CN101702521A - State estimation method for electric power system considering influences of multi-balancing machine - Google Patents
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Abstract
The invention discloses a state estimation method for an electric power system considering the influences of a multi-balancing machine. The method comprises the following steps of: firstly, according to the needs of the system, setting a group of multi-balancing machines for commonly sharing the imbalanced power of the system; secondly, deriving a computational formula of a measurement vector according to the setting of the multi-balancing machines, solving a Jacobian matrix of the measurement vector with respect to a quantity of state, and estimating the state of the system by using a least squares estimation criteria . Because the influences the multi-balancing machine is considered, the imbalanced power of the system is commonly shared by setting a group of multi-balancing machines, and the result of the state estimation accords with the practical situation better. In addition, the method can realize the state estimation considering the influences of the multi-balancing machine only by slightly amending the measurement function and the Jacobian matrix parts of the prior state estimation software. The invention has definite physical meaning, is convenient to realize in the traditional state estimation software and satisfies the requirements of engineering on the estimation precision.
Description
Technical Field
The invention relates to a power system state estimation method considering the influence of a multi-balancing machine, and belongs to the technical field of power system operation and control.
Background
The state estimation is also called filtering, and the redundancy of a real-time measurement system is utilized to improve the data accuracy, automatically eliminate error information caused by random interference and estimate or forecast the running state of the system. With implementation of western and east power transmission and rapid promotion of the power market, the ultra-high voltage, long-distance and alternating-current and direct-current hybrid power transmission technology develops rapidly in a power grid in China, and the automation level of a power system dispatching center needs to be gradually improved. As an important component of an Energy Management System (EMS) of each level of a modern large-scale power system, state estimation provides reliable and complete system running state information for the EMS, and a database required by various high-level application software is established by using the data and is known as the heart of the application software, so the state estimation is the basis of the aspects of power system running, control, safety evaluation and the like.
In conventional state estimation, only one balancing node is usually provided, corresponding to one balancing machine, to balance unbalanced power in the system, but this is not consistent with the actual situation of the power system. In an actual power system, when the system has small unbalanced power, the unbalanced power is distributed by all the generators with capacity margins and all the loads together according to respective active frequency characteristic coefficients, namely primary frequency modulation; when the system has larger unbalanced power, the unbalanced power can be adjusted by primary frequency modulation, and a generating set with secondary frequency modulation capability can be used for secondary frequency modulation. Therefore, when the unbalanced power of the system is small, the conventional state estimation method adopting the balance generator cannot generate great influence on the running state of the system; when the unbalanced power of the system is large, it is not appropriate to adopt the conventional state estimation method in which only one balanced generator is provided, and the resulting system operation state may deviate from the actual state greatly. The state estimation method considering the influence of the multi-balancing machine overcomes the defects, and a group of balancing generator sets are arranged to share the unbalanced power of the system, so that the state estimation result is more in line with the actual situation. At present, the concept of a multi-balancing machine is mostly seen in power flow calculation of a power system, and the state estimation research of the power system under the multi-balancing machine is not reported in documents.
Disclosure of Invention
The invention aims to solve the technical problem of providing a power system state estimation method considering the influence of a multi-balancing machine aiming at the defect that the balance requirement on unbalanced power is difficult to meet by setting a single balancing machine of an interconnected power grid.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a power system state estimation method considering the influence of a multi-balancing machine, which is characterized by comprising the following steps of:
(1) acquiring network parameters of an electric power system, comprising: the branch number, the head end node and the tail end node number of the power transmission line, the series resistance, the series reactance, the parallel conductance, the parallel susceptance, the transformer transformation ratio and the impedance;
(2) initializing, including: setting an initial value for the state quantity, optimizing the node sequence, forming a node admittance matrix, setting a threshold value and distributing a memory;
(3) inputting telemetering data z, including voltage amplitude, generator active power, generator reactive power, load active power, load reactive power, line head end active power, line head end reactive power, line tail end active power and line tail end reactive power;
(4) the power system is provided with n nodes, wherein generators where the nodes n, … and n-m are located form a balance unit and bear unbalanced power of the power system;
(5) recovering the iteration number k of the iteration counter to be 1;
(6) from the existing state quantity x(k)The calculated value h (x) of each measurement is calculated according to the following formula(k))；
The voltage amplitude of the node i is Vi＝vi：
Node i injected power:
starting power on lines i-j:
end power on lines i-j:
the power of the upper starting end of the transformer line i-j is as follows:
power at the upper end of the transformer line i-j:
in the formula vi、vjVoltage amplitudes of the node i and the node j are respectively; thetaijIs the voltage phase angle difference of node i and node j; gij、BijThe real part and the imaginary part of the admittance matrix; g. b, ycRespectively the conductance, susceptance and grounding susceptance of the line; k is the nonstandard transformation ratio of the transformer; bTThe standard susceptance of the transformer is measured; p, Q represent the active and reactive power of the generator, respectively; i. j is 1, 2, …, n-m-1, i, j, m and n are natural numbers which are larger than zero, and m is less than n;
(7) is divided intoDerivation of state quantities to obtain a measured Jacobian matrix H (x)(k))：
And (3) injecting power into the node:
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
starting power on lines i-j
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(8) Determining a state correction amount
SelectingAnd correcting the state quantity to obtain
Wherein x is a 2n-1 dimensional state variable of the power system;is an estimate of the state quantity; z is a vector of measurement values, namely telemetry data; h (x) is a non-linear function of x; h (x) a Jacobian matrix which is a measurement function; r-1A weighting matrix for the measurement vector; t is a rank conversion symbol; (k) representing an iteration number;
(9) when in use
And (4) ending the state estimation if the convergence standard is smaller than the set convergence standard, otherwise returning to the step (6) to carry out the (k +1) th estimation.
The method for estimating the state of the power system considering the influence of the multi-balancing machine, which is provided by the invention, ensures that the state estimation result is more in line with the actual situation by arranging a group of balanced generator sets to bear the unbalanced power of the system together, can realize the state estimation considering the influence of the multi-balancing machine only by slightly correcting the measurement function and the Jacobian matrix part of the existing state estimation software, has clear physical significance, is convenient to realize on the existing state estimation software, and meets the requirement of engineering on the estimation precision.
Drawings
FIG. 1: the method of the invention is a flow chart.
FIG. 2: the invention adopts an element equivalent circuit diagram, wherein: the diagram (a) is a circuit diagram of a circuit pi-shaped equivalent circuit, and the diagram (b) is a circuit diagram of a transformer pi-shaped equivalent circuit.
FIG. 3: the state estimation method considering the influence of the multi-balancing machine provided by the invention is applied to two small example systems, wherein: FIG. (a) is an IEEE-14 node system, and FIG. (b) is an IEEE-30 node system.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings:
the most basic algorithm for estimating the state of a power system, namely a basic weighted two-times state estimation algorithm (WLS), was proposed by the institute of technology, massachusetts, usa in 1969 as a permissive paste (f.c. schweppe), and the basic idea is an estimation method using the minimum sum of squares of differences between measured values and measured estimated values as a target criterion. The method is widely applied by the characteristics of simple model, good convergence performance and high estimation quality. The method for estimating the state of the power system considering the influence of the multi-balance machine is provided on the basis of a WLS algorithm.
As shown in fig. 1, given the network wiring, branch parameters and measurement system, the nonlinear measurement equation can be expressed as:
z＝h(x)+v
in the formula, z is a measurement value vector, namely telemetering data, most of the data are obtained through telemetering, and a small part of the data are manually set; h (x) is a measurement function established by the basic circuit law of kirchhoff and the like; x is a system state variable; v is the measured random error, assuming that it obeys a mean of zero and a variance of σ2Is normally distributed. The system is provided with n nodes, the voltage amplitude and the voltage phase angle of the nodes are used as state variables, and the generator where the nodes n, …, n-m are located meets the selection requirement of a balancing machineIf the balance unit is formed (namely, the generator serving as the balance machine should have larger adjustment margin), then
…，
In the state estimation of the power system, the types of measurement configurations are more than the conventional power flow, and not only the injection power measurement P of each node is includedi、QiIt may also include power measurement P of the branchij、Qij、Pji、QjiAnd voltage amplitude measurement V of the nodeiThe measurement equation is shown as follows:
and (3) injecting power into the node:
starting power on lines i-j:
end power on lines i-j:
the power of the upper starting end of the transformer line i-j is as follows:
power at the upper end of the transformer line i-j:
voltage amplitude of node i:
Vi＝vi，i、j＝1，2，…，n-m-1
in the above measurement equation, vi、vjVoltage amplitudes of the node i and the node j are respectively; thetaijIs the voltage phase angle difference of node i and node j; gij、BijThe real part and the imaginary part of the admittance matrix; g. b, ycThe conductance, susceptance and grounding susceptance of the line are adopted; k is the nonstandard transformation ratio of the transformer; bTThe standard susceptance of the transformer.
Given a measurement vector z, the state estimation problem is to solve an objective function
J(x)＝[z-h(x)]TR-1[z-h(x)]
The value of x at the minimum is reached. Wherein R is σi 2The matrix is a measurement error variance matrix of diagonal elements, and the inverse matrix is taken as a weighting matrix of measurement vectors in state estimation.
Since h (x) is a non-linear function of x, it cannot be directly calculated
To find out
First, h (x) is linearized. Let x0Is some approximation of x, at x0And (3) performing Taylor expansion on h (x) nearby, and neglecting higher-order terms of more than two times to obtain:
h(x)≈h(x0)+H(x0)Δx
wherein Δ x is x-x0， <math><mrow><mi>H</mi><mrow><mo>(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mo>∂</mo><mi>x</mi></mrow></mfrac><msub><mo>|</mo><mrow><mi>x</mi><mo>=</mo><msub><mi>x</mi><mn>0</mn></msub></mrow></msub><mo>.</mo></mrow></math>
Taking the node injection power and the initial power on the line i-j as an example, the corresponding elements of the Jacobian matrix H (x) of the measurement vector are:
node injected power
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
Starting power on lines i-j
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
It can be seen that there are m +1 balanced nodes in the system, and the Jacobian matrix will be reduced by 2(m +1) orders.
Substituting the linearized expression of h (x) into the objective function, which can be solved iteratively by the following mathematical induction:
where (k) represents an iteration number.
As shown in FIG. 2, the diagram (a) is the equivalent of the line IIIn the circuit diagram, an admittance g + j 'b is connected between a node i and a node j in series, and the output ends of the nodes i and j are respectively connected with a grounding susceptance j' y in seriescAnd then grounded.
The diagram (b) is a pi-shaped equivalent circuit diagram of the transformer, and the node i and the node j are connected in series
Node i is connected in series toRear ground, j output end connected in series to oneAnd then grounded. j' represents an imaginary part.
Two embodiments of the invention are described below:
the first embodiment is as follows:
the invention adopts the standard example of IEEE-14 node shown in figure 3(a), and simulates the example with a single balancing machine and a multi-balancing machine respectively, the system parameters are shown in table 1, and the simulation results are shown in table 2:
TABLE 1 System parameter Table
| Type (B) | | Redundancy | |
| 1 | 1 | 2.15 | |
| 2 | 1，2 | 2.33 | |
| 3 | 1，2，3，8 | 2.80 |
TABLE 2 simulation results Table
| |
|
Type 3 | |
| J | 0.002062 | 0.002155 | 0.002232 |
| EMI | 0.010031 | 0.010031 | 0.010031 |
| EEI | 0.007070 | 0.006931 | 0.006748 |
| EMO | 0.008536 | 0.008536 | 0.008536 |
| EEO | 0.006031 | 0.005902 | 0.005736 |
Example two:
the invention adopts the standard example of IEEE-30 node shown in figure 3(b), and simulates the example with a single balancing machine and a multi-balancing machine respectively, the system parameters are shown in table 3, and the simulation results are shown in table 4:
TABLE 3 System parameters Table
| Type (B) | | Redundancy | |
| 1 | 1 | 2.07 | |
| 2 | 1，2，5 | 2.22 | |
| 3 | 1，2，5，8，11 | 2.40 |
Table 4 simulation results table
| |
|
Type 3 | |
| J | 0.003482 | 0.003665 | 0.003681 |
| EMI | 0.008891 | 0.008891 | 0.008891 |
| EEI | 0.006351 | 0.006212 | 0.006164 |
| EMO | 0.007513 | 0.007513 | 0.007513 |
| EEO | 0.005251 | 0.005130 | 0.005087 |
Wherein, <math><mrow><mi>J</mi><mo>=</mo><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><msup><mrow><mo>[</mo><mfrac><mrow><msub><mi>z</mi><mi>i</mi></msub><mo>-</mo><msub><mi>h</mi><mi>i</mi></msub><mrow><mo>(</mo><mover><mi>x</mi><mo>^</mo></mover><mo>)</mo></mrow></mrow><msub><mi>σ</mi><mi>i</mi></msub></mfrac><mo>]</mo></mrow><mn>2</mn></msup></mrow></math>
in the formula, EMi＝MEAi-MTRiIs a measurement error; EEi＝ESTi-MTRiTo estimate the error; MEA (membrane electrode assembly)iA measured value measured for the ith quantity; EST (expressed sequence tag)iAn estimate measured for the ith quantity; MTRiTrue value of the ith quantity measurement.
On one hand, compared with the conventional single-balance machine state estimation method, the multi-balance machine state estimation method has the advantages that the calculation accuracy is high, and the estimation result is more consistent with the actual state of the power system; on the other hand, the structure of the overall method has definite physical significance, protects the existing mature state estimation program, only corrects the measurement vector and the Jacobian matrix part thereof, has little modification to the existing state estimation software, and is easy to realize.
Claims (1)
1. A power system state estimation method considering multi-balancing machine influence is characterized by comprising the following steps:
(1) acquiring network parameters of an electric power system, comprising: the branch number, the head end node and the tail end node number of the power transmission line, the series resistance, the series reactance, the parallel conductance, the parallel susceptance, the transformer transformation ratio and the impedance;
(2) initializing, including: setting an initial value for the state quantity, optimizing the node sequence, forming a node admittance matrix, setting a threshold value and distributing a memory;
(3) inputting telemetering data z, including voltage amplitude, generator active power, generator reactive power, load active power, load reactive power, line head end active power, line head end reactive power, line tail end active power and line tail end reactive power;
(4) the power system is provided with n nodes, wherein generators where the nodes n, … and n-m are located form a balance unit and bear unbalanced power of the power system;
(5) recovering the iteration number k of the iteration counter to be 1;
(6) from the existing state quantity x(k)The calculated value h (x) of each measurement is calculated according to the following formula(k))；
The voltage amplitude of the node i is Vi＝vi：
Node i injected power:
starting power on lines i-j:
end power on lines i-j:
the power of the upper starting end of the transformer line i-j is as follows:
power at the upper end of the transformer line i-j:
in the formula vi、vjVoltage amplitudes of the node i and the node j are respectively; thetaijIs the voltage phase angle difference of node i and node j; gij、BijThe real part and the imaginary part of the admittance matrix; g. b, ycRespectively the conductance, susceptance and grounding susceptance of the line; k is the nonstandard transformation ratio of the transformer; bTThe standard susceptance of the transformer is measured; p, Q represent the active and reactive power of the generator, respectively; i. j is 1, 2, …, n-m-1, i, j, m and n are natural numbers which are larger than zero, and m is less than n;
(7) respectively carrying out derivation on the state quantities in the step (6) to obtain a Jacobian matrix H (x) for measuring the quantity(k))：
And (3) injecting power into the node:
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
starting power on lines i-j
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(i＝1，2，…，n-m-1)
(j＝1，2，…，n-m-1)
(8) Determining a state correction amount
Selecting
And correcting the state quantity to obtain
Wherein x is a 2n-1 dimensional state variable of the power system;
is an estimate of the state quantity; z is a vector of measurement values, namely telemetry data; h (x) is a non-linear function of x; h (x) a Jacobian matrix which is a measurement function; r-1Is measured byMeasuring a weighting array of the vectors; t is a rank conversion symbol; (k) representing an iteration number;
(9) when in useAnd (4) ending the state estimation if the convergence standard is smaller than the set convergence standard, otherwise returning to the step (6) to carry out the (k +1) th estimation.
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| CN102623993A (en) * | 2012-04-12 | 2012-08-01 | 河海大学 | Distributed power system state estimation method |
| CN102623993B (en) * | 2012-04-12 | 2013-12-25 | 河海大学 | Distributed power system state estimation method |
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