CN103246804B - Obtain the method and device of Electric Power System Node Voltage - Google Patents

Abstract

The invention discloses a kind of method and device obtaining Electric Power System Node Voltage, belong to electrical distribution field.Described method includes: obtain network structure and the component parameters of each node of power system；The iteration general equation of PV node, the iteration general equation of PQ node and the iterative equation of slow convergence PQ node is generated according to network structure and component parameters；The iterative equation of iteration general equation, the iteration general equation of PQ node and slow convergence PQ node according to this PV node calculates PV node and the voltage of PQ node.The present invention generates the iteration general equation of PV node, the iteration general equation of PQ node and the iterative equation of slow convergence PQ node by the network structure according to power system and component parameters, and calculate PV node and the voltage of PQ node according to the iterative equation of the iteration general equation of PV node, the iteration general equation of PQ node and slow convergence PQ node, reach to improve the purpose of node voltage computational convergence.

Description

Method and device for acquiring node voltage of power system

Technical Field

The invention relates to the field of power transmission, in particular to a method and a device for acquiring node voltage of a power system.

Background

The tidal current calculation is the calculation of the distribution of active power, reactive power and voltage in the power grid under the given power system network topology, element parameters and power generation and load parameters. The calculation of the voltage amplitude and the voltage phase angle of each node is the most core part in the power flow calculation.

Nodes in the power system may include at least one PV node, at least one PQ node, and a balancing node. The active power P and the voltage amplitude V of the PV node are known, the active power P and the reactive power Q of the PQ node are known, and the voltage amplitude V and the voltage phase angle theta of the balance node are known. When load flow calculation is carried out on each node, only the voltage amplitude and the voltage phase angle of the PQ node and the voltage phase angle of the PV node need to be calculated. The existing method for calculating the voltage amplitude and the voltage phase angle of the PQ node and the voltage phase angle of the PV node mainly comprises the following steps:

firstly, generating an iterative equation of a PV node and an iterative equation of a PQ node according to a network structure and element parameters of a power system; secondly, calculating the reactive power injected into the PV node according to preset initial voltage values of all the nodes, calculating the injection current of the PV node according to the reactive power injected into the PV node and substituting the injection current into an iterative equation of the PV node, and finally correcting the calculation result of the iterative equation of the PV node according to the given voltage amplitude of the PV node to obtain the voltage of the PV node (the node voltage comprises the voltage amplitude and the voltage phase angle); and thirdly, calculating the voltage of the PQ node according to the obtained voltage of the PV node and an iterative equation of the PQ node.

In the process of implementing the invention, the inventor finds that the prior art has at least the following problems:

the existing method for calculating the voltage of the PQ node and the PV node needs to calculate the reactive power of the PV node when the PV node is processed, and when the number of the PV nodes in the power system is large, the calculation convergence of the reactive power of the PV node is poor or even does not converge, so that the convergence of the calculation of the node iterative equation is further influenced.

Disclosure of Invention

In order to solve the problem of poor convergence of node voltage calculation in the prior art, the embodiment of the invention provides a method and a device for acquiring node voltage of a power system. The technical scheme is as follows:

in one aspect, a method for obtaining a node voltage of a power system is provided, and the method includes:

acquiring network structure and element parameters of each node of a power system, wherein the node at least comprises: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the active power and the voltage amplitude of the PV node are known, the active power and the reactive power of the PQ node are known, and the PQ node comprises at least one slow convergence PQ node;

generating an iteration general equation of the PV node and an iteration general equation of the PQ node according to the network structure and element parameters, and generating an iteration equation of the slow convergence PQ node according to the network structure and element parameters;

calculating the current injection quantity of each node according to the preset initial voltage value of each node;

calculating the actual active power of the PV node according to the current injection quantity of each node, and calculating the voltage of the PV node according to the actual active power of the PV node and an iterative general equation of the PV node;

calculating the voltage of the PQ node according to the voltage of the PV node, the general iterative equation of the PQ node and the iterative equation of the slow converged PQ node.

Prior to the generating an iterative equation for the slow converged PQ node from the network fabric and element parameters, the method further comprises:

calculating a convergence factor of the PQ node;

and sequencing the PQ nodes according to the descending order of the convergence factors, and determining n nodes in the front sequence as the slow convergence PQ nodes, wherein n is a preset proportion.

The calculating the convergence factor of the PQ node comprises:

calculating the convergence factor of the PQ node according to a convergence factor calculation formula, wherein the convergence factor calculation formula is as follows:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{\left(\mathrm{\∞}\right)}\right|}^2};$

wherein α is the convergence factor, Z is the self-impedance of PQ node, S is the sum of the self-active power and reactive power of PQ node, U^(∞)Is the final solution for the voltage at the PQ node.

The iterative equation for generating the slow converged PQ node from the network fabric and element parameters includes:

generating an impedance matrix of the PQ node according to the network structure and element parameters;

generating an iterative equation for the slow converged PQ node from the impedance matrix for the PQ node;

wherein the iterative equation of the slow convergence PQ node is as follows:

$U_B^{(k+1)}=Z_{BA}{I}_A^{(k+1)}+Z_{BB}{I}_B^{\left(k\right)};$

wherein,the voltage of the slow converged PQ node calculated for the k +1 th iteration, the Z_BAFor fast converging PQ nodes to slow converging PQ nodesImpedance matrix, said Z_BBFor the slow converging PQ node's own impedance matrix,the resulting current injection amount for the fast converging PQ node is calculated for the (k + 1) th iteration,calculating the current injection amount of the slow convergent PQ node for the k-th iteration, wherein the fast convergent PQ node is a PQ node except the slow convergent PQ node.

The calculating the voltage of the PQ node according to the voltage of the PV node, the general iterative equation of the PQ node, and the iterative equation of the slow converged PQ node includes:

performing q iterative computations on the voltage of the PQ node, wherein q is an integer greater than 1;

when the 1 st iteration calculation is carried out, solving an iteration general equation of the PQ node according to the voltage of the PV node to obtain the voltage of the fast convergence PQ node obtained by the 1 st calculation and the voltage of the slow convergence PQ node obtained by the 1 st calculation before correction; correcting the voltage of the slow convergence PQ node obtained by the 1 st calculation before correction according to the iterative equation of the slow convergence PQ node to obtain the corrected voltage of the slow convergence PQ node obtained by the 1 st calculation; determining the obtained voltage of the fast convergence PQ node obtained by the 1 st calculation and the corrected voltage of the slow convergence PQ node obtained by the 1 st calculation as the voltage obtained by the 1 st calculation;

when the q-th iterative computation is carried out, recalculating the current injection quantity of each node according to the voltage obtained by the q-1-th iterative computation and the voltage of the PV node, recalculating the actual active power of the PV node according to the recalculated current injection quantity of each node, recalculating the voltage of the PV node according to the recalculated actual active power of the PV node and the iterative total equation of the PV node, solving the iterative total equation of the PQ node according to the recalculated voltage of the PV node, and obtaining the voltage of the fast convergence PQ node obtained by the q-th computation and the voltage of the slow convergence PQ node obtained by the q-th computation before correction; correcting the voltage of the slow convergence PQ node obtained by the calculation of the q times before correction according to the iterative equation of the slow convergence PQ node to obtain the corrected voltage of the slow convergence PQ node obtained by the calculation of the q times; determining the obtained fast convergence PQ node voltage obtained by the q-th calculation and the corrected slow convergence PQ node voltage obtained by the q-th calculation as the voltage obtained by the q-th calculation;

judging whether the voltage change module value calculated for the q times is smaller than a preset value or not, wherein the voltage change module value calculated for the q times is the module value of the difference between the voltage obtained by the q times of calculation and the voltage obtained by the q-1 times of iterative calculation;

if the voltage change modulus calculated for the q-th time is smaller than a preset value, determining the voltage obtained by the q-th time calculation as the voltage of the PQ node;

and if the voltage change module value calculated for the q th time is not less than the preset value, continuing to perform iterative calculation for the q +1 th time.

The correcting the voltage of the slow convergence PQ node obtained by the calculation of the q times before correction according to the iterative equation of the slow convergence PQ node to obtain the corrected voltage of the slow convergence PQ node obtained by the calculation of the q times comprises the following steps:

keeping the voltage of the fast converging PQ node obtained by the q-th calculation unchanged, performing m times of iterative calculation on the voltage of the slow converging PQ node according to an iterative equation of the slow converging PQ node by taking the voltage of the fast converging PQ node obtained by the q-th calculation as an initial value, and taking the voltage of the slow converging PQ node obtained by the m-th iterative calculation as the corrected voltage of the slow converging PQ node, wherein m is an integer greater than or equal to 1.

In another aspect, an apparatus for obtaining a node voltage of a power system is provided, where the apparatus includes:

an obtaining module, configured to obtain a network structure and element parameters of each node of a power system, where the node at least includes: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the active power and the voltage amplitude of the PV node are known, the active power and the reactive power of the PQ node are known, and the PQ node comprises at least one slow convergence PQ node;

the first equation generation module is used for generating an iteration general equation of the PV node and an iteration general equation of the PQ node according to the network structure and the element parameters acquired by the acquisition module;

the second equation generation module is used for generating an iterative equation of the slow convergent PQ node according to the network structure and the element parameters acquired by the acquisition module;

the current calculation module is used for calculating the current injection quantity of each node according to the preset initial voltage value of each node;

the active power calculation module is used for calculating the actual active power of the PV node according to the current injection quantity of each node calculated by the current calculation module;

the first voltage calculation module is used for calculating the voltage of the PV node according to the actual active power of the PV node and the iterative overall equation of the PV node generated by the first equation generation module;

and the second voltage calculation module is used for calculating the voltage of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module, the total iterative equation of the PQ node generated by the first equation generation module and the iterative equation of the slow convergence PQ node generated by the second equation generation module.

The device further comprises:

a convergence factor calculation module, configured to calculate a convergence factor of the PQ node before the second equation generation module generates the iterative equation of the slow convergence PQ node according to the network structure and the element parameters acquired by the acquisition module;

and the node determining module is used for sequencing the PQ nodes according to the descending order of the convergence factors calculated by the convergence factor calculating module, and determining n nodes in the front of the sequence as the slow convergence PQ nodes, wherein n is a preset proportion.

The convergence factor calculation module is configured to calculate a convergence factor of the PQ node according to a convergence factor calculation formula, where the convergence factor calculation formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{\left(\mathrm{\∞}\right)}\right|}^2};$

wherein α is the convergence factor, Z is the self-impedance of PQ node, S is the sum of the self-active power and reactive power of PQ node, U^(∞)Is the final solution for the voltage at the PQ node.

The second equation generation module includes:

an impedance matrix generating unit for generating an impedance matrix of the PQ node according to the network structure and the element parameters;

the iterative equation generating unit is used for generating an iterative equation of the slow converged PQ node according to the impedance matrix of the PQ node generated by the impedance matrix generating unit;

wherein the iterative equation of the slow convergence PQ node is as follows:

$U_B^{(k+1)}=Z_{BA}{I}_A^{(k+1)}+Z_{BB}{I}_B^{\left(k\right)};$

wherein,the voltage of the slow converged PQ node calculated for the k +1 th iteration, the Z_BAAn impedance matrix for the fast converging PQ node to the slow converging PQ node, the Z_BBFor the slow converging PQ node's own impedance matrix,the resulting current injection amount for the fast converging PQ node is calculated for the (k + 1) th iteration,calculating the current injection amount of the slow convergent PQ node for the k-th iteration, wherein the fast convergent PQ node is other than the slow convergent PQ nodeThe PQ node of (a).

The second voltage calculation module includes:

the voltage calculation unit is used for performing q times of iterative calculation on the voltage of the PQ node, wherein q is an integer greater than 1;

the voltage calculation unit includes:

the voltage calculation subunit is configured to, when performing iterative calculation for the 1 st time, solve an iterative total equation of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module, and obtain a voltage of the fast convergence PQ node calculated for the 1 st time and a voltage of the slow convergence PQ node calculated for the 1 st time before correction;

the voltage correction subunit is configured to correct, according to the iterative equation of the slow convergence PQ node, the voltage before correction of the slow convergence PQ node obtained by the voltage calculation subunit at the 1 st time, and obtain a corrected voltage of the slow convergence PQ node obtained by the 1 st time;

a voltage determining subunit, configured to determine, as the voltage obtained by the 1 st calculation, the voltage of the fast converging PQ node obtained by the voltage calculating subunit and the voltage obtained by the voltage correcting subunit, after correction, of the slow converging PQ node obtained by the 1 st calculation;

when the q-th iterative computation is performed, the current computation module is further configured to recalculate the current injection amount of each node according to the voltage obtained by the q-1-th iterative computation determined by the voltage determination subunit and the voltage of the PV node computed by the first voltage computation module;

the active power calculation module is further configured to recalculate the actual active power of the PV node according to the current injection amount of each node recalculated by the current calculation module;

the first voltage calculation module is further used for recalculating the voltage of the PV node according to the actual active power of the PV node recalculated by the active power calculation module and the iterative overall equation of the PV node;

the voltage calculation subunit is configured to, when performing iterative calculation for the q-th time, solve an iterative total equation of the PQ node according to the voltage of the PV node recalculated by the first voltage calculation module, and obtain a voltage of the fast convergence PQ node calculated for the q-th time and a voltage of the slow convergence PQ node calculated for the q-th time before correction;

the voltage correction subunit is configured to correct, according to the iterative equation of the slow convergence PQ node, the voltage before correction of the slow convergence PQ node obtained by the voltage calculation subunit for the q-th calculation, and obtain a corrected voltage of the slow convergence PQ node obtained by the q-th calculation;

the voltage determining subunit is configured to determine, as the voltage obtained by the q-th calculation, the voltage of the fast converging PQ node obtained by the voltage calculating subunit and the corrected voltage of the slow converging PQ node obtained by the q-th calculation obtained by the voltage correcting subunit;

the second voltage calculating module further includes:

the judging unit is used for judging whether the voltage change module value calculated for the q times is smaller than a preset value or not, wherein the voltage change module value calculated for the q times is a module value of the difference between the voltage obtained by the q times of calculation determined by the voltage determining subunit and the voltage obtained by the q-1 th iteration calculation determined by the voltage determining subunit;

a voltage determining unit, configured to determine the voltage obtained through the q-th computation as the voltage of the PQ node if the determining unit determines that the voltage change modulus calculated through the q-th computation is smaller than a preset value;

and the voltage calculation unit is used for continuing to carry out iterative calculation for the (q + 1) th time if the judgment unit judges that the voltage change modulus value calculated for the (q) th time is not less than the preset value.

And the voltage correction subunit is configured to keep the voltage of the fast converging PQ node calculated by the voltage calculation subunit q times unchanged, perform iterative calculation on the voltage of the slow converging PQ node m times according to an iterative equation of the slow converging PQ node by using the voltage of the slow converging PQ node calculated by the voltage calculation subunit q times before correction as an initial value, and use the voltage of the slow converging PQ node calculated by the iterative calculation m times as a corrected voltage of the slow converging PQ node, where m is an integer greater than or equal to 1.

The technical scheme provided by the embodiment of the invention has the following beneficial effects:

the method comprises the steps of generating an iteration total equation of a PV node, an iteration total equation of a PQ node and an iteration equation of a slow convergence PQ node according to a received network structure and element parameters of the power system, calculating the voltage of the PV node according to the actual active power of the PV node and the iteration total equation of the PV node, and further calculating the voltage of the PQ node according to the voltage of the PV node, the iteration total equation of the PQ node and the iteration equation of the slow convergence PQ node, so that the aim of improving the node voltage calculation convergence is fulfilled.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a flowchart of a method for obtaining a node voltage of an electrical power system according to an embodiment of the present invention;

fig. 2 is a flowchart of a method for obtaining a node voltage of an electrical power system according to a second embodiment of the present invention;

fig. 3 is a device structure diagram of a device for obtaining node voltage of an electric power system according to a third embodiment of the present invention;

fig. 4 is a device structure diagram of a device for obtaining a node voltage of an electric power system according to a fourth embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

Example one

Referring to fig. 1, a flowchart of a method for obtaining a node voltage of an electrical power system according to an embodiment of the present invention is shown. The method can be applied to calculating the voltage of each node in the power system, wherein the nodes in the power system can comprise: at least one PQ node, at least one PV node, and a balancing node. The method for acquiring the node voltage of the power system can comprise the following steps:

step 101, obtaining network structure and element parameters of each node of a power system, wherein the node at least comprises: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the PV node has known active power and voltage amplitude, the PQ node has known active power and reactive power, and the PQ node comprises at least one slow convergence PQ node;

102, generating an iteration general equation of the PV node and an iteration general equation of the PQ node according to the network structure and the element parameters;

103, generating an iterative equation of the slow convergence PQ node according to a network structure and element parameters;

104, calculating the current injection quantity of each node according to the preset initial voltage value of each node;

step 105, calculating the actual active power of the PV node according to the current injection quantity of each node, and calculating the voltage of the PV node according to the actual active power of the PV node and the iterative overall equation of the PV node;

and 106, calculating the voltage of the PQ node according to the voltage of the PV node, the iteration general equation of the PQ node and the iteration equation of the slowly-converged PQ node.

In summary, according to the method for obtaining the node voltage of the power system provided in the first embodiment of the present invention, the total iteration equation of the PV node, the total iteration equation of the PQ node, and the iteration equation of the slow convergence PQ node are generated according to the received network structure and the element parameters of the power system, the voltage of the PV node is calculated according to the actual active power of the PV node and the total iteration equation of the PV node, and the voltage of the PQ node is further calculated according to the voltage of the PV node, the total iteration equation of the PQ node, and the iteration equation of the slow convergence PQ node, so as to achieve the purpose of improving the convergence of the calculation of the node voltage.

Example two

To further describe the method for obtaining the node voltage of the power system according to the first embodiment of the present invention, please refer to fig. 2, which shows a flowchart of the method for obtaining the node voltage of the power system according to the second embodiment of the present invention. The method may be used to calculate voltages at nodes in a power system comprising: at least one PQ node, at least one PV node, and a balancing node; wherein, since the voltage amplitude and the voltage phase angle of the balance node are known quantities, only the voltage amplitude and the voltage phase angle of the PQ node and the voltage phase angle of the PV node need to be calculated. The method for acquiring the node voltage of the power system can comprise the following steps:

step 201, a voltage calculation device receives network structures and element parameters of nodes of a power system;

step 202, writing a power system flow equation according to each node network structure and element parameter column, and generating an iteration general equation of a PQ node and an iteration general equation of a PV node according to the power system flow equation;

network nodes can be generally classified into 3 types according to the difference of node injection conditions: PQ nodes, PV nodes, and balancing nodes.

The PQ node is usually a load node or a network connection node, the active power P and the reactive power Q of the PQ node are known, and the voltage amplitude U and the voltage phase angle theta are to be solved; the PV node is usually a generator outlet node, the active power P and the voltage amplitude U of the PV node are known, and the voltage phase angle theta is to be solved; the balancing node is typically a generator outlet node, with a known voltage magnitude U and voltage phase angle θ, and there is one and only one balancing node in the power system.

The known conditions and the variables to be required of the PQ node, the PV node and the balance node are different, so that the node voltage equation is required to be processed respectively aiming at different node forms when being constructed.

202a, PQ node processing:

for an n-node power system, firstly, it is assumed that the network does not include PV nodes, 1 balancing node is provided, and the serial number of the balancing node is set as n. Constructing a node admittance matrix Y, and further constructing a node voltage equation as follows:

$\left[\begin{array}{cc}{Y}_{PQPQ}& Y_{PQVV}\\ 0& Y_{VVVV}\end{array}\right]\left[\begin{array}{c}{U}_{PQ}\\ U_{VV}\end{array}\right]=\left[\begin{array}{c}{I}_{PQ}\\ U_{VV}\end{array}\right]---(2-1)$

wherein U is_PQ＝[U₁…U_n-1]^T，U_i＝[U_iAU_iBU_iC]^Ti＝1,2,……,n-1。U_iA、U_iB、U_iCA, B, C three-phase voltages respectively corresponding to nodes i。U_VV＝[U_VVAU_VVBU_VVC]^T。I_PQ＝[I₁…I_n-1]^TInjecting a current into the node, I_i＝[I_iAI_iBI_iC]^Ti＝1,2,……,n-1， $I_{i\mathrm{\ψ}}=\frac{P_{i\mathrm{\ψ}}-{\mathrm{jQ}}_{i\mathrm{\ψ}}}{U_{i\mathrm{\ψ}}^{*}},\mathrm{\ψ}=A,B,C,$ P, Q inject power for the node.

202b, PV node processing:

because the number of known conditions of the PV node is less than that of unknown conditions, an internal potential node of a generator of an equivalent power supply is required to be connected to the PV node, and the PV node is converted into a PQ node.

Because the internal resistance of the generator is pure reactance, zero sequence reactance values, positive sequence reactance values and negative sequence reactance values are generally given, and are respectively: xGi0, xGi1, xGi2, there is no coupling between the three sequences. By conversion, a transformer three-phase admittance matrix YGi is obtained.

$Y_{Gi}=T\left[\begin{array}{ccc}\frac{1}{{\mathrm{jx}}_{Gi1}}& & \\ & \frac{1}{{\mathrm{jx}}_{Gi2}}& \\ & & \frac{1}{{\mathrm{jx}}_{Gi0}}\end{array}\right]T^{-1}---(2-2)$

Wherein: $T=\left[\begin{array}{ccc}1& 1& 1\\ {\mathrm{\α}}^2& \mathrm{\α}& 1\\ \mathrm{\α}& {\mathrm{\α}}^2& 1\end{array}\right],$ α＝e^j120°，T^-1is the inverse of the matrix T.

The voltage equation of the PV node and the potential node column in the generator is as follows:

$\left[\begin{array}{cc}{Y}_{Gi}& -Y_{Gi}\\ -Y_{Gi}& Y_{Gi}\end{array}\right]\left[\begin{array}{c}{U}_{PVi}\\ U_{Gi}\end{array}\right]=\left[\begin{array}{c}{I}_{PVLi}\\ I_{Gi}\end{array}\right]---(2-3)$

$U_{PVi}=\left[\begin{array}{c}{U}_{PViA}\\ U_{PViB}\\ U_{PViC}\end{array}\right],U_{Gi}=\left[\begin{array}{c}{U}_{GiA}\\ U_{GiB}\\ U_{GiC}\end{array}\right],I_{PVLi}=\left[\begin{array}{c}{S^{*}}_{PVLiA}/U_{PViA}^{*}\\ {S^{*}}_{PVLiB}/{U^{*}}_{PViB}\\ {S^{*}}_{PVLiC}/{U^{*}}_{PViC}\end{array}\right],I_{Gi}=\left[\begin{array}{c}{S^{*}}_{GiA}/{U^{*}}_{GiA}\\ {S^{*}}_{GiB}/U_{GiB}^{*}\\ {S^{*}}_{GiC}/U_{GiC}^{*}\end{array}\right].$

wherein U is_GiA、U_GiB、U_GiCA, B, C three-phase voltage phasors, U, of potential nodes in the generator to which the PV node i is connected_PViA、U_PViB、U_PViCA, B, C three-phase voltage phasors at PV node i, respectively. Since YGi is a purely reactive component and does not consume active power, there are:

$\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{P}_{Gi\mathrm{\β}}=\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{P}_{PVGi\mathrm{\β}}---(2-4)$

definition of

Then there is

Therefore, there are:

wherein $U_{PVi}=\left[\begin{array}{c}{U}_{PViA}\\ U_{PViB}\\ U_{PViC}\end{array}\right],$ $I_{PVLi}={\left[\begin{array}{c}-S_{PVLiA}/U_{PViA}\\ -S_{PVLiB}/U_{PViB}\\ -S_{PVLiC}/U_{PViC}\end{array}\right]}^{*},$ $I_{GiA}=\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{S^{*}}_{Gi\mathrm{\β}}/U_{GiA}^{*}.$

Adding generator nodes to all PV nodes according to the formula (2-9), and correcting the formula (2-1) to obtain

$\left[\begin{array}{cccc}{Y}_{PQPQ}& Y_{PQPV}& Y_{PQVV}& \\ Y_{PVPQ}& Y_{PVPV}+Y_{PVPV}^{\′}& Y_{PVVV}& Y_{PVGA}\\ Y_{VVPQ}& Y_{VVPV}& Y_{VVVV}& \\ & Y_{GAPV}& & Y_{GAGA}\end{array}\right]\left[\begin{array}{c}{U}_{PQ}\\ U_{PV}\\ U_{VV}\\ U_{GA}\end{array}\right]=\left[\begin{array}{c}{I}_{PQ}\\ I_{PVL}\\ I_{VV}\\ I_{GA}\end{array}\right]---(2-10)$

202c, processing of balance nodes:

the voltage amplitude and phase angle of the balance node are given values and are not directly connected with a load. Applying the equations (2-9), the equation for the equilibrium node column can be obtained

Wherein $U_{VV}=\left[\begin{array}{c}{U}_{VVA}\\ U_{VVB}\\ U_{VVC}\end{array}\right],$ $I_{VV}=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right],$ $I_{GVVA}=\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{S^{*}}_{GVV\mathrm{\β}}/U_{GVVA}^{*}.$

By modifying the formula (2-10) with the formula (2-11), the following results are obtained:

$\left[\begin{array}{ccccc}{Y}_{PQPQ}& Y_{PQPV}& Y_{PQVV}& & \\ Y_{PVPQ}& Y_{PVPV}+Y_{PVPV}^{\′}& Y_{PVVV}& Y_{PVGA}& \\ Y_{VVPQ}& Y_{VVPV}& Y_{VVVV}+Y_{VVVV}^{\′}& & Y_{VVGVVA}\\ & Y_{GAPV}& & Y_{GAGA}& \\ & & Y_{GVVAVV}& & Y_{GVVAGVVA}^{\′}\end{array}\right]\left[\begin{array}{c}{U}_{PQ}\\ U_{PV}\\ U_{VV}\\ U_{GA}\\ U_{GVVA}\end{array}\right]=\left[\begin{array}{c}{I}_{PQ}\\ I_{PVL}\\ I_{VV}\\ I_{GA}\\ I_{GVVA}\end{array}\right]---(2-12)$

wherein Y'_VVVV,Y_VVGVVA,Y_GVVAVV,Y′_GVVAGVVAA modification matrix to the node admittance matrix for the balanced nodes.

202d, establishing a power flow equation of the power system:

according to the above formula, the total number of network nodes is n, wherein the total number of PV nodes is m, and the total number of balance nodes is 1. An equation is established according to the formula (2-12), and the matrix on the left side of the equation is subjected to elementary transformation, which is abbreviated as the following formula:

$\left[\begin{array}{ccccc}{Y}_{PQPQ}^{\′}& Y_{PQPV}^{\′}& Y_{PQVV}^{\′}& Y_{PQPVA}^{\′}& Y_{PQVVA}^{\′}\\ Y_{PVPQ}^{\′}& Y_{PVPV}^{\′}& Y_{PVVV}^{\′}& Y_{PVPVA}^{\′}& Y_{PVVVA}^{\′}\\ Y_{VVPQ}^{\′}& Y_{VVPV}^{\′}& Y_{VVVV}^{\′}& Y_{VVPVA}^{\′}& Y_{VVVVA}^{\′}\\ Y_{PVAPQ}^{\′}& Y_{PVAPV}^{\′}& Y_{PVAVV}^{\′}& Y_{PVAPVA}^{\′}& Y_{PVAVVA}^{\′}\\ Y_{VVAPQ}^{\′}& Y_{VVAPV}^{\′}& Y_{VVAVV}^{\′}& Y_{VVAPVA}^{\′}& Y_{VVAVVA}^{\′}\end{array}\right]\left[\begin{array}{c}{U}_{PQ}\\ U_{PV}^{\′}\\ U_{VV}^{\′}\\ U_{PVA}\\ U_{VVA}\end{array}\right]=\left[\begin{array}{c}{I}_{PQ}\\ I_{PVL}\\ I_{VV}\\ I_{GA}\\ I_{GVVA}\end{array}\right]---(2-13)$

wherein

$U_{PQ}=\left[\begin{array}{c}\left[\begin{array}{c}{U}_{PQ1A}\\ U_{PQ1B}\\ U_{PQ1C}\end{array}\right]\\ ...\\ \left[\begin{array}{c}{U}_{PQ(n-m-1)A}\\ U_{PQ(n-m-1)B}\\ U_{PQ(n-m-1)C}\end{array}\right]\end{array}\right],$ $U_{PV}^{\′}=\left[\begin{array}{c}\left[\begin{array}{c}{U}_{G1A}\\ U_{PV1B}\\ U_{PV1C}\end{array}\right]\\ ...\\ \left[\begin{array}{c}{U}_{GmA}\\ U_{PVmB}\\ U_{PVmC}\end{array}\right]\end{array}\right],$ $U_{VV}^{\′}=\left[\begin{array}{c}{U}_{GVVA}\\ U_{VVB}\\ U_{VVC}\end{array}\right],$ $U_{PVA}=\left[\begin{array}{c}{U}_{PV1A}\\ ...\\ U_{PVmA}\end{array}\right]$

In the formula, the equation left side U_PQ、U′_PV、U′_VVThe amplitude and phase angle of each variable in the (1) are all to be solved, U_PVAThe amplitude of each variable is known, the phase angle is unknown, U_VVAAre known. I is_PQ、I_PVL、I_VVThe active power and the reactive power in the equation are known; i is_GAThe active power in the equation is known and the reactive power is unknown. Combining terms with the same known conditions, the conditions to be solved, and simplifying the formula (2-13) as follows:

$\left[\begin{array}{ccc}{Y}_{\mathrm{\ω}\mathrm{\ω}}& Y_{\mathrm{\ω}\mathrm{\ϵ}}& Y_{\mathrm{\ω}\mathrm{\ξ}}\\ Y_{\mathrm{\ϵ}\mathrm{\ω}}& Y_{\mathrm{\ϵ}\mathrm{\ϵ}}& Y_{\mathrm{\ϵ}\mathrm{\ξ}}\\ Y_{\mathrm{\ξ}\mathrm{\ω}}& Y_{\mathrm{\ξ}\mathrm{\ϵ}}& Y_{\mathrm{\ξ}\mathrm{\ξ}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{\ω}}\\ U_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{\ω}}\\ I_{\mathrm{\ϵ}}\\ I_{\mathrm{\ξ}}\end{array}\right]---(2-14)$

wherein, U_ω＝[U_PQU′_PVU′_VV]，U ＝[U_PVA]，Wherein, U_ξFor known conditions, the rewritten formula (2-14) is:

$\left[\begin{array}{ccc}{Y}_{\mathrm{\ω}\mathrm{\ω}}& Y_{\mathrm{\ω}\mathrm{\ϵ}}& Y_{\mathrm{\ω}\mathrm{\ξ}}\\ Y_{\mathrm{\ϵ}\mathrm{\ω}}& Y_{\mathrm{\ϵ}\mathrm{\ϵ}}& Y_{\mathrm{\ϵ}\mathrm{\ξ}}\\ & & 1\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{\ω}}\\ U_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{\ω}}\\ I_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]---(2-15)$

gaussian elimination of formula (2-15) gives:

$\left[\begin{array}{ccc}{Y}_{\mathrm{\ω}\mathrm{\ω}}& Y_{\mathrm{\ω}\mathrm{\ϵ}}& Y_{\mathrm{\ω}\mathrm{\ξ}}\\ & Y_{\mathrm{\ϵ}\mathrm{\ϵ}}^{\′}& Y_{\mathrm{\ϵ}\mathrm{\ξ}}^{\′}\\ & & 1\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{\ω}}\\ U_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{\ω}}\\ I_{\mathrm{\ϵ}}^{\′}\\ U_{\mathrm{\ξ}}\end{array}\right]---(2-16)$

wherein, the equation (2-16) is the Gaussian power flow equation of the power system.

The expansion (2-16) is:

$\left\{\begin{array}{c}{r}_{\mathrm{\ω}\mathrm{\ω}}{U}_{\mathrm{\ω}}+Y_{\mathrm{\ω}\mathrm{\ϵ}}{U}_{\mathrm{\ϵ}}+Y_{\mathrm{\ω}\mathrm{\ξ}}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ω}}\\ Y_{\mathrm{\ϵ}\mathrm{\ϵ}}^{\′}{U}_{\mathrm{\ϵ}}+Y_{\mathrm{\ϵ}\mathrm{\ξ}}^{\′}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ϵ}}^{\′}\end{array}\right.---(2-17)$

the total iterative equation for constructing the PQ node and the total iterative equation for the PV node are as follows:

$\left\{\begin{array}{c}{Y}_{\mathrm{\ω}\mathrm{\ω}}{U}_{\mathrm{\ω}}^{(k+1)}+Y_{\mathrm{\ω}\mathrm{\ϵ}}{U}_{\mathrm{\ϵ}}^{(k+1)}+Y_{\mathrm{\ω}\mathrm{\ξ}}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ω}}^{\left(k\right)}\\ Y_{\mathrm{\ϵ}\mathrm{\ϵ}}^{\′}{U}_{\mathrm{\ϵ}}^{(k+1)}+Y_{\mathrm{\ϵ}\mathrm{\ξ}}^{\′}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ϵ}}^{\′\left(k\right)}\end{array}\right.---(2-18)$

in the formula (2-18), the upper half part is an iteration general equation of a PQ node, the lower half part is an iteration general equation of a PV node, and k corresponds to the kth iteration calculation.Calculating according to the active power, the reactive power and the kth iteration voltage value of the node;active power injected into the middle node is known, and reactive power is unknown.

Step 203, the voltage calculation device generates an iterative equation for converging the PQ node at a slow speed according to the network structure and the element parameters;

the voltage calculation device first needs to determine which of the PQ nodes are slow converging PQ nodes before generating an iterative equation for the slow converging PQ nodes based on network structure and element parameters.

Specifically, the voltage calculation means first calculates a convergence factor of each PQ node; the PQ nodes are sorted in the order of descending convergence factors, and n nodes in the top of the order are determined as slow-converging PQ nodes, where n is the total number of PQ nodes at a predetermined ratio, that is, a node with the maximum convergence factor among the PQ nodes at a predetermined ratio is used as a slow-converging PQ node, for example, a node with the maximum convergence factor of 20% among all PQ nodes is used as a slow-converging PQ node, and PQ nodes other than the slow-converging PQ nodes are called fast-converging PQ nodes.

Specifically, the node equations for an n-node system are written in matrix form, where subscript E denotes all nodes except node i

$\left[\begin{array}{cc}{Y}_{EE}& Y_{Ei}\\ Y_{iE}& Y_{ii}\end{array}\right]\left[\begin{array}{c}{U}_E\\ U_i\end{array}\right]=\left[\begin{array}{c}{I}_E\\ I_i\end{array}\right]---(2-19)$

Inverting and substituting the admittance matrix into an expression (2-19) to obtain

$\left[\begin{array}{c}{U}_E\\ U_i\end{array}\right]=\left[\begin{array}{cc}{Z}_{EE}& Z_{Ei}\\ Z_{iE}& Z_{ii}\end{array}\right]\left[\begin{array}{c}{I}_E\\ I_i\end{array}\right]---(2-20)$

Iterative formula of node i in equation solving process

$U_i^{(k+1)}=Z_{ii}\frac{P_i-{\mathrm{jQ}}_i}{{\[U_i^{\left(k\right)}\]}^{*}}+Z_{iE}{I}_E^{\left(k\right)}---(2-21)$

The node i is inspected, and the final solution of the power flow of the node is set asWhich satisfies

$U_i^{\left(\mathrm{\∞}\right)}=Z_{ii}\frac{P_i-{\mathrm{jQ}}_i}{{\[U_i^{\left(\mathrm{\∞}\right)}\]}^{*}}+Z_{iE}{I}_E^{\left(\mathrm{\∞}\right)}---(2-22)$

The voltage at the k and k +1 iterations can be expressed as the sum of the final value and the deviation, i.e. let

$U_i^{(k+1)}=U_i^{\left(\mathrm{\∞}\right)}+{\mathrm{\ΔU}}_i^{(k+1)}---(2-23)$

$U_i^{\left(k\right)}=U_i^{\left(\mathrm{\∞}\right)}+{\mathrm{\ΔU}}_i^{\left(k\right)}---(2-24)$

The formulas (2-24) can be converted into a form represented by voltage final solution and deviation quantity

$U_i^{\left(\mathrm{\∞}\right)}+{\mathrm{\ΔU}}_i^{(k+1)}=Z_{ii}\frac{P-{\mathrm{jQ}}_i}{{\[U_i^{\left(\mathrm{\∞}\right)}+{\mathrm{\ΔU}}_i^{\left(k\right)}\]}^{*}}+Z_{iE}\[I_E^{\left(\mathrm{\∞}\right)}+{\mathrm{\ΔI}}_E^{\left(k\right)}\]---(2-25)$

To obtain

${\mathrm{\ΔU}}_i^{(k+1)}=Z_{ii}\frac{P_i-{\mathrm{jQ}}_i}{{\[U_i^{\left(\mathrm{\∞}\right)}+{\mathrm{\ΔU}}_i^{\left(k\right)}\]}^{*}{\[U_i^{\left(\mathrm{\∞}\right)}\]}^{*}}{\[{\mathrm{\ΔU}}_i^{\left(\mathrm{\∞}\right)}\]}^{*}+Z_{iE}{\mathrm{\ΔI}}_E^{\left(k\right)}---(2-26)$

In this case, if it is satisfied that the voltage difference of other nodes in the network is significantly smaller than the voltage difference of node i, that is, the latter term can be ignored, and at the same time, it is defined that

$p=\frac{\left|U_i^{\left(k\right)}\right|}{\left|U_i^{\left(\mathrm{\∞}\right)}\right|}---(2-27)$

Under the assumed conditions, can be obtained

$\left|{\mathrm{\ΔU}}_i^{(k+1)}\right|=\left|Z_{ii}\right|\frac{\left|S_i\right|}{{\left|U_i^{\left(\mathrm{\∞}\right)}\right|}^{2}p}\left|{\mathrm{\ΔU}}_i^{\left(k\right)}\right|---(2-28)$

When in useWhen the power flow approaches convergence, the voltage amplitude of node i follows the slope α if the influence of other node errors is ignored_iThe linearity converges, wherein,

${\mathrm{\α}}_i=\left|Z_{ii}\right|\frac{\left|S_i\right|}{{\left|U_i^{\left(\mathrm{\∞}\right)}\right|}^2}---(2-29)$

alpha is defined as a convergence factor, and the smaller the convergence factor is, the faster the convergence speed of the load flow calculation is.

Therefore, when calculating the convergence factor of the PQ node, the convergence factor of the PQ node may be calculated according to a convergence factor calculation formula:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{\left(\mathrm{\∞}\right)}\right|}^2};$

wherein α is the convergence factor, Z is the self-impedance of PQ node, S is the sum of the self-active power and reactive power of PQ node, U^(∞)Is the final solution for the voltage at the PQ node.

In addition, the voltage calculation means may generate an impedance matrix of the PQ node from the network structure and the element parameters, and generate an iterative equation to slowly converge the PQ node from the impedance matrix of the PQ node. The calculation method is as follows:

$\left[\begin{array}{c}{U}_A^{(k+1)}\\ U_B^{(k+1)}\end{array}\right]=\left[\begin{array}{cc}{Z}_{AA}& Z_{AB}\\ Z_{BA}& Z_{BB}\end{array}\right]\left[\begin{array}{c}{I}_A^{\left(k\right)}\\ I_B^{\left(k\right)}\end{array}\right]---(2-30)$

in the formula, subscript a corresponds to a fast converging PQ node, and subscript B corresponds to a slow converging PQ node. The iterative equation for constructing the slow convergent PQ node is:

$U_B^{(k+1)}=Z_{BA}{I}_A^{(k+1)}+Z_{BB}{I}_B^{\left(k\right)}---(2-31)$

wherein,voltage, Z, of slowly converging PQ node calculated for the (k + 1) th iteration_BAImpedance matrix for fast converging PQ nodes to slow converging PQ nodes, Z_BBTo slowly converge the impedance matrix of the PQ node itself,the resulting current injection amount for the fast converging PQ node is calculated for the (k + 1) th iteration,the resulting current injection amount for the slowly converging PQ node is calculated for the kth iteration.

Step 204, assigning initial values to the voltages of all the nodes;

since there are unknown quantities in the voltage amplitude and the voltage phase angle of each node, an initial value of the unknown voltage amplitude is usually set to 1, and an initial value of the unknown voltage phase angle is set to 0.

Step 205, calculating the current injection amount of each node according to the voltage of each node;

specifically, the voltage calculating means may calculate the current injection amount of each node according to the following equation,

YU＝I(2-32)

wherein U is a node voltage column vector; y is a node admittance matrix; i is the node injection current column vector.

Step 206, calculating the equivalent injection current of the PV node according to the current injection amount of each node;

specifically, the calculation result of step 205 may be substituted into equation (2-16), and the equivalent injection current of the PV node may be obtained by gradually substituting the current injection amount of each node.

Step 207, calculating the actual active power of the PV node;

the actual active power of the PV node comprises the active power injected by the PV node and the active power of the PV node; the PV node injection active power can be obtained by calculating the equivalent injection current of the PV node; the PV node active power itself is a known quantity that is contained in the element parameters and depends on the PV node voltage.

Specifically, the voltage calculation device may calculate the PV node injection active power according to the PV node equivalent injection current, and calculate the PV node actual active power according to the PV node injection active power and the PV node own active power carried in the element parameter.

Step 208, solving an iterative total equation of the PV node according to the actual active power of the PV node to obtain the voltage of the PV node;

specifically, for any node i, the column write node active power equation is as follows:

$U_i\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j(G_{ij}{\mathrm{cos\δ}}_{ij}+B_{ij}{\mathrm{sin\δ}}_{ij})=P_i---(2-33)$

expanding the equation (2-33) and moving the cosine part of the equation to the right of the equation, we get:

$\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{ij}{\mathrm{sin\δ}}_{ij}=\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{ij}{\mathrm{cos\δ}}_{ij}---(2-34)$

by modifying the formula (2-34), we obtain:

$\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{ij}({\mathrm{sin\δ}}_i{\mathrm{cos\δ}}_j-{\mathrm{cos\δ}}_i{\mathrm{sin\δ}}_j)=\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{ij}{\mathrm{cos\δ}}_{ij}---(2-35)$

by modifying the formula (2-35), we obtain:

$-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{ij}{\mathrm{sin\δ}}_j=\frac{1}{{\mathrm{cos\δ}}_i}(\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{ij}{\mathrm{cos\δ}}_{ij}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{ij}{\mathrm{sin\δ}}_i{\mathrm{cos\δ}}_j)---(2-36)$

the phase angle unknown node iterative equation is constructed according to the formula (2-36) as follows:

B′()U′()＝I′()(2-37)

wherein, $B^{\′}\left(\mathrm{\δ}\right)=\left[\begin{array}{ccccc}{B}_{1j}& ...& -B_{1i}& ...& -B_{1m}\\ ...& ...& ...& ...& ...\\ -B_{i1}& ...& B_{ij}& ...& -B_{im}\\ ...& ...& ...& ...& ...\\ -B_{m1}& ...& -B_{mi}& ...& B_{mj}\end{array}\right],$ $U^{\′}\left(\mathrm{\δ}\right)=\left[\begin{array}{c}{U}_1{\mathrm{sin\δ}}_1\\ ...\\ U_i{\mathrm{sin\δ}}_i\\ ...\\ U_m{\mathrm{sin\δ}}_m\end{array}\right],$

$I^{\′}\left(\mathrm{\δ}\right)=\left[\begin{array}{c}\frac{1}{{\mathrm{cos\δ}}_1}(\frac{P_1}{U_1}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{1j}{\mathrm{cos\δ}}_{1j}-{\mathrm{sin\δ}}_1\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{1j}{\mathrm{cos\δ}}_j)\\ ...\\ \frac{1}{{\mathrm{cos\δ}}_i}(\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{ij}{\mathrm{cos\δ}}_{ij}-{\mathrm{sin\δ}}_i\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{ij}{\mathrm{cos\δ}}_j)\\ ...\\ \frac{1}{{\mathrm{cos\δ}}_m}(\frac{P_m}{U_m}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{mj}{\mathrm{cos\δ}}_{mj}-{\mathrm{sin\δ}}_m\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{mj}{\mathrm{cos\δ}}_j)\end{array}\right].$

the PV node voltage phase angle can be calculated according to equation (2-36) and the PV node voltage is obtained from the PV node voltage phase angle and the known PV node voltage magnitude.

Step 209, determining whether the PV node voltage change modulus is smaller than a preset PV node voltage change threshold, if so, entering step 210, otherwise, returning to step 207;

specifically, the voltage calculation device needs to perform p times of iterative calculation on the voltage of the PV node, where p is an integer greater than 1; when the 1 st iterative computation is carried out, solving an iterative general equation of the PV node according to the actual active power of the PV node to obtain a voltage phase angle obtained by the 1 st computation, and calculating a voltage obtained by the 1 st iterative computation according to the voltage phase angle obtained by the 1 st computation and the voltage amplitude of the PV node; when the iterative computation is performed for the p time, returning to step 207, correcting the actual active power of the PV node according to the voltage obtained by the iterative computation for the p-1 time, solving an iterative total equation of the PV node according to the corrected actual active power of the PV node, obtaining a voltage phase angle obtained by the p time of computation, and calculating the voltage obtained by the p time of iterative computation according to the voltage phase angle obtained by the p time of computation and the voltage amplitude of the PV node; when the actual active power of the PV node is corrected according to the voltage obtained by the p-1 iteration calculation, the own active power of the PV node is recalculated according to the voltage obtained by the p-1 iteration calculation, and the actual active power of the PV node is corrected according to the recalculated own active power of the PV node.

The voltage change module value calculated for the p time is the module value of the difference between the voltage obtained by the p time calculation and the voltage obtained by the p-1 time calculation;

if the voltage change module value calculated for the p time is smaller than the preset PV node voltage change threshold value, taking the voltage obtained by the p time calculation as the voltage of the PV node;

and if the voltage change module value calculated for the p time is not less than the preset PV node voltage change threshold value, returning to step 207, and continuing to calculate for the p +1 time.

Step 210, calculating the PQ node voltage according to the PV node voltage, the total iteration equation of the PQ node and the iteration equation of the slow converged PQ node;

specifically, the voltage calculation device substitutes the PV node voltage obtained in step 209 into the overall iterative equation for the PQ node to obtain the PQ node voltage.

Step 211, determining whether the PQ node voltage change modulus is smaller than a preset PQ node voltage change threshold, if so, entering step 212, otherwise, returning to step 205;

similar to PV node voltage calculation, the voltage calculation means needs to perform q iterations of the voltage of the PQ node, where q is an integer greater than 1; when the 1 st iteration calculation is carried out, solving an iteration general equation of a PQ node according to the voltage of the PV node, and obtaining the voltage of the fast convergence PQ node obtained by the 1 st calculation and the voltage of the slow convergence PQ node obtained by the 1 st calculation before correction; correcting the voltage of the slow convergence PQ node obtained by the 1 st calculation before correction according to an iterative equation of the slow convergence PQ node to obtain the voltage of the slow convergence PQ node obtained by the 1 st calculation after correction; the obtained voltage of the fast converging PQ node calculated at the 1 st time and the corrected voltage of the slow converging PQ node calculated at the 1 st time are determined as the voltage calculated at the 1 st time.

When the q-th iterative computation is performed, returning to step 205, recalculating the current injection amount of each node according to the voltage obtained by the q-1-th iterative computation and the voltage of the PV node, recalculating the actual active power of the PV node according to the recalculated current injection amount of each node, recalculating the voltage of the PV node according to the recalculated actual active power of the PV node and the iterative overall equation of the PV node, solving the iterative overall equation of the PQ node according to the recalculated voltage of the PV node, and obtaining the voltage of the PQ node subjected to the q-th computation and the voltage of the PQ node subjected to the slow convergence computation and before the correction; correcting the voltage of the slow convergence PQ node obtained by the calculation of the q times before correction according to an iterative equation of the slow convergence PQ node to obtain the voltage of the slow convergence PQ node obtained by the calculation of the q times after correction; the obtained fast converging PQ node voltage obtained by the q-th calculation and the corrected voltage of the slow converging PQ node obtained by the q-th calculation are determined as the voltage obtained by the q-th calculation.

The voltage calculation device judges whether the voltage change module value calculated for the q time is smaller than a preset PQ node voltage change threshold value or not, wherein the voltage change module value calculated for the q time is the module value of the difference between the voltage calculated for the q time and the voltage calculated for the q-1 time iteration; if the voltage change module value calculated for the q-th time is smaller than a preset PQ node voltage change threshold value, taking the voltage obtained by the q-th time calculation as the voltage of the PQ node; and if the voltage change module value calculated in the q th time is not less than the preset PQ node voltage change threshold value, continuing to calculate in the q +1 th time.

The voltage calculation device corrects the voltage of the slow convergent PQ node before correction obtained by the q-th calculation according to the iterative equation of the slow convergent PQ node, keeps the voltage of the fast convergent PQ node obtained by the q-th calculation unchanged when obtaining the voltage of the slow convergent PQ node after correction obtained by the q-th calculation, performs iterative calculation on the voltage of the slow convergent PQ node for m times according to the iterative equation of the slow convergent PQ node, and uses the voltage of the slow convergent PQ node obtained by the m-th iterative calculation as the voltage of the slow convergent PQ node after correction, wherein m is an integer greater than or equal to 1.

Please refer to formula (2-31), wherein Z_BAAnd Z_BBAs is known, when the voltage at the fast converging PQ node obtained from the q-th calculation is kept constant, there areAt this time, only calculation is neededI.e. the voltage of the slow converging PQ node can be calculated iteratively by equation (2-31) alone. Specifically, the voltage of the slow converged PQ node may be iterated m times separately, where m is a predetermined value and m is an integer greater than or equal to 1.

When the voltage of the slowly converging PQ node is iteratively calculated 1 st time, the current injection amount of the rapidly converging PQ node can be calculated from the voltage of the rapidly converging PQ node calculated q times and the voltage of the slowly converging PQ node before correction calculated q timesAnd slow convergence of the amount of current injected into the PQ nodeDue to the fact thatThen according toAnd the iterative equation for the slowly converging PQ node may calculate the voltage of the slowly converging PQ node as calculated by performing a single iteration on the voltage of the slowly converging PQ node at time 1. When the voltage of the slow converging PQ node is iteratively calculated the mth time, the current injection amount of the slow converging PQ node can be calculated according to the voltage of the slow converging PQ node obtained by singly and iteratively calculating the voltage of the slow converging PQ node the mth-1 timeAnd according toAnd the iterative equation for the slowly converging PQ node may calculate the voltage of the slowly converging PQ node obtained by iteratively calculating the voltage of the slowly converging PQ node m times, and finally determine the voltage of the slowly converging PQ node obtained by iteratively calculating the voltage of the slowly converging PQ node m times as the corrected voltage of the slowly converging PQ node obtained by calculating the voltage of the PQ node q times.

Since the PV node voltage amplitude in the power system is known and is easy to converge with respect to the PQ node, the convergence performance of the algorithm is mainly determined by the PQ node, and the node with the larger convergence factor among the PQ nodes has the slower convergence speed, so the core idea of step 210 in the embodiment of the present invention is: when the PQ node voltage is subjected to iterative computation, after the voltage of each PQ node is computed according to the general iterative equation of the PQ node each time, the voltage of the fast convergence PQ node is kept unchanged, the voltage of the slow convergence PQ node is subjected to iterative computation for a preset number of times according to the iterative equation of the slow convergence PQ node, and the voltage of the slow convergence PQ node computed each time is corrected, so that the convergence rate of the voltage computation of the whole node is improved.

In step 212, the voltage of the PV node and the voltage of the PQ node are determined as the calculation results.

The voltage calculation means outputs the finally obtained PV node voltage and PQ node voltage as calculation results.

The calculation method provided by the embodiment may involve a large number of matrices and their calculations. According to the grid structure, only a few elements in the matrixes are non-zero matrixes. Therefore, only non-zero elements are calculated during calculation, and zero elements are not calculated, so that the calculation speed of the algorithm can be greatly improved. Meanwhile, only non-zero elements are stored in the data storage process, and the memory can be greatly saved.

In practical applications, a storage format of triangle search is usually adopted to store data, such as a certain matrix a, the non-zero elements of the upper triangle part of a are stored according to rows, and the non-zero elements of the lower triangle part of a are stored according to columns. If A is an n × n-order square matrix, the storage method is as follows:

u-storing the non-zero element value of the upper triangular part of A, and storing the values in sequence according to rows;

JU-the column number of the non-zero element of the upper triangular portion of A;

IU-position of the first non-zero element in each row of the upper triangular part in the storage A;

l-storing the values of the lower triangular non-zero elements in A by columns;

IL-store the row number of the lower triangular non-zero element in A by column;

JL-the position in L of the first non-zero element in each column of the lower triangular part in A;

d-store the value of the diagonal element of A, whose index does not need to be stored.

In summary, in the method for obtaining the node voltage of the power system provided in the second embodiment of the present invention, the total iteration equation of the PV node, the total iteration equation of the PQ node, and the iteration equation of the PQ node with slow convergence are generated according to the received network structure and the element parameters of the power system, the voltage of the PV node is calculated according to the actual active power of the PV node and the total iteration equation of the PV node, and the voltage of the PQ node is further calculated according to the voltage of the PV node, the total iteration equation of the PQ node, and the iteration equation of the PQ node with slow convergence, so as to achieve the purpose of improving the convergence of the calculation of the node voltage; in addition, in the method for calculating the node voltage of the power system according to the second embodiment of the present invention, after the voltage of each PQ node is calculated according to the general iterative equation of the PQ node each time, the voltage of the slowly converged PQ node is separately subjected to iterative calculation for a predetermined number of times according to the iterative equation of the slowly converged PQ node, so as to achieve the purpose of increasing the convergence rate of the voltage calculation of the whole node.

EXAMPLE III

Referring to fig. 3, a device structure diagram of a device for obtaining a node voltage of an electrical power system according to a third embodiment of the present invention is shown. The device for acquiring the node voltage of the power system can be used for calculating the voltage of each node in the power system. The device for acquiring the node voltage of the power system can comprise:

an obtaining module 301, configured to obtain a network structure and element parameters of each node of a power system, where the node at least includes: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the active power and the voltage amplitude of the PV node are known, the active power and the reactive power of the PQ node are known, and the PQ node comprises at least one slow convergence PQ node;

a first equation generating module 302, configured to generate an iterative summation equation of the PV node and an iterative summation equation of the PQ node according to the network structure and the element parameters acquired by the acquiring module 301;

a second equation generating module 303, configured to generate an iterative equation of a slow converged PQ node according to the network structure and the element parameters acquired by the acquiring module 301;

the current calculating module 304 is configured to calculate a current injection amount of each node according to a preset initial voltage value of each node;

an active power calculation module 305, configured to calculate an actual active power of the PV node according to the current injection amount of each node calculated by the current calculation module 304;

a first voltage calculation module 306, configured to calculate a voltage of the PV node according to the actual active power of the PV node and the iterative overall equation of the PV node generated by the first equation generation module 302;

a second voltage calculation module 307, configured to calculate the voltage of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module 306, the total iterative equation of the PQ node generated by the first equation generation module 302, and the iterative equation of the slow-convergence PQ node generated by the second equation generation module 303.

In summary, in the apparatus for obtaining node voltage of an electrical power system provided in the third embodiment of the present invention, the total iteration equation of the PV node, the total iteration equation of the PQ node, and the iteration equation of the PQ node with slow convergence are generated according to the received network structure and the element parameters of the electrical power system, the voltage of the PV node is calculated according to the actual active power of the PV node and the total iteration equation of the PV node, and the voltage of the PQ node is further calculated according to the voltage of the PV node, the total iteration equation of the PQ node, and the iteration equation of the PQ node with slow convergence, so as to achieve the purpose of improving the convergence of node voltage calculation.

Example four

To further describe the device for obtaining node voltage of an electrical power system according to the third embodiment of the present invention, please refer to fig. 4, which shows a device structure diagram of a device for calculating node voltage of an electrical power system according to the fourth embodiment of the present invention. The device for acquiring the node voltage of the power system can comprise:

an obtaining module 301, configured to obtain a network structure and element parameters of each node of a power system, where the node at least includes: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the active power and the voltage amplitude of the PV node are known, the active power and the reactive power of the PQ node are known, and the PQ node comprises at least one slow convergence PQ node;

a first equation generating module 302, configured to generate an iterative summation equation of a PV node and an iterative summation equation of a PQ node according to the network structure and the element parameters acquired by the acquiring module 301;

a second equation generating module 303, configured to generate an iterative equation of a slow converged PQ node according to the network structure and the element parameters acquired by the acquiring module 301;

the current calculating module 304 is configured to calculate a current injection amount of each node according to a preset initial voltage value of each node;

an active power calculation module 305, configured to calculate an actual active power of the PV node according to the current injection amount of each node calculated by the current calculation module 304;

a first voltage calculation module 306, configured to calculate a voltage of the PV node according to the actual active power of the PV node and the iterative overall equation of the PV node generated by the first equation generation module 302;

a second voltage calculation module 307, configured to calculate the voltage of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module 306, the total iterative equation of the PQ node generated by the first equation generation module 302, and the iterative equation of the slow-convergence PQ node generated by the second equation generation module 303.

The device also includes:

a convergence factor calculating module 308, configured to calculate a convergence factor of the PQ node before the second equation generating module 303 generates an iterative equation of a PQ node converged at a slow speed according to the network structure and the element parameters acquired by the acquiring module 301;

a node determining module 309, configured to rank the PQ nodes in order from large to small according to the convergence factor calculated by the convergence factor calculating module 308, and determine n nodes ranked in the front as slow converged PQ nodes, where n is a predetermined ratio.

A convergence factor calculating module 308, configured to calculate a convergence factor of the PQ node according to a convergence factor calculation formula, where the convergence factor calculation formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{\left(\mathrm{\∞}\right)}\right|}^2};$

wherein α is the convergence factor, Z is the self-impedance of PQ node, S is the sum of the self-active power and reactive power of PQ node, U^(∞)Is the final solution for the voltage at the PQ node.

A second equation generating module 303, comprising:

an impedance matrix generating unit 3031, configured to generate an impedance matrix of the PQ node according to the network structure and the element parameters acquired by the acquiring module 301;

an iterative equation generating unit 3032, configured to generate an iterative equation converging the PQ node at a slow speed according to the impedance matrix of the PQ node generated by the impedance matrix generating unit 3031;

the iteration equation of the slow convergence PQ node is as follows:

$U_B^{(k+1)}=Z_{BA}{I}_A^{(k+1)}+Z_{BB}{I}_B^{\left(k\right)};$

wherein,voltage, Z, of slowly converging PQ node calculated for the (k + 1) th iteration_BAImpedance matrix for fast converging PQ nodes to slow converging PQ nodes, Z_BBTo slowly converge the impedance matrix of the PQ node itself,the resulting current injection amount for the fast converging PQ node is calculated for the (k + 1) th iteration,and calculating the current injection quantity of the slow convergence PQ node for the k-th iteration, wherein the fast convergence PQ node is the PQ node except the slow convergence PQ node.

A second voltage calculation module 307, comprising:

a voltage calculation unit 3071, configured to perform q iterative calculations on the voltage of the PQ node, where q is an integer greater than 1;

the voltage calculation unit 3071 includes:

the voltage calculation subunit 3071a is configured to, when performing iterative calculation for the 1 st time, solve an iterative general equation of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module 306, and obtain a voltage of the PQ node converged quickly obtained by the calculation for the 1 st time and a voltage of the PQ node converged slowly obtained by the calculation for the 1 st time before correction;

a voltage correction subunit 3071b, configured to correct, according to an iterative equation of the slow convergence PQ node, the voltage before correction of the slow convergence PQ node obtained by the voltage calculation subunit 3071a in the 1 st calculation, and obtain a corrected voltage of the slow convergence PQ node obtained by the 1 st calculation;

a voltage determining subunit 3071c, configured to determine, as the voltage obtained by the 1 st calculation, the voltage of the fast converging PQ node obtained by the voltage calculating subunit 3071a and the voltage obtained by the voltage correcting subunit 3071b after correction of the slow converging PQ node obtained by the 1 st calculation;

when the q-th iterative computation is performed, the current computation module 304 is further configured to recalculate the current injection amount of each node according to the voltage obtained by the q-1-th iterative computation determined by the voltage determination subunit 3071c and the voltage of the PV node computed by the first voltage computation module 306;

the active power calculation module 305 is further configured to recalculate the actual active power of the PV node according to the current injection amount of each node recalculated by the current calculation module 304;

a first voltage calculation module 306, further configured to recalculate the voltage of the PV node according to the actual active power of the PV node recalculated by the active power calculation module 305 and the iterative sum equation of the PV node;

the voltage calculation subunit 3071a is configured to, when performing iterative calculation for the q-th time, solve an iterative general equation of the PQ node according to the voltage of the PV node recalculated by the first voltage calculation module 306, and obtain a voltage of the PQ node converged quickly obtained by the q-th time calculation and a voltage of the PQ node converged slowly obtained by the q-th time calculation before correction;

a voltage correction subunit 3071b, configured to correct, according to an iterative equation of the slow convergence PQ node, the voltage before correction of the slow convergence PQ node obtained by the voltage calculation subunit 3071a in the q-th calculation, and obtain a corrected voltage of the slow convergence PQ node obtained by the q-th calculation;

a voltage determining subunit 3071c, configured to determine, as the voltage obtained by the q-th calculation, the voltage of the fast converging PQ node obtained by the voltage calculating subunit 3071a and the corrected voltage of the slow converging PQ node obtained by the q-th calculation and obtained by the voltage correcting subunit 3071 b;

the second voltage calculating module 307 further includes:

a determining unit 3072, configured to determine whether the voltage change modulus calculated for the q-th time is smaller than a preset PQ node voltage change threshold, where the voltage change modulus calculated for the q-th time is a modulus of a difference between a voltage obtained by the q-th calculation determined by the voltage determining subunit 3071c and a voltage obtained by the q-1-th iterative calculation determined by the voltage determining subunit 3071 c;

a voltage determining unit 3073, configured to determine the voltage obtained by the q-th calculation as the voltage of the PQ node if the determining unit 3072 determines that the voltage change modulus calculated for the q-th calculation is smaller than the preset PQ node voltage change threshold;

the voltage calculating unit 3071 is configured to continue to perform iterative calculation for the (q + 1) th time if the determining unit 3073 determines that the voltage change modulus calculated for the q-th time is not less than the preset PQ node voltage change threshold.

Voltage correcting subunit 3071b is configured to hold the voltage of the fast converging PQ node calculated by voltage calculating subunit 3071a q-th time as an integer greater than or equal to 1, perform iterative calculation on the voltage of the slow converging PQ node m times according to an iterative equation of the slow converging PQ node, using the voltage of the slow converging PQ node calculated by voltage calculating subunit 3071a q-th time before correction as an initial value, and use the voltage of the slow converging PQ node calculated by iterative calculation m times as the voltage of the slow converging PQ node after correction.

Specifically, please refer to formula (2-31), wherein, Z_BAAnd Z_BBAs is known, when the voltage at the fast converging PQ node obtained from the q-th calculation is kept constant, there areAt this time, only calculation is neededI.e. the voltage of the slow converging PQ node can be calculated iteratively by equation (2-31) alone. Specifically, the voltage of the slow converged PQ node may be iterated m times separately, where m is a predetermined value and m is an integer greater than or equal to 1.

When the voltage of the slowly converging PQ node is iteratively calculated 1 st time, the voltage correction subunit 3071b may calculate the current injection amount of the rapidly converging PQ node from the voltage of the rapidly converging PQ node calculated q times on the voltage of the PQ node and the voltage before correction of the slowly converging PQ node calculated q timesAnd slow convergence of the amount of current injected into the PQ nodeDue to the fact thatThe voltage correction subunit 3071bAnd the iterative equation for the slowly converging PQ node may calculate the voltage of the slowly converging PQ node as calculated by performing a single iteration on the voltage of the slowly converging PQ node at time 1. When the voltage of the slowly converging PQ node is iteratively calculated m times, the voltage correction subunit 3071b may calculate the voltage of the slowly converging PQ node from the m-1 times of individual iterations of the voltage of the slowly converging PQ nodeCalculating current injection amount of slow convergence PQ nodeAnd according toAnd the iterative equation of the slowly converging PQ node may calculate the voltage of the slowly converging PQ node obtained by iteratively calculating the voltage of the slowly converging PQ node m times, and finally, the voltage corrector subunit 3071b determines the voltage of the slowly converging PQ node obtained by iteratively calculating the voltage of the slowly converging PQ node m times as the corrected voltage of the slowly converging PQ node obtained by calculating the voltage of the PQ node q times.

In summary, in the apparatus for obtaining node voltage of an electrical power system provided in the fourth embodiment of the present invention, the total iteration equation of the PV node, the total iteration equation of the PQ node, and the iteration equation of the PQ node with slow convergence are generated according to the received network structure and the element parameters of the electrical power system, the voltage of the PV node is calculated according to the actual active power of the PV node and the total iteration equation of the PV node, and the voltage of the PQ node is further calculated according to the voltage of the PV node, the total iteration equation of the PQ node, and the iteration equation of the PQ node with slow convergence, so as to achieve the purpose of improving the convergence of node voltage calculation; in addition, the node voltage calculation device of the power system according to the fourth embodiment of the present invention separately performs iterative calculations on the voltage of the slowly converging PQ node for a predetermined number of times according to the iterative equation of the slowly converging PQ node after calculating the voltage of each PQ node according to the iterative general equation of the PQ node each time, so as to achieve the purpose of increasing the convergence rate of the voltage calculation of the entire node.

It should be noted that: in the above-described embodiment, when calculating the voltage of each node of the power system, the device for obtaining the node voltage of the power system is only illustrated by dividing the functional modules, and in practical applications, the function distribution may be completed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules, so as to complete all or part of the functions described above. In addition, the apparatus for obtaining the node voltage of the power system and the method for obtaining the node voltage of the power system provided in the above embodiments belong to the same concept, and specific implementation processes thereof are detailed in the method embodiments and are not described herein again.

The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.

It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, where the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A method of deriving a power system node voltage, the method comprising:

acquiring network structure and element parameters of each node of a power system, wherein the node at least comprises: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the active power and the voltage amplitude of the PV node are known, the active power and the reactive power of the PQ node are known, and the PQ node comprises at least one slow convergence PQ node;

generating an iteration general equation of the PV node and an iteration general equation of the PQ node according to the network structure and element parameters, and generating an iteration equation of the slow convergence PQ node according to the network structure and element parameters;

calculating the current injection quantity of each node according to the preset initial voltage value of each node;

calculating the actual active power of the PV node according to the current injection quantity of each node, and calculating the voltage of the PV node according to the actual active power of the PV node and an iterative general equation of the PV node;

calculating the voltage of the PQ node according to the voltage of the PV node, the general iterative equation of the PQ node and the iterative equation of the slow converged PQ node;

prior to the generating an iterative equation for the slow converged PQ node from the network fabric and element parameters, the method further comprises:

calculating a convergence factor of the PQ node;

and sequencing the PQ nodes according to the descending order of the convergence factors, and determining n nodes in the front sequence as the slow convergence PQ nodes, wherein n is a preset proportion.

2. The method of claim 1, wherein the calculating the convergence factor for the PQ node comprises:

calculating the convergence factor of the PQ node according to a convergence factor calculation formula, wherein the convergence factor calculation formula is as follows:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{|U^{\left(\mathrm{\∞}\right)}{|}^2};$

wherein α is the convergence factor, Z is the self-impedance of PQ node, S is the sum of the self-active power and reactive power of PQ node, U^(∞)Is the final solution for the voltage at the PQ node.

3. The method of any of claims 1-2, wherein the generating an iterative equation for the slow converging PQ node from the network structure and element parameters comprises:

generating an impedance matrix of the PQ node according to the network structure and element parameters;

generating an iterative equation for the slow converged PQ node from the impedance matrix for the PQ node;

wherein the iterative equation of the slow convergence PQ node is as follows:

$U_B^{(k+1)}=Z_{BA}{I}_A^{(k+1)}+Z_{BB}{I}_B^{\left(k\right)};$

wherein,the voltage of the slow converged PQ node calculated for the k +1 th iteration, the Z_BAImpedance of the slowly converging PQ node for a rapidly converging PQ nodeMatrix, said Z_BBFor the slow converging PQ node's own impedance matrix,the resulting current injection amount for the fast converging PQ node is calculated for the (k + 1) th iteration,calculating the current injection amount of the slow convergent PQ node for the k-th iteration, wherein the fast convergent PQ node is a PQ node except the slow convergent PQ node.

4. The method of claim 3, wherein said calculating the voltage of the PQ node from the voltage of the PV node, the overall iterative equation of the PQ node, and the iterative equation of the slow converged PQ node comprises:

performing q iterative computations on the voltage of the PQ node, wherein q is an integer greater than 1;

when the 1 st iteration calculation is carried out, solving an iteration general equation of the PQ node according to the voltage of the PV node to obtain the voltage of the fast convergence PQ node obtained by the 1 st calculation and the voltage of the slow convergence PQ node obtained by the 1 st calculation before correction; correcting the voltage of the slow convergence PQ node obtained by the 1 st calculation before correction according to the iterative equation of the slow convergence PQ node to obtain the corrected voltage of the slow convergence PQ node obtained by the 1 st calculation; determining the obtained voltage of the fast convergence PQ node obtained by the 1 st calculation and the corrected voltage of the slow convergence PQ node obtained by the 1 st calculation as the voltage obtained by the 1 st calculation;

when the q-th iterative computation is carried out, recalculating the current injection quantity of each node according to the voltage obtained by the q-1-th iterative computation and the voltage of the PV node, recalculating the actual active power of the PV node according to the recalculated current injection quantity of each node, recalculating the voltage of the PV node according to the recalculated actual active power of the PV node and the iterative total equation of the PV node, solving the iterative total equation of the PQ node according to the recalculated voltage of the PV node, and obtaining the voltage of the fast convergence PQ node obtained by the q-th computation and the voltage of the slow convergence PQ node obtained by the q-th computation before correction; correcting the voltage of the slow convergence PQ node obtained by the calculation of the q times before correction according to the iterative equation of the slow convergence PQ node to obtain the corrected voltage of the slow convergence PQ node obtained by the calculation of the q times; determining the obtained fast convergence PQ node voltage obtained by the q-th calculation and the corrected slow convergence PQ node voltage obtained by the q-th calculation as the voltage obtained by the q-th calculation;

judging whether the voltage change module value calculated for the q times is smaller than a preset value or not, wherein the voltage change module value calculated for the q times is the module value of the difference between the voltage obtained by the q times of calculation and the voltage obtained by the q-1 times of iterative calculation;

if the voltage change modulus calculated for the q-th time is smaller than a preset value, determining the voltage obtained by the q-th time calculation as the voltage of the PQ node;

and if the voltage change module value calculated for the q th time is not less than the preset value, continuing to perform iterative calculation for the q +1 th time.

5. The method of claim 4, wherein the modifying the pre-modified voltage of the slowly converging PQ node calculated q times according to the iterative equation for the slowly converging PQ node to obtain a modified voltage of the slowly converging PQ node calculated q times comprises:

keeping the voltage of the fast converging PQ node obtained by the q-th calculation unchanged, performing m times of iterative calculation on the voltage of the slow converging PQ node according to an iterative equation of the slow converging PQ node by taking the voltage of the fast converging PQ node obtained by the q-th calculation as an initial value, and taking the voltage of the slow converging PQ node obtained by the m-th iterative calculation as the corrected voltage of the slow converging PQ node, wherein m is an integer greater than or equal to 1.

6. An apparatus for obtaining a node voltage of a power system, the apparatus comprising:

an obtaining module, configured to obtain a network structure and element parameters of each node of a power system, where the node at least includes: the photovoltaic power generation system comprises at least one PV node and at least one PQ node, wherein the active power and the voltage amplitude of the PV node are known, the active power and the reactive power of the PQ node are known, and the PQ node comprises at least one slow convergence PQ node;

the first equation generation module is used for generating an iteration general equation of the PV node and an iteration general equation of the PQ node according to the network structure and the element parameters acquired by the acquisition module;

the second equation generation module is used for generating an iterative equation of the slow convergent PQ node according to the network structure and the element parameters acquired by the acquisition module;

the current calculation module is used for calculating the current injection quantity of each node according to the preset initial voltage value of each node;

the active power calculation module is used for calculating the actual active power of the PV node according to the current injection quantity of each node calculated by the current calculation module;

the first voltage calculation module is used for calculating the voltage of the PV node according to the actual active power of the PV node and the iterative overall equation of the PV node generated by the first equation generation module;

a second voltage calculation module, configured to calculate the voltage of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module, the total iterative equation of the PQ node generated by the first equation generation module, and the iterative equation of the slow-convergence PQ node generated by the second equation generation module;

a convergence factor calculation module, configured to calculate a convergence factor of the PQ node before the second equation generation module generates the iterative equation of the slow convergence PQ node according to the network structure and the element parameters acquired by the acquisition module;

and the node determining module is used for sequencing the PQ nodes according to the descending order of the convergence factors calculated by the convergence factor calculating module, and determining n nodes in the front of the sequence as the slow convergence PQ nodes, wherein n is a preset proportion.

7. The apparatus of claim 6, wherein the convergence factor calculating module is configured to calculate the convergence factor of the PQ node according to a convergence factor calculation formula:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{|U^{\left(\mathrm{\∞}\right)}{|}^2};$

wherein α is the convergence factor, Z is the self-impedance of PQ node, S is the sum of the self-active power and reactive power of PQ node, U^(∞)Is the final solution for the voltage at the PQ node.

8. The apparatus of any of claims 6 to 7, wherein the second equation generation module comprises:

an impedance matrix generating unit for generating an impedance matrix of the PQ node according to the network structure and the element parameters;

the iterative equation generating unit is used for generating an iterative equation of the slow converged PQ node according to the impedance matrix of the PQ node generated by the impedance matrix generating unit;

wherein the iterative equation of the slow convergence PQ node is as follows:

$U_B^{(k+1)}=Z_{BA}{I}_A^{(k+1)}+Z_{BB}{I}_B^{\left(k\right)};$

wherein,the voltage of the slow converged PQ node calculated for the k +1 th iteration, the Z_BAAn impedance matrix for the fast converging PQ node to the slow converging PQ node, the Z_BBFor the slow converging PQ node's own impedance matrix,the resulting current injection amount for the fast converging PQ node is calculated for the (k + 1) th iteration,calculating the current injection amount of the slow convergent PQ node for the k-th iteration, wherein the fast convergent PQ node is a PQ node except the slow convergent PQ node.

9. The apparatus of claim 8, wherein the second voltage calculation module comprises:

the voltage calculation unit is used for performing q times of iterative calculation on the voltage of the PQ node, wherein q is an integer greater than 1;

the voltage calculation unit includes:

the voltage calculation subunit is configured to, when performing iterative calculation for the 1 st time, solve an iterative total equation of the PQ node according to the voltage of the PV node calculated by the first voltage calculation module, and obtain a voltage of the fast convergence PQ node calculated for the 1 st time and a voltage of the slow convergence PQ node calculated for the 1 st time before correction;

the voltage correction subunit is configured to correct, according to the iterative equation of the slow convergence PQ node, the voltage before correction of the slow convergence PQ node obtained by the voltage calculation subunit at the 1 st time, and obtain a corrected voltage of the slow convergence PQ node obtained by the 1 st time;

a voltage determining subunit, configured to determine, as the voltage obtained by the 1 st calculation, the voltage of the fast converging PQ node obtained by the voltage calculating subunit and the voltage obtained by the voltage correcting subunit, after correction, of the slow converging PQ node obtained by the 1 st calculation;

when the q-th iterative computation is performed, the current computation module is further configured to recalculate the current injection amount of each node according to the voltage obtained by the q-1-th iterative computation determined by the voltage determination subunit and the voltage of the PV node computed by the first voltage computation module;

the active power calculation module is further configured to recalculate the actual active power of the PV node according to the current injection amount of each node recalculated by the current calculation module;

the first voltage calculation module is further used for recalculating the voltage of the PV node according to the actual active power of the PV node recalculated by the active power calculation module and the iterative overall equation of the PV node;

the voltage calculation subunit is configured to, when performing iterative calculation for the q-th time, solve an iterative total equation of the PQ node according to the voltage of the PV node recalculated by the first voltage calculation module, and obtain a voltage of the fast convergence PQ node calculated for the q-th time and a voltage of the slow convergence PQ node calculated for the q-th time before correction;

the voltage correction subunit is configured to correct, according to the iterative equation of the slow convergence PQ node, the voltage before correction of the slow convergence PQ node obtained by the voltage calculation subunit for the q-th calculation, and obtain a corrected voltage of the slow convergence PQ node obtained by the q-th calculation;

the voltage determining subunit is configured to determine, as the voltage obtained by the q-th calculation, the voltage of the fast converging PQ node obtained by the voltage calculating subunit and the corrected voltage of the slow converging PQ node obtained by the q-th calculation obtained by the voltage correcting subunit;

the second voltage calculating module further includes:

the judging unit is used for judging whether the voltage change module value calculated for the q times is smaller than a preset value or not, wherein the voltage change module value calculated for the q times is a module value of the difference between the voltage obtained by the q times of calculation determined by the voltage determining subunit and the voltage obtained by the q-1 th iteration calculation determined by the voltage determining subunit;

a voltage determining unit, configured to determine the voltage obtained through the q-th computation as the voltage of the PQ node if the determining unit determines that the voltage change modulus calculated through the q-th computation is smaller than a preset value;

and the voltage calculation unit is used for continuing to carry out iterative calculation for the (q + 1) th time if the judgment unit judges that the voltage change modulus value calculated for the (q) th time is not less than the preset value.

10. The apparatus of claim 9, wherein the voltage correction subunit is configured to keep the voltage of the fast converging PQ node calculated by the voltage calculation subunit q times constant, perform m iterative calculations on the voltage of the slow converging PQ node according to an iterative equation of the slow converging PQ node using a voltage before correction of the slow converging PQ node calculated by the voltage calculation subunit q times as an initial value, and use the voltage of the slow converging PQ node calculated by the m iterative calculations as a corrected voltage of the slow converging PQ node, where m is an integer greater than or equal to 1.