CN112653134B - Power distribution network voltage stability judgment method based on HELM voltage sensitivity - Google Patents

Power distribution network voltage stability judgment method based on HELM voltage sensitivity Download PDF

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CN112653134B
CN112653134B CN202011458402.8A CN202011458402A CN112653134B CN 112653134 B CN112653134 B CN 112653134B CN 202011458402 A CN202011458402 A CN 202011458402A CN 112653134 B CN112653134 B CN 112653134B
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voltage
sensitivity
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power
order
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CN112653134A (en
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高慧敏
钟毅
陈健琳
赵嘉敏
罗平
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Hangzhou Dianzi University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • 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
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • 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]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

Abstract

The invention discloses a distribution network voltage stability judgment method based on HELM voltage sensitivity. According to the method, firstly, the power flow of the power distribution network is calculated by using the HELM, and then the sensitivity of voltage to the injection power of each node is calculated according to a sensitivity calculation method based on the HELM. Secondly, judging the sensitivity of each order of the injected power of each node according to the voltage, and if the high-order sensitivity is greater than the low-order sensitivity, the voltage is unstable; if the high-order sensitivity is equal to the low-order sensitivity, the voltage is critical and stable; if the high-order sensitivity is smaller than the low-order sensitivity, the difference is the voltage stability margin. The invention utilizes the HELM method to consider the nonlinear factors of the sensitivity, calculates the nonlinear sensitivity of each order and is used for judging the voltage stability of the power distribution network.

Description

Power distribution network voltage stability judgment method based on HELM voltage sensitivity
Technical Field
The invention belongs to the technical field of electric power information, and particularly relates to a distribution network voltage stability judgment method based on HELM holo-function embedded voltage sensitivity.
Background
The existing power distribution network has heavier system load along with the expansion of scale and the access of distributed power generation, and the problem of voltage instability is easy to occur. The conventional static voltage stability analysis and judgment method of the power distribution network is to calculate the maximum load causing voltage instability according to a continuous power flow method, compare the current power flow with the maximum load, and consider the voltage to be stable if the current power flow is smaller than the maximum load. This analysis method has the following problems: 1) the calculation amount of continuous calculation is large, the calculation time is long, and the real-time requirement of online voltage stability judgment is not met; 2) as the DG or FACT access and the node load are not increased proportionally, the maximum load is changed, and the maximum load calculated by using the continuous power flow method is not accurate.
Some of which have also been proposed in the literatureThe indexes are used for judging whether the voltage of the power distribution network is stable, such as line breakdown indexes, line voltage stability indexes and the like, but the indexes are derived based on a two-machine system, a complex power distribution network load model accessed into DG or FACT equipment and the like cannot be considered, or line resistance or grounding capacitance and the like are ignored, and evaluation is not accurate enough[1-5]。
The sensitivity calculation method based on the jacobian matrix is often used in preventive control of voltage stabilization, but a problem that calculation cannot be performed in the case of encountering pathological power flow often occurs.
A load flow calculation method based on the embedding of Holomorphic embedding method full-pure functions is proposed in the last two years, the load flow method completely subverts the traditional cow pulling method, and whether a load flow solution exists or not can be determined without depending on the initial value of a node[6-10]. The method can completely solve the problems of load flow calculation, reactive power optimization, voltage stability analysis and the like of the traditional power system. However, no relevant literature research exists at present on how to judge whether the voltage of the power distribution network is stable by calculating the voltage sensitivity through the HELM.
Reference to the literature
[1] Comprehensive voltage instability prevention control strategy for power system considering response [ J ] institute of Fuzhou university, 2017, 11 (10): 74-86.
[2] Arrowanz, Yaohai, research on static voltage stability of cloud and precious power grid based on sensitivity analysis [ J ] North China power technology, 2017, (5): 9-l4.
[3] Yuanhao, li fang xing, ginger billow, jia macrojie wide area load margin sensitivity based on coupled single port network theory and its application in voltage stabilization control [ J ] south grid technology, 2017, 11 (10): 74-86.
[4]Banerjee S,Das D,Chanda CK,“Voltage stability of radial distribution networks for different types of loads”.Int J Power Energy Convers,vol.5,no.1,pp.70-87,2014.
[5]Seyed Eshagh Sadeghi,Asghar Akbari Foroud,“A new approach for static voltage stability assessment in distribution networks”,Int Trans Electr Energ Syst,e12203,2019.
[6]Shruti Rao,Yang Feng,Daniel J.Tylavsky,Muthu Kumar Subramanian,“The Holomorphic Embedding Method Applied to the power-Flow Problem”,IEEE TRANSACTIONS ON POWER SYSTEMS,vol.31,no.5,pp.3816-3828,2016.
[7]Antonio Trias and JoséLuis Marín,“The Holomorphic Embedding Load flow Method for DC Power Systems and Nonlinear DC Circuits”,IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS,vol.63,no.2,pp.322-333,2016.
[8]Bin Wang，Chengxi Liu,Kai Sun,“Multi-Stage Holomorphic Embedding Method for Calculating the Power-Voltage Curve”,IEEE TRANSACTIONS ON POWER SYSTEMS,vol.33,no.1,pp.1127-1129,2018.
[9]Rui Yao,Kai Sun,Di Shi,Xiaohu Zhang,“Voltage Stability Analysis of Power Systems with Induction Motors Based on Holomorphic Embedding”,IEEE TRANSACTIONS ON POWER SYSTEMS,vol.33,no.1,pp.1127-1129,2018.
[10]Baran M E and Wu F F,“Network reconfiguration in distribution systems for loss reduction and load balancing”,IEEE Trans on Power Delivery,pp.1401-1407,1989.
Disclosure of Invention
The method for judging the voltage stability of the power distribution network based on the HELM voltage sensitivity is provided for overcoming the defects in the prior art, the voltage sensitivity is calculated by the HELM method, the method is suitable for various load models, can be used for judging the voltage stability of the power distribution network on line and preventing and controlling the voltage stability of the power distribution network, is high in calculation speed and simple in calculation, and has higher theoretical significance and application value.
The method for judging the voltage stability of the power distribution network based on the HELM voltage sensitivity specifically comprises the following steps:
step one, establishing a mathematical model of the power distribution network.
Assuming that no grounding branch circuit exists in the power distribution network, the root node is a balance node, and no PV node exists except the root node, establishing a mathematical model of power flow calculation of the power distribution network by a node power equation:
Figure GDA0003506269380000021
wherein Y isikRepresenting the mutual admittance between an i node and a j node in a node admittance matrix, wherein i is 1,2, … N, j is 1,2, … N, and N represents the number of network nodes; vkRepresents the injection voltage at node k, k being 1,2 … N;
Figure GDA0003506269380000031
representing the conjugate of the injected apparent power at the i-node, Vi *Representing the conjugate of the i-node injection voltage and m represents all the nodes of the network.
And step two, calculating the power flow of the power distribution network by using an HELM method.
Because the node voltage is related to the node injection power and the like, the injection power comprises active power and reactive power and is usually expressed by complex numbers, and the holomorphic function is a complex analysis method, an embedded pure imaginary function can be constructed according to the embedded holomorphic function method:
Figure GDA0003506269380000032
in the formula: s is an embedded parameter operator, ci(s) is the s-series expansion of the i-node, n is the s-series order, ci[n]Is the coefficient of the s-order and n-order terms of the voltage of the i node. snThe n-th order term representing the inline parametric operator s.
The formula (2) can be substituted for the formula (1):
Figure GDA0003506269380000033
wherein s is*Meaning the conjugation of the s operator.
Yik,transIs the admittance between the non-grounded branch nodes i, k; vk(s) represents a voltage holo-functional expression of the k node;
Figure GDA0003506269380000034
Yik,shuntrepresenting the ground admittance of the i-node. When s is 0, letting both the constant power and the ground load be 0, a linear, balanced node only network solution can be obtained for a pure transmission network. And when s is 1, the solution of the original trend equation is obtained.
Suppose that:
Figure GDA0003506269380000035
Figure GDA0003506269380000036
wherein d isi[n]As an inverse function of the voltage expressed as an all-pure function
Figure GDA0003506269380000037
The coefficient corresponding to the n-th order term of s;
Figure GDA0003506269380000038
is a ground branch current;
the formula (3) can be substituted with the formulae (2) and (4):
Figure GDA0003506269380000039
wherein the content of the first and second substances,
Figure GDA0003506269380000041
is a ground branch current; when no grounding branch is assumed in the distribution network
Figure GDA0003506269380000042
Yik,tran＝Yik。
When s is 0, formula (4) is substituted, or coefficients of 0 th order of the s series according to formula (5) are equal, and the following can be obtained:
Figure GDA0003506269380000043
from this equation (6), c can be determinedk[0]。
Figure GDA0003506269380000044
According to the equality of coefficients of the S series, the following can be obtained:
dk[0]＝1/ck[0] (8)
when the order of s is 1
Figure GDA0003506269380000045
Wherein the content of the first and second substances,
Figure GDA0003506269380000046
inverse function V representing i-node voltage expressed by holo-pure functioni -1(s) the conjugation of coefficients corresponding to the 0 th order term of s; can find ck[1]。
According to the equality of coefficients of the S series, the following can be obtained:
Figure GDA0003506269380000048
according to a formula (11)
Figure GDA0003506269380000049
Thereby, it is possible to obtain:
Figure GDA00035062693800000410
when s is 1, a solution to the trend can be obtained.
The HELM power flow solution is not set by an initial value, and the HELM can clearly inform whether the power flow solution exists or not and predict a voltage collapse point.
And thirdly, calculating the sensitivity of the voltage to the node injection power by using a HELM method.
To determine the sensitivity of the voltage to the injection of active and reactive power into the node, i.e. the requirement
Figure GDA0003506269380000051
Wherein P isjRepresenting the active power injected at node j, QjRepresenting the reactive power injected at node j.
As can be seen from the calculation of equation (6), ci[0]Independent of the injected power at node i, and therefore,
Figure GDA0003506269380000052
are all 0.
In the formula (9) on both sides to Pj，QjThe partial derivatives are calculated to obtain the final product,
when j ═ i:
Figure GDA0003506269380000053
when j ≠ i:
Figure GDA0003506269380000054
the simultaneous formulas (14) and (15) can be solved
Figure GDA0003506269380000055
From the solving process, it can be seen that
Figure GDA0003506269380000056
And
Figure GDA0003506269380000057
independent of the system power flow distribution, onlyThe network structure is related to the electrical distance and is referred to as the voltage structure sensitivity.
From the formula (11)
Figure GDA0003506269380000058
Thereby deducing:
Figure GDA0003506269380000061
similarly, P is paired on both sides of equation (10)j，QjCalculating the partial derivative, obtaining:
when j ═ i:
Figure GDA0003506269380000062
when j ≠ i:
Figure GDA0003506269380000063
can find out
Figure GDA0003506269380000064
Can be derived from formula (11)
Figure GDA0003506269380000065
Equations (14) - (20) are computed cyclically, so that all of them can be computed
Figure GDA0003506269380000066
Then, the total nonlinear sensitivity of the voltage to the injected power is calculated by substituting the equation (13).
The analysis finds that the raw materials are mixed with the raw materials,
Figure GDA0003506269380000067
proportional to the load first power, because when n is 2, the first term on the right of equation (18) is constant, and the second term is proportional to the load;
Figure GDA0003506269380000071
proportional to the load squared and so on, which are defined herein as the voltage partial sensitivity. In the normal case of the operation of the device,
Figure GDA0003506269380000072
and
Figure GDA0003506269380000073
and becomes smaller as the value of n increases.
Finally, the overall voltage sensitivity
Figure GDA0003506269380000074
And
Figure GDA0003506269380000075
can be obtained from the formula (14).
The voltage structure sensitivity is irrelevant to load and only relevant to the network structure, in the strong network structure, the structure sensitivity can be used as the basis of voltage control and reactive power optimization decision, the online voltage control is accurate, repeated calculation is not needed, and the calculation speed is high. The voltage part sensitivity is related to the load and can be used for measuring the non-linearity degree of the voltage sensitivity.
Step four, judging voltage stability by using HELM voltage to inject reactive power sensitivity to the node;
firstly, a voltage stability judgment principle is deduced by using a two-machine system:
the two-machine system voltage vector diagram can be obtained:
Figure GDA0003506269380000076
wherein the content of the first and second substances,
Figure GDA0003506269380000077
represents the equivalent voltage vector of the system,
Figure GDA0003506269380000078
Represents the current flowing through the system,
Figure GDA0003506269380000079
Representing the extreme voltage of a system equivalent generator, R representing the system equivalent resistance and X representing the system equivalent reactance;
suppose that
Figure GDA00035062693800000710
The magnitude of the voltage solution can be:
Figure GDA00035062693800000711
wherein P represents active power, Q represents reactive power, ZSRepresenting the equivalent impedance of the system; when Z isL＝ZSWhile obtaining the inflection point, Z, of the PV or QV curveLRepresenting the equivalent impedance of the load;
namely, it is
Figure GDA00035062693800000712
And (3) pushing out:
Figure GDA00035062693800000713
wherein R isLRepresenting the equivalent resistance, X, of the loadLRepresenting the equivalent reactance of the load;
when X is 0, P is E4/(4R)
For a two-machine system, HELM method is adopted to calculate the nonlinear sensitivity of each order
②
Figure GDA0003506269380000081
To obtain C2[0]＝C1[0]
② by
Figure GDA0003506269380000082
Figure GDA0003506269380000083
To obtain
Figure GDA0003506269380000084
③ composed of
Figure GDA0003506269380000085
Figure GDA0003506269380000086
To obtain
Figure GDA0003506269380000087
④
Figure GDA0003506269380000088
Figure GDA0003506269380000089
To obtain
Figure GDA00035062693800000810
Therefore, from C2[0]、C2[1]、C2[2]、C2[3]To obtain
Figure GDA00035062693800000811
Figure GDA00035062693800000812
Figure GDA00035062693800000813
Let R be 0 or more,
Figure GDA00035062693800000814
to obtain
Figure GDA00035062693800000815
Namely, it is
The real solution is obtained from the solution of this one-dimensional quadratic equation:
Figure GDA00035062693800000816
from the above it is seen that in the normal case,
Figure GDA0003506269380000091
is less than
Figure GDA0003506269380000092
As the load increases in the course of time,
Figure GDA0003506269380000093
and
Figure GDA0003506269380000094
and increased until it is satisfied
Figure GDA0003506269380000095
Figure GDA0003506269380000096
And
Figure GDA0003506269380000097
the cross-over is carried out,
Figure GDA0003506269380000098
is initially greater than
Figure GDA0003506269380000099
This condition is the condition for determining the inflection point of the voltage stability
Figure GDA00035062693800000910
Very close so we can use
Figure GDA00035062693800000911
Is greater than
Figure GDA00035062693800000912
This determination is used as a determination condition for voltage stabilization.
Obtaining voltage sensitivity of each order by using HELM calculation, and then subtracting high-order sensitivity from low-order sensitivity, wherein the low-order sensitivity is larger than the high-order sensitivity under the normal condition, namely the difference value is positive; when the load is increased, if the difference value is negative, the voltage instability is judged; in the voltage stabilization prevention control, a threshold value is set for the difference value, and if the value obtained by subtracting the high-order sensitivity from the low-order sensitivity exceeds the threshold value, it is considered that the voltage is about to be destabilized, and the voltage prevention control is started.
Preferably, after the voltage sensitivity of 6 th order is calculated, the voltage sensitivity of the higher order is subtracted from the voltage sensitivity of the lower order to determine whether the voltage is unstable or not
The invention has the following beneficial effects:
the distribution network voltage stability judgment method based on the HELM voltage sensitivity is provided, can be used for online voltage stability judgment of the distribution network and voltage stability prevention control of the distribution network, solves the problem that the online voltage of the distribution network is not easy to calculate, and is high in calculation speed, simple in calculation and high in theoretical significance and application value.
Drawings
FIG. 1 is a flow chart of a method for determining voltage stability of a power distribution network based on HELM voltage sensitivity;
FIG. 2 is a schematic diagram of a 33-node grid;
FIG. 3 is a schematic diagram showing a comparison between the results of the HELM power flow calculation and the results of the forward-backward substitution;
FIG. 4 is a graph of voltage versus reactive power sensitivity calculated using HELM under base tidal conditions, where FIG. 4(a) is the voltage versus reactive power total sensitivity and voltage structure sensitivity, and FIG. 4(b) is the voltage partial versus reactive power sensitivity;
FIG. 5 is a graph of voltage part to reactive power sensitivity as the load scale increases, where FIG. 5(a) is the voltage to reactive power sensitivity and FIGS. 5(b) - (f) are the voltage part to reactive power sensitivity from C2-C6;
FIG. 6 is a schematic diagram of a two-machine system;
FIG. 7 is a λ V curve for node 30 in a 33-node system;
fig. 8 is a plot of the 30-node voltage portions versus reactive power sensitivity.
Detailed Description
The invention is further explained below with reference to the drawings;
as shown in fig. 1, the method for determining the voltage stability of the power distribution network based on the voltage sensitivity of the HELM comprises the following steps:
step one, establishing a mathematical model of a power distribution network according to data of a 33-node power grid shown in fig. 2:
Figure GDA0003506269380000101
Figure GDA0003506269380000102
wherein, Pi、Qi、ViRespectively injecting active power, reactive power and voltage at the node i; gij、Bij、δijRespectively, conductance, susceptance and phase angle difference between the nodes i and j; and N is the total number of nodes.
And step two, performing load flow calculation by using the HELM, wherein the result is shown in fig. 3, and as can be seen from fig. 3, the result based on the HELM load flow calculation is basically consistent with the result obtained by the forward-backward substitution calculation, which proves that the method for performing load flow calculation by using the HELM is feasible.
And step three, calculating the voltage sensitivity by using the HELM, wherein the result is shown in figure 4. The load of the 33-node power distribution network is increased according to the proportion lambda, and the voltage sensitivity is calculated through the HELM, and the result is shown in figure 5.
And step four, deducing a voltage stability judgment principle according to the two-machine system shown in the figure 6, and judging whether the voltage is stable or not by using the voltage sensitivity calculated by the HELM. The graph of λ V for a 33 node system plotted using Matpower, with λ on the abscissa being the load increase factor. As is clear from fig. 7, the breakdown voltage of the node 30 is about 0.5, and the active load at this time is about 2.4 times the initial value.
Fig. 8 is a graph showing the sensitivity of each portion of the voltage at the 30 node as the total grid load increases proportionally.
As can be seen from fig. 8, the reactive sensitivities of the voltage parts C (2), C (3), C (4), C (5) and C (6) are gradually increased along with the increase of the load, and when the load value is about 2.5 times of the initial value, the voltage-reactive sensitivities of the voltage parts C (5) and C (6) are crossed first, and at this time, the voltage-reactive sensitivity of the voltage part C (6) starts to exceed the voltage-reactive sensitivity of the voltage part C (5), and is increased along with the increase of the load. After this crossed load point, the voltage sensitivity of the voltage parts to reactive power is greater and greater, and the system voltage has already become unstable. This point is very close to the voltage inflection point calculated by the mather, and we can use this point as the determination point of voltage stability and instability when calculating the voltage sensitivity.

Claims (5)

1. A distribution network voltage stability judgment method based on HELM voltage sensitivity is characterized by comprising the following steps: the method specifically comprises the following steps:
step one, establishing a mathematical model of a power distribution network;
when no grounding branch circuit exists in the power distribution network, the root node is a balance node, and no PV node exists except the root node, a mathematical model of power distribution network load flow calculation is established:
Figure FDA0003504818970000011
wherein Y isikRepresenting the transadmittance between node i and node j in the node admittance matrix, i ═1,2, … N, j-1, 2, … N, N being the total number of nodes, VkIndicating the injection voltage at node k, k-1, 2, … N,
Figure FDA0003504818970000012
representing the conjugate of the injected apparent power at the i-node, Vi *Represents the conjugate of the i-node injection voltage, and m represents all nodes of the network;
calculating the power flow of the power distribution network by using an HELM method;
constructing an embedded purely imaginary function:
Figure FDA0003504818970000013
wherein c isi[n]Nth voltage component, s, representing i-node voltage in HELM power flow calculationnAn n-th order representing an embedded parameter operator s; substituting the formula (2) into the node power equation of the formula (1), solving the formula (2) according to the equality of the S-level coefficients, and substituting S into 1 to obtain the solution of the power flow of the power distribution network;
thirdly, calculating the sensitivity of voltage to node injection power by using a HELM method;
calculating the sensitivity of voltage to the active power and reactive power injected into the node:
Figure FDA0003504818970000014
wherein P isjRepresenting the active power injected at node j, QjRepresents the reactive power injected at node j;
according to the calculation result of the step three, all the obtained results are solved
Figure FDA0003504818970000015
Obtaining the sensitivity of each order of voltage to the injection power of each node;
step four, judging voltage stability by using HELM voltage to inject reactive power sensitivity to the node;
and (3) deriving a voltage stability judgment principle by using a two-machine system: under normal conditions
Figure FDA0003504818970000021
Is less than
Figure FDA0003504818970000022
As the load increases in the course of time,
Figure FDA0003504818970000023
and
Figure FDA0003504818970000024
and also increased until
Figure FDA0003504818970000025
When the temperature of the water is higher than the set temperature,
Figure FDA0003504818970000026
and
Figure FDA0003504818970000027
the curves are crossed with each other,
Figure FDA0003504818970000028
is initially greater than
Figure FDA0003504818970000029
While
Figure FDA00035048189700000210
And condition for determining voltage stabilization inflection point
Figure FDA00035048189700000211
Are very close to each other and thus use
Figure FDA00035048189700000212
Is greater than
Figure FDA00035048189700000213
This determination is taken as a determination condition for voltage stabilization, where X represents the system equivalent reactance;
obtaining voltage sensitivity of each order by using HELM calculation, and then subtracting high-order sensitivity from low-order sensitivity, wherein the low-order sensitivity is larger than the high-order sensitivity under the normal condition, namely the difference value is positive; when the load is increased, if the difference value is negative, the voltage instability is judged; in the voltage stabilization prevention control, a threshold value is set for the difference value, and if the value obtained by subtracting the high-order sensitivity from the low-order sensitivity exceeds the threshold value, it is considered that the voltage is about to be destabilized, and the voltage prevention control is started.
2. The distribution network voltage stability determination method based on the HELM voltage sensitivity of claim 1, wherein: the calculation process of the power flow of the power distribution network in the second step is as follows:
substituting the embedded pure imaginary function of the formula (2) into the formula (1) to obtain:
Figure FDA00035048189700000214
wherein s is*Means to conjugate the s operator; y isik,transIs the admittance between the non-grounded branch nodes i, k; vk(s) is a voltage holomorphic expression of the k node; y isik,shuntRepresenting the ground admittance of the i-node;
definition of
Figure FDA00035048189700000215
Wherein d isi[n]As an inverse function V of the i-node voltage expressed as an all-pure functioni -1Coefficient corresponding to the n-th order of s of(s), ci(s) is an s-series expansion of a fully pure function expression of the i-node voltage;
substituting s-0 into equation (4) to obtain:
Figure FDA00035048189700000216
calculating c from equation (6)k[0]：
Figure FDA0003504818970000031
The coefficients according to the S series are equal:
dk[0]＝1/ck[0] (8)
when the order of s is 1, the equation (4) is calculated according to the equality of coefficients of the n-th order of s:
Figure FDA0003504818970000032
wherein the content of the first and second substances,
Figure FDA0003504818970000033
is a ground branch current; when there is no ground branch in the distribution network
Figure FDA0003504818970000034
Yik,tran＝Yik；
Figure FDA0003504818970000035
Inverse function V representing i-node voltage expressed by holo-pure functioni -1(s) the conjugation of coefficients corresponding to the 0 th order term of s; solved to obtain ck[1]：
The coefficients of the s series of equation (4) are equal:
Figure FDA0003504818970000036
the nth power coefficients of the s series according to equation (7) are equal:
Figure FDA0003504818970000037
calculated according to the formula (11)
Figure FDA0003504818970000038
C is calculated according to the formula (10)k[n]；
Thus, when s is equal to 1, equation (12) is solved to obtain a solution of the power flow:
Figure FDA0003504818970000039
3. the distribution network voltage stability determination method based on the HELM voltage sensitivity of claim 2, wherein: in the third step, the HELM method is utilized to calculate the sensitivity of the voltage to the node injection power, namely, the solution formula (3) is obtained, and the process is as follows:
c is obtained from the formula (6)i[0]Independent of the injected power at node i, and therefore,
Figure FDA00035048189700000310
are all 0;
in the formula (9) on both sides to Pj，QjDerivation of the deviation
When j ═ i:
Figure FDA0003504818970000041
when j ≠ i:
Figure FDA0003504818970000042
simultaneous equations (13) and (14) are solved
Figure FDA0003504818970000043
Obtained by equation (11):
Figure FDA0003504818970000044
thereby deducing:
Figure FDA0003504818970000045
similarly, P is paired on both sides of equation (10)j，QjCalculating a partial derivative to obtain:
when j ═ i:
Figure FDA0003504818970000046
when j ≠ i:
Figure FDA0003504818970000051
find out
Figure FDA0003504818970000052
Is pushed out by formula (11)
Figure FDA0003504818970000053
Calculating the formula (13) to the formula (19) circularly, and calculating all
Figure FDA0003504818970000054
Then, the total nonlinear sensitivity of the voltage to the injected power is calculated by substituting the equation (3).
4. The distribution network voltage stability determination method based on HELM voltage sensitivity of claim 3, characterized in that: in the fourth step, the process of deriving the voltage stability determination principle by using the two-machine system comprises the following steps:
obtaining the following voltage vector diagram according to a two-machine system:
Figure FDA0003504818970000055
wherein the content of the first and second substances,
Figure FDA0003504818970000056
represents the equivalent voltage vector of the system,
Figure FDA0003504818970000057
Represents the current flowing through the system,
Figure FDA0003504818970000058
Representing the extreme voltage of a system equivalent generator, R representing the system equivalent resistance and X representing the system equivalent reactance;
suppose that
Figure FDA0003504818970000059
The magnitude of the voltage is solved as:
Figure FDA00035048189700000510
wherein P represents active power, Q represents reactive power, ZSRepresenting the equivalent impedance of the system; when Z isL＝ZSWhile obtaining the inflection point, Z, of the PV or QV curveLRepresenting the equivalent impedance of the load;
namely, it is
Figure FDA00035048189700000511
And (3) pushing out:
Figure FDA0003504818970000061
wherein R isLRepresenting the equivalent resistance, X, of the loadLRepresenting the equivalent reactance of the load;
when X is 0, P is E4/(4R)
For a two-machine system, HELM method is adopted to calculate the nonlinear sensitivity of each order
First order:
by
Figure FDA0003504818970000062
To obtain C2[0]＝C1[0]
Second order:
by
Figure FDA0003504818970000063
To obtain
Figure FDA0003504818970000064
Third order:
by
Figure FDA0003504818970000065
To obtain
Figure FDA0003504818970000066
Fourth step:
by
Figure FDA0003504818970000067
Figure FDA0003504818970000068
To obtain
Figure FDA0003504818970000069
So from C2[0]、C2[1]、C2[2]、C2[3]To obtain
Figure FDA00035048189700000610
Figure FDA00035048189700000611
Let R be 0 or more,
Figure FDA0003504818970000071
to obtain
Figure FDA0003504818970000072
That is, a real solution is obtained from the solution of this one-dimensional quadratic equation:
Figure FDA0003504818970000073
5. the distribution network voltage stability determination method based on the HELM voltage sensitivity of claim 1, wherein: and in the fourth step, after 6-order voltage sensitivity is obtained by using HELM calculation, the high-order voltage sensitivity is subtracted from the low-order voltage sensitivity, and whether the voltage is unstable or not is judged.
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