The method for processing the PV nodes is characterized in that: when a plurality of power supplies in a power distribution system supply power together (such as the situation of distributed power supplies and the like), firstly judging whether the PV node can be used as a PQ node for calculation or the error is controlled to be two percentage points under the situation that the PV node is used as the PQ node for calculation, and then a special processing method for the PV node is not needed; if the calculation cannot be performed as a PQ node, special processing of the PV node is performed.
The method for processing the PV nodes comprises the following specific steps:
1) and setting the initial value of the reactive power output of the PV node power supply to be 0, and converting the initial value of the reactive power output into a PQ node.
2) And (4) calculating the calculated voltage of the upper-layer parent node (except the balance node and the root node, any other node can find the parent node) connected with the PV node through load flow calculation.
3) According to fig. 3, the correction amount of the reactive power output of the PV node connected to the power supply is obtained from the calculated voltage of the parent node of the PV node, the impedance of the branch connecting the PV node and the parent node thereof, the constant voltage of the PV node and the active power:
wherein, λ is the calculation step length, -1<λ<1, typically 0.1; q2、P2Calculating reactive and active power for PV nodesPower; qdReactive power for all branches and nodes connected to the PV node; u shaper1、Ur2The total node voltage component of the PV node and the father node thereof; u shape2An input voltage at the PV node; r, x is the impedance on the branch between the PV node and its parent node.
4) If the forward pushing is carried out for load flow calculation convergence, the convergence reactive power of the PV node can be obtained; otherwise, the reactive power output of the PV node accessed power supply is corrected according to the formula (4), and the step 2) is switched to continue the next iterative calculation.
Example (b):
taking a classic IEEE33 node system and a 10kV system as examples, the load flows of the forward-backward substitution algorithm and the improved algorithm are respectively calculated, and the effectiveness and the feasibility of the improved algorithm are verified by comparing the calculation results of the forward-backward substitution algorithm and the improved algorithm.
1. IEEE33 node system simulation:
the IEEE33 node standard system topology is shown in FIG. 4, and is programmed with MATLAB simulation software and performs load flow calculations. Load flow calculation is performed by the original method and the improved method provided by the article, and the first ten and average absolute error values with the largest comparison error between the network voltage distribution and the power distribution and the actual result are respectively shown in tables 4 to 9:
TABLE 4 Voltage distribution and error (original method)
TABLE 5 active distribution and error (original method)
TABLE 6 reactive distribution and error (original method)
TABLE 7 Voltage distribution and error (improvement method of the present technical solution)
Table 8 active power distribution and error (improvement method of the present technical scheme)
TABLE 9 reactive distribution and error (improvement method of the present technical solution)
As can be seen from tables 4 to 6, when the IEEE33 node system power flow is calculated by using the ordinary forward-backward substitution algorithm, most of the errors of the node voltage amplitudes are between 1% and 3%, and the positions with larger errors are concentrated on the line from the node 6 to the node 17; and the error in power occurs mostly at nodes with more than two children, such as node 1, node 2.
From tables 7 to 9, when the improved method of the technical scheme is used for calculating the power flow of the IEEE33 node system, the absolute average error of the node voltage amplitude is 0.02 percent and is far less than 1.17 percent of the original method; the absolute average error of active power distribution is 0.33 percent and is slightly less than 0.8 percent of the original method; the absolute average error of the node voltage amplitude is 0.69 percent and is less than 1.77 percent of the original method. Therefore, under the condition of calculating the same configuration network, the method has smaller error and better accuracy.
2)10kV system simulation:
the 10kV system performs load flow calculation by the former method and the improved method proposed by the article respectively with the configuration, and gives the first ten and average absolute error values of the maximum comparison error between the network voltage distribution and the power distribution and the actual result as shown in tables 10 to 16 respectively:
TABLE 10 Voltage distribution and error
TABLE 11 active distribution and error
TABLE 12 reactive distribution and error
TABLE 13 Voltage distribution and error
TABLE 14 Power distribution and error (active)
As can be seen from tables 10 to 12, when the general forward-backward substitution algorithm is used to calculate the power flow of the 10kV system, the average absolute error of the active power reaches 25.95% and the absolute error of the reactive power reaches 61.11% due to the existence of the PV node in the system, so the original algorithm loses the effectiveness and feasibility of the calculation and needs to perform corresponding special processing on the PV.
As can be seen from tables 13 to 15, when the improved method of the technical scheme is used to calculate the power flow of the 10kV system, the absolute average errors of the voltage amplitude, the active power distribution and the reactive power distribution are respectively as follows: 1.06%, 3.29%, 2.93%, all within acceptable ranges.
Therefore, compared with the existing method, the improved method adopted in the technical scheme not only has better accuracy, but also has better application prospect for a system with PV nodes.
In the technical scheme of the invention, firstly, full-automatic numbering is realized on each node of the power distribution network by generating the node data table, the matrix A and the matrix B, PV nodes are automatically identified, and the step that a common algorithm needs to number the nodes according to certain requirements before iterative computation can be omitted; secondly, the load of the transformer is converted to a high-voltage side, so that a power distribution network can be changed into a simple single line diagram, and the scale of the system is reduced; in addition, the node injection power in the back substitution process is replaced by the node injection current, so that the time for calculating the branch loss can be saved; finally, the power distribution network containing the PV nodes can be effectively processed through the reactive power correction equation of the PV nodes, and the problem that the PV nodes in the power distribution network system cannot be processed in the prior art is solved.
By adopting the technical scheme of the invention, the practical improvement is made aiming at the defects of the existing method; the method can be matched with the characteristics of the power distribution network, and a relatively accurate result can be calculated; meanwhile, the numbering time is saved by generating three matrixes; simplifying the node iteration scale; and converting the PV node into a PQ node by adopting a reactive power correction calculation formula for calculation. As can be seen from the comparison result, in the IEEE33 node system, the error of the technical scheme improvement method is obviously reduced; in a 10kV system, the PV nodes can be processed to control the error to be about +/-3%, and the error is much smaller than that of the traditional forward-backward substitution method.
The invention can be widely applied to the field of planning and management of the power distribution network.
Claims (10)
1. A power distribution network load flow calculation method of an improved forward-backward substitution method comprises the step of performing load flow calculation on a power distribution network by adopting the forward-backward substitution method, and is characterized in that when the load flow calculation of the power distribution network is performed, the following steps are performed:
1) firstly, drawing a system node structure diagram of a power distribution network, and generating a corresponding power distribution network related parameter table by looking up impedance parameters of related lines, impedance of each branch and load of each node;
2) the node numbering processing rules are adopted to carry out full-automatic numbering on each node of the power distribution network, the node type is determined, and PV nodes are automatically identified;
3) generating a matrix A and a matrix B by adopting iterative node scale simplification processing according to a related parameter table of the power distribution network, and performing load flow calculation by utilizing the matrix A and the matrix B in cooperation with a traditional forward-backward substitution method;
4) converting the low-voltage side load of the transformer into a high-voltage side load for iterative computation by adopting a practical processing mode of simplifying the scale of iterative nodes through simple equivalent operation, so that the nodes participating in the iterative computation only contain all the high-voltage side nodes of the transformer branch and do not contain the low-voltage side nodes of the transformer branch, and further special processing on the PV nodes is realized;
5) in the algorithm back-substitution process, the node injection power is replaced by the node injection current, so that the branch power loss is prevented from being calculated during each iterative calculation, and the calculation speed is increased;
the power distribution network load flow calculation method can change a power distribution network into a simple single line diagram, thereby reducing the system scale; the node injection power in the regeneration process is replaced by the node injection current, so that the time for calculating the branch loss can be saved; the power distribution network containing the PV nodes is effectively processed through the reactive power correction equation of the PV nodes, and the problem that the PV nodes in the power distribution network system cannot be processed in the prior art is solved; under the condition of calculating the same configuration network, the method has the advantages of smaller error, better accuracy and higher calculation speed.
2. The method for calculating power flow in a power distribution network according to claim 1, wherein said node numbering process comprises:
naming nodes, starting from a root node along the direction of a radiation feeder, wherein the nodes connected with the root node through branches are child nodes of the root node, the root node is a father node of the node, and if one node is connected with different nodes through different branches, the nodes are brother nodes;
and forming a node data table through node traversal, wherein the table needs to record the load, the node voltage and the node type of a father node, and also needs to record the load, the node voltage, the node type information of a child node and relevant parameters of a branch between two points.
3. The method of power flow calculation for a power distribution network using the improved push-forward substitution method as claimed in claim 2, wherein said node types include PQ nodes and PV nodes;
the relevant parameters of the branch between the two points at least comprise branch impedance, branch current or power.
4. The method as claimed in claim 1, wherein an n × 2 matrix is generated during the power flow calculation, n is the number of network nodes, after a certain node is calculated, the corresponding second column in the matrix is automatically marked with 1, and the node marked with 1 skips the calculation, so as to avoid calculation errors caused by repeated calculation of the same node.
5. The method according to claim 1, wherein the matrix a is an a x b matrix, a is the number of the endmost child nodes of the network, b is the number of the network nodes, and the number after the leaf node in the matrix represents the number of the node passing from the leaf node to the root node via the shortest path;
the matrix B is a matrix of c multiplied by d, c is the number of nodes in the network, and d is the number of nodes with the most child nodes in a father node in the network.
6. The method for calculating power flow in a power distribution network according to claim 1, wherein said iterative calculation is performed according to the following conversion formula:
wherein, P1、Q1Active and reactive power, P, for the high-voltage side of the transformer2、Q2Active and reactive power, Δ P, for the low-voltage side of the transformer0、ΔPkRated no-load loss and rated short-circuit loss in a transformer nameplate parameter table, I0％、Us% is the percent of no-load current and the percent of short circuit voltage; u shape1、UNAnd SNThe voltage, the rated voltage and the rated capacity of the high-voltage side of the transformer are respectively; u shapes％、Ur% is the percentage of the voltage drop across the resistance and reactance when the current value in the transformer is exactly equal to the nominal current value.
7. The method according to claim 1, wherein the special processing of the PV nodes comprises reactive power modification of the PV nodes, and the reactive power modification of the PV nodes comprises the following steps:
1) setting the initial value of reactive power output of the PV node power supply to be 0, and converting the initial value of the reactive power output into a PQ node;
2) calculating the calculated voltage of the upper-layer parent node connected with the PV node through load flow calculation;
3) and calculating the correction quantity of the reactive power output of the PV node accessed to the power supply according to the calculated voltage of the parent node of the PV node, the impedance of the connection branch of the PV node and the parent node thereof, and the constant voltage and the active power of the PV node:
wherein, λ is the calculation step length, -1<λ<1, typically 0.1; q2、P2Calculating reactive power and active power for the PV node; qdReactive power for all branches and nodes connected to the PV node; u shaper1、Ur2The total node voltage component of the PV node and its parent node; u shape2An input voltage at the PV node; r, x is the impedance on the branch between the PV node and its parent node;
4) if the forward pushing is carried out for load flow calculation convergence, the convergence reactive power of the PV node can be obtained; otherwise, correcting the reactive power output of the PV node accessed power supply according to the formula, and turning to the step 2) to continue the next iterative calculation.
8. The method for calculating the power distribution network load flow according to the improved forward-backward substitution method of claim 1, wherein the method for calculating the power distribution network load flow fully automatically numbers each node of the power distribution network through the power distribution network related parameter table, the matrix a and the matrix B to realize forward traversal and reverse traversal of the node, and can accelerate the calculation speed when processing power distribution network load flow calculation with more nodes, and can automatically identify PV nodes without performing matrix operation when encountering a complex power distribution network.
9. The method for calculating the power flow of the power distribution network by the improved forward-backward substitution method according to claim 1, wherein the method for calculating the power flow of the power distribution network converts the load on the low-voltage side of the transformer into the load on the high-voltage side of the transformer for iterative calculation by simplifying a practical processing mode with an iterative node scale, so that the power distribution network is changed into a simple single line diagram, thereby reducing the system scale; the occupied space of the computer memory is small, the trouble of nodes at the low-voltage side of the iterative transformer can be saved, the number of iterative nodes is greatly reduced, and the calculation speed is favorably accelerated.
10. The method for calculating the power flow of the power distribution network according to the improved forward-backward substitution method of claim 1, wherein in the algorithm backward substitution process, the node injection power is replaced by the node injection current, so that the branch power loss is prevented from being calculated in each iterative calculation, and the calculation speed is increased.
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