CN111884226A - Power grid probabilistic power flow analysis method based on generalized semi-invariant and maximum entropy method - Google Patents

Power grid probabilistic power flow analysis method based on generalized semi-invariant and maximum entropy method Download PDF

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CN111884226A
CN111884226A CN202010655327.8A CN202010655327A CN111884226A CN 111884226 A CN111884226 A CN 111884226A CN 202010655327 A CN202010655327 A CN 202010655327A CN 111884226 A CN111884226 A CN 111884226A
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power
invariant
formula
new energy
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卫志农
廖星星
孙国强
臧海祥
陈�胜
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Hohai University HHU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy

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Abstract

The invention discloses a power grid probability power flow analysis method based on a generalized semi-invariant and maximum entropy method, which comprises the following steps: s1: establishing a power flow model of the power system considering frequency; s2: establishing a load random output model based on a normal distribution function; s3: establishing a new energy random output model by adopting a Gaussian mixture model; s4: calculating the probability load flow of the power system based on a generalized semi-invariant method; s5: and fitting the probability density curve of the output variable by adopting a maximum entropy method. The method can effectively process the problem of frequency and voltage fluctuation of the power system under the influence of randomness of the input variables, has the advantages of accuracy, practicability and high efficiency, can comprehensively evaluate the out-of-limit risk of large-scale new energy accessed to the power system, finds weak links of the power system and promotes further consumption of the new energy.

Description

Power grid probabilistic power flow analysis method based on generalized semi-invariant and maximum entropy method
Technical Field
The invention belongs to the field of operation and safety analysis of a power system considering frequency, and particularly relates to a power grid probability load flow analysis method based on a generalized semi-invariant and maximum entropy method.
Background
In recent years, with the continuous development of new energy grid connection technology in China, the new energy grid connection capacity is continuously increased, and large-scale new energy grid connection becomes an important scene under a modern smart grid. However, the inertia of the system is reduced due to the access of new energy, and the uncertainty and the volatility of the power system are further aggravated due to the strong randomness of the new energy, so that a series of safety and stability problems of the power system, such as voltage and frequency out-of-limit, are caused. Based on this, the research on the uncertain influence caused by the fact that large-scale new energy is merged into the power grid has great significance for promoting the safety and the rapid development of the power grid.
Therefore, a new technical solution is needed to solve this problem.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a power grid probability load flow analysis method based on generalized semi-invariant and maximum entropy method aiming at the problem that the current power system load and new energy randomness are aggravated to cause the out-of-limit risk level of system voltage and frequency to be increased.
The technical scheme is as follows: the invention provides a power grid probability power flow analysis method based on a generalized semi-invariant and maximum entropy method, which comprises the following steps:
s1: establishing a power flow model of the power system considering frequency;
s2: acquiring load and new energy output data through the established power flow model of the power system, and establishing a load random output model by adopting a normal distribution function;
s3: based on the new energy output data, a new energy random output model is established by adopting a Gaussian mixture model;
s4: considering the uncertainty of the output variable, calculating the probability load flow of the power system based on a generalized semi-invariant method, and solving each-order semi-invariant of the output variable;
s5: and fitting the probability density curve of the output variable by adopting a maximum entropy method.
Further, the power system power flow model of the frequency counted in step S1 includes the following models:
the primary frequency regulation characteristic of the generator can be expressed as:
PGi＝-KGi(f-fN) i＝1,2,...,g
in the formula: pGiThe active power of the ith generator; kGiThe primary frequency modulation coefficient of the ith generating set; f. ofNThe rated frequency is the normal state of the system; f is the system frequency.
The primary frequency regulation characteristic of the grid load may be expressed as:
PDi＝PDNi+KDi(f-fN)
in the formula: pDiAnd PDNiAt frequency f and nominal frequency f for node i respectivelyNThe active power of the power; kDiIs the primary frequency modulation coefficient of the node i load.
Considering a new energy output model for droop control:
Figure BDA0002576558740000021
in the formula: pNEW_iAnd QNEW_iRespectively representing active power and reactive power of a new energy access system of a node i; p0NEW_iAnd Q0NEW_iRespectively representing the rated active power and the rated reactive power of the new energy of the node i; m ispi，nqiA droop gain representing new energy power control; u shape0iRepresents a no-load voltage; u shapeiAnd the voltage of the new energy during the operation of the power grid is accessed.
Considering a power system power flow model of primary frequency modulation:
Figure BDA0002576558740000023
ΔPi＝PGi+PNew_i-PDi-Pi＝0
ΔQi＝QGi+QNEW_i-QDi-Qi＝0
in the formula: viAnd thetaiRespectively, the voltage amplitude and the voltage phase angle of the node i, where thetaij＝θi-θj；GijAnd BijRespectively representing the real part value and the imaginary part value of the jth column element of the ith row in the node admittance matrix; delta PiAnd Δ QiRespectively the active unbalance amount and the reactive unbalance amount of the node i; qGiAnd QDiThe generator reactive power and the load reactive power of the node i are respectively.
Further, in step S1, the equation set of each model is solved by using a newton-raphson method, and the modified equation is:
Figure BDA0002576558740000022
in the formula: delta theta is a phase angle correction quantity; Δ f is a frequency correction amount; Δ V is a voltage correction amount; j is a Jacobian matrix; Δ X is an output variable correction amount; Δ F is the input variable correction amount.
Further, the specific process of establishing the load random output model by using the normal distribution function in the step S2 is as follows:
the uncertainty of the load can be generally described by a normal distribution with a probability density function of:
Figure BDA0002576558740000031
in the formula: mu.sPAnd σPRespectively the expected and standard deviation of the load.
Further, the step S3 includes the following steps:
the GMM is formed by linearly combining a plurality of Gaussian distributions, and the probability distribution function of the GMM is as follows:
Figure BDA0002576558740000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002576558740000033
is the probability distribution of the jth part; omegajA weight of the jth component which is a Gaussian mixture function; mu.sjAnd σjRespectively, the expectation and standard deviation of the jth component; n is a radical oftThe number of fitting components; wherein the weights satisfy the following constraints:
Figure BDA0002576558740000034
further, the step S4 is specifically:
s4-1: the power flow calculation model of the power system considering the frequency is a nonlinear function, and the mathematical expression of the power flow calculation model can be expressed as follows:
Figure BDA0002576558740000035
in the formula: a isi、aij、aijkIs a nonlinear function coefficient, i, j, k ═ 1,2,. D; Δ XiIs the ith independent variable; Δ Y is a dependent variable.
S4-2: solving semi-invariants of each order of output variables:
Figure BDA0002576558740000036
Figure BDA0002576558740000037
Figure BDA0002576558740000038
Figure BDA0002576558740000039
in the formula: kappaY,νNu (nu ═ 1,2,3) order of dependent variable Δ YA semi-invariant;
Figure BDA00025765587400000310
is DeltaXi,ΔXjA joint expectation of (c);
Figure BDA00025765587400000311
are each Xi' first, second, third order semi-invariant; k represents the degree of non-linearity.
S4-3: solving the coefficient a of a nonlinear functioni、aij、aijkThe following corresponding relation can be obtained by calculating the power series of the voltage amplitude:
Figure BDA0002576558740000041
in the formula: vf(s1,s2…,sj…,sD) In the form of a voltage power series; mf[·]Is the voltage amplitude component under the corresponding power series; sjThe coefficients j, which are multidimensional power series, are 1, 2.
The above formula is corresponded to step S4-1, wherein Δ XiThe item can be associated with SiThe terms correspond to each other, then the coefficient a can be obtainedi、aij、aijk。
Further, the step S5 is specifically:
s5-1: the mathematical model for establishing the maximum entropy method is as follows:
Figure BDA0002576558740000042
in the formula: h (x) is the information entropy of the variable; p (x) is a probability density function of the variable;
Figure BDA0002576558740000043
αnis the n-th order origin moment of the variable.
S5-2: the empirical solution for p (x) is expressed as:
Figure BDA0002576558740000044
in the formula: lambda [ alpha ]n(N-0, 1, … N) is a lagrange multiplier.
S5-3: substituting the formula of the step S5-2 into the formula of the step S5-1 can obtain N +1 equations:
Figure BDA0002576558740000045
solving the equation by adopting a Newton iteration method, and finally obtaining a result lambdanSubstituting (N-0, 1, … N) into step S5-1 results in the probability density function of the variable.
The method can effectively process the problem of frequency and voltage fluctuation of the power system under the influence of randomness of the input variables, has the advantages of accuracy, practicability and high efficiency, can comprehensively evaluate the out-of-limit risk of large-scale new energy accessed to the power system, finds weak links of the power system and promotes further consumption of the new energy.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) the method has the advantages of accuracy and effectiveness in calculating the probability load flow of the large-scale new energy access power system considering the frequency;
(2) compared with MPPT control, the droop control mode can reduce the standard difference of system frequency and voltage fluctuation, thereby reducing the out-of-limit probability and ensuring the safer operation of the system;
(3) the method can effectively calculate the probability density function of the output variable, and can further provide a basis for risk assessment and optimized scheduling of a large-scale new energy access system and grid-connected active support.
Drawings
FIG. 1 is a flow chart of the method calculation of the present invention;
FIG. 2 is a simplified wiring topology diagram of an actual power grid in a certain area;
FIG. 3 is a graph of the voltage distribution at system 43 nodes;
FIG. 4 is a graph of a system frequency probability distribution;
FIG. 5 is a comparison of different fitting methods;
FIG. 6 is a graph of node 43 voltage probability density under different control modes;
FIG. 7 is a voltage diagram of each node of the system under different control modes;
fig. 8 is a frequency probability density graph under different control modes.
Detailed Description
The invention is further elucidated with reference to the drawings and the embodiments.
In this embodiment, the method of the present invention is applied to a power system, as shown in fig. 1, and the specific calculation method includes the following steps:
s1: establishing a power system power flow model considering frequency, wherein the power system power flow model comprises the following models:
the primary frequency regulation characteristic of the generator can be expressed as:
PGi＝-KGi(f-fN) i＝1,2,...,g
in the formula: pGiThe active power of the ith generator; kGiThe primary frequency modulation coefficient of the ith generating set; f. ofNThe rated frequency is the normal state of the system; f is the system frequency.
The primary frequency regulation characteristic of the grid load may be expressed as:
PDi＝PDNi+KDi(f-fN)
in the formula: pDiAnd PDNiAt frequency f and nominal frequency f for node i respectivelyNThe active power of the power; kDiIs the primary frequency modulation coefficient of the node i load.
Considering a new energy output model for droop control:
Figure BDA0002576558740000051
in the formula: pNEW_iAnd QNEW_iRespectively representing active power and reactive power of a new energy access system of a node i; p0NEW_iAnd Q0NEW_iRespectively representing the rated active power and the rated reactive power of the new energy of the node i; m ispi，nqiA droop gain representing new energy power control; u shape0iRepresents a no-load voltage; u shapeiAnd the voltage of the new energy during the operation of the power grid is accessed.
Considering a power system power flow model of primary frequency modulation:
Figure BDA0002576558740000061
ΔPi＝PGi+PNew_i-PDi-Pi＝0
ΔQi＝QGi+QNEW_i-QDi-Qi＝0
in the formula: viAnd thetaiRespectively, the voltage amplitude and the voltage phase angle of the node i, where thetaij＝θi-θj；GijAnd BijRespectively representing the real part value and the imaginary part value of the jth column element of the ith row in the node admittance matrix; delta PiAnd Δ QiRespectively the active unbalance amount and the reactive unbalance amount of the node i; qGiAnd QDiThe generator reactive power and the load reactive power of the node i are respectively.
The Newton-Raphson method is adopted for solving, and the correction equation is as follows:
Figure BDA0002576558740000062
in the formula: delta theta is a phase angle correction quantity; Δ f is a frequency correction amount; Δ V is a voltage correction amount; j is a Jacobian matrix; Δ X is an output variable correction amount; Δ F is the input variable correction amount.
S2: the specific process of establishing the load random output model by adopting the normal distribution function is as follows:
the uncertainty of the load can be generally described by a normal distribution with a probability density function of:
Figure BDA0002576558740000063
in the formula: mu.sPAnd σPRespectively the expected and standard deviation of the load.
S3: the specific process of establishing the random probability density function of the new energy output by adopting the Gaussian mixture model comprises the following steps:
the GMM is formed by linearly combining a plurality of Gaussian distributions, and the probability distribution function of the GMM is as follows:
Figure BDA0002576558740000064
in the formula (I), the compound is shown in the specification,
Figure BDA0002576558740000065
is the probability distribution of the jth part; omegajA weight of the jth component which is a Gaussian mixture function; mu.sjAnd σjRespectively, the expectation and standard deviation of the jth component; n is a radical oftThe number of fitting components; wherein the weights satisfy the following constraints:
0＜ωj≤1,
Figure BDA0002576558740000066
s4: solving the probability density function of the output variable by adopting the generalized semi-invariant specifically comprises the following steps:
s4-1: the power flow calculation model of the power system considering the frequency is a nonlinear function, and the mathematical expression of the power flow calculation model can be expressed as follows:
Figure BDA0002576558740000071
in the formula: a isi、aij、aijkIs the nonlinear function coefficient, i, j, k is 1,2, …, D; Δ XiIs the ith independent variable; Δ Y is a dependent variable.
S4-2: solving semi-invariants of each order of output variables:
Figure BDA0002576558740000072
Figure BDA0002576558740000073
Figure BDA0002576558740000074
Figure BDA0002576558740000075
in the formula: kappaY,νν (ν ═ 1,2,3) order semi-invariant for the dependent variable Δ Y;
Figure BDA0002576558740000076
is DeltaXi,ΔXjA joint expectation of (c);
Figure BDA0002576558740000077
are each Xi' first, second, third order semi-invariant; k represents the degree of non-linearity.
S4-3: solving the coefficient a of a nonlinear functioni、aij、aijkThe following corresponding relation can be obtained by calculating the power series of the voltage amplitude:
Figure BDA0002576558740000078
in the formula: vf(s1,s2…,sj…,sD) In the form of a voltage power series; mf[·]Is the voltage amplitude component under the corresponding power series; sjThe coefficients j, which are multidimensional power series, are 1, 2.
The above formula is corresponded to step S4-1, wherein Δ XiThe item can be associated with SiThe terms correspond to each other, then the coefficient a can be obtainedi、aij、aijk。
S5: after obtaining each order of semi-invariants of the output variables, fitting a probability density curve of the output variables by adopting a maximum entropy method, specifically:
s5-1: establishing a mathematical model of a maximum entropy method:
Figure BDA0002576558740000081
in the formula: h (x) is the information entropy of the variable; p (x) is a probability density function of the variable;
Figure BDA0002576558740000082
αnis the n-th order origin moment of the variable.
S5-2: the empirical solution for p (x) is expressed as:
Figure BDA0002576558740000083
in the formula: lambda [ alpha ]n(N-0, 1, … N) is a lagrange multiplier.
S5-3: substituting the formula S5-2 into S5-1 to obtain N +1 equations:
Figure BDA0002576558740000084
solving the equation by adopting a Newton iteration method, and finally obtaining a result lambdanAnd (N is 0,1, … N) is substituted into the equation S5-1 to obtain the probability density function of the variable.
As shown in fig. 2, based on the above method and process, the present embodiment adopts an actual power grid simplification system in a certain area to perform example analysis, and considers the wind power and photovoltaic new energy access, wherein the wind power generation system is accessed at nodes 4, 17, 35, and 42, the photovoltaic power generation system is accessed at nodes 24, 30, 40, and 43, the new energy access permeability reaches 52.42%, and the requirement of a large-scale new energy scene is met. In order to consider randomness of new energy and load power, the load power prediction error is assumed to follow a normal distribution, the expected value is the actual power, and the standard deviation is 5% of the expected value. The value range of the active power droop gain is 0.0032-0.0053 (per unit value), the value range of the reactive power droop gain is 0.08-0.12 (per unit value), the normal range of the voltage is 1 +/-5% p.u., and the normal range of the frequency is [0.996,1.004] p.u.
In this embodiment, in order to verify the actual effect of the method of the present invention, the following simulation experiment is performed:
1. method validity verification
Comparing the calculated value of GCM with different K values with the reference value, wherein the relative error indexes of the mean value and the standard deviation of the voltage V and the frequency f
Figure BDA0002576558740000085
And maximum error index
Figure BDA0002576558740000086
As shown in table 1 below, the accuracy comparison of the remaining power flow calculation results can be seen in the appendix part of this document. In the table, CM represents GCM when K is 1, i.e. conventional semi-invariant method, GCM2And GCM3Respectively, the generalized semi-invariant method when K is 2 and 3. Wherein CM and GCM are calculated in mean2Maximum error is 1.708% and 0.635%, respectively, and GCM is used3The maximum error is 0.039%; CM and GCM in standard deviation calculations2Maximum error is 45.42% and 5.686%, respectively, while GCM3The maximum error is 0.129%, so that the digital statistical characteristic precision can be greatly improved in the PPF calculation of the large-scale new energy access power grid along with the increase of the value of K.
TABLE 1 output variable relative error index
Figure BDA0002576558740000091
Table 2 shows the average value of ARMS indexes
Figure BDA0002576558740000092
And maximum value
Figure BDA0002576558740000093
In the use of GCM3The method has ARMS value of 0.243% at most, and CM and GCM are adopted2The ARMS values in the method reach 2.899% and 1.583% at most, which shows that the increase of the value of K can improve the probability distribution accuracy of the PPF calculation result.
Table 3 shows comparison of calculation time of different methods, and the calculation complexity of the analysis may be further increased with the increase of K, resulting in an increase of calculation time, but the calculation efficiency of the proposed method still has a great advantage compared to the MCS method, so that K is taken as 3 in the subsequent research in consideration of the comprehensive calculation accuracy and time.
TABLE 2 ARMS indices
Figure BDA0002576558740000094
TABLE 3 comparison of calculation times by different methods
Figure BDA0002576558740000095
Taking the node (node 43) with the maximum system frequency and voltage test error as an example, drawing a corresponding distribution function curve, specifically as shown in fig. 3 and 4, calculating accuracy degrees of different K values can be intuitively obtained from the probability distribution curve in the graph.
FIG. 5 is a comparison graph of fitting by different methods, when a Gram-charlier (GC) series is adopted, the probability of being less than 0 and greater than 1 occurs at the head end and the tail end of the probability distribution function, and the defect is effectively avoided and the fitting accuracy is improved when the maximum entropy method fitting is adopted.
2. Effect of droop control on node voltage
Compared with different new energy access control modes, when the MPPT control method is adopted, the access of new energy is processed by PQ nodes, and the voltage fluctuation of partial nodes of the power system is increased, so that the out-of-limit part of the power system appears. The invention introduces a droop control method, and the new energy is accessed in a droop control mode. Fig. 6 is a probability density curve of the node 43 voltage under different control modes, from which it can be obtained that when MPPT control is adopted, a larger out-of-limit probability, specifically 30.80%, occurs, and the voltage is within a normal range by adopting the droop control method.
A single section is selected for comparative analysis of system voltage, and as shown in FIG. 7, different node voltages of the system under a single section are shown. When MPPT control is adopted, the voltages of the nodes 23, 24, 40 and 43 exceed the allowable value, and the comparison of a network wiring diagram shows that the four nodes are all new energy access nodes or access points close to the new energy access nodes, while droop control adopted by the invention enables the voltages of the system nodes to be in a normal range, and the important effect of the droop control on voltage regulation during new energy access is reflected on the basis of the analysis.
3. Effect of droop control on grid frequency
In the aspect of frequency response, when the MPPT control method is adopted, the new energy does not participate in the frequency response of the system, so that the system frequency fluctuation is increased along with the large-scale access of the new energy to the system. As shown in fig. 8, which is a probability density curve of the system frequency under different control modes, the system frequency out-of-limit probability is 22.31% when the MPPT control mode is adopted, and the system frequency is within a normal range when the droop control mode is adopted, and the above analysis shows that the droop control plays an important role in the frequency response when new energy is accessed. The new energy has active supporting capacity through the droop control technology, so that the consumption of the new energy can be further increased, and important technical support is provided for comprehensive utilization of multiple energy sources.
The simulation results verify the effectiveness and the practicability of the method provided by the invention, the probability density function of the output variable can be effectively calculated, and a basis can be further provided for risk assessment, optimized scheduling and grid-connected active support of a large-scale new energy access system.

Claims (7)

1. A power grid probability power flow analysis method based on a generalized semi-invariant and maximum entropy method comprises the following steps: the method comprises the following steps:
s1: establishing a power flow model of the power system considering frequency;
s2: acquiring load and new energy output data through the established power flow model of the power system, and establishing a load random output model by adopting a normal distribution function;
s3: based on the new energy output data, a new energy random output model is established by adopting a Gaussian mixture model;
s4: considering the uncertainty of the output variable, calculating the probability load flow of the power system based on a generalized semi-invariant method, and solving each-order semi-invariant of the output variable;
s5: and fitting the probability density curve of the output variable by adopting a maximum entropy method.
2. The power grid probabilistic power flow analysis method based on the generalized semi-invariant and maximum entropy method according to claim 1, wherein: the power system power flow model of the frequency counted in the step S1 includes the following models:
the primary frequency regulation characteristic of the generator is expressed as:
PGi＝-KGi(f-fN) i＝1,2,...,g
in the formula: pGiThe active power of the ith generator; kGiThe primary frequency modulation coefficient of the ith generating set; f. ofNThe rated frequency is the normal state of the system; f is the system frequency;
the primary frequency regulation characteristic of the grid load is expressed as:
PDi＝PDNi+KDi(f-fN)
in the formula: pDiAnd PDNiAt frequency f and nominal frequency f for node i respectivelyNThe active power of the power; kDiThe primary frequency modulation coefficient of the node i load;
designing a new energy output model for droop control:
Figure FDA0002576558730000011
in the formula: pNEW_iAnd QNEW_iRespectively representing active power and reactive power of a new energy access system of a node i; p0NEW_iAnd Q0NEW_iRespectively representing the rated active power and the rated reactive power of the new energy of the node i; m ispi，nqiA droop gain representing new energy power control; u shape0iRepresents a no-load voltage; u shapeiAnd the voltage of the new energy during the operation of the power grid is accessed.
Designing a power flow model of a primary frequency modulation electric power system:
Figure FDA0002576558730000012
ΔPi＝PGi+PNew_i-PDi-Pi＝0
ΔQi＝QGi+QNEW_i-QDi-Qi＝0
in the formula: viAnd thetaiRespectively, the voltage amplitude and the voltage phase angle of the node i, where thetaij＝θi-θj；GijAnd BijRespectively representing the real part value and the imaginary part value of the jth column element of the ith row in the node admittance matrix; delta PiAnd Δ QiRespectively the active unbalance amount and the reactive unbalance amount of the node i; qGiAnd QDiThe generator reactive power and the load reactive power of the node i are respectively.
3. The power grid probabilistic power flow analysis method based on the generalized semi-invariant and maximum entropy method according to claim 2, wherein: in step S1, the newton-raphson method is used to solve the equation set of each model, and the modified equation is:
Figure FDA0002576558730000021
in the formula: delta theta is a phase angle correction quantity; Δ f is a frequency correction amount; Δ V is a voltage correction amount; j is a Jacobian matrix; Δ X is an output variable correction amount; Δ F is the input variable correction amount.
4. The power grid probabilistic power flow analysis method based on the generalized semi-invariant and maximum entropy method according to claim 1, wherein: the specific process of establishing the load random output model by using the normal distribution function in the step S2 is as follows:
the load uncertainty is described by normal distribution, and the probability density function is as follows:
Figure FDA0002576558730000022
in the formula: mu.sPAnd σPRespectively the expected and standard deviation of the load.
5. The power grid probabilistic power flow analysis method based on the generalized semi-invariant and maximum entropy method according to claim 1, wherein: the new energy random output model in the step S3 is established in the following process:
the Gaussian mixture model is formed by linearly combining a plurality of Gaussian distributions, and the probability distribution function of the Gaussian mixture model is as follows:
Figure FDA0002576558730000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002576558730000024
is the probability distribution of the jth part; omegajA weight of the jth component which is a Gaussian mixture function; mu.sjAnd σjRespectively, the expectation and standard deviation of the jth component; n is a radical oftThe number of fitting components; wherein the weight ω isjThe following constraints are satisfied:
0＜ωj≤1,
Figure FDA0002576558730000025
6. the power grid probabilistic power flow analysis method based on the generalized semi-invariant and maximum entropy method according to claim 1, wherein: the step S4 specifically includes:
s4-1: the power flow calculation model of the power system considering the frequency is a nonlinear function, and the mathematical expression is represented as follows:
Figure FDA0002576558730000031
in the formula: a isi、aij、aijkIs a nonlinear function coefficient, i, j, k ═ 1,2,. D; deltaXiIs the ith independent variable; Δ Y is a dependent variable;
s4-2: solving semi-invariants of each order of output variables:
Figure FDA0002576558730000032
Figure FDA0002576558730000033
Figure FDA0002576558730000034
Figure FDA0002576558730000035
in the formula: kappaY,νν (ν ═ 1,2,3) order semi-invariant for the dependent variable Δ Y;
Figure FDA0002576558730000036
is DeltaXi,ΔXjA joint expectation of (c);
Figure FDA0002576558730000037
is DeltaXi,ΔXjA joint semi-invariant of (a);
Figure FDA0002576558730000038
are each Xi' first, second, third order semi-invariant; k represents the degree of non-linearity;
s4-3: solving the coefficient a of a nonlinear functioni、aij、aijkAnd calculating the power series of the voltage amplitude to obtain the corresponding relation as follows:
Figure FDA0002576558730000039
in the formula: vf(s1,s2…,sj…,sD) In the form of a voltage power series; mf[·]Is the voltage amplitude component under the corresponding power series; sjA coefficient j, which is a multidimensional power series, is 1, 2.
The above formula is corresponded to step S4-1, wherein Δ XiThe item can be associated with SiThe terms correspond to each other, then the coefficient a can be obtainedi、aij、aijk。
7. The power grid probabilistic power flow analysis method based on the generalized semi-invariant and maximum entropy method according to claim 1, wherein: the step S5 specifically includes:
s5-1: establishing a mathematical model of a maximum entropy method:
Figure FDA0002576558730000041
in the formula: h (x) is the information entropy of the variable; p (x) is a probability density function of the variable;
Figure FDA0002576558730000042
αnis the n-order origin moment of the variable;
s5-2: the empirical solution for p (x) is expressed as:
Figure FDA0002576558730000043
in the formula: lambda [ alpha ]n(N ═ 0,1, … N) is the lagrange multiplier;
s5-3: substituting the formula of step S5-2 into step S5-1 results in N +1 equations:
Figure FDA0002576558730000044
solving the equation by adopting a Newton iteration method, and finally obtaining a result lambdanSubstituting (N-0, 1, … N) into step S5-1 results in the probability density function of the variable.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113315132A (en) * 2021-06-02 2021-08-27 贵州电网有限责任公司 Three-phase load flow calculation method for island micro-grid with droop nodes
TWI790743B (en) * 2021-09-14 2023-01-21 台灣電力股份有限公司 Calculation method of grid-connectable capacity of feeder

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113315132A (en) * 2021-06-02 2021-08-27 贵州电网有限责任公司 Three-phase load flow calculation method for island micro-grid with droop nodes
CN113315132B (en) * 2021-06-02 2023-07-28 贵州电网有限责任公司 Island micro-grid three-phase power flow calculation method with sagging nodes
TWI790743B (en) * 2021-09-14 2023-01-21 台灣電力股份有限公司 Calculation method of grid-connectable capacity of feeder

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