CN108736475B - Interconnected power grid subsystem operation reliability assessment method based on PMU monitoring - Google Patents

Interconnected power grid subsystem operation reliability assessment method based on PMU monitoring Download PDF

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CN108736475B
CN108736475B CN201810618472.1A CN201810618472A CN108736475B CN 108736475 B CN108736475 B CN 108736475B CN 201810618472 A CN201810618472 A CN 201810618472A CN 108736475 B CN108736475 B CN 108736475B
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CN108736475A (en
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张大波
连帅
朱志鹏
王乃静
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Hefei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

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Abstract

The invention discloses an interconnected power grid subsystem operation reliability assessment method based on PMU monitoring, which comprises the following steps: s1, simplifying an external network subsystem A by adopting an external network static equivalence method; s2, obtaining the voltage of the boundary node of the selected subsystem B based on the PMU (phasor measurement Unit)utAnd current i of boundary nodetCalculating the optimal static equivalent initial value of the external network subsystem A; s3, simulating the failure of the subsystem based on the non-sequential Monte Carlo method, and calculating the optimal power flow of the selected subsystem B in the simulation state after updating the initial value of the static equivalent corresponding to each simulation based on the asynchronous iteration method; s4, after the selected subsystem B is simulated for n times, judging whether the simulated state is a failure state each time, and finally calculating the reliability of the power system, wherein the reliability of the power system comprises a load reduction probability LOLP and an expected power shortage amount EENS. The invention has the advantages that: an effective path is provided for the evaluation method for solving the problem of the reliability of the subsystems under the influence of the interconnected power grid.

Description

Interconnected power grid subsystem operation reliability assessment method based on PMU monitoring
Technical Field
The invention relates to the field of interconnected power systems, in particular to a PMU (phasor measurement Unit) monitoring-based interconnected power grid subsystem operation reliability assessment method.
Background
In order to realize resource complementation and improve the operation safety of an electric power system, it is necessary to interconnect small and medium-sized power grids through tie lines to form a multi-domain interconnected electric power system, the interconnection of the power grids can improve the operation reliability of the network, but the risk of the interconnected system can be shared, and the fault of a local power grid can influence the whole interconnected system.
In order to grasp the operation state of the power grid in time and adjust the operation mode in time to reduce the risk when the power grid faces the risk, the online evaluation of the operation reliability of the power grid in each region to the power grid in the jurisdiction becomes particularly important.
The operation reliability evaluation of a local power grid in an interconnected power grid mainly faces two difficulties, and on one hand, the analytic or simulated reliability calculation method must master the topology and operation parameters of the whole interconnected power grid; on the other hand, information cannot be transmitted in time due to the fact that regional power grids belong to different companies and dispatching operation centers, and difficulty is brought to operation reliability evaluation of interconnected power grids.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a method for evaluating the operation reliability of an interconnected power grid subsystem based on PMU monitoring.
In order to achieve the purpose, the invention adopts the following technical scheme:
PMU monitoring-based interconnected power grid subsystem operation reliability assessment method, wherein the interconnected power grid subsystem comprises a selected subsystem B and an external network subsystem A, and N is included between the selected subsystem B and the external network subsystem ABA border node, the method comprising the steps of:
s1, simplifying an external network subsystem A by adopting an external network static equivalence method based on sensitivity consistency;
s2 obtaining boundary node voltage u of selected subsystem B based on PMUtAnd current i of boundary nodetCalculating the optimal static equivalent initial value of the external network subsystem A;
s3, simulating the selected subsystem B to have a fault based on a non-sequential Monte Carlo method, setting the simulation times as n, calculating the load flow result of the selected subsystem B in the simulation state after updating the static equivalent initial value corresponding to each simulation based on an asynchronous iteration method, judging whether the simulated state is a failure state or not according to the load flow calculation result, performing optimal load flow calculation if the simulated state is the failure state, and not performing optimal load flow calculation if the simulated state is not the failure state;
and S4, after the selected subsystem B is simulated for n times, calculating the reliability of the power system, wherein the reliability of the power system comprises the load reduction probability LOLP and the expected power shortage EENS.
In detail, in step S1, the external network subsystem a is simplified by using an external network static equivalence method based on sensitivity consistency, and the initial static equivalence value of the external network subsystem a is as follows:
voltage current of boundary node: voltage u of ith boundary nodet iAnd the current i of the ith boundary nodet iVoltage u of jth boundary nodet jAnd the current i of the j-th boundary nodet jI ≠ j, i, j take 1, 2, 3 … NB；
Equivalent motor node voltage vector: equivalent motor node voltage vector E corresponding to ith boundary nodeiJ boundary node pairCorresponding equivalent motor node voltage vector EjI ≠ j, i, j take 1, 2, 3 … NB；
Equivalent branch impedance: impedance Z between the ith boundary node and the corresponding equivalent motor nodeeqiThe impedance Z between the jth boundary node and the corresponding equivalent motor nodeeqjImpedance Z between the equivalent motor node corresponding to the ith boundary node and the equivalent motor node corresponding to the jth boundary nodeeqGijImpedance Z between the ith and jth boundary nodeseqijI ≠ j, i, j take 1, 2, 3 … NB；
Injection power at the equivalent boundary: equivalent injection power S of ith boundary nodeLiThe equivalent injection power S of the jth boundary nodeLjActive power P of equivalent motor node motor corresponding to ith boundary nodeeqiActive power P of equivalent motor node motor corresponding to jth boundary nodeeqjI ≠ j, i, j take 1, 2, 3 … NB；
The equivalent ground branch admittance of the ith boundary node to the ground branch admittance biThe jth boundary node admittances b to the ground branchjI ≠ j, i, j take 1, 2, 3 … NB。
In detail, the step S2 includes the following steps:
s21, obtaining the voltage u of M groups of boundary nodes with the time interval sampling times of PMU being MtAnd current i of boundary nodetSubstituting into the measurement equation to calculate the optimal static equivalent initial value,
x represents the static equivalent initial values of M groups to be measured:
Figure GDA0002823361860000031
the measurement equation is:
Figure GDA0002823361860000032
Figure GDA0002823361860000033
in the formula:
Figure GDA0002823361860000034
Figure GDA0002823361860000041
Zeqikrepresenting an impedance between the kth boundary node and the ith boundary node;
s22, obtaining a static equivalent initial value x under the maximum running state of the external network subsystem AmaxAnd the static equivalent initial value x under the minimum running stateminConstructing an inequality constraint equation
Figure GDA0002823361860000042
Figure GDA0002823361860000043
Inequality constraint equation
xmin≤x≤xmax (8)
S23, constructing a least square model of the static equivalent initial values based on the measurement equation to obtain the optimal static equivalent initial values, wherein the least square model is
Figure GDA0002823361860000044
In detail, in step S3, the static equivalent initial value corresponding to each simulation is updated based on the asynchronous iterative method, and the specific steps are as follows,
s31, calculating information matrixes G corresponding to boundary nodes after reactive power decoupling and active power decoupling respectively corresponding to the selected subsystem B and the external network subsystem A, and further calculating merging parameters, wherein a merging parameter calculation formula is as follows:
Figure GDA0002823361860000051
in the formula: r denotes the selected subsystem B and the extranet subsystem A, pirRepresenting a voltage merging parameter, σ, of the ith boundary node of the selected subsystem B or the outer network subsystem AirA phase angle merging parameter, theta, representing the ith boundary node of the selected subsystem B or the extranet subsystem AirAnd upsilonirRespectively representing diagonal elements of an inverse matrix of the information matrix G corresponding to the boundary node after decoupling of reactive power and active power in the selected subsystem B or the external network subsystem A;
s32, carrying out load flow calculation on the selected subsystem B and the external network subsystem A, carrying out merging update on the voltage amplitude and the phase angle of the boundary node through the merging formula by the merging parameter calculated in the step S31, and correspondingly calculating the equivalent injection power S of the ith boundary node according to the boundary injection power calculation formula and the equivalent motor active power output calculation formula by the boundary voltage amplitude and the phase angle obtained by new calculationLiAnd the active power P of the equivalent motor node motor corresponding to the ith boundary nodeeqiAnd then the current is calculated next time by taking the static equivalent initial value as the updated initial value,
the voltage amplitude and phase angle are combined into a formula:
Figure GDA0002823361860000052
in the formula: u. ofiAnd deltaiRespectively representing the combined voltage amplitude and phase angle u of the ith boundary node connected with the selected subsystem B and the external network subsystem AirAnd deltairRepresenting the combination of the voltage amplitude and the phase angle before the ith boundary node connected with the selected subsystem B and the external network subsystem A is combined;
boundary injection power calculation formula:
Figure GDA0002823361860000053
in the formula: m represents the number of system nodes, gilRepresenting the conductance between the ith and the l-th boundary nodes, bilRepresenting susceptance, δ, between the ith and the l-th boundary nodesilRepresents the phase angle difference between the ith boundary node and the l boundary node, uiRepresenting the combined voltage amplitude of the ith boundary node, and ul representing the voltage amplitude of the ith boundary node;
the equivalent motor active power output calculation formula is as follows:
Figure GDA0002823361860000061
wherein u ist iRepresents the voltage of the ith boundary node;
Eirepresenting the equivalent motor node voltage vector corresponding to the ith boundary node, EjRepresenting an equivalent motor node voltage vector corresponding to the jth boundary node;
Zeqirepresenting the impedance between the ith boundary node and the corresponding equivalent motor node;
ZeqGijrepresenting the impedance between the equivalent motor node corresponding to the ith boundary node and the equivalent motor node corresponding to the jth boundary node;
i ≠ j, i, j take 1, 2, 3 … NB；
S33, comparing the difference between the voltage amplitude and the phase angle after the combination for the first time and the difference between the phase angle and the last time, judging whether the difference meets the convergence precision, if so, stopping iteration, taking the static equivalent initial value obtained for the first time as the updated static equivalent initial value, otherwise, turning to the step S32.
Specifically, the specific steps of step S4 are as follows:
s41, adopting a minimum load shedding model based on the alternating current power flow to cut down the load,
the target equation:
Figure GDA0002823361860000062
s42, determining a constraint equation, and judging whether the state of each simulation is a failure state:
Figure GDA0002823361860000071
in the formula: py、QyRespectively the injected active power and the injected reactive power of the bus y; u and δ are the voltage magnitude and phase angle vectors of the bus, respectively; u. ofyIs an element of u; PD (photo diode)y、QDyRespectively an active load and a reactive load on the bus y; cyIs the load shedding variable for bus y;
Figure GDA0002823361860000072
the lower limit and the upper limit of active power injection and reactive power injection on the bus y are respectively; t ishIs the megavolt-ampere current on line h;
Figure GDA0002823361860000073
is the rated capacity of the line h;
Figure GDA0002823361860000074
respectively, a lower limit and an upper limit of the voltage amplitude on the bus y; ND, NG, L and U are respectively a load bus, a power generation bus, a set of all lines and a set of all buses in the system;
s43, reliability calculation index:
load shedding probability LOLP:
Figure GDA0002823361860000075
wherein F represents all failure states of the system, S represents the S-th failure state, and P (S) represents the probability of the S-th failure state;
desired starved power EENS:
Figure GDA0002823361860000076
where c (S) represents the amount of load reduction in the S-th failure state.
Optimally, the value of the time interval sampling times M of the PMU is not less than 7.
The invention has the advantages that:
(1) the influence of the interconnected external network on the subsystem is fully considered when the reliability of the interconnected power grid subsystem is calculated, the selected subsystem B and the external network subsystem A connected with the selected subsystem B are taken as examples, the problem of information isolation of the interconnected power grid is effectively solved by estimating the initial value of the static equivalence based on PMU monitoring data, and the problem that the initial value of the static equivalence cannot adapt to the change of the running state of the system in the conventional evaluation method is solved by adopting the to-be-updated method of the initial value of the static equivalence.
(2) In the aspect of theoretical analysis, the reliability evaluation theory of the interconnected power grid subsystem is further improved, the reliability evaluation method has an important role in the theoretical analysis and engineering application of the interconnected power grid reliability, and an effective path is provided for the evaluation method for the reliability of the subsystem under the influence of the interconnected power grid.
(3) The static equivalent initial value is estimated based on PMU real-time measurement data, the PMU real-time measurement data records running state data of the power system at a certain moment, and therefore the static equivalent initial value estimated based on the PMU real-time measurement data is the static equivalent initial value at the running state at the certain moment.
When the reliability of the power system is evaluated, the fault operation mode of the power grid needs to be simulated continuously, so that the fault element needs to be sampled, the operation state of the power system is changed, and equivalent parameters of an external grid are different necessarily under different operation states. The static equivalent initial value estimated by real-time PMU measurement data is only a parameter when the power grid normally runs, and when the reliability of the internal grid is evaluated in a fault simulation mode, errors of results are inevitably caused. Changes in the operating state of the intranet can cause two types of non-linear errors: a. when the operation state of the internal network changes, the injected power of the external network is assumed to be unchanged, and the voltage of the boundary node and the voltage of the equivalent node of the external network change, which is a first type of nonlinear error. b. When the operation state of the internal network changes, the action of the external network on the ground branch and the generator node with the speed regulator causes the injection power of the external network to change, which is a second type of nonlinear error. For the reliability calculation method for reducing the load by adopting the alternating current load flow, the two nonlinear errors can generate adverse effects on the calculation result and cannot be ignored. In order to ensure the precision and accuracy of the reliability calculation result, the influence caused by two types of nonlinear errors needs to be eliminated, and the static equivalent initial value is updated after the operation state of the internal network is changed. The method updates the static equivalent initial value through an asynchronous iteration method, and ensures the accuracy of the reliability calculation result.
Drawings
FIG. 1 is a system diagram after the static equivalence method of the external network;
FIG. 2 is a flow chart of an asynchronous iterative method of static equivalence initial values;
FIG. 3 is a flow chart of interconnected network subsystem operational reliability assessment based on PMU monitoring;
FIG. 4 is a diagram of an IEEE-RTS-96 node topology;
FIG. 5 is a static equivalence initial value error versus iteration number curve.
Detailed Description
A PMU monitoring-based interconnected power grid subsystem operation reliability assessment method includes that an interconnected power grid system comprises a selected subsystem B and an external network subsystem A, and N is included between the selected subsystem B and the external network subsystem ABA border node, as shown in fig. 3, the method comprising the steps of:
s1, as shown in figure 1, simplifying the external network subsystem A by adopting the external network static equivalence method based on sensitivity consistency. The static equivalent initial value of the external network subsystem A is as follows:
voltage current of boundary node: voltage u of ith boundary nodet iAnd the current i of the ith boundary nodet iVoltage u of jth boundary nodet jAnd the current i of the j-th boundary nodet j(i ≠ j, i, j take 1, 2, 3 … NB)；
Equivalent motor node voltage vector: motor node voltage vector E corresponding to ith boundary nodeiMotor node voltage vector E corresponding to jth boundary nodej(i ≠ j, i, j take 1, 2, 3 … NB)；
Equivalent branch impedance: impedance Z between the ith boundary node and the corresponding equivalent motor nodeeqiThe impedance Z between the jth boundary node and the corresponding equivalent motor nodeeqjImpedance Z between the equivalent motor node corresponding to the ith boundary node and the equivalent motor node corresponding to the jth boundary nodeeqGijImpedance Z between the ith and jth boundary nodeseqij(i ≠ j, i, j take 1, 2, 3 … NB)；
Injection power at the equivalent boundary: equivalent injection power S of ith boundary nodeLiThe equivalent injection power S of the jth boundary nodeLjActive power P of equivalent motor node motor corresponding to ith boundary nodeeqiActive power P of equivalent motor node motor corresponding to jth boundary nodeeqj(i ≠ j, i, j take 1, 2, 3 … NB)；
The equivalent ground branch admittance of the ith boundary node to the ground branch admittance biThe jth boundary node admittances b to the ground branchj(i ≠ j, i, j take 1, 2, 3 … NB)。
S2, obtaining the voltage u of the boundary node of the selected subsystem B based on the PMU (phasor measurement Unit)tAnd current i of boundary nodetCalculating the optimal static equivalent initial value of the external network subsystem A;
the method comprises the following specific steps:
s21, obtaining the voltage u of M groups of boundary nodes with the time interval sampling times of PMU being MtAnd current i of boundary nodetSubstituting into the measurement equation to calculate the optimal static equivalent initial value,
x represents M groups of static equivalent initial values to be measured, namely:
Figure GDA0002823361860000101
measurement equation obtained by kirchhoff's current theorem
Figure GDA0002823361860000102
The equation (2) is respectively expanded according to the real part of the imaginary part, and can be obtained:
Figure GDA0002823361860000103
Figure GDA0002823361860000104
in the formula:
Figure GDA0002823361860000105
Figure GDA0002823361860000111
Zeqikrepresenting an impedance between the kth boundary node and the ith boundary node;
s22, obtaining a static equivalent initial value x under the maximum running state of the external network subsystem AmaxAnd the static equivalent initial value x under the minimum running stateminIn order to ensure that the measurement equation is reasonably solved, an inequality constraint equation is constructed
Figure GDA0002823361860000112
Figure GDA0002823361860000113
Inequality constraint equation
xmin≤x≤xmax (8)
S23, constructing a least square model of the static equivalent initial values based on the measurement equation to obtain the optimal static equivalent initial values, wherein the least square model is
Figure GDA0002823361860000114
In order to ensure the redundancy of the measurement equation and the validity of the solution of the measurement equation, the value of the time period sampling number M must be greater than a certain critical value. The following describes a method for calculating the critical value of the segment sampling number M. The number of boundary nodes is NBThe number of corresponding motor nodes is also NBThe number of the parameters x to be estimated is 8, and M groups of static equivalent initial values to be measured need to calculate two quantities of the real part of the imaginary part and record the two quantities as two unknowns, so that the number of the known estimators is 14NBAccording to the above description, in order to ensure that the equation number is greater than the number of the parameters to be solved, the following relation is required to be satisfied between the measurement equation and the number of the estimators:
2NBM≥14NB (10)
simplifying to obtain:
M≥7 (11)
herein, M is calculated by taking an integer of not less than 7.
Based on the equation, the static equivalent model parameters of the external network are calculated by adopting an interior point method.
S3, as shown in fig. 2, simulating the selected subsystem B to have a fault based on the non-sequential monte carlo method, where the number of times of simulation is set to n, calculating the result of the power flow of the selected subsystem B in the simulation state after updating the initial static equivalent value corresponding to each simulation based on the asynchronous iterative method, determining whether the simulated state is a failure state according to the result of the power flow calculation, performing optimal power flow calculation if the simulated state is the failure state, and not performing optimal power flow calculation if the simulated state is not the failure state, where the specific steps of updating the initial static equivalent value corresponding to each simulation based on the asynchronous iterative method are as follows:
s31, calculating information matrixes G corresponding to boundary nodes after reactive power decoupling and active power decoupling respectively corresponding to the selected subsystem B and the external network subsystem A, and further calculating merging parameters, wherein a merging parameter calculation formula is as follows:
Figure GDA0002823361860000121
in the formula: r denotes the selected subsystem B and the extranet subsystem A, pirRepresenting a voltage merging parameter, σ, of the ith boundary node of the selected subsystem B or the outer network subsystem AirA phase angle merging parameter, theta, representing the ith boundary node of the selected subsystem B or the extranet subsystem AirAnd upsilonirRespectively representing diagonal elements of an inverse matrix of the information matrix G corresponding to the boundary node after decoupling of reactive power and active power in the selected subsystem B or the external network subsystem A;
s32, carrying out load flow calculation on the selected subsystem B and the external network subsystem A, carrying out merging update on the voltage amplitude and the phase angle of the boundary node through the merging formula by the merging parameter calculated in the step S31, and correspondingly calculating the equivalent injection power S of the ith boundary node according to the boundary injection power calculation formula and the equivalent motor active power output calculation formula by the boundary voltage amplitude and the phase angle obtained by new calculationLiAnd the active power P of the equivalent motor node motor corresponding to the ith boundary nodeeqiAnd then the current is calculated next time by taking the static equivalent initial value as the updated initial value,
the voltage amplitude and phase angle are combined into a formula:
Figure GDA0002823361860000131
in the formula: u. ofiAnd deltaiRespectively representing the combined voltage amplitude and phase angle u of the ith boundary node connected with the selected subsystem B and the external network subsystem AirAnd deltairRepresenting the combination of the voltage amplitude and the phase angle before the ith boundary node connected with the selected subsystem B and the external network subsystem A is combined;
boundary injection power calculation formula:
Figure GDA0002823361860000132
in the formula: m represents the number of system nodes, gilRepresenting the conductance between the ith and the l-th boundary nodes, bilRepresenting susceptance, δ, between the ith and the l-th boundary nodesilRepresents the phase angle difference between the ith boundary node and the l boundary node, uiRepresenting the combined voltage amplitude of the ith boundary node, and ul representing the voltage amplitude of the ith boundary node;
the equivalent motor active power output calculation formula is as follows:
Figure GDA0002823361860000133
wherein u ist iRepresents the voltage of the ith boundary node;
Eirepresenting the equivalent motor node voltage vector corresponding to the ith boundary node, EjRepresenting an equivalent motor node voltage vector corresponding to the jth boundary node;
Zeqirepresenting the impedance between the ith boundary node and the corresponding equivalent motor node;
ZeqGijrepresenting the impedance between the equivalent motor node corresponding to the ith boundary node and the equivalent motor node corresponding to the jth boundary node;
i ≠ j, i, j take 1, 2, 3 … NB；
S33, comparing the difference between the voltage amplitude and the phase angle after the combination for the first time and the difference between the phase angle and the last time, judging whether the difference meets the convergence precision, if so, stopping iteration, taking the static equivalent initial value obtained for the first time as the updated static equivalent initial value, otherwise, turning to the step S32.
And S4, after the selected subsystem B is simulated for n times, calculating the reliability of the power system, wherein the reliability of the power system comprises the load reduction probability LOLP and the expected power shortage EENS. The method comprises the following specific steps:
s41, adopting a minimum load shedding model based on the alternating current power flow to cut down the load,
the target equation:
Figure GDA0002823361860000141
s42, determining a constraint equation, and judging whether the state of each simulation is a failure state:
Figure GDA0002823361860000142
in the formula: py、QyRespectively the injected active power and the injected reactive power of the bus y; u and δ are the voltage magnitude and phase angle vectors of the bus, respectively; u. ofyIs an element of u; PD (photo diode)y、QDyRespectively an active load and a reactive load on the bus y; cyIs the load shedding variable for bus y;
Figure GDA0002823361860000143
the lower limit and the upper limit of active power injection and reactive power injection on the bus y are respectively; t ishIs the megavolt-ampere current on line h;
Figure GDA0002823361860000144
is the rated capacity of the line h;
Figure GDA0002823361860000145
respectively, a lower limit and an upper limit of the voltage amplitude on the bus y; ND, NG, L and U are respectively a load bus, a power generation bus, a set of all lines and a set of all buses in the system;
s43, reliability calculation index:
load shedding probability LOLP:
Figure GDA0002823361860000146
wherein F represents all failure states of the system, S represents the S-th failure state, and P (S) represents the probability of the S-th failure state;
desired starved power EENS:
Figure GDA0002823361860000151
where c (S) represents the amount of load reduction in the S-th failure state.
The embodiment takes an improved IEEE-RTS-96 node system as an example, and a network topology diagram of the system is shown in fig. 4. The selection of the boundary node, the external node and the internal node is as follows:
boundary nodes: 27,39, 41;
an external node: 1-24
Internal nodes: 25-26,28-38,40,42-48
Three methods were used to compare with the method proposed by the present invention:
(1) and simplifying an external network, and performing reliability calculation on the selected subsystem B power grid by using complete and accurate whole-network data, wherein the method is taken as M0, the calculation result is taken as a standard result, and the standard result is compared with other methods to verify the accuracy of the results of various methods.
(2) The method for calculating the reliability of the interconnected power grid subsystem based on the estimated static equivalent initial value of the PMU monitoring data calculates the reliability of the power grid of the selected subsystem B, and the reliability is taken as M1.
(3) And calculating the reliability of the power grid of the selected subsystem B by using an improved equivalent support capacity method, and taking the reliability as M2.
(4) And directly performing reliability calculation without updating the static equivalent initial value of the external network, and taking the value as M3.
E1 and e2 were selected as the error of various reliability calculation methods and standard results
Absolute error e1
e1＝|x0-xi|(i＝1,2,3) (20)
Relative error e2
Figure GDA0002823361860000152
In the formula x0、xiRepresenting the reliability calculation results of methods M0-M3, respectively.
TABLE 1 initial value of static equivalence estimation
Figure GDA0002823361860000153
Figure GDA0002823361860000161
TABLE 2 reliability calculation results
Figure GDA0002823361860000162
TABLE 3 reliability calculation result error
Figure GDA0002823361860000163
The reliability of the interconnected power grid subsystem is calculated by adopting the method provided by the invention. From table 2 and table 3, it can be seen that, when the reliability calculation is performed by using the M2 method, the reliability calculation result has a larger error than the reliability calculation results of the methods M1 and M3 because the outer network equivalent is too simple; by using the method M3, namely the static equivalent initial value is not updated, the static equivalent initial value is regarded as an invariant value to carry out reliability calculation, and the error of the calculation result is still large; through updating of the static equivalent initial value, as shown in fig. 5, as the iteration times increase, the static equivalent initial value tends to be stable, the reliability calculation is performed by using the method M1, the error of the reliability calculation result is greatly reduced compared with that of the method M3, the result calculated by the method close to M0 is close to the true value, and the effectiveness of the method provided by the invention is demonstrated.
The invention is not to be considered as limited to the specific embodiments shown and described, but is to be understood to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. The interconnected power grid subsystem operation reliability assessment method based on PMU monitoring is characterized in that the interconnected power grid subsystem comprises a selected subsystem B and an external network subsystem A, and N is included between the selected subsystem B and the external network subsystem ABA border node, the method comprising the steps of:
s1, simplifying an external network subsystem A by adopting an external network static equivalence method based on sensitivity consistency;
s2 obtaining boundary node voltage u of selected subsystem B based on PMUtAnd current i of boundary nodetCalculating the optimal static equivalent initial value of the external network subsystem A;
s3, simulating the selected subsystem B to have a fault based on a non-sequential Monte Carlo method, setting the simulation times as n, calculating the load flow result of the selected subsystem B in the simulation state after updating the static equivalent initial value corresponding to each simulation based on an asynchronous iteration method, judging whether the simulated state is a failure state or not according to the load flow calculation result, performing optimal load flow calculation if the simulated state is the failure state, and not performing optimal load flow calculation if the simulated state is not the failure state;
s4, after the selected subsystem B is simulated for n times, calculating the reliability of the power system, wherein the reliability of the power system comprises a load reduction probability LOLP and an expected power shortage amount EENS;
in step S3, the static equivalent initial value corresponding to each simulation is updated based on the asynchronous iterative method, and the specific steps are as follows,
s31, calculating information matrixes G corresponding to boundary nodes after reactive power decoupling and active power decoupling respectively corresponding to the selected subsystem B and the external network subsystem A, and further calculating merging parameters, wherein a merging parameter calculation formula is as follows:
Figure FDA0002823361850000011
in the formula: r denotes the selected subsystem B and the extranet subsystem A, pirRepresenting a voltage merging parameter, σ, of the ith boundary node of the selected subsystem B or the outer network subsystem AirA phase angle merging parameter, theta, representing the ith boundary node of the selected subsystem B or the extranet subsystem AirAnd upsilonirRespectively representing diagonal elements of an inverse matrix of the information matrix G corresponding to the boundary node after decoupling of reactive power and active power in the selected subsystem B or the external network subsystem A;
s32, carrying out load flow calculation on the selected subsystem B and the external network subsystem A, carrying out merging update on the voltage amplitude and the phase angle of the boundary node through the merging formula by the merging parameter calculated in the step S31, and correspondingly calculating the equivalent injection power S of the ith boundary node according to the boundary injection power calculation formula and the equivalent motor active power output calculation formula by the boundary voltage amplitude and the phase angle obtained by new calculationLiAnd the active power P of the equivalent motor node motor corresponding to the ith boundary nodeeqiAnd then the current is calculated next time by taking the static equivalent initial value as the updated initial value,
the voltage amplitude and phase angle are combined into a formula:
Figure FDA0002823361850000021
in the formula: u. ofiAnd deltaiRespectively representing the combined voltage amplitude and phase angle u of the ith boundary node connected with the selected subsystem B and the external network subsystem AirAnd deltairRepresenting the combination of the voltage amplitude and the phase angle before the ith boundary node connected with the selected subsystem B and the external network subsystem A is combined;
boundary injection power calculation formula:
Figure FDA0002823361850000022
in the formula: m represents the number of system nodes, gilRepresenting the ith boundary node and the ith boundary nodeConductance between points, bilRepresenting susceptance, δ, between the ith and the l-th boundary nodesilRepresents the phase angle difference between the ith boundary node and the l boundary node, uiRepresenting the combined voltage amplitude of the ith boundary node, and ul representing the voltage amplitude of the ith boundary node; biRepresenting the i-th boundary node to the terrestrial path admittance;
the equivalent motor active power output calculation formula is as follows:
Figure FDA0002823361850000023
wherein u ist iRepresents the voltage of the ith boundary node;
Eirepresenting the equivalent motor node voltage vector corresponding to the ith boundary node, EjRepresenting an equivalent motor node voltage vector corresponding to the jth boundary node;
Zeqirepresenting the impedance between the ith boundary node and the corresponding equivalent motor node;
ZeqGijrepresenting the impedance between the equivalent motor node corresponding to the ith boundary node and the equivalent motor node corresponding to the jth boundary node;
i ≠ j, i, j take 1, 2, 3 … NB；
S33, comparing the difference between the voltage amplitude and the phase angle after the combination for the first time and the difference between the phase angle and the last time, judging whether the difference meets the convergence precision, if so, stopping iteration, taking the static equivalent initial value obtained for the first time as the updated static equivalent initial value, otherwise, turning to the step S32.
2. The PMU-monitoring-based interconnected network subsystem operation reliability assessment method according to claim 1, wherein the step S1 is to simplify the external network subsystem A by using an external network static equivalence method based on sensitivity consistency, and the initial static equivalence values of the external network subsystem A are as follows:
voltage current of boundary node: voltage u of ith boundary nodet iAnd the current i of the ith boundary nodet iVoltage u of jth boundary nodet jAnd the current i of the j-th boundary nodet jI ≠ j, i, j take 1, 2, 3 … NB；
Equivalent motor node voltage vector: equivalent motor node voltage vector E corresponding to ith boundary nodeiEquivalent motor node voltage vector E corresponding to jth boundary nodejI ≠ j, i, j take 1, 2, 3 … NB；
Equivalent branch impedance: impedance Z between the ith boundary node and the corresponding equivalent motor nodeeqiThe impedance Z between the jth boundary node and the corresponding equivalent motor nodeeqjImpedance Z between the equivalent motor node corresponding to the ith boundary node and the equivalent motor node corresponding to the jth boundary nodeeqGijImpedance Z between the ith and jth boundary nodeseqijI ≠ j, i, j take 1, 2, 3 … NB；
Injection power at the equivalent boundary: equivalent injection power S of ith boundary nodeLiThe equivalent injection power S of the jth boundary nodeLjActive power P of equivalent motor node motor corresponding to ith boundary nodeeqiActive power P of equivalent motor node motor corresponding to jth boundary nodeeqjI ≠ j, i, j take 1, 2, 3 … NB；
The equivalent ground branch admittance of the ith boundary node to the ground branch admittance biThe jth boundary node admittances b to the ground branchjI ≠ j, i, j take 1, 2, 3 … NB。
3. The PMU-monitoring-based interconnected network subsystem operation reliability assessment method according to claim 2, wherein the step S2 specifically comprises the following steps:
s21, obtaining the voltage u of M groups of boundary nodes with the time interval sampling times of PMU being MtAnd current i of boundary nodetSubstituting into the measurement equation to calculate the optimal static equivalent initial value,
x represents the static equivalent initial values of M groups to be measured:
Figure FDA0002823361850000041
the measurement equation is:
Figure FDA0002823361850000042
Figure FDA0002823361850000043
in the formula:
Figure FDA0002823361850000044
Figure FDA0002823361850000051
Zeqikrepresenting an impedance between the kth boundary node and the ith boundary node;
s22, obtaining a static equivalent initial value x under the maximum running state of the external network subsystem AmaxAnd the static equivalent initial value x under the minimum running stateminAnd constructing an inequality constraint equation:
Figure FDA0002823361850000052
Figure FDA0002823361850000053
inequality constraint equation
xmin≤x≤xmax (8)
S23, constructing a least square model of the static equivalent initial values based on the measurement equation to obtain the optimal static equivalent initial values, wherein the least square model is
Figure FDA0002823361850000054
4. The PMU monitoring-based interconnected network subsystem operation reliability assessment method according to claim 3, characterized in that, the specific steps of step S4 are as follows:
s41, adopting a minimum load shedding model based on the alternating current power flow to cut down the load,
the target equation:
Figure FDA0002823361850000055
s42, determining a constraint equation, and judging whether the state of each simulation is a failure state:
Figure FDA0002823361850000061
in the formula: py、QyRespectively the injected active power and the injected reactive power of the bus y; u and δ are the voltage magnitude and phase angle vectors of the bus, respectively; u. ofyIs an element of u; PD (photo diode)y、QDyRespectively an active load and a reactive load on the bus y; cyIs the load shedding variable for bus y;
Figure FDA0002823361850000062
the lower limit and the upper limit of active power injection and reactive power injection on the bus y are respectively; t ishIs the megavolt-ampere current on line h;
Figure FDA0002823361850000063
is the rated capacity of the line h;
Figure FDA0002823361850000064
respectively, a lower limit and an upper limit of the voltage amplitude on the bus y; ND, NG, L and U are respectively a load bus, a power generation bus, a set of all lines and a set of all buses in the system;
s43, reliability calculation index:
load shedding probability LOLP:
Figure FDA0002823361850000065
wherein F represents all failure states of the system, S represents the S-th failure state, and P (S) represents the probability of the S-th failure state;
desired starved power EENS:
Figure FDA0002823361850000066
where c (S) represents the amount of load reduction in the S-th failure state.
5. The interconnected network subsystem operation reliability assessment method based on PMU monitoring of claim 3, characterized by that, the value of the time interval sampling times M of PMU is not less than 7.
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