CN107124000B - Power function model-based power distribution network distributed power supply accepting capacity analysis method - Google Patents

Power function model-based power distribution network distributed power supply accepting capacity analysis method Download PDF

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CN107124000B
CN107124000B CN201710233349.3A CN201710233349A CN107124000B CN 107124000 B CN107124000 B CN 107124000B CN 201710233349 A CN201710233349 A CN 201710233349A CN 107124000 B CN107124000 B CN 107124000B
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李妍
黄彦璐
盛梦雨
杨晨光
杨秉臻
王少荣
叶玮佳
余珏
刘婉兵
熊嘉丽
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Abstract

The invention relates to the technical field of power distribution networks of power systems, and provides a method for analyzing the capability of a power distribution network for accepting a distributed power supply based on a power function model, wherein the method is characterized in that the power function model of the distributed power supply is obtained based on an open running power distribution network model for accessing the distributed power supply from a user side, sensitivity indexes of distributed power supply access power to various factors under different power distribution network states are obtained based on the power function model, and the influence of single-factor change on the accepting capability of the distributed power supply of the power distribution network is analyzed based on the sensitivity indexes; the method comprises the steps of calculating three indexes of single-factor partial increment, basic partial increment and cooperative increment by using a partial increment analysis model of a power function, analyzing the comprehensive influence of multi-factor change on the receiving capacity of the distributed power supply of the power distribution network based on index results, and realizing quantitative analysis of influence factors of the power distribution network on the receiving capacity of the distributed power supply.

Description

Power function model-based power distribution network distributed power supply accepting capacity analysis method
Technical Field
The invention relates to the technical field of power distribution networks of power systems, in particular to a power function model-based method for analyzing distributed power supply accepting capacity of a power distribution network.
Background
In recent years, with the wide application and development of distributed power generation technology, the structure of a power system is changed by accessing a large-scale distributed power source to a power distribution network, and the power distribution network system is changed from a simple powered network to a complex active network, so that some adverse effects are brought, such as overvoltage at an access point, branch transmission capacity exceeding an allowable limit and the like. In order to ensure reliable and continuous operation of the power distribution network, research and analysis on the acceptance capacity of the power distribution network are urgently needed.
The admission capacity of the distributed power supply of the power distribution network is limited by a plurality of factors such as operating conditions, distributed power supply and load characteristics, grid structure, management means and the like, the existing research mainly focuses on calculation and optimization of the upper limit value of the admission capacity, for example, the upper limit value of the admission capacity is evaluated by considering the operation constraint conditions of the power distribution network such as power quality, protection configuration and the like, or a calculation method for researching the maximum admission capacity and an optimal planning scheme for site selection and volume fixing of the distributed power supply.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a power function model-based power distribution network distributed power supply accepting capability analysis method, wherein a sensitivity index can be used for quantitatively evaluating the influence of single-factor change on the power distribution network distributed power supply accepting capability, and a bias increment model, a single-factor bias increment, a basic bias increment and a cooperative increment can quantify the independent influence quantity of a single factor and the cooperative influence quantity of all factors and quantitatively evaluate the comprehensive influence of multi-factor change on the accepting capability.
The object of the invention is achieved by the following technical measures.
A power function model-based power distribution network admission distributed power supply capacity analysis method comprises the following steps:
(1) based on an open-type operation distribution network model of a user side access distributed power supply, calculating equivalent impedance of the transformer according to model parameters of the transformer to obtain an expression of access power of the distributed power supply; and giving the variation range of each variable and the voltage upper limit value of the distributed power supply access point, and converting the access power complex function into a real function to obtain a power function model of the user side access distributed power supply. The specific mode is as follows:
step 1-1, calculating equivalent impedance of a transformer according to model parameters of the transformer based on a power distribution network model of a user side access distributed power supply, and substituting the equivalent impedance into formula (1) to obtain an expression of a distributed power supply access power complex function. The model of a power distribution network with a user side connected to a distributed power supply is shown in fig. 1, and the model of the power distribution network with an equivalent branch of a transformer is shown in fig. 2.
Figure BDA0001267267800000021
Figure BDA0001267267800000022
The symbols in fig. 1 and formula (1) are defined as follows: pDG、QDGGenerating active power and reactive power for the distributed power supply;
Figure BDA0001267267800000023
accessing a power complex function for the distributed power supply;
Figure BDA0001267267800000024
is the conjugate of the voltage of the distributed power access point;
Figure BDA0001267267800000025
is the conjugate of the operating voltage of the power supply point; rT、XTIs the equivalent impedance of the transformer; rL、XLIs the equivalent impedance of the power supply line; pL、QLThe power distribution network is loaded with active power and reactive power.
The derivation process of equation (1) is as follows:
because the impedance ratio of the power distribution network is generally greater than 1, the resistance of the power supply line cannot be ignored when calculating the voltage drop like a power transmission network, but the resistance and the reactance of the power supply line need to be considered at the same time, and meanwhile, it is assumed that the distributed power supply is connected to the power distribution network to cause the power supply line to be connectedReverse power flow occurs, and then the current of the power supply line can be obtained according to the circuit diagram shown in figure 1
Figure BDA0001267267800000026
The expression of (2) is shown in formula (2).
Figure BDA0001267267800000027
Step 1-2, setting the operating voltage of a power supply point, the impedance of a power supply line and the variation range x of load power accessed by a power supply areaimin≤xi≤ximax(i ═ 1,2,3), verifying whether constraint condition formula (4) -formula (6) is satisfied, and selecting a power distribution network state set satisfying the condition as a domain of the power function; giving a voltage upper limit value of a distributed power supply access point, a ratio of a line equivalent reactance to a line equivalent resistance, and a power factor of an access load; and (3) converting the complex function shown in the distributed power access power complex function expression formula (1) obtained in the step into a real function, and obtaining a multivariate function expression shown in a formula (3) of the distributed power access power with respect to the power point operating voltage, the power supply line impedance and the load accessed to the power supply area, namely a distributed power access power function model.
y＝f(x1,x2,x3)＝abs[g(x1,x2,x3)]＝abs[A(A-x1)/(B+x2-jCx2)+x3+jDx3],(x1,x2,x3∈M) (3)
The constraint conditions are as follows:
real[g(x1,x2,x3)]≥0 (4)
cosθ≥0.9 (5)
|(A*-x1 *)/(B*+x2+jCx2)|≤Imax(6)
in the formula (3), xi(i ═ 1,2,3) is defined as x1＝US*,x2＝RL,x3＝PL，
Figure BDA0001267267800000031
Representing an upper voltage limit for a given distributed power access point,
Figure BDA0001267267800000032
representing the equivalent impedance of the transformer, C ═ XL/RLThe ratio of the equivalent reactance of the line to the equivalent resistance of the line is expressed, D ═ QL/PLA, B, C, D are constants representing the ratio of reactive power to active power of the load accessing the distribution grid. The formula (4) represents that the output active power of the distributed power supply is constantly a non-negative value; the formula (5) represents that the power factor of the distributed power supply is not lower than 0.9; equation (6) represents the constraint of branch ampacity.
The distributed power supply access power multivariate function is defined in detail as follows:
the independent variable is xi(i＝1,2,3)|x1＝US *,x2＝RL,x3＝PLM is a non-empty multi-element ordered array and represents the operating voltage of a power supply point of the power distribution network, the impedance of a power supply line and the load connected to a power supply area in ximin≤xi≤ximax(i is 1,2,3) and satisfies the constraint conditions (4) to (6), and f is a correspondence rule such that for each ordered array (x)1,x2,x3E.m) has a uniquely determined value y corresponding to it, so the distributed power accessed by the user side can be expressed as a multivariate function defined on M and related to the operating voltage of the power point, the impedance of the power supply line and the load accessed by the power supply area, which is abbreviated as y (f) (M), as shown in formula (3). The dependent variable y represents the distributed power supply power accessed by the user side under the limit condition
Figure BDA0001267267800000033
y＝{y|y＝f(x1,x2,x3),(x1,x2,x3E.g. M) is the value range of the function.
(2) Based on the power function model obtained in the step (1), obtaining sensitivity indexes of distributed power supply access power to all factors according to different power distribution network states; analyzing the influence of single factors, namely the operating voltage of a power supply point, the impedance of a power supply line or the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network based on the sensitivity index; the specific mode is as follows:
based on the power function model obtained in the step (1), according to different power distribution network states, obtaining the sensitivity index S of the distributed power supply access power to each factor according to the formula (7)iThe method is used for quantitatively measuring the influence of a single factor on the access power in the initial state of a certain power distribution network. And analyzing the influence of single factors (power supply point operating voltage, power supply line impedance or load accessed in a power supply area) on the receiving capacity of the distributed power supply of the power distribution network based on the calculated sensitivity index.
Figure BDA0001267267800000041
Wherein the sensitivity index is defined as follows:
pair function to argument xiThe first partial derivative of (A) is defined as a distributed power supply access power pair variable xiSensitivity S ofiThe physical meaning is the variation trend of the distributed power supply access power in the direction of the coordinate axis of the variable. Thus, given a certain operating state (x) of the distribution network10,x20,x30) E.g. M, the sensitivity index of the distributed power supply access power to each variable can be obtained according to the formula (7).
(3) Based on the power function model obtained in the step (1), calculating three indexes of single-factor partial increment, basic partial increment and cooperative increment by using a partial increment analysis model of the power function; analyzing the comprehensive influence of a plurality of factors, namely the power supply point operating voltage, the power supply line impedance and the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network based on the index calculation result; the specific mode is as follows:
step 3-1 giving initial state X of power distribution network0＝(x10,x20,x30) And the increase DeltaX of each dependent variable10＝(Δx1,Δx2,Δx3) Can beObtaining the final value state X of the power distribution network1＝(x11,x21,x31) And (3) calculating to obtain the full increment of the power function according to the formula (8) based on the power function model obtained in the step (1).
Δy10＝f(x11,x21,x31)-f(x10,x20,x30) (8)
And 3-2, decomposing the obtained access power full increment by using a partial increment analysis model of the power function based on the power function model obtained in the step (1): determination of the Power function for the variables at the Point X0The n-order partial derivative (taking n as 7, which is accurate enough in practical engineering application) is calculated according to the formula (15) - (17) to obtain three indexes of single-factor partial increment, basic partial increment and cooperative increment, so that the full increment is decomposed into independent influence quantity of a single factor and cooperative influence quantity of all factors, and further the comprehensive influence of a plurality of factors of the operating voltage of a power supply point, the impedance of a power supply line and the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network is analyzed based on the index calculation result.
The definition formula and the analysis method of each index are as follows:
(a) single factor partial increment PIi
Single factor partial increment PIiThe formula for defining (A) is as follows,
Figure BDA0001267267800000051
in the formula (I), the compound is shown in the specification,
Figure BDA0001267267800000052
denotes the power function y ═ f (M) versus the argument xiPartial differential of order m, Δ xiDenotes the independent variable xiThe amount of change in (c).
The analysis method using this index is as follows,
can quantitatively calculate independent variable xiThe influence degree in the total variation of the admission capacity is used for measuring the access power variation of the distributed power supply caused by the independent of single variable, whereinPositive values indicate that the argument favors an increase in the acceptance, negative values indicate a decrease in the acceptance, and absolute values of the index indicate the magnitude of the influence. (b) Basic partial increment PA
The basic bias delta PA is defined as follows,
Figure BDA0001267267800000053
defining basic partial increment PA as single-factor partial increment PI of all independent variables of power functioniAnd the sum is used for measuring the influence on the distributed power supply access power caused by the independence of all independent variables.
(c) Cooperative incremental CA
The formula for defining the cooperative increment CA is as follows,
CA＝Δy10-PA (17)
and defining the cooperative increment CA as the difference between the full increment and the basic deviation increment for measuring the influence of the cooperative action of all variables on the access power.
The mathematical demonstration process of the partial increment analysis model of the power function in the step (3) is as follows:
arranged in a defined field M of the power function, the distribution network is operated from a certain operating state X0＝(x10,x20,x30) Change to another operating state X1＝(x11,x21,x31) And the increase of each dependent variable is DeltaX10＝(Δx1,Δx2,Δx3) If the power function y ═ f (m) at point X0＝(x10,x20,x30) With a continuous partial derivative of order n +1, the power function is taken from state X0Change to state X1Full increment of Δ y10The delta deltax of each argument can be used according to the taylor formulaiPower function for each variable at point X0All possible partial derivatives of the respective order of (A) and (B) the Lagrangian remainder RnThe expression is shown in formula (9).
Figure BDA0001267267800000061
In the formula, Lagrangian remainder RnRepresents the remainder after the omitted n term, as shown in equation (10), where δ is between X0And X1A state point in between.
Figure BDA0001267267800000062
From equation 9, full increment Δ y10Except for the lagrange remainder RnIn addition, the argument x is then pair by functioniAnd the mixed partial differential of each order for all independent variables. By Delta CiIndicates when only the argument x is presentiVariation Δ xiThe expression of the sum of the first n-order bias increments of the power function caused by the individual change amounts is shown in formula (11), and it can be seen that the sum is related to the independent variable increment Δ xiIs subjected to the initial state of the distribution network, the power function and the independent variable xiPartial derivatives of each order and independent variable increments Δ xiIndependent of the increments of other independent variables;
Figure BDA0001267267800000063
let Δ CA represent the sum of the first n-order increments to the power function under the common variation of all factors, and its expression is shown in formula (12), which represents the synergy of all factors to the power function, and is affected by the initial state of the distribution network, the power function to the independent variable xiThe mixed partial derivatives of each order and the effect of all independent variable increments.
Figure BDA0001267267800000064
Thus, a full increment can be written as shown in equation (13).
Figure BDA0001267267800000071
Can prove the peace in mathematicsWhen the number n of terms of the expansion approaches infinity, the Lagrangian remainder RnApproaches zero, so as long as n is large enough, the full increment of the power function can be approximated by the function to the variable xiThe sum of the first nth order increments of the function over all variables is approximately represented with an error of the remainder RnTherefore, a partial increment analysis model of the distributed power supply access power can be obtained, as shown in a formula (14).
Δy10≈ΔC1+ΔC2+ΔC3+ΔCA (14)
TABLE 1 relationship of partial incremental model analysis results to the number of terms n
Number of terms n 1 2 3 4 5 6 7 8
ΔC1 -0.1188 -0.1030 -0.0882 -0.0754 -0.0654 -0.0584 -0.0546 -0.0538
ΔC2 -0.0045 -0.0041 -0.0041 -0.0041 -0.0042 -0.0042 -0.0042 -0.0042
ΔC3 0.0080 0.0081 0.0081 0.0081 0.0081 0.0081 0.0081 0.0081
ΔCA 0.0409 0.0246 0.0098 -0.0030 -0.0129 -0.0199 -0.0237 -0.0245
As the value of n increases, the smaller the lagrangian error remainder, the more accurate the decomposition result of the full increment of the function obtained by using the partial increment analysis model of equation (14) will tend to be, as can be seen from table 1, when n is greater>At 6, Δ CiAnd the delta CA tends to be stable, and the partial increment analysis model of the distributed power supply access power is considered to be accurate enough in practical engineering application. Therefore, n can be taken to be 7 in the analysis of the distributed power source acceptance capability.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides an analysis method of distributed power supply accepting capability of a power distribution network based on a power function sensitivity index and a partial increment model, wherein the power function model of a distributed power supply is obtained based on an open running power distribution network model of a user side accessed distributed power supply, the sensitivity index of distributed power supply access power to each factor under different power distribution network states is obtained based on the power function model, and the influence of single factor change on the accepting capability of the distributed power supply of the power distribution network is analyzed based on the sensitivity index; the method comprises the steps of calculating three indexes of single-factor partial increment, basic partial increment and cooperative increment by using a partial increment analysis model of a power function, analyzing the comprehensive influence of multi-factor change on the receiving capacity of the distributed power supply of the power distribution network based on index results, and realizing quantitative analysis of influence factors of the power distribution network on the receiving capacity of the distributed power supply.
Drawings
Fig. 1 is a power distribution network model with a user side accessing a distributed power supply.
Fig. 2 is a power distribution network model with transformer equivalent branches obtained by transformation of the model in fig. 1.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, but the embodiments of the present invention are not limited thereto.
The embodiment of the invention provides a power function model-based method for analyzing distributed power supply accepting capacity of a power distribution network, which comprises the following steps of:
(1) based on an open-type operation distribution network model of a user side access distributed power supply, calculating equivalent impedance of the transformer according to model parameters of the transformer to obtain an expression of access power of the distributed power supply; and giving the variation range of each variable and the voltage upper limit value of the distributed power supply access point, and converting the access power complex function into a real function to obtain a power function model of the user side access distributed power supply. The specific mode is as follows:
step 1-1, calculating equivalent impedance of a transformer according to model parameters of the transformer based on a power distribution network model of a user side access distributed power supply, and substituting the equivalent impedance into formula (1) to obtain an expression of a distributed power supply access power complex function. The model of a power distribution network with a user side connected to a distributed power supply is shown in fig. 1, and the model of the power distribution network with an equivalent branch of a transformer is shown in fig. 2.
Figure BDA0001267267800000081
Figure BDA0001267267800000082
The symbols in fig. 1 and formula (1) are defined as follows: pDG、QDGGenerating active power and reactive power for the distributed power supply;
Figure BDA0001267267800000083
accessing a power complex function for the distributed power supply;
Figure BDA0001267267800000084
is the conjugate of the voltage of the distributed power access point;
Figure BDA0001267267800000085
is the conjugate of the operating voltage of the power supply point; rT、XTIs the equivalent impedance of the transformer; rL、XLIs the equivalent impedance of the power supply line; pL、QLThe power distribution network is loaded with active power and reactive power.
The derivation process of equation (1) is as follows:
due to the distribution networkThe impedance ratio is generally greater than 1, so that the resistance of a power supply line cannot be ignored when calculating the voltage drop like a power transmission network, but the resistance and the reactance of the power supply line need to be considered at the same time, and meanwhile, the condition that a distributed power supply is connected to a power distribution network to cause the reverse power flow of the power supply line is assumed, so that the current of the power supply line can be obtained according to the circuit diagram shown in fig. 1
Figure BDA0001267267800000091
The expression of (2) is shown in formula (2).
Figure BDA0001267267800000092
Step 1-2, setting the operating voltage of a power supply point, the impedance of a power supply line and the variation range x of load power accessed by a power supply areaimin≤xi≤ximax(i ═ 1,2,3), verifying whether constraint condition formula (4) -formula (6) is satisfied, and selecting a power distribution network state set satisfying the condition as a domain of the power function; giving a voltage upper limit value of a distributed power supply access point, a ratio of a line equivalent reactance to a line equivalent resistance, and a power factor of an access load; and (3) converting the complex function shown in the distributed power access power complex function expression formula (1) obtained in the step into a real function, and obtaining a multivariate function expression shown in a formula (3) of the distributed power access power with respect to the power point operating voltage, the power supply line impedance and the load accessed to the power supply area, namely a distributed power access power function model.
y＝f(x1,x2,x3)＝abs[g(x1,x2,x3)]＝abs[A(A-x1)/(B+x2-jCx2)+x3+jDx3],(x1,x2,x3∈M) (3)
The constraint conditions are as follows:
real[g(x1,x2,x3)]≥0 (4)
cosθ≥0.9 (5)
|(A*-x1 *)/(B*+x2+jCx2)|≤Imax(6)
in the formula (3), xi(i ═ 1,2,3) is defined as x1＝US *,x2＝RL,x3＝PL，
Figure BDA0001267267800000093
Representing an upper voltage limit for a given distributed power access point,
Figure BDA0001267267800000094
representing the equivalent impedance of the transformer, C ═ XL/RLThe ratio of the equivalent reactance of the line to the equivalent resistance of the line is expressed, D ═ QL/PLA, B, C, D are constants representing the ratio of reactive power to active power of the load accessing the distribution grid. The formula (4) represents that the output active power of the distributed power supply is constantly a non-negative value; the formula (5) represents that the power factor of the distributed power supply is not lower than 0.9; equation (6) represents the constraint of branch ampacity.
The distributed power supply access power multivariate function is defined in detail as follows:
the independent variable is xi(i＝1,2,3)|x1＝US *,x2＝RL,x3＝PLM is a non-empty multi-element ordered array and represents the operating voltage of a power supply point of the power distribution network, the impedance of a power supply line and the load connected to a power supply area in ximin≤xi≤ximax(i is 1,2,3) and satisfies the constraint conditions (4) to (6), and f is a correspondence rule such that for each ordered array (x)1,x2,x3E.m) has a uniquely determined value y corresponding to it, so the distributed power accessed by the user side can be expressed as a multivariate function defined on M and related to the operating voltage of the power point, the impedance of the power supply line and the load accessed by the power supply area, which is abbreviated as y (f) (M), as shown in formula (3). The dependent variable y represents the distributed power supply power accessed by the user side under the limit condition
Figure BDA0001267267800000101
y＝{y|y＝f(x1,x2,x3),(x1,x2,x3E.g. M) is the value range of the function.
(2) Based on the power function model obtained in the step (1), obtaining sensitivity indexes of distributed power supply access power to all factors according to different power distribution network states; analyzing the influence of single factors, namely the operating voltage of a power supply point, the impedance of a power supply line or the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network based on the sensitivity index; the specific mode is as follows:
based on the power function model obtained in the step (1), according to different power distribution network states, obtaining the sensitivity index S of the distributed power supply access power to each factor according to the formula (7)iThe method is used for quantitatively measuring the influence of a single factor on the access power in the initial state of a certain power distribution network. And analyzing the influence of single factors (power supply point operating voltage, power supply line impedance or load accessed in a power supply area) on the receiving capacity of the distributed power supply of the power distribution network based on the calculated sensitivity index.
Figure BDA0001267267800000102
Wherein the sensitivity index is defined as follows:
pair function to argument xiThe first partial derivative of (A) is defined as a distributed power supply access power pair variable xiSensitivity S ofiThe physical meaning is the variation trend of the distributed power supply access power in the direction of the coordinate axis of the variable. Thus, given a certain operating state (x) of the distribution network10,x20,x30) E.g. M, the sensitivity index of the distributed power supply access power to each variable can be obtained according to the formula (7).
(3) Based on the power function model obtained in the step (1), calculating three indexes of single-factor partial increment, basic partial increment and cooperative increment by using a partial increment analysis model of the power function; analyzing the comprehensive influence of a plurality of factors, namely the power supply point operating voltage, the power supply line impedance and the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network based on the index calculation result; the specific mode is as follows:
step 3-1 giving initial state X of power distribution network0＝(x10,x20,x30) And the increase DeltaX of each dependent variable10＝(Δx1,Δx2,Δx3) Obtaining the final value state X of the power distribution network1＝(x11,x21,x31) And (3) calculating to obtain the full increment of the power function according to the formula (8) based on the power function model obtained in the step (1).
Δy10＝f(x11,x21,x31)-f(x10,x20,x30) (8)
And 3-2, decomposing the obtained access power full increment by using a partial increment analysis model of the power function based on the power function model obtained in the step (1): determination of the Power function for the variables at the Point X0The n-order partial derivative (taking n as 7, which is accurate enough in practical engineering application) is calculated according to the formula (15) - (17) to obtain three indexes of single-factor partial increment, basic partial increment and cooperative increment, so that the full increment is decomposed into independent influence quantity of a single factor and cooperative influence quantity of all factors, and further the comprehensive influence of a plurality of factors of the operating voltage of a power supply point, the impedance of a power supply line and the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network is analyzed based on the index calculation result.
The definition formula and the analysis method of each index are as follows:
(a) single factor partial increment PIi
Single factor partial increment PIiThe formula for defining (A) is as follows,
Figure BDA0001267267800000111
in the formula (I), the compound is shown in the specification,
Figure BDA0001267267800000112
denotes the power function y ═ f (M) versus the argument xiPartial differential of order m, Δ xiDenotes the independent variable xiThe amount of change in (c).
The analysis method using this index is as follows,
can quantitatively calculate independent variable xiAnd the influence degree in the total variation of the admission capacity is used for measuring the access power change of the distributed power supply caused by the independent single variable, wherein a positive value indicates that the independent variable is beneficial to the improvement of the admission capacity, a negative value indicates that the admission capacity is weakened, and an absolute value of the index indicates the influence degree. (b) Basic partial increment PA
The basic bias delta PA is defined as follows,
Figure BDA0001267267800000121
defining basic partial increment PA as single-factor partial increment PI of all independent variables of power functioniAnd the sum is used for measuring the influence on the distributed power supply access power caused by the independence of all independent variables.
(c) Cooperative incremental CA
The formula for defining the cooperative increment CA is as follows,
CA＝Δy10-PA (17)
and defining the cooperative increment CA as the difference between the full increment and the basic deviation increment for measuring the influence of the cooperative action of all variables on the access power.
The mathematical demonstration process of the partial increment analysis model of the power function in the step (3) is as follows:
arranged in a defined field M of the power function, the distribution network is operated from a certain operating state X0＝(x10,x20,x30) Change to another operating state X1＝(x11,x21,x31) And the increase of each dependent variable is DeltaX10＝(Δx1,Δx2,Δx3) If the power function y ═ f (m) at point X0＝(x10,x20,x30) With a continuous partial derivative of order n +1, the power function is taken from state X0Change to state X1Full increment of Δ y10The delta deltax of each argument can be used according to the taylor formulaiPower function for each variable at point X0All of (A) to (B)Partial derivatives of the respective order, if any, and Lagrangian residuals RnThe expression is shown in formula (9).
Figure BDA0001267267800000122
In the formula, Lagrangian remainder RnRepresents the remainder after the omitted n term, as shown in equation (10), where δ is between X0And X1A state point in between.
Figure BDA0001267267800000123
From equation 9, full increment Δ y10Except for the lagrange remainder RnIn addition, the argument x is then pair by functioniAnd the mixed partial differential of each order for all independent variables. By Delta CiIndicates when only the argument x is presentiVariation Δ xiThe expression of the sum of the first n-order bias increments of the power function caused by the individual change amounts is shown in formula (11), and it can be seen that the sum is related to the independent variable increment Δ xiIs subjected to the initial state of the distribution network, the power function and the independent variable xiPartial derivatives of each order and independent variable increments Δ xiIndependent of the increments of other independent variables;
Figure BDA0001267267800000131
let Δ CA represent the sum of the first n-order increments to the power function under the common variation of all factors, and its expression is shown in formula (12), which represents the synergy of all factors to the power function, and is affected by the initial state of the distribution network, the power function to the independent variable xiThe mixed partial derivatives of each order and the effect of all independent variable increments.
Figure BDA0001267267800000132
Thus, a full increment can be written as shown in equation (13).
Figure BDA0001267267800000133
It can be mathematically proven that the Lagrangian remainder R is taken as the number of terms n of the Taylor expansion approaches infinitynApproaches zero, so as long as n is large enough, the full increment of the power function can be approximated by the function to the variable xiThe sum of the first nth order increments of the function over all variables is approximately represented with an error of the remainder RnTherefore, a partial increment analysis model of the distributed power supply access power can be obtained, as shown in a formula (14).
Δy10≈ΔC1+ΔC2+ΔC3+ΔCA (14)
TABLE 1 relationship of partial incremental model analysis results to the number of terms n
Figure BDA0001267267800000134
Figure BDA0001267267800000141
As the value of n increases, the smaller the lagrangian error remainder, the more accurate the decomposition result of the full increment of the function obtained by using the partial increment analysis model of equation (14) will tend to be, as can be seen from table 1, when n is greater>At 6, Δ CiAnd the delta CA tends to be stable, and the partial increment analysis model of the distributed power supply access power is considered to be accurate enough in practical engineering application. Therefore, n can be taken to be 7 in the analysis of the distributed power source acceptance capability.
The following embodiments are further illustrated by the following examples:
firstly, quantitatively analyzing the influence of a single factor on the receiving capacity of a power distribution network based on a sensitivity index, and setting the voltage of a power supply point to operate between 0.93 and 1.07 times of rated voltage; based on the longest power supply radius specified by power distribution network planning, the radius of a power supply line is set to be changed between 10% and 400% of the reference power supply radius, and the section of the line is taken as70-240 mm2, and taking the limiting current value of the maximum line section as the maximum current-carrying capacity constraint; setting the load rate between 0% and 125%, and checking the constraint condition according to the formulas (4) to (6), thereby obtaining a definition domain M of a power function meeting the constraint condition and an arbitrarily determined running state X (X) of the power distribution network1,x2,x3) E to the distributed power supply access power y (x) accessed by the user side corresponding to the M1,x2,x3)。
According to equation (7), the distributed power supply switches in power y ═ f (x)1,x2,x3) Sensitivity index S of distributed power supply access power to each variable can be calculatediThus, the sensitivity index S of each operation state of the power distribution network and the corresponding distributed power supply access power to the power supply point operation voltage is obtained as shown in Table 21。
TABLE 2 sensitivity distribution of distributed power access power to power point operating voltage under different operating conditions
Distribution network state The radius of the power supply line is 10 to 200 percent The radius of the power supply line is 200 to 400 percent
Sensitivity index S1 -2.5～-0.75 -0.75～-0.6
Distribution network state Power supply point operating voltage 0.93 to 0.95 Power supply point operating voltage 0.95 to 1.07
Sensitivity index S1 -2.5～-1.5 -1.5～0
As can be seen from Table 2, when the voltage at the power supply point fluctuates within + -7% of the rated voltage, if the line impedance is large, the sensitivity S of the power function to the operating voltage at the power supply point1The variation range is small, so that the receiving capacity is not greatly influenced by the voltage of a power supply point; if the line impedance is small, the sensitivity S1The voltage at the access point of the distributed power supply is easier to exceed the limit when the voltage at the power supply point is higher, so that the receiving capacity is gradually reduced along with the increase of the voltage at the power supply point.
Therefore, in the same situation, the power distribution network with lower line impedance has a larger influence on the receptivity of the distributed power source on the operating voltage of the power source point than the power distribution network with higher line impedance. Compared with the power distribution network with higher load rate, the power distribution network with lower load rate has the advantage that the receiving capacity of the power distribution network with lower load rate is not greatly influenced by the operating voltage of a power supply point.
And then analyzing the influence of multi-factor change on the acceptance capacity of the distributed power supply of a certain power distribution network based on a power function partial increment model, and confirming the existence of multi-factor synergy and the effectiveness of the model. Assuming that the distribution network is in a certain initial operation state, each variable increment is 10% at the moment, so that the distribution network is changed to another operation state, and the calculation results of the single-factor partial increment, the basic partial increment and the cooperative increment indexes are obtained by using a partial increment model of the power function are shown in the following table.
TABLE 3 calculation results (per unit value) of indices
PI1 PI2 PI3 PA CA Full increment
-0.0538 -0.0042 0.0081 -0.0499 -0.0245 -0.0744
As can be seen from table 3, the access power of the distributed power supply is reduced by-0.0744 as the operating voltage of the power supply point, the impedance of the power supply line and the load connected to the power supply area are simultaneously increased, wherein the access power of the distributed power supply is reduced by-0.0538 and-0.0042 as the operating voltage of the power supply point and the impedance of the power supply line are respectively increased, the access power of the distributed power supply is improved by 0.0081 as the weight of the access load is increased, the access power of the distributed power supply changes to-0.0499 as the three factors change independently, and the access power of the distributed power supply changes to-0.0245 as the three factors change cooperatively.

Claims (1)

1. A power function model-based power distribution network admission distributed power supply capacity analysis method is characterized by comprising the following steps:
(1) based on an open-type operation distribution network model of a user side access distributed power supply, calculating equivalent impedance of the transformer according to model parameters of the transformer to obtain an expression of access power of the distributed power supply; giving the variation range of each variable and the voltage upper limit value of a distributed power supply access point, converting an access power complex function into a real function, and obtaining a power function model of a user side access distributed power supply;
the expression of the distributed power supply access power complex function is as follows:
Figure FDA0002209192160000011
Figure FDA0002209192160000012
wherein, PDG、QDGGenerating active power and reactive power for the distributed power supply;
Figure FDA0002209192160000013
as a complex function of the distributed power supply access power,
Figure FDA0002209192160000014
is the conjugate of the voltage of the distributed power access point;
Figure FDA0002209192160000015
is the conjugate of the operating voltage of the power supply point; rT、XTIs the equivalent impedance of the transformer; rL、XLIs the equivalent impedance of the power supply line; pL、QLLoad active and reactive power for the distribution network;
converting the distributed power supply access power complex function into a real function, wherein the expression is as follows:
y＝f(x1,x2,x3)＝abs[g(x1,x2,x3)]＝abs[A(A-x1)/(B+x2-jCx2)+x3+jDx3],(x1,x2,x3∈M)
the constraint conditions are as follows:
real[g(x1,x2,x3)]≥0
cosθ≥0.9
|(A*-x1 *)/(B*+x2+jCx2)|≤Imax
wherein x isi(i ═ 1,2,3) is defined as x1＝US *,x2＝RL,x3＝PL，
Figure FDA0002209192160000016
Representing an upper voltage limit for a given distributed power access point,
Figure FDA0002209192160000017
representing the equivalent impedance of the transformer, C ═ XL/RLThe ratio of the equivalent reactance of the line to the equivalent resistance of the line is expressed, D ═ QL/PLA, B, C, D are constants, which represent the ratio of the reactive power and the active power of the load accessed to the distribution network; the constraint condition I indicates that the output active power of the distributed power supply is constantly a non-negative value; constraint two represents that the power factor of the distributed power supply is not lower than 0.9; the constraint condition represents the constraint of branch current-carrying capacity;
the above multivariate function of the distributed power access power is defined in detail as follows:
the independent variable is xi(i＝1,2,3)|x1＝US *,x2＝RL,x3＝PLM is a non-empty multi-element ordered array and represents the operating voltage of a power supply point of the power distribution network, the impedance of a power supply line and the load connected to a power supply area in ximin≤xi≤ximax(i ═ 1,2,3) and satisfying a set of three constraints, and f is a rule of correspondence such that for each ordered array (x)1,x2,x3E.m) has a uniquely determined value y corresponding to it, so that the distributed power accessed by the user side can be expressed as a multivariate function defined on M and related to the operating voltage of a power supply point, the impedance of a power supply line and the load accessed by a power supply area, which is abbreviated as y (f) (M), and the dependent variable y represents the work of the distributed power accessed by the user side under the limit conditionRate of change
Figure FDA0002209192160000021
y＝{y|y＝f(x1,x2,x3),(x1,x2,x3E.g. M) is the value range of the function;
(2) based on the power function model obtained in the step (1), obtaining sensitivity indexes of distributed power supply access power to all factors according to different power distribution network states; analyzing the influence of single factors, namely the operating voltage of a power supply point, the impedance of a power supply line or the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network based on the sensitivity index;
the expression of the sensitivity index of the distributed power supply access power to each factor is as follows:
Figure FDA0002209192160000022
wherein the sensitivity index is defined as follows:
pair function to argument xiThe first partial derivative of (A) is defined as a distributed power supply access power pair variable xiSensitivity S ofiThe physical meaning is the variation trend of the distributed power supply access power in the direction of the coordinate axis of the variable; given a certain operating state (x) of the distribution network10,x20,x30) E, obtaining the sensitivity index of the distributed power supply access power to each variable according to the formula;
(3) based on the power function model obtained in the step (1), calculating three indexes of single-factor partial increment, basic partial increment and cooperative increment by using a partial increment analysis model of the power function; analyzing the comprehensive influence of a plurality of factors, namely the power supply point operating voltage, the power supply line impedance and the load accessed in a power supply area on the receiving capacity of the distributed power supply of the power distribution network based on the index calculation result;
the three index formulas and the analysis method of the single-factor partial increment, the basic partial increment and the cooperative increment are as follows:
(a) single factor partial increment PIi
Single factor partial increment PIiThe formula for defining (A) is as follows,
Figure FDA0002209192160000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002209192160000032
denotes the power function y ═ f (M) versus the argument xiPartial differential of order m, Δ xiDenotes the independent variable xiThe amount of change in (c);
the analysis method using this index is as follows,
can quantitatively calculate independent variable xiThe influence degree in the total variation of the admission capacity is used for measuring the access power variation of the distributed power supply caused by the independence of a single variable, wherein a positive value indicates that the independent variable is beneficial to the improvement of the admission capacity, a negative value indicates that the admission capacity is weakened, and an absolute value of the index indicates the influence degree;
(b) basic partial increment PA
The basic bias delta PA is defined as follows,
Figure FDA0002209192160000033
defining basic partial increment PA as single-factor partial increment PI of all independent variables of power functioniThe sum is used for measuring the influence on the distributed power supply access power caused by all independent arguments;
(c) cooperative incremental CA
The formula for defining the cooperative increment CA is as follows,
CA＝Δy10-PA
defining a cooperative increment CA as the difference between a full increment and a basic offset increment, and measuring the influence of the cooperative action of all variables on access power;
initial state X of given distribution network0＝(x10,x20,x30) And the increase DeltaX of each dependent variable10＝(Δx1,Δx2,Δx3) Obtaining the final value state X of the power distribution network1＝(x11,x21,x31) Calculating to obtain the full increment of the power function based on the power function model obtained in the step (1),
Δy10＝f(x11,x21,x31)-f(x10,x20,x30)。
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