CN109149583B - Simple forward-push backward-replace power flow calculation method for active power distribution network - Google Patents

Simple forward-push backward-replace power flow calculation method for active power distribution network Download PDF

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CN109149583B
CN109149583B CN201811129927.XA CN201811129927A CN109149583B CN 109149583 B CN109149583 B CN 109149583B CN 201811129927 A CN201811129927 A CN 201811129927A CN 109149583 B CN109149583 B CN 109149583B
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CN109149583A (en
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董张卓
张倍倍
白翰林
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Xian Shiyou University
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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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • 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
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Abstract

The invention discloses a simple forward-backward substitution power flow calculation method for an active power distribution network. The method comprises the following steps: determining the forward-pushing and backward-replacing sequence of the branch, performing forward-pushing calculation according to the sequence, performing backward-replacing calculation according to the branch sequence to finish one-time load flow calculation, and obtaining a load flow solution through multiple forward-pushing and backward-replacing cycles; forward calculation: calculating for the first time, setting the initial value of each node voltage as the first node voltage, calculating for the subsequent time, taking the node voltage of the last iterative calculation, starting from the last node, taking or calculating the active power and the reactive power of the node or substituting the calculated reactive power of the node power according to different node types, and calculating the current of each branch circuit from the tail end of the radiation-shaped network; and (3) back substitution calculation: calculating the voltage of a downstream node or a voltage phase angle and reactive power from the voltage of the root node according to different node voltages, and calculating the voltage of each node to the tail end; the method solves the problem of tidal current oscillation caused by the adjustment quantity, is simple and convenient, has small calculated quantity, and can reliably converge.

Description

Simple forward-push backward-replace power flow calculation method for active power distribution network
Technical Field
The invention belongs to the technical field of power distribution networks, and particularly relates to a simple forward-backward substitution load flow calculation method for an active power distribution network.
Background
The forward-backward substitution method is one of effective methods for calculating the power flow of the power distribution network. According to the operating characteristics and states of different types of Distributed power supplies (Distributed Generation-DGs) connected into a power distribution network, when a forward-backward substitution method is used for calculating power flow, the power flow can be used as four types of nodes PQ, PV, PI and PQ (V). Among the four types of nodes, the PI node and the PQ (V) node can be converted into the PQ node according to the given parameters of the nodes in the forward pushing process, and the reactive power Q of the node is calculatedi. PV node with reactive reserve, reactive power Q of the nodeiDepending on the distribution network parameters and the voltage of the system node, the reactive power of the node cannot be directly obtained from the electrical quantity of the node. When the load flow calculation is carried out on the power distribution network accessed to the DG by using a forward-backward substitution method,the processing of the PV nodes is the key to load flow calculation.
At present, in the calculation of the generation load flow before the power distribution network accessing the DG is pushed back, two methods are provided for processing the PV node. One method is a node reactive power and voltage sensitivity compensation algorithm, or a branch current and voltage sensitivity method. Another method is a node virtual branch addition method.
And a node reactive power and voltage sensitivity compensation algorithm derives a reactive power and voltage sensitivity equation through a PV node voltage equation. And when one-time forward-backward substitution calculation is completed, calculating the reactive power adjustment quantity of all PV nodes through a sensitivity matrix, wherein the sensitivity matrix is a sub-matrix of a system node impedance matrix. By improving a node reactive power and node voltage sensitivity algorithm, a branch current and voltage sensitivity method is provided, the adjustment quantity of node voltage and the correction quantity of branch current are considered to be associated with a node admittance matrix, a voltage variation quantity of each PV node and a branch current variation quantity equation in a power distribution network are established, the calculated node reactive variation quantity is changed into a variation quantity of branch current directly calculated through the voltage variation quantity, and therefore the calculation is used for calculating the forward branch current. According to the method for solving the node reactive power or current correction quantity based on the sensitivity algorithm, the calculation process involves the formation of a sensitivity matrix of a network, and the defects of complex calculation and large calculation amount exist.
The virtual branch adding method is characterized in that a reactance type virtual branch is connected to a given PV node to maintain the voltage of the node constant, and the reactive power regulating quantity of the node is calculated according to the voltage deviation quantity of the node. The method for determining the impedance value of the virtual branch lacks strict theoretical support and has larger impedance calculation amount.
Disclosure of Invention
The invention aims to provide a simple forward-backward substitution load flow calculation method for an active power distribution network, so as to solve the technical problem.
In order to achieve the purpose, the invention adopts the following technical scheme:
the method for calculating the succinct forward-backward substitution load flow of the active power distribution network comprises the following steps: determining the forward-pushing and backward-replacing sequence of the branch, performing forward-pushing calculation according to the sequence, performing backward-replacing calculation according to the branch sequence to finish one-time load flow calculation, and obtaining a load flow solution through multiple forward-pushing and backward-replacing cycles;
the branch forward-pushing and backward-replacing sequence is obtained by adopting a power distribution network operation topology and branch sequence algorithm;
forward calculation: calculating for the first time, setting the initial value of each node voltage as the first node voltage, calculating for the subsequent time, taking the node voltage of the last iterative calculation, starting from the last node, taking or calculating the active power and the reactive power of the node or substituting the calculated reactive power of the node power according to different node types, and calculating the current of each branch circuit from the tail end of the radiation-shaped network;
and (3) back substitution calculation: calculating the voltage of a downstream node or a voltage phase angle and reactive power from the voltage of the root node according to different node voltages, and calculating the voltage of each node to the tail end;
an iterative process is completed through the two steps, and the process is repeated.
As a further scheme of the invention, the specific steps of the forward calculation are as follows:
when load flow calculation is carried out on a power distribution network accessed to a DG, a first node is considered to be a balance node, a load node is a PQ node, the node accessed to the DG is divided into four nodes of PQ, PV, PI and PQ (V) according to different running characteristics and states of the DG, when load flow is calculated by a forward-backward substitution method, other nodes except the balance node need to calculate injection current, wherein the injection active power and the injection reactive power of the nodes are respectively Pi、QiAt a node voltage of
Figure GDA0003492312050000021
A PQ node;
considering the requirements of environmental protection, economy and the like, the wind turbine generator operated under the rated condition can make the power factor constant by automatic switching of the parallel capacitor, so that the power factor is taken as a PQ node, and the node P, Q is constant:
Figure GDA0003492312050000031
in the formula: pi、QiThe active and reactive injected power is given to the node,
Figure GDA0003492312050000032
is the node voltage at the (k-1) th iteration;
a PV node;
both a photovoltaic grid-connected inverter using a voltage control type strategy and a synchronous machine with field regulation can be used as P, V constant PV nodes, which are generally known as the upper and lower reactive limits,
when the first forward pushing is carried out, the reactive power of the PV node is taken as follows:
Figure GDA0003492312050000033
in the formula: qimax、QiminThe upper limit and the lower limit are reactive;
reactive power Q of node i in the forward calculation of the subsequent kth iterationiThe PV node injection current is calculated during the back substitution of (k-1), the last iteration, as:
Figure GDA0003492312050000034
a PI node;
the grid-connected inverter adopting the current control mode can be equivalent to a PI node with constant active power and constant effective current value, and the effective value of the injected current of the PI node is set as IiThen, the injection current is:
Figure GDA0003492312050000035
in the formula: i isiThe effective value of the current is injected into the node,
Figure GDA0003492312050000036
injecting a phase angle of the current for the node;
during the push-forward process, the node voltage vector is known to be
Figure GDA0003492312050000037
The reactive power of the node can be calculated by the formula (10)
Figure GDA0003492312050000038
Figure GDA0003492312050000039
To obtain QiThe current phase angle theta can then be calculated from the following equationi：
Figure GDA0003492312050000041
A PQ (V) node;
considering the active power P emitted by the asynchronous generator, the reactive power Q absorbed from the system varies with the variation of the port voltage V, and is therefore taken as PQ (V) node, ReIs a mechanical load equivalent resistance; r is rotor resistance; xσIs leakage reactance; xmIs an excitation reactance; i isrIs the rotor current; i issIs the stator current; i ismIs an excitation current; s is slip, and the tangent calculation formulas of the active power output by the generator and the power factor angle are respectively as follows:
Figure GDA0003492312050000042
Figure GDA0003492312050000043
from equation (12), when the generator port voltage V and the generator output P are given, the slip s is obtained, and the reactive power of the node can be calculated by the following equation:
Figure GDA0003492312050000044
in the formula:
Figure GDA0003492312050000045
node reactive power, P, for the kth iterationiActive power is provided to the node, so:
Figure GDA0003492312050000046
namely: the PQ (V) node is temporarily converted to a PQ node, and the injection current of the node is calculated by equation (15).
As a further scheme of the invention, the back substitution calculation comprises the following specific steps:
calculating the current of each branch through a forward-pushing process, and a backward-replacing process starts from a source node, gradually pushes out the voltage of a downstream node of the branch according to branch parameters, but for the branch of which the downstream node is a PV node, when the voltage of the node calculated according to gradual pushing is compared with the given node voltage, a deviation occurs, and different calculation methods are adopted for PQ, PI and PQ (V) type nodes and the PV node backward-replacing process;
calculating the voltage of nodes PQ, PI and PQ (V);
during the back-substitution process, the voltage of the node i is known from the first branch, such as the branch (ij)
Figure GDA0003492312050000051
Branch current
Figure GDA0003492312050000052
Node j voltage when node j is PQ, PI, PQ (V) node
Figure GDA0003492312050000053
Can be calculated by the formula (5);
calculating the voltage of a PV node;
in a branch of the distribution network, the voltage of the left end node i is
Figure GDA0003492312050000058
And active power P of right end node jjAnd an effective value of voltage VjKnowing the voltage phase angle theta of node jjAnd reactive power QjUnknown, in theory, the voltage of the node j is constant, the current, the active power and the reactive power of the downstream branch of the node j are determined by the voltage of the node, the voltage of each node of the upstream branch and the reactive power of the node determine the voltage of the node j, namely the PV node, therefore, when the voltage of the node j is given, the voltage of the node j can be ensured to be constant by adjusting the reactive power of the node j in the iterative process of load flow calculation, and the reactive power regulating quantity delta Q of the node is introducedj；
The calculated Delta Q is obtained through one branchjThe left side of the branch is close to the upper system side, the node of the branch is numbered i, the node on the right side is a PV node, the node is numbered j, the impedance of the branch is ZijR + jX, reactive power variation Δ Q by regulation nodejThe branch current is changed, so that the node voltage is changed, and the capacitance effect of the line to the ground is not considered and the equivalent circuit is obtained;
from this the following equation can be written as follows:
Figure GDA0003492312050000054
in the formula:
Figure GDA0003492312050000055
power flowing into node j for a branch;
both sides of equation (16) are multiplied by
Figure GDA0003492312050000056
Obtaining:
Figure GDA0003492312050000057
order:
Figure GDA0003492312050000061
substituting into (17), and separating the real part and the imaginary part to obtain an equation:
Figure GDA0003492312050000062
in the system of equations set forth in the above description,
Figure GDA0003492312050000063
Vj,
Figure GDA0003492312050000064
r, X are known quantities, theta, delta QjThe unknown quantity is two unknown quantities of two equations, and the equations can be solved;
the solving process of the equation is given below;
is represented by the formula (18):
Figure GDA0003492312050000065
substituting the formula (19) to obtain:
Figure GDA0003492312050000066
the two sides of the equation are multiplied by X:
Figure GDA0003492312050000067
the above formula is written in order:
Figure GDA0003492312050000068
order:
Figure GDA0003492312050000069
then equation (23) can be simplified to:
Figure GDA00034923120500000610
namely:
Figure GDA00034923120500000611
wherein:
Figure GDA00034923120500000612
thus, the phase angle of the PV node voltage is:
Figure GDA0003492312050000071
obtaining:
Figure GDA0003492312050000072
further, it can be obtained from the formula (19):
Figure GDA0003492312050000073
calculated by the formula (26)
Figure GDA0003492312050000074
Then by
Figure GDA0003492312050000075
Calculated to obtain theta(k)By substituting the formula (27)
Figure GDA0003492312050000076
The reactive power regulating quantity can make the voltage of the PV node constant, the reactive power correcting direction is determined, if the voltage is regular, the reactive power injection of the node needs to be reduced, and if the voltage is negative, the reactive power injection of the node needs to be increased;
the reactive power of the PV node is taken as:
Figure GDA0003492312050000077
in the formula: k is a radical ofpFor the correction coefficient, it is generally 0.05 to 0.1.
As a further scheme of the present invention, the node voltage error is defined as an absolute value of a difference between a current iteration voltage and a last iteration voltage of the node i, that is:
Figure GDA0003492312050000078
in the formula: n is a node number set;
obtaining the maximum value of the node voltage error:
emax＝max(ei|i∈N) (30)；
when the maximum value of the node voltage error is smaller than the error precision epsilon set in the calculation, namely emaxThe iteration converges when < epsilon.
The specific flow of the forward-pushing-back generation load flow calculation of the power distribution network accessed to the DG is as follows:
(1) given convergence accuracyεTotal number of nodes and branches n, nbInputting original parameters of the distribution network;
(2) obtaining forward-pushing branch sequences seq _ forward and backward-substituting branch sequences seq _ back and seq _ back according to a power distribution network operation topology and branch sequence algorithm;
(3) iterating the voltage rated values of all nodes for the first time, wherein the current of each branch is 0;
(4) a forward pushing process:
1) the current branch number m is equal to 0;
2) obtaining a branch from seq _ forward (m);
3) calculating reactive power and injection current of a node on the left side of the branch circuit according to the forward-pushing time node injection current and the reactive power;
4) calculating the right side current and the left side current of the branch circuit;
5) adding a left current to the left node;
6) judging whether m is equal to nbIf yes, go to (5), if m is equal to m +1, return to 2);
(5) the back substitution process:
1) the current branch number m is equal to 0;
2) obtaining a branch from seq _ back (m);
3) calculating the voltage or the reactive power of the right node according to the back substitution process;
4) judging whether m is equal to n, is equal to the revolution (6), is not equal to m +1, and returns to 2);
(6) and (3) error discrimination: calculating the absolute value of the node voltage error
Figure GDA0003492312050000081
i 1,2 … n, if max (e)1,e2…en) If the value is less than epsilon, the iteration is converged, the calculation is finished and the result is output, otherwise, the step (4) is switched to continue the next iteration.
The invention has the beneficial effects that: the method solves the problem of tidal current oscillation caused by the regulating quantity, introduces the regulating coefficient, and multiplies the regulating quantity with the regulating coefficient to obtain a new node reactive regulating quantity; in the back substitution process, the voltage phase angle and the reactive power can be obtained through the calculation of the algorithm; the method is simple and convenient, has small calculated amount and can reliably converge.
Drawings
FIG. 1 is an equivalent circuit diagram of a local distribution network according to the present invention;
FIG. 2 is a diagram of a model of the PV node voltage calculation of the present invention;
FIG. 3 is a flow chart of the DG load flow calculation according to the present invention;
FIG. 4 is a 33-node power distribution system connection diagram of the present invention;
FIG. 5 is a graph of the node voltage conditions of the 33-node distribution network of the present invention (where a is the voltage amplitude profile at IEEE33 node and b is the voltage phase angle profile at IEEE33 node);
FIG. 6 is a graph of correction factor versus convergence time for the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely explained below with reference to the drawings in the embodiments of the present invention.
The calculation principle of the forward-backward substitution method of the invention is as follows: when the forward-backward substitution method is used for calculating the power flow, the forward-backward substitution method is divided into a forward-backward substitution process and a backward substitution process. During forward pushing, assuming that the voltage of each node in the power distribution network is known, and starting from a tail end branch, calculating the left current and the right current of each branch. When the branch current is known, the voltage of the subsequent node is calculated in sequence from the node at the head end, namely the balanced node (power supply). And repeating iteration until the voltage change of each node and the last iteration is smaller than a specified value, and finishing the load flow calculation.
FIG. 1 is an equivalent circuit of a local distribution network, wherein a left superior is supposed to be connected with a power supply, and a right superior is supposed to be connected with a load; the calculation principle of the forward and backward iterations is given below with reference to fig. 1, where the number of iterations is denoted by the variable k, where k is 1,2 …, and all variables denoted by (k) denote the value of the kth iteration.
A forward pushing process: assuming that the load current of the node j of the subsequent branch of branch (ij) is calculated in fig. 1, the injection current of branch (ij) is:
Figure GDA0003492312050000091
Figure GDA0003492312050000092
Figure GDA0003492312050000093
the current outflow is taken as a reference direction in the formula:
Figure GDA0003492312050000094
the outgoing current for branch (ij);
Figure GDA0003492312050000095
a load current at node j;
Figure GDA0003492312050000096
an injection current at node j;
Figure GDA0003492312050000097
an injection current for a subsequent branch, where ν is 1,2 … n, n is the number of subsequent branches of branch (ij);
Figure GDA0003492312050000098
is the impedance branch current;
Figure GDA0003492312050000099
an injection current for branch (ij);
Figure GDA00034923120500000910
respectively, the ground current at both ends of the branch (ij).
And sequentially calculating the current of each branch to the first branch according to the given branch sequence, namely finishing the forward pushing process.
The back substitution process: starting from the first branch, the right voltage is calculated from the left voltage and the branch current of the known branch until the last branch. In the context of figure 1 of the drawings,
Figure GDA0003492312050000101
the result of the calculation is that,
Figure GDA0003492312050000102
and (5) waiting for calculation. When node j is not a PV node, represented by equation (4):
Figure GDA0003492312050000103
get node j node voltage:
Figure GDA0003492312050000104
when the node j is the PV node, the node voltage calculation method is described in detail in the back-generation process.
The method for calculating the succinct forward-backward substitution load flow of the active power distribution network comprises the following steps: determining the forward-pushing and backward-replacing sequence of the branch, performing forward-pushing calculation according to the sequence, performing backward-replacing calculation according to the branch sequence to finish one-time load flow calculation, and obtaining a load flow solution through multiple forward-pushing and backward-replacing cycles;
the branch forward-pushing and backward-replacing sequence is obtained by adopting a power distribution network operation topology and branch sequence algorithm;
forward calculation: calculating for the first time, setting the initial value of each node voltage as the first node voltage, calculating for the subsequent time, taking the node voltage obtained by the last iteration, taking or calculating the active power and the reactive power of the node or substituting the calculated reactive power of the node power according to different node types from the last node, and calculating the current of each branch circuit from the tail end of the radiation-shaped network;
the forward calculation comprises the following specific steps:
when load flow calculation is carried out on a power distribution network accessed to a DG, a first node is considered to be a balance node, a load node is a PQ node, the node accessed to the DG is divided into four nodes of PQ, PV, PI and PQ (V) according to different running characteristics and states of the DG, when load flow is calculated by a forward-backward substitution method, other nodes except the balance node need to calculate injection current, wherein the injection active power and the injection reactive power of the nodes are respectively Pi、QiAt a node voltage of
Figure GDA0003492312050000105
A PQ node;
considering the requirements of environmental protection, economy and the like, the wind turbine generator operated under the rated condition can make the power factor constant by automatic switching of the parallel capacitor, so that the power factor is taken as a PQ node, and the node P, Q is constant:
Figure GDA0003492312050000111
in the formula: pi、QiThe active and reactive injected power is given to the node,
Figure GDA0003492312050000112
is the node voltage at the (k-1) th iteration;
a PV node;
both a photovoltaic grid-connected inverter using a voltage control type strategy and a synchronous machine with field regulation can be used as P, V constant PV nodes, which are generally known as the upper and lower reactive limits,
when the first forward pushing is carried out, the reactive power of the PV node is taken as follows:
Figure GDA0003492312050000113
in the formula: qimax、QiminThe upper limit and the lower limit are reactive;
reactive power Q of node i in the forward calculation of the subsequent kth iterationiThe calculation is carried out in the back substitution process of (k-1), namely the last iteration, the calculation method is given in the calculation of the PV node voltage, and the PV node injection current is as follows:
Figure GDA0003492312050000114
a PI node;
the grid-connected inverter adopting the current control mode can be equivalent to a PI node with constant active power and constant effective current value, and the effective value of the injected current of the PI node is set as IiThen, the injection current is:
Figure GDA0003492312050000115
in the formula: i isiThe effective value of the current is injected into the node,
Figure GDA0003492312050000116
injecting a phase angle of the current for the node;
during the push-forward process, the node voltage vector is known to be
Figure GDA0003492312050000117
The reactive power of the node can be calculated by the formula (10)
Figure GDA0003492312050000121
Figure GDA0003492312050000122
To obtain QiThe current phase angle theta can then be calculated from the following equationi：
Figure GDA0003492312050000123
A PQ (V) node;
considering the active power P emitted by the asynchronous generator, and the reactive power Q absorbed from the system varies with the variation of the port voltage V, it is taken as PQ (V) node, the approximate equivalent circuit diagram of the asynchronous generator, ReIs a mechanical load equivalent resistance; r is rotor resistance; xσIs leakage reactance; xmIs an excitation reactance; i isrIs the rotor current; i issIs the stator current; i ismIs an excitation current; s is slip, and the tangent calculation formulas of the active power output by the generator and the power factor angle can be deduced as follows:
Figure GDA0003492312050000124
Figure GDA0003492312050000125
from equation (12), when the generator port voltage V and the generator output P are given, the slip s is obtained, and the reactive power of the node can be calculated by the following equation:
Figure GDA0003492312050000126
in the formula:
Figure GDA0003492312050000127
node reactive power, P, for the kth iterationiActive power is provided to the node, so:
Figure GDA0003492312050000128
namely: the PQ (V) node is temporarily converted to a PQ node, and the injection current of the node is calculated by equation (15).
And (3) back substitution calculation: calculating the voltage of a downstream node or a voltage phase angle and reactive power from the voltage of the root node according to different nodes, and calculating the voltage of each node to the tail end;
the back substitution calculation comprises the following specific steps:
calculating the current of each branch through a forward-pushing process, and a backward-replacing process starts from a source node, gradually pushes out the voltage of a downstream node of the branch according to branch parameters, but for the branch of which the downstream node is a PV node, when the voltage of the node calculated according to gradual pushing is compared with the given node voltage, a deviation occurs, and different calculation methods are adopted for PQ, PI and PQ (V) type nodes and the PV node backward-replacing process;
calculating the voltage of nodes PQ, PI and PQ (V);
in the backward substitution process, as shown in FIG. 1, the voltage of node i is known from the first branch, i.e. branch (ij)
Figure GDA0003492312050000131
Branch current
Figure GDA0003492312050000132
Node j voltage when node j is PQ, PI, PQ (V) node
Figure GDA0003492312050000133
Can be calculated by the formula (5);
calculating the voltage of a PV node;
in a branch of the distribution network shown in fig. 1, the voltage of the left end node i is
Figure GDA0003492312050000134
And active power P of right end node jjAnd an effective value of voltage VjKnowing the voltage phase angle theta of node jjAnd reactive power QjUnknown, in theory, the voltage of the node j is constant, the current, the active power and the reactive power of the downstream branch of the node j are determined by the voltage of the node, the voltage of each node of the upstream branch and the reactive power of the node determine the voltage of the node j, namely the PV node, therefore, when the voltage of the node j is given, the voltage of the node j can be ensured to be constant by adjusting the reactive power of the node j in the iterative process of load flow calculation, and the reactive power regulating quantity delta Q of the node is introducedj；
To simplify the calculation, the Δ Q is calculated by only considering one branchjThe left side of the branch is close to the upper system side, the node of the branch is numbered i, the node on the right side is a PV node, the node is numbered j, the impedance of the branch is ZijR + jX, reactive power variation Δ Q by regulation nodejThe branch current is changed, so that the node voltage is changed, and the capacitance effect of the line to the ground is not considered, and the node voltage is changed according to the equivalent circuit, as shown in FIG. 2;
from this the following equation can be written as follows:
Figure GDA0003492312050000141
in the formula:
Figure GDA0003492312050000142
power flowing into node j for a branch;
both sides of equation (16) are multiplied by
Figure GDA0003492312050000143
Obtaining:
Figure GDA0003492312050000144
order:
Figure GDA0003492312050000145
substituting into (17), and separating the real part and the imaginary part to obtain an equation:
Figure GDA0003492312050000146
in the system of equations set forth in the above description,
Figure GDA0003492312050000147
Vj,
Figure GDA0003492312050000148
r, X are known quantities, theta, delta QjThe unknown quantity is two unknown quantities of two equations, and the equations can be solved;
the solving process of the equation is given below;
is represented by the formula (18):
Figure GDA0003492312050000149
substituting the formula (19) to obtain:
Figure GDA00034923120500001410
the two sides of the equation are multiplied by X:
Figure GDA0003492312050000151
the above formula is written in order:
Figure GDA0003492312050000152
order:
Figure GDA0003492312050000153
then equation (23) can be simplified to:
Figure GDA0003492312050000154
namely:
Figure GDA0003492312050000155
wherein:
Figure GDA0003492312050000156
thus, the phase angle of the PV node voltage is:
Figure GDA0003492312050000157
obtaining:
Figure GDA0003492312050000158
further, it can be obtained from the formula (19):
Figure GDA0003492312050000159
calculated by the formula (26)
Figure GDA00034923120500001510
Then by
Figure GDA00034923120500001511
Calculated to obtain theta(k)By substituting the formula (27)
Figure GDA00034923120500001512
The reactive power regulating quantity can make the voltage of the PV node constant, the reactive power correcting direction is determined, if the voltage is regular, the reactive power injection of the node needs to be reduced, and if the voltage is negative, the reactive power injection of the node needs to be increased;
the reactive power of the PV node is taken as:
Figure GDA0003492312050000161
in the formula: k is a radical ofpFor the correction coefficient, it is generally 0.05 to 0.1.
An iterative process is completed through the two steps, and the process is repeated.
Defining the node voltage error as the absolute value of the difference between the current iteration voltage and the last iteration voltage of the node i, namely:
Figure GDA0003492312050000162
in the formula: n is a node number set;
obtaining the maximum value of the node voltage error:
emax＝max(ei|i∈N) (30)；
when the maximum value of the node voltage error is smaller than the error precision epsilon set in the calculation, namely emaxThe iteration converges when < epsilon.
As shown in fig. 3, the specific flow of forward-backward substitution load flow calculation of the power distribution network connected to the DG is as follows:
(1) given convergence accuracy epsilon, total number n and n of nodes and branchesbInputting original parameters of the distribution network;
(2) obtaining forward-pushing branch sequences seq _ forward and backward-substituting branch sequences seq _ back and seq _ back according to a power distribution network operation topology and branch sequence algorithm;
(3) iterating the voltage rated values of all nodes for the first time, wherein the current of each branch is 0;
(4) a forward pushing process:
1) the current branch number m is equal to 0;
2) obtaining a branch from seq _ forward (m);
3) calculating reactive power and injection current of a node on the left side of the branch circuit according to the forward-pushing time node injection current and the reactive power;
4) calculating the right side current and the left side current of the branch circuit;
5) adding a left current to the left node;
6) judging whether m is equal to nbIf yes, go to (5), if m is equal to m +1, return to 2);
(5) the back substitution process:
1) the current branch number m is equal to 0;
2) obtaining a branch from seq _ back (m);
3) calculating the voltage or the reactive power of the right node according to the back substitution process;
4) judging whether m is equal to n, is equal to the revolution (6), is not equal to m +1, and returns to 2);
(6) and (3) error discrimination: calculating the absolute value of the node voltage error
Figure GDA0003492312050000171
i 1,2 … n, if max (e)1,e2…en) If the value is less than epsilon, the iteration is converged, the calculation is finished and the result is output, otherwise, the step (4) is switched to continue the next iteration.
In order to verify the correctness of the program and the convergence characteristic of the algorithm, the verification program is programmed under the VS2013C + + environment according to the specific flow of the generation load flow calculation pushed back before the power distribution network accessing the DG. A distribution network with 33 nodes shown in FIG. 4 is used as a test system.
In fig. 4, system nodes 9, 15, 26 and 32 access 4 groups of DG, where 9 and 15 are PV nodes, 26 is PI nodes, and 32 is pq (v) nodes. The basic parameters of the distributed power supply are shown in table 1.
TABLE 1 distributed Power supply parameters
Figure GDA0003492312050000172
The following tests were performed: functional test and convergence test are performed, and the power flow calculation result is shown in fig. 5, the voltage distribution of each node and the convergence error are 10-4As can be seen from fig. 5, a sudden increase in voltage occurs at the PV node.
When the correction coefficients are different values, the convergence of the program is tested, the test curves are shown in FIG. 6, and the convergence errors are 10 respectively-4、10-5The calculation result shows that the correction coefficient has great influence on the convergence speed, when the correction factor is taken out, the convergence is good, but the iteration times are many, the correction factor is taken out of a large value, and the program can be diverged; the relation curve of the correction coefficient and the convergence times is in a parabola shape.
The method takes the characteristics of the PV node into consideration, maintains the voltage of the PV node constant, is related to the power supply voltage and the impedance of the upstream branch of the PV node, and can calculate the voltage phase angle and the reactive power of the PV node only by the information of the upstream node of the branch in the back-substitution process. By means of a method for directly solving node reactive power correction, a C + + program is written in a compiling environment of VS2013, and a proposed algorithm is verified through a 33-node distribution example.
The following conclusions were reached:
1) when the node of the radiation type power distribution network is PV, the node voltage is related to the source node voltage and the branch impedance.
2) By adjusting the reactive power of the node, the voltage of the node can be ensured to be constant.
3) And the reactive power correction coefficient of the PV node in the power flow calculation is related to the convergence of the power flow.
4) The calculation example results show that the calculation amount of the proposed method is small and the convergence can be reliably realized.
The PV node has the defects of complex calculation and large calculation amount when the reactive power is calculated by adopting a sensitivity method, and the calculation method of the PV node is improved and designed. The new forward-backward substitution load flow calculation method is provided, wherein in the backward substitution process, only branch upstream node information is needed, and the PV node voltage phase angle and the reactive power are directly calculated. When the reactive power of the PV node is calculated in the method, a reactive power correction coefficient is introduced, and the convergence of calculation is ensured. The method is programmed and verified by using an IEEE33 power distribution system example, and the calculation result shows that the method overcomes the defects of complex calculation and large calculation amount caused by the fact that a sensitivity matrix needs to be established in PV node calculation in the forward-backward flow calculation process, and is simple, convenient, small in calculation amount and capable of reliably converging.
The foregoing is a preferred embodiment of the present invention, and it will be apparent to those skilled in the art that variations, modifications, substitutions and alterations can be made in the embodiment without departing from the principles and spirit of the invention.

Claims (3)

1. The method for calculating the succinct forward-backward substitution load flow of the active power distribution network is characterized by comprising the following steps of: determining the forward-pushing and backward-replacing sequence of the branch, performing forward-pushing calculation according to the sequence, performing backward-replacing calculation according to the branch sequence to finish one-time load flow calculation, and obtaining a load flow solution through multiple forward-pushing and backward-replacing cycles;
the branch forward-pushing and backward-replacing sequence is obtained by adopting a power distribution network operation topology and branch sequence algorithm;
forward calculation: calculating for the first time, setting the initial value of each node voltage as the first node voltage, calculating for the subsequent time, taking the node voltage of the last iterative calculation, starting from the last node, taking or calculating the active power and the reactive power of the node or substituting the calculated reactive power of the node power according to different node types, and calculating the current of each branch circuit from the tail end of the radiation-shaped network;
and (3) back substitution calculation: calculating the voltage of a downstream node or a voltage phase angle and reactive power from the voltage of the root node according to different node voltages, and calculating the voltage of each node to the tail end;
an iterative process is completed through the forward-pushing calculation and the back-substitution calculation, and the forward-pushing calculation and the back-substitution calculation are repeated;
the forward calculation comprises the following specific steps:
when load flow calculation is carried out on a power distribution network accessed to a DG, a first node is considered to be a balance node, a load node is a PQ node, the node accessed to the DG is divided into four nodes of PQ, PV, PI and PQV according to different running characteristics and states of the DG, when load flow is calculated by a forward-backward substitution method, other nodes except the balance node need to calculate injection current, wherein the injection active power and the injection reactive power of the nodes are respectively Pi、QiAt a node voltage of
Figure FDA0003492312040000011
A PQ node;
considering the requirements of environmental protection and economy, the wind turbine generator operated under the rated condition can make the power factor constant by the automatic switching of the parallel capacitor, so the power factor is used as a PQ node, and the active power and the reactive power of the node are constant:
Figure FDA0003492312040000012
in the formula: pi、QiThe active and reactive injected power is given to the node,
Figure FDA0003492312040000013
is the node voltage at the k-1 iteration,
Figure FDA0003492312040000021
injecting a current into the node;
a PV node;
both a photovoltaic grid-connected inverter adopting a voltage control type strategy and a synchronous machine with excitation regulation can be used as PV nodes with constant active power and constant voltage, the upper limit and the lower limit of reactive power are generally known,
when the first forward pushing is carried out, the reactive power of the PV node is taken as follows:
Figure FDA0003492312040000022
in the formula: qi max、Qi minThe upper limit and the lower limit are reactive;
reactive power of node i in the forward calculation of the subsequent k-th iteration
Figure FDA0003492312040000023
Calculated during the back substitution of k-1, the last iteration, PV sectionThe point injection current is:
Figure FDA0003492312040000024
a PI node;
the grid-connected inverter adopting the current control mode can be equivalent to a PI node with constant active power and constant effective current value, and the effective value of the injected current of the PI node is set as IiThen, the injection current is:
Figure FDA0003492312040000025
in the formula: i isiThe effective value of the current is injected into the node,
Figure FDA0003492312040000026
injecting a phase angle of the current for the node;
during the push-forward process, the node voltage vector is known to be
Figure FDA0003492312040000027
The reactive power of the node can be calculated by the formula (10)
Figure FDA0003492312040000028
Figure FDA0003492312040000029
To obtain
Figure FDA00034923120400000210
The current phase angle can then be calculated from the following equation
Figure FDA00034923120400000211
For the voltage at node i:
Figure FDA00034923120400000212
a PQV node;
the active power drawn from the system, taking into account the determination of the active power delivered by the asynchronous generator, varies as the port voltage V varies, and is therefore taken as the PQV node, ReIs a mechanical load equivalent resistance; r is rotor resistance; xσIs leakage reactance; xmIs an excitation reactance; i isrIs the rotor current; i issIs the stator current; i ismIs an exciting current; s is slip, and the tangent calculation formulas of the active power output by the generator and the power factor angle are respectively as follows:
Figure FDA0003492312040000031
Figure FDA0003492312040000032
from equation (12), when the generator port voltage V and the generator output P are appliediWhen given, the slip rate s can be obtained, and the reactive power of the node can be calculated through the following formula:
Figure FDA0003492312040000033
in the formula:
Figure FDA0003492312040000034
node reactive power, P, for the kth iterationiFor node active power, s(k)Is the slip for the kth iteration, so:
Figure FDA0003492312040000035
namely: temporarily converting the PQV node into a PQ node, and calculating the injection current of the node by using an equation (15);
the back substitution calculation comprises the following specific steps:
calculating the current of each branch through a forward-pushing process, and gradually pushing out the voltage of a downstream node of the branch according to branch parameters in a backward-replacing process from a root node, wherein for the branch of which the downstream node is a PV node, the voltage of the node calculated according to gradual pushing is compared with the given voltage of the node, and different calculation methods are adopted for PQ, PI and PQV type nodes and the PV node backward-replacing process;
calculating the voltage of nodes PQ, PI and PQV;
during the back-substitution process, the voltage V of the node i is known from the first branch, such as the branch iji (k)Branch current
Figure FDA0003492312040000036
Node j voltage when node j side is PQ, PI, PQV node
Figure FDA0003492312040000037
Can be calculated by the formula (5);
Figure FDA0003492312040000041
calculating the voltage of a PV node;
in a branch of the distribution network, the voltage of the left end node i is
Figure FDA0003492312040000042
And active power P of right end node jjAnd an effective value of voltage VjKnowing the voltage phase angle theta of node jjAnd reactive power QjUnknown, in theory, the voltage of the node j is constant, the current, active power and reactive power of the branch at the downstream of the node j are all determined by the voltage of the node, the voltage of each node of the branch at the upstream and the reactive power of the node determine the voltage of the node j, namely the PV node, therefore, the voltage of the node j is supplied to the PV nodeThe voltage of the node j can be ensured to be constant by adjusting the reactive power of the node j in the iterative process of timing and load flow calculation, and the reactive power regulating quantity delta Q of the node is introducedj；
The calculated Delta Q is obtained through one branchjThe left side of the branch is close to the upper system side, the node of the branch is numbered i, the node on the right side is a PV node, the node is numbered j, the impedance of the branch is ZijR + jX, by adjusting the reactive power of the node by an amount Δ QjThe branch current is changed, so that the node voltage is changed, the capacitance effect of the line to the ground is not considered, and the following equation is obtained according to the equivalent circuit of the line:
Figure FDA0003492312040000043
in the formula:
Figure FDA0003492312040000044
the active and reactive power flowing into node j for the branch,
Figure FDA0003492312040000045
the adjustment quantity of the reactive power at the kth iteration is;
both sides of equation (16) are multiplied by
Figure FDA0003492312040000046
Obtaining:
Figure FDA0003492312040000047
order:
Figure FDA0003492312040000048
substituted into formula (17);
and separating the real part and the imaginary part to obtain an equation:
Figure FDA0003492312040000051
in this system of equations, Vi (k),Vj,
Figure FDA0003492312040000052
R, X are known quantities, theta(k)，
Figure FDA0003492312040000053
Solving the equation for unknown quantity;
obtained by the formula (18):
Figure FDA0003492312040000054
substituting formula (19) to obtain:
Figure FDA0003492312040000055
the two sides of the equation are multiplied by X:
Figure FDA0003492312040000056
the above formula is written in order:
Figure FDA0003492312040000057
order:
Figure FDA0003492312040000058
equation (23) is simplified to:
Figure FDA0003492312040000059
namely:
Figure FDA00034923120400000510
wherein:
Figure FDA00034923120400000511
from the above formula:
Figure FDA0003492312040000061
thus, the voltage phase angle at the PV node is:
Figure FDA0003492312040000062
and then obtained by the formula (19):
Figure FDA0003492312040000063
calculated by the formula (26)
Figure FDA0003492312040000064
Then by
Figure FDA0003492312040000065
Calculated to obtain theta(k)By substituting the formula (27)
Figure FDA0003492312040000066
The reactive power regulating quantity can make the voltage of the PV node constant, the reactive power correcting direction is determined, if the voltage is regular, the reactive power injection of the PV node needs to be reduced, and if the voltage is negative, the reactive power injection of the PV node needs to be increased;
the reactive power of the PV node is taken as:
Figure FDA0003492312040000067
in the formula: k is a radical ofpFor the correction coefficient, it is 0.05-0.1.
2. The active power distribution network compact forward-backward flow calculation method according to claim 1, wherein the node voltage error is defined as an absolute value of a difference between a current iteration voltage and a last iteration voltage of the node i, that is:
ei＝|Vi (k)-Vi (k-1)|i∈N (29)；
in the formula: n is a node number set, and the voltage V of the node ii (k)；
Obtaining the maximum value of the node voltage error:
emax＝max(ei|i∈N) (30)；
when the maximum value of the node voltage error is smaller than the error precision epsilon set in the calculation, namely emaxThe iteration converges when < epsilon.
3. The method for calculating the succinct forward-backward flow of the active power distribution network according to claim 2, wherein the forward-backward flow calculation of the power distribution network accessing the DG comprises the following specific procedures:
(1) giving the precision of error epsilon, total number of nodes and branches n and nbInputting original parameters of the distribution network;
(2) obtaining forward-pushing branch sequences seq _ forward and backward-substituting branch sequences seq _ back and seq _ back according to a power distribution network operation topology and branch sequence algorithm;
(3) iterating the rated value of each node voltage for the first time, wherein the current of each branch is 0;
(4) a forward pushing process:
1) the current branch number m is equal to 0;
2) obtaining a branch from seq _ forward;
3) calculating reactive power and injection current of a node on the left side of the branch circuit according to the forward-pushing time node injection current and the reactive power;
4) calculating the right side current and the left side current of the branch circuit;
5) adding a left current to the left node;
6) judging whether m is equal to nbIf yes, go to (5), if m is equal to m +1, return to 2);
(5) the back substitution process:
1) the current branch number m is equal to 0;
2) obtaining a branch from seq _ back;
3) calculating the voltage or the reactive power of the right node according to the back substitution process;
4) judging whether m is equal to nbEqual to revolution (6), not equal to m +1, return 2);
(6) and (3) error discrimination: calculating the absolute value e of the node voltage errori＝|Vi (k)-Vi (k-1)1,2 … n, if max (e)1,e2…en) If the value is less than epsilon, the iteration is converged, the calculation is finished and the result is output, otherwise, the step (4) is switched to continue the next iteration.
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