CN106786536B - A State Estimation Method Considering External Network Extended Ward Equivalent - Google Patents
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Abstract
本发明的目的是针对现有考虑外网状态估计研究方法的不足，提出了一种考虑外网扩展Ward等值的状态估计方法。具体步骤包括：读入电网的参数和SCADA量测数据；结合外网典型断面网络信息构造扩展Ward等值模型；考虑外网扩展Ward模型，形成新的量测信息；单独对内网进行带等式约束的加权最小二乘状态估计。
The purpose of the present invention is to propose a state estimation method considering the external network expansion Ward equivalence in view of the deficiencies of the existing research methods for state estimation considering the external network. The specific steps include: reading the parameters of the power grid and SCADA measurement data; constructing an extended Ward equivalent model based on the typical cross-section network information of the external network; expanding the Ward model considering the external network to form new measurement information; formula-constrained weighted least squares state estimation.
Description
Technical field
The invention belongs to dispatching automation of electric power systems field, in particular to a kind of shape for considering outer net extended Ward equivalent
State estimation method.
Background technique
Power system state estimation is an important ring of EMS, has a direct impact to the scheduling decision of power grid, can improve electric power
System safe and economical operation is horizontal.Its main task is to calculate by best estimate criterion raw data, obtains power grid shape
The best estimate of state amount.
The electric system in China is mainly by Two large pools --- and national grid and south electric network form, and in addition there are some small
The regional power grid of range, such as Hong Kong power grid and Macao's power grid.Exist between Two large pools and between small range regional power grid
Competitive relation, the topological structure and operation conditions of both sides can only share some essential informations according to regulation, or even cannot share.
Therefore when being based on measurement progress state estimation to separate subnet, need to carry out outer net simply and effectively equivalent, Cai Nengzhun
True carry out state estimation.
Based on this, when being based on measurement progress state estimation to separate subnet in practical power systems at present, often outer
Net processing is the mode of the check-ins such as extension, and the influence of the internal net state estimation of the topological structure for not accounting for outer net, therefore not
Quantity of state can be modified in time when Intranet contains bad data.Further to excavate the available effective information of outer net,
By introducing outer net extended Ward equivalent model, the constraint relationship in the estimation of interior net state is increased, to effectively distinguish not
Good data improve the precision of Intranet state estimation, to meet the needs of Practical Project utilization.
Summary of the invention
The purpose of the present invention is propose outside a kind of consideration for the existing deficiency for considering outer net State Estimation Study method
The state estimation of net extended Ward equivalent model.Specific steps include: to read in the parameter and SCADA metric data of power grid；In conjunction with
The outer net typical section network information constructs extended Ward equivalent model；Consider that outer net extends Ward model, forms new measurement letter
Breath；The weighted least-squares state estimation with equality constraint individually is carried out to Intranet.
Purpose and the technical solution that uses to realize the present invention, the following steps are included:
1) parameter and SCADA metric data of power grid are read in:
The parameter of power grid refers to outer net typical section, Intranet topological structure and component parameters；The SCADA measurement information is
Information under intranet and extranet collective effect, measuring point is in Intranet, comprising: branch power, injecting power and node voltage amplitude.
2) the outer net typical section network information is combined to construct extended Ward equivalent model:
Outer net topological structure and parameter 2-1) are utilized, outer net node admittance matrix Y is calculated based on formula (1):
In formula, node i and the node that node j is that any two are different in outer net；YiiFor the diagonal line of node admittance matrix
Element, YijFor the off diagonal element of node admittance matrix；yijFor the branch admittance between node i and node j；Symbol j ∈ i
When indicating that node j and node i are connected directly, and should also include the case where when node i has ground branch j=0.
Outer net node admittance matrix Y is organized into following form by node type:
In formula: Q represents the PQ node in external network, and V represents the PV node in external network, and B represents boundary node, E
Represent external node, YαβFor submatrix, wherein α=Q, V, B, β=Q, V, B；
2-2) disregard outer net parallel branch, eliminates former external network node admittance matrix with Gaussian elimination method based on (2)
(2) all PQ nodes in formula, the admittance matrix Y after obtaining abbreviation*, solve power extension branch parameters:
In formula, " 0 ", which represents, is eliminated part, and "-" is represented without being melted into 0 part； For (2) formula
By 2-2) operation after need to retain part.
Wherein YQQ、YQV、YQB、YVQ、YVV、YVB、YBQ、YBV、YBBIt is in the outer net node admittance matrix of (2) formula Central Plains
Element.
By the outer net admittance matrix after abbreviation, the sum of the branch admittance between boundary node and outer net PV node is sought, i.e.,
Every a line value is added, and after taking opposite number, can obtain the admittance value of power extension branch.
Outer net PV node further 2-3) is eliminated using Gaussian elimination to formula (3), obtains (4)
Ask admittance between equivalent boundary node:
In formula, " 0 ", which represents, is eliminated part, and "-" is represented without being melted into 0 part；Equivalent between boundary node is led
It receives.
Wherein For the equivalent admittance in (3) formula.
2-4) calculate the equivalent injecting power of boundary node:
The power between boundary node is calculated based on formula (5)；It is calculated in real time in view of online, equivalent power supply voltage is equal to side
Boundary's node voltage, power branch power are 0；And the power on interconnection can be obtained in real time by measuring, according to node power
Balance, can calculate the equivalent power on boundary node.
P in formulaij, QijActive power and reactive power respectively between boundary node i and j；uiFor the voltage amplitude of node i
Value, ujFor the voltage magnitude of node j；θiFor the voltage phase angle of node i, θjFor the voltage phase angle of node j, and θij=θi-θj, table
Show the phase difference of voltage of node i and node j；gijConductance, b for boundary point i and boundary point jijFor boundary point i's and boundary point j
Susceptance.
2-5) in Equivalent Model, the check-ins such as boundary point is respectively hung, medium value machine power is
0, voltage magnitude is the boundary point voltage magnitude that is connected.
3) consider outer net extended Ward equivalent model, form new measurement information:
By 2 equivalent power supply voltage magnitudes in outer net extended Ward equivalent model, increase to measurement as voltage measurement
In information, two boundary node injecting powers are measured, are needed former boundary node injecting power measuring value plus 2-2)
Medium value function injection rate forms new boundary node injecting power measurement.
4) the weighted least-squares state estimation with equality constraint individually is carried out to Intranet:
, neither generator node is also not the injecting power of load bus, equation will be injected as zero in Intranet measurement
Constraint equation indicates are as follows:
C (x)=0 (4)
In formula, c (x) is the measurement equation of zero injection node, the node injection active power and reactive power value indicated
It can be calculated by formula (5)；X is the quantity of state of n dimension, and n is actual state variable number in state estimation.The calculating of c (x)
Formula are as follows:
In formula, Pi' the active power injected for node i；Qi' the reactive power injected for node i；uiFor the voltage of node i
Amplitude, ujFor the voltage magnitude of node j；θiFor the voltage phase angle of node i, θjFor the voltage phase angle of node j, and θij=θi-θj,
Indicate the phase difference of voltage of node i and node j；Gij、BijElement between corresponding node i and j respectively in node admittance matrix
Real and imaginary parts；N is the node number of power grid.
Traditional WLS considers that zero energy equivalence restricted problem, mathematical model can be described as formula (6):
In formula, z is metric data, and h (x) is measurement equation, and R weight matrix is assigned to 1.
Problem with equality constraint is transformed to unconstrained problem with method of Lagrange multipliers, recycles extremum conditions to obtain non-
System of linear equations obtains quantity of state finally by iterative solution formula (7).
In formula, time is to calculate the number of iterations；x(time)Quantity of state when for the time times iteration；R-1For weight diagonal matrix.For the Jacobian matrix of measurement, HTFor its transposition.c(x(time)) be iterative value be x(time)When zero injection etc.
Formula constraint,It is the Jacobian matrix of zero injection equality constraint, CTFor its transposition.z-h(x(time)) indicate iterative value
For x(time)When residual error；λ(time)Lagrange multiplier vector when for the time times iteration.
The present invention is after adopting the above technical scheme, mainly have the following effects:
It is often the check-ins such as extension outer net processing when with carrying out state estimation to separate subnet in practical power systems at present
Mode compare, the present invention considers outer net extended Ward equivalent model, by further excavating the available effective letter of outer net
Breath increases the constraint relationship in the estimation of interior net state and improves Intranet state estimation so as to effectively distinguish bad data
Precision.
The present invention can replace and lose interest in original power system by using the method for estimating state of extended Ward equivalent
Or the part of network state information can not be obtained in real time, it is substantially reduced the scale of state estimation.
Due between practical interacted system there may be competitive relation, both sides can only share some basic topological structures with
Health information.In this case, the present invention extends Ward by the topology information using outer net typical section, construction outer net
Equivalent Model, so that independent carry out state estimation to Intranet, to meet the needs of Practical Project utilization.
In the outer net extended Ward equivalent model that the present invention considers, the equivalent impedance between boundary node is to Intranet transfer power
With correcting action, equivalence power generation function, which is internally netted, carries out corresponding reactive compensation, supports Intranet voltage, shape on this basis
State estimation, accuracy and Robustness least squares can effectively be embodied.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Fig. 1 is the flow diagram for considering the method for estimating state of outer net extended Ward equivalent；
Fig. 2 is outer net node admittance matrix；
Fig. 3 is the admittance matrix that outer net PQ node is eliminated using Gaussian elimination；
Fig. 4 is outer net extended Ward equivalent model；
Fig. 5 is the virtual external network equivalent parameter calculated result of IEEE39 node system；
Fig. 6 is the wiring diagram of IEEE39 node system.
Specific embodiment
Below with reference to embodiment, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention only
It is limited to following embodiments.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and used
With means, various replacements and change are made, should all include within the scope of the present invention.
It is a kind of consider outer net extended Ward equivalent estimation method specific step is as follows in embodiment:
(1) it is measured with modular system digital simulation intranet and extranet and SCADA
By taking 39 node system of IEEE as an example, node 3 and 17 is used as boundary point, and node 1,2,25~30 and 37~39 is made
For outer net node, remaining node is Intranet node, simultaneously switches off branch 9~39, and the load of node 17 is set as 10-
J20MVA forms the analogue system of two-port interconnected network.
For network measurement, obtained using true value superposition random error.The whole network trend meter first is carried out to the example system
It calculates, then is superimposed random error in measurement on the basis of trend true value and constitutes Intranet measuring value, can use injecting power, branch function herein
Rate, the standard deviation of the error in measurement of voltage magnitude are respectively 0.01,0.008 and 0.004.
(2) solution of ward parameter is extended
The node admittance matrix of outer net is first calculated based on formula (1), the transadmittance on equivalent boundary is calculated based on formula (2)Power between boundary node is first calculated based on formula (3), then goes out equivalent injecting power according to power equilibrium calculationWith
Concrete outcome such as Fig. 4:
(3) consider outer net extended Ward equivalent, form new measurement
Measurement information variation includes: that form two nodes in conjunction with the measurement injecting power of node 3,17 and equivalent injecting power new
Injecting power, while node 3 and 17 voltage magnitude of node are incorporated into new measurement as measurement information.
(4) the WLS state estimation of equality constraint is individually carried out to Intranet
By described in step, belonging to having for zero energy node: 1,2,5,6,9,10,11,13,14,19,22 being based on formula (5)
Calculate the calculated value of injecting power.
For the superiority of process in detail, explanation is compared using two schemes:
Scheme is 1.: being the mode for the check-ins such as hanging by outer net processing, i.e., is calculated outside at boundary node by Intranet measurement information
The equivalent injecting power of net；It is computed
Scheme is 2.: the method for the present invention handles outer net for extended Ward equivalent model.
Finally, carry out Intranet as a result, subtracting each other to obtain error with the true value of Load flow calculation after state estimation, and relatively on
State the error size of two schemes.
Experiment effect comparative analysis
A. the analysis of the accuracy of model
In the case where there is no bad data in Intranet measurement, after state estimation with the maximum value of trend true value error and
Average value is as shown in Table 1 and Table 2, and each parameter is per unit value, reference power 100MVA in table.And er_Vm、er_Pi、er_Qi、
er_Pij、er_QijIndicate that voltage magnitude, injection active power, injection reactive power, branch active power, branch reactive power are missed
The maximum value of difference；es_Vm、es_Pi、es_Qi、es_Pij、es_QijIndicate voltage magnitude, injection active power, injection reactive power, branch
The average value of road active power, branch reactive power error.
Intranet state estimation max value of error when table 1 is without bad data
Intranet state estimation average error when table 2 is without bad data
As can be seen from Table 1 and Table 2, when not having bad data in Intranet measurement, the error of two schemes is smaller, table
Bright outer net can accurately estimate Intranet trend using the check-ins methods such as extension or extended Ward equivalent method；Outer net extension
In the result that Ward equivalent method calculates, error in addition to voltage magnitude is slightly larger than hanging equivalent method, other errors, such as injecting power and
The error of branch power is respectively less than the check-ins methods such as extension, illustrates that outer net extended Ward equivalent method is high compared with the estimated accuracy of the check-ins such as extension.
In order to enable those skilled in the art to better understand the present invention and understand the present invention compared with the advantages of the prior art, Shen
It asks someone further to be illustrated in conjunction with specific embodiments.
B. the Robustness least squares analysis of model
Correcting action of the B1 to Intranet transfer power
It is verifying outer net extended Ward equivalent model to the correcting action of Intranet transfer power, looped network between present boundary node
Bad data is constructed in the power measurement of branch.In IEEE39 node system, it is assumed that form ring between boundary node 3 and 17
In Intranet route 3-4,4-14,14-15,15-16, the 16-17 on road, branch power measures the negative for being set as true value, then shape
As shown in Table 3 and Table 4 with the maximum value and average value of trend true value error after state estimation, each parameter is per unit value, base in table
Quasi- power is 100MVA.
Intranet state estimation error is most when containing bad data in 3 power measurement of table
Big value
Intranet state estimation average error when containing bad data in 4 power measurement of table
Can be seen that from table 3 and table 4, when between Intranet boundary node in characteristic of loop branches there are when bad data, outer net extension
The check-ins such as the error of Ward equivalence either maximum value or average value, respectively less than outer net extension illustrate to extend Ward etc. in outer net
It is worth in model, the equivalent impedance between boundary node has correcting action to Intranet transfer power, when ring between Intranet boundary node
It, can internally net state carries out estimation calculating on more accurate ground there are when bad data in net branch.
Supporting role of the B2 to Intranet voltage
Supporting role for verifying outer net extended Ward equivalent model to Intranet voltage, considers boundary node or adjacent thereto
The voltage of node constructs bad data in measuring.Assuming that voltage measurement is set as 0, i.e., in Intranet node 3,4,16,17,18
The point sensor does not get voltage value or loss of data occurs in transmission process.Scheme 1., the state estimation of scheme 2.
As a result as shown in table 5 below:
Estimated result when in the measurement of 5 voltage of table containing bad data
As can be seen from Table 5, when voltage is measured containing bad data in Intranet measurement, estimated with check-ins methods such as outer net extensions
The resultant error counted out is all larger than outer net using extended Ward equivalent.To find out its cause, in outer net extended Ward equivalent, it is equivalent
Power supply can provide Intranet voltage support effect, to can also estimate when containing bad data in the measurement of the voltage of Intranet
Its true value out.For check-ins methods such as outer net extensions, due to only the injecting power that external network equivalent is at boundary node, not having
Voltage support effect.
More clearly to show that extended Ward equivalent surveys equivalent precision when the error occurs in Intranet voltage, now it is arranged
The voltage of 1/2 number of nodes of Intranet is 0, then the maximum value of the whole network trend error after state estimation and average value are shown such as table 6
With table 7.
Intranet state estimation max value of error when containing bad data in the measurement of 6 voltage of table
Intranet state estimation average error when containing bad data in the measurement of 7 voltage of table
From table 6 and table 7 as can be seen that when the number of nodes that Intranet voltage magnitude is bad measurement increases, two kinds of outer nets etc.
The state estimation result error of value model can all increase.But outer net uses error when extended Ward equivalent to be respectively less than and hangs equivalence
Machine illustrates the supporting role of external network equivalent power supply, keeps the precision of extended Ward equivalent model higher, estimated result is more quasi-
Really.
Claims (1)
1. a kind of method for estimating state for considering outer net extended Ward equivalent, it is characterised in that: the following steps are included:
1) parameter and SCADA metric data of power grid are read in:
The parameter of power grid refers to outer net typical section, Intranet topological structure and component parameters；The SCADA measurement information is inside and outside
Information under net collective effect, measuring point is in Intranet, comprising: branch power, injecting power and node voltage amplitude；
2) the outer net typical section network information is combined to construct extended Ward equivalent model:
Outer net topological structure and parameter 2-1) are utilized, outer net node admittance matrix Y is calculated based on formula (1):
In formula, node i and the node that node j is that any two are different in outer net；YiiFor the diagonal entry of node admittance matrix,
YijFor the off diagonal element of node admittance matrix；yijFor the branch admittance between node i and node j；Symbol j ∈ i indicates section
Point j and node i are connected directly, and when should also include the case where when node i has ground branch j=0；
Outer net node admittance matrix Y is organized into following form by node type:
In formula: Q represents the PQ node in external network, and V represents the PV node in external network, and B represents boundary node, and E is represented
External node, YαβFor submatrix, wherein α=Q, V, B, β=Q, V, B；
2-2) disregard outer net parallel branch, is eliminated in former outer net node admittance matrix (2) formula based on (2) with Gaussian elimination method
All PQ nodes, the admittance matrix Y after obtaining abbreviation*, solve power extension branch parameters:
In formula, " 0 ", which represents, is eliminated part, and "-" is represented without being melted into 0 part, For (2) formula process
It needs to retain part after 2-2) operating；
Wherein YQQ、YQV、YQB、YVQ、YVV、YVB、YBQ、YBV、YBBIt is first in the outer net node admittance matrix of (2) formula Central Plains
Element；
By the outer net admittance matrix after abbreviation, the sum of the branch admittance between boundary node and outer net PV node is sought, i.e.,It is each
Row value is added, and after taking opposite number, can obtain the admittance value of power extension branch；
Matrix (3) 2-3) are based on, further eliminate outer net PV node using Gaussian elimination, (4) is obtained and asks between equivalent boundary node
Admittance:
In formula, " 0 ", which represents, is eliminated part, and "-" is represented without being melted into 0 part；Equivalent admittance between boundary node；
Wherein For the equivalent admittance in (3) formula；
2-4) calculate the equivalent injecting power of boundary node:
Based on formula (5), the power between boundary node is calculated；It is calculated in real time in view of online, equivalent power supply voltage is equal to boundary
Node voltage, power branch power are 0；And the power on interconnection can be obtained in real time by measuring, it is flat according to node power
Weighing apparatus, can calculate the equivalent power on boundary node；
P in formulaij, QijActive power and reactive power respectively between boundary node i and j；uiFor the voltage magnitude of node i,
ujFor the voltage magnitude of node j；θiFor the voltage phase angle of node i, θjFor the voltage phase angle of node j, and θij=θi-θj, indicate section
The phase difference of voltage of point i and node j；gijConductance, b for boundary point i and boundary point jijFor the electricity of boundary point i and boundary point j
It receives；
2-5) in Equivalent Model, the check-ins such as boundary point is respectively hung, medium value machine power is 0, and voltage magnitude is the boundary that is connected
Point voltage magnitude；
3) consider outer net extended Ward equivalent model, form new measurement information:
By 2 equivalent power supply voltage magnitudes in outer net extended Ward equivalent model, increase to measurement information as voltage measurement
In, two boundary node injecting powers are measured, are needed former boundary node injecting power measuring value plus 2-4) medium value
Injecting power forms new boundary node injecting power measurement；
4) the weighted least-squares state estimation with equality constraint individually is carried out to Intranet:
, neither generator node is also not the injecting power of load bus, equality constraint will be injected as zero in Intranet measurement
Equation indicates are as follows:
C (x)=0 (6)
In formula, c (x) is the measurement equation of zero injection node, and the node injection active power and reactive power value indicated can be by
Formula (5) is calculated；X is the quantity of state of n dimension, and n is actual state variable number in state estimation；The calculation formula of c (x)
Are as follows:
In formula, Pi' the active power injected for node i；Q′iFor the reactive power of node i injection；uiFor the voltage amplitude of node i
Value, ujFor the voltage magnitude of node j；θiFor the voltage phase angle of node i, θjFor the voltage phase angle of node j, and θij=θi-θj, table
Show the phase difference of voltage of node i and node j；Gij、BijRespectively in node admittance matrix between corresponding node i and j element reality
Portion and imaginary part；N is the node number of power grid；
Traditional WLS considers that zero energy equivalence restricted problem, mathematical model can be described as formula (8):
In formula, z is metric data, and h (x) is measurement equation, and R weight matrix is assigned to 1；
Problem with equality constraint is transformed to unconstrained problem with method of Lagrange multipliers, recycles extremum conditions to obtain non-linear
Equation group obtains quantity of state finally by iterative solution formula (9)；
In formula, time is to calculate the number of iterations；x(time)Quantity of state when for the time times iteration；R-1For weight diagonal matrix；For the Jacobian matrix of measurement, HTFor its transposition；c(x(time)) be iterative value be x(time)When zero injection etc.
Formula constraint,It is the Jacobian matrix of zero injection equality constraint, CTFor its transposition；z-h(x(time)) indicate iterative value
For x(time)When residual error；λ(time)Lagrange multiplier vector when for the time times iteration.
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