CN108711851B - Method for evaluating safety of medium-voltage distribution network closed-loop operation - Google Patents

Method for evaluating safety of medium-voltage distribution network closed-loop operation Download PDF

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CN108711851B
CN108711851B CN201810568104.0A CN201810568104A CN108711851B CN 108711851 B CN108711851 B CN 108711851B CN 201810568104 A CN201810568104 A CN 201810568104A CN 108711851 B CN108711851 B CN 108711851B
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closed
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load
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CN108711851A (en
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周自强
张焰
冯楠
郭强
连鸿波
陈旸
余颖辉
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Shanghai Jiaotong University
State Grid Shanghai Electric Power Co Ltd
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State Grid Shanghai Electric Power Co Ltd
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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
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Abstract

The invention discloses a method for evaluating the safety of medium-voltage distribution network closed-loop operation, which comprises the following steps: acquiring a topological structure, equipment parameters and real-time operation data of a closed loop network, and performing state estimation on a high-voltage distribution network to obtain a voltage amplitude and a phase angle of a 10kV bus at the head end of a closed loop feeder line; selecting the ratio of the active and reactive loads of each load point on the closed loop feeder line to the active and reactive powers of the head end of the feeder line as an input variable, and calculating each-order semi-invariant of the input variable based on historical load data; performing deterministic load flow and closed loop current calculation; calculating each-order semi-invariant of closed-loop current; calculating the cumulative probability distribution of closed loop current; and calculating out-of-limit probability of each closed loop current, and evaluating the safety of closed loop operation. The invention can quantitatively evaluate the safety of the medium-voltage distribution network closed-loop operation; the problem that real-time load data of each load point of a feeder line cannot be obtained in practice is solved; the problem that the probability distribution function of the input variable is required to be known when the semi-invariant is solved by the traditional numerical method is also solved.

Description

Method for evaluating safety of medium-voltage distribution network closed-loop operation
Technical Field
The invention relates to the field of safe and stable operation of a power system, in particular to a method for evaluating the safety of closed-loop operation of a medium-voltage distribution network.
Background
The medium-voltage distribution network adopts a power supply mode of closed-loop design and open-loop operation. Under normal conditions, the interconnection switch is turned on, and the power distribution network operates in a radiation structure; when equipment is overhauled or an accident is handled, the load can be transferred without power failure through the loop closing operation of the interconnection switch. The loop closing operation of the medium voltage distribution network may generate a large loop closing current in the loop closing network, which causes a line current protection action or overload of some electrical equipment, resulting in a larger range of power failure accidents. Therefore, the operator needs to evaluate the safety of the loop closing operation before the loop closing operation.
Currently, there is no systematic method for evaluating the safety of the closed-loop operation of the medium voltage distribution network, and in actual production, workers generally consider the following conditions to be safe according to experience:
(1) before closing the loop, the difference of the voltage amplitude of the 10kV bus of the feeder line where the fractures on the two sides of the tie switch are located is less than 10 percent;
(2) before loop closing, the load difference of feeder lines on two sides of the tie switch is small, and the total load is not greater than the upper limit of the transmission capacity of any feeder line;
therefore, to ensure safety, the loop closing and load reversing operation of the medium-voltage distribution network is mostly performed at night when the load is light.
However, this production experience-based evaluation method lacks a corresponding theoretical support. Theoretical analysis shows that the magnitude of the loop closing current is greatly influenced by the voltage amplitude difference and the phase angle difference on two sides of the fracture of the interconnection switch. Therefore, there is no scientific basis for evaluating the safety of the loop closing operation only according to the voltage amplitude difference of the 10kV buses on both sides of the loop closing point. In addition, the method for comparing the total load of the loop closing feeder line with the upper limit of the transmission capacity of the line leads to conservative loop closing safety evaluation results, and has limited reference value for final loop closing decision making.
Related researches propose to evaluate the safety of closed loop by calculating the steady-state current and the transient impact current of the closed loop. However, the existing power distribution network measuring device is limited in configuration range, so that the voltage phase angle information of a 10kV bus in the power distribution network and the voltage amplitude and phase angle difference of two sides of a contact switch fracture cannot be obtained, and in addition, real-time load data of each load point on a feeder line required by calculating closed loop current cannot be obtained, so that the practicability of the researches is limited.
Disclosure of Invention
The invention aims to provide a method for evaluating the safety of closed-loop operation of a medium-voltage distribution network, which aims at solving the problem that voltage phase angle data of each bus in the distribution network cannot be acquired and adopts a method for carrying out state estimation on the high-voltage distribution network to obtain bus phase angle information. Aiming at the problem that real-time load data of feeder load points required by loop closing current calculation cannot be obtained, probability distribution characteristics of load values of all the load points are analyzed based on historical load data, then a half-step variable method is adopted to obtain an accumulated distribution curve of the loop closing current based on a probability load flow theory, and finally the safety of the loop closing operation is evaluated by obtaining the out-of-limit probability of the loop closing current.
In order to achieve the aim, the invention discloses a method for evaluating the safety of closed-loop operation of a medium-voltage distribution network, which takes the load point load on a closed-loop feeder line as a random variable, calculates the out-of-limit probability of closed-loop steady-state current and transient impact current based on a probability power flow theory and evaluates the safety of the closed-loop operation, and comprises the following steps:
s1, acquiring a topological structure, equipment parameters and real-time operation data before loop closing of the loop closing network, and performing state estimation on the high-voltage distribution network to obtain the voltage amplitude and phase angle of 10kV buses at the head ends of two loop closing feeders;
s2, selecting the ratio of the active load of each load point on the loop closing feed line to the active power of the head end of the feed line and the ratio of the reactive load of each load point on the loop closing feed line to the reactive power of the head end of the feed line as input variables, and calculating each-order semiinvariant of each input variable in the season and time period of the loop closing time based on the historical load data of each load point;
s3, performing deterministic load flow calculation and closed-loop current calculation at the reference operating point to obtain a closed-loop network system state variable reference value, a closed-loop current reference value and a conversion matrix;
s4, calculating each-order semi-invariant of the loop closing current according to each-order semi-invariant of the input variables and the conversion matrix;
s5, calculating the cumulative probability distribution of the loop closing current according to each-order semi-invariant of the loop closing current;
and S6, taking the maximum allowable current-carrying capacity of the feeder line and the current protection setting value as limit values, calculating the out-of-limit probability of each loop closing current, and evaluating the safety of the loop closing operation.
Preferably, the step S1 further includes:
and performing state estimation on the high-voltage distribution network by adopting a weighted least square criterion to obtain the voltage amplitude and phase angle of 10kV buses at the head ends of the two closed-loop feeders, and identifying and correcting bad measurement data.
Preferably, the step S2 further includes:
and considering the load value of each load point as a random variable, selecting the ratio of the active load of each load point to the active power of the head end of the feeder line and the ratio of the reactive load of each load point on the closed-loop feeder line to the reactive power of the head end of the feeder line as input variables to perform probability load flow calculation, and solving each-order semi-invariant of the input variables based on historical load data.
Preferably, the method for obtaining each order of semi-invariants of input variables based on historical load data comprises the following processes:
setting an input variable kPIs the ratio of the active load of any load point to the active power of the head end of the feeder line; sorting the load point and the annual 96-point daily load historical data of the outgoing line to obtain annual discrete measured data of the input variable, and constructing the historical data for solving the input variable kPThe sample set S of each order of semi-invariant;
dividing a sample set S into a plurality of sub-sample sets according to seasons and time periods, and solving an input variable k through analysis of any one sub-sample setPSemi-invariants of each step in seasons and time periods of loop closing time;
if the sub-sample set corresponding to the loop closing time has N discrete historical data { k }P1,kP2,kP3,…,kPNAt first, calculate its origin moment of each order αv：
Figure BDA0001685051310000031
Then by halfCalculating the relationship between the invariant and the origin moment, and calculating the semi-invariant gamma of each orderv：
Figure BDA0001685051310000032
Wherein, α1And αjThe origin moments when v is 1 and v is j respectively;
Figure BDA0001685051310000033
is the number of different combinations of j elements out of v elements.
Preferably, the step S3 further includes:
the voltage difference between two sides of the fracture of the interconnection switch is set to
Figure BDA0001685051310000041
Total impedance of closed loop is Z∑Then loop-closing steady-state circulation
Figure BDA0001685051310000042
Comprises the following steps:
Figure BDA0001685051310000043
is provided with
Figure BDA0001685051310000044
And
Figure BDA0001685051310000045
the initial current of the head ends of the two side feed lines before loop closing is respectively, X ═ theta1,V1,θ2,V2,…,θn,Vn]TFor the state variable of the closed-loop network system, according to the superposition theorem, the effective value I of the steady-state current of the head ends of the two side feeder lines after the loop is closed1'and I'2Respectively as follows:
Figure BDA0001685051310000046
Figure BDA0001685051310000047
let I1And I2Are respectively as
Figure BDA0001685051310000048
And
Figure BDA0001685051310000049
effective value of (1), maximum impact current effective value I appearing at the head ends of the feeder lines at two sides in the transient process of loop closing1MAnd I2MRespectively as follows:
I1M＝I1+1.51Ic＝g3(X) (6)
I2M＝I2+1.51Ic＝g4(X) (7)
let Z be ═ I1',I'2,I1M,I2M]TIf the loop closing current is a variable, the loop closing current equation is as follows:
Z＝g(X) (8)
setting K as an input variable of probability load flow calculation; w represents the injection power of each node in the closed loop network system, and W is AK, wherein A is a diagonal matrix formed by active power and reactive power at the head ends of two feeders; the closed loop network system flow equation can be expressed as:
W＝f(X) (9)
the input variable K is a random variable, which can be expressed as K0+ Δ K, where K0The expected value of the random variable K is a reference operating point of the closed-loop network system; delta K is random disturbance; the closed-loop network system state variable X can be expressed as X0+ΔX，X0The state variable is an expected value of a closed loop network system state variable, and delta X is random disturbance; each node injected power W may be represented as W0+ΔW，W0Injecting a power expected value for the node, wherein delta W is random disturbance corresponding to delta X; the loop closing current variable Z can be expressed as Z0+ΔZ，Z0The variable expectation value of the closed-loop current is shown, and the delta Z is random disturbance corresponding to the delta X;
performing Taylor series expansion on a power flow equation (9) and a closed loop current equation (8) of the closed loop network system and omitting high-order terms to obtain a linear relation between delta Z and delta K:
Figure BDA0001685051310000051
wherein, Jacobian matrix
Figure BDA0001685051310000052
Coefficient matrix
Figure BDA0001685051310000053
Preferably, the step S3 further includes: firstly, at a reference operating point K0Performing deterministic load flow calculation according to a formula (9) to obtain a state variable X of the closed-loop network system0And Jacobian matrix J0Wherein W is0＝AK0(ii) a Then at X0Calculating the loop closing current according to a formula (8) to obtain a loop closing current variable Z0And a coefficient matrix G0(ii) a Finally, a conversion matrix T is obtained0。
Preferably, the step S4 further includes: let Δ K(v)A v-order semi-invariant representing an input variable,
Figure BDA0001685051310000054
represents T0The coefficient matrix formed by v powers of the elements in (1) is composed of the property of semi-invariants
Figure BDA0001685051310000055
Determining v-order semi-invariants Delta Z of closed-loop current variables(v)。
Preferably, the step S5 further includes: the cumulative probability distribution of the closed-loop current is solved by adopting a Cornish-Fisher series, and the method comprises the following steps:
the cumulative distribution function of the closed-loop current variable Z is represented by F (Z), the α quantiles of the standard normal distribution function of phi (Z), F (Z) and phi (Z) can be respectively represented by Z (α) and phi (Z)
Figure BDA0001685051310000056
I.e. z (α) ═ F-1(α)，
Figure BDA0001685051310000057
Then z (α) and
Figure BDA0001685051310000058
the following relationship is satisfied:
Figure BDA0001685051310000059
wherein, gvNormalizing the v-order semi-invariant of the closed-loop current variable Z if the v-order semi-invariant of the random variable Z is gammavWith a standard deviation of σ, then
Figure BDA0001685051310000061
The cumulative probability distribution function can be obtained from the semi-invariants of each order of the closed-loop current through the formula (11).
Preferably, the step S6 further includes:
the loop closing current variable Z comprises a steady-state current effective value I of the head ends of the feeder lines at two sides after loop closing1'and I'2And the maximum impact current effective value I appearing at the head ends of the feeder lines at two sides1MAnd I2M；
Set variable I1'、I'2、I1M、I2MRespectively, is F1(x)、F2(x)、F3(x)、F4(x) The maximum allowable current-carrying capacity of the feeder lines on both sides of the loop closing point is Imax,1And Imax,2The protection setting values of the current I sections at two sides are respectively IsetI,1And IsetI,2Then, the out-of-limit probability of each loop closing current is respectively:
P1＝P(I1'≥Imax,1)＝1-F1(Imax,1)
P2＝P(I'2≥Imax,2)＝1-F2(Imax,2)
P3＝P(I1M≥IsetI,1)＝1-F3(IsetI,1)
P4＝P(I2M≥IsetI,2)＝1-F4(IsetI,2)
quantitatively evaluating the safety of the medium-voltage distribution network loop closing operation according to the out-of-limit probability of each loop closing current: if the out-of-limit probabilities are all less than 5%, the safety of the loop closing operation is determined to be high, otherwise, the safety of the loop closing operation is determined not to be guaranteed.
Compared with the prior art, the invention has the beneficial effects that:
(1) according to the invention, the safety of the loop closing operation of the medium voltage distribution network can be quantitatively evaluated by calculating the loop closing steady-state current and the transient state impact current generated by the loop closing operation, and the evaluation result has a theoretical basis and can provide reference for the loop closing operation of operators.
(2) The invention takes the load point load on the closed loop feeder line as a random variable, and obtains the probability distribution characteristic of the closed loop steady-state current and the transient impact current based on the probability load flow theory, thereby solving the problem that the real-time load data of each load point can not be obtained at present.
(3) According to the method, each-order semi-invariant of the input variable is solved through analysis of historical load data, and the problem that the probability distribution function of the input variable needs to be known when the semi-invariant is solved in the traditional numerical method is solved.
Drawings
Fig. 1 is a schematic diagram of a closed loop operation of a medium voltage distribution network of the present invention;
fig. 2 is a technical route diagram of the method for evaluating the safety of the closed-loop operation of the medium-voltage distribution network according to the present invention.
Detailed Description
The invention discloses a method for evaluating the loop closing operation safety of a medium voltage distribution network, which is further explained by combining an attached drawing and a specific implementation mode in order to make the invention more obvious and understandable.
As shown in fig. 1, the system transmission network (220kV and higher voltage class network) operates in a ring structure, and the distribution network with 110kV and lower voltage class operates in an open loop. Q1 and Q2 are outlet breakers that communicate the feeders on either side of the switch, respectively. The two 10kV feeder lines are connected through a communication switch Q3; when the system is operating normally, the tie switch Q3 is open; when the operation mode is adjusted or an emergency accident occurs, the connection switch Q3 can be closed, and the load is turned over by the loop.
As shown in fig. 2, the method for evaluating the safety of the medium voltage distribution network closed loop operation provided by the present invention is divided into 6 main steps, as follows:
step A, estimating the state of a high-voltage distribution network;
in the step A, on the basis of obtaining the topological structure of the loop closing network, equipment parameters and real-time operation data before loop closing, state estimation is carried out on the high-voltage distribution network to obtain the voltage amplitude and the phase angle of the 10kV bus at the head end of the two loop closing feeders.
Specifically, the method comprises the following steps:
when the closed-loop current calculation of the press-fit power grid is carried out, a 10kV bus node at the head end of the closed-loop feeder line is generally selected as a reference node, so that the voltage amplitude and the phase angle of 10kV buses at two sides of the interconnection switch are required to be known. At present, a measurement system of a medium-voltage distribution network can acquire a voltage amplitude, but phase angle information of the voltage amplitude cannot be acquired. For the situation, on the basis of acquiring topological structures, equipment parameters and real-time operation data before loop closing of the power transmission network and the high-voltage distribution network in the loop closing network, a Weighted Least square criterion (WLS) is adopted to carry out state estimation on the high-voltage distribution network, and the Weighted Least square method has the advantages of simple model and small calculated amount. Therefore, the voltage amplitude and the phase angle of the 10kV bus at the head end of the loop closing feeder line can be obtained through the state estimation of the high-voltage distribution network, and meanwhile, poor measurement data can be identified and corrected.
B, calculating semi-invariants of each order of input variables;
in the step B, the ratio of the active load of each load point on the closed-loop feeder to the active power of the head end of the feeder and the ratio of the reactive load of each load point on the closed-loop feeder to the reactive power of the head end of the feeder are selected as input variables, and each-order semi-invariant of each input variable in the season and time period of the closed-loop time is calculated based on 96-point daily load historical data of each load point in the year.
Specifically, before the medium voltage distribution network closed loop operation, the real-time load of each load point is generally difficult to obtain. And in view of the above, the load value of each load point is taken as a random variable, and the ratio of the active load of each load point to the active power of the head end of the feeder line and the ratio of the reactive load of each load point on the closed-loop feeder line to the reactive power of the head end of the feeder line are selected as input variables to perform probabilistic load flow calculation. When each order of semi-invariant of the input variable is solved, the traditional method adopts a numerical method to solve according to the probability distribution function of the variable. However, the distribution function of these input variables is unknown in engineering. Therefore, the invention adopts a method for solving each-order semi-invariant of the input variable based on historical load data, and the method is described as follows:
setting an input variable kPIs the ratio of the active load at a certain load point to the active power at the head end of the feeder line. Sorting the load point and the annual 96-point daily load historical data of the outgoing line to obtain annual discrete measured data of the input variable, and constructing the historical data for solving the input variable kPOf each order of the semi-invariant sample set S. Considering that the load may exhibit different characteristics in different seasons and different time periods each day, the sample set S is divided into 12(4 × 3 ═ 12) sub-sample sets (S) by seasons (spring, summer, autumn, and winter) and time periods (00:00-08:00, 08:00-18:00, 18:00-24:00)1，S2，…，S12). By analyzing a certain subsample set, the input variable k is obtainedPAnd each step is semi-invariable in the season and time period of the loop closing time.
If there are N discrete historical data in the sub-sample set corresponding to the loop closing time, it can be expressed as { k }P1,kP2,kP3,…,kPN}. first calculate its origin moments α of each orderv：
Figure BDA0001685051310000081
Then, the relationship between the semi-invariant and the origin moment is used to calculate the semi-invariant gamma of each orderv：
Figure BDA0001685051310000082
Wherein,
Figure BDA0001685051310000083
for different combinations of j elements out of v elements α1And αjThe origin moments when v is 1 and v is j, respectively.
Step C, deterministic load flow calculation and closed loop current calculation;
and C, combining the topological information and the operation data of the closed-loop network, and performing deterministic load flow calculation and closed-loop current calculation at a reference operation point to obtain a system state variable reference value, a closed-loop current reference value and a coefficient matrix of the closed-loop network.
Specifically, let the voltage difference between the two sides of the break of the interconnection switch be
Figure BDA0001685051310000091
Total impedance of closed loop is Z∑Then loop-closing steady-state circulation
Figure BDA0001685051310000092
Comprises the following steps:
Figure BDA0001685051310000093
is provided with
Figure BDA0001685051310000094
And
Figure BDA0001685051310000095
the initial current of the head ends of the two side feed lines before loop closing is respectively, X ═ theta1,V1,θ2,V2,…,θn,Vn]TFor the state variable of the closed-loop network system, according to the superposition theorem, the effective value I of the steady-state current of the head ends of the two side feeder lines after the loop is closed1'and I'2Respectively as follows:
Figure BDA0001685051310000096
Figure BDA0001685051310000097
let I1And I2Are respectively as
Figure BDA0001685051310000098
And
Figure BDA0001685051310000099
effective value of (1), maximum impact current effective value I possibly appearing at the head ends of the feeder lines at two sides in the transient process of loop closing1MAnd I2MRespectively as follows:
I1M＝I1+1.51Ic＝g3(X) (6)
I2M＝I2+1.51Ic＝g4(X) (7)
let Z be ═ I1',I'2,I1M,I2M]TIf the loop closing current is a variable, the loop closing current equation is as follows:
Z＝g(X) (8)
setting K as an input variable of probability load flow calculation, and representing the ratio of active power and reactive power of each node to the active power and reactive power of the head end of the line; and W represents the injected power of each node in the closed loop network system, and W is AK, wherein A is a diagonal matrix consisting of active power and reactive power at the head ends of two feeders. The closed loop network system flow equation can be expressed as:
W＝f(X) (9)
the input variable K is a random variable, which can be expressed as K0+ Δ K, where K0The expected value of the random variable K is a reference operation point of the closed-loop network system, and delta K is random disturbance. Similarly, the closed-loop network system state variable X can be represented as X0+ΔX，X0And delta X is a random disturbance value which is a state variable expected value of the closed-loop network system. Each node injected power W may be represented as W0+ΔW，W0Injecting a power expectation value for the node, Δ W being the random perturbation corresponding to Δ X. The loop closing current variable Z can be expressed as Z0+ΔZ，Z0For closed loop current variable desired values, Δ Z is the random perturbation corresponding to Δ X.
Performing Taylor series expansion on a power flow equation (9) and a closed loop current equation (8) of the closed loop network system and omitting high-order terms to obtain a linear relation between delta Z and delta K:
Figure BDA0001685051310000101
wherein, Jacobian matrix
Figure BDA0001685051310000102
Coefficient matrix
Figure BDA0001685051310000103
In this step C, first at a reference operating point K0Where (W at this time)0＝AK0) Performing deterministic load flow calculation according to a formula (9) to obtain a state variable X of the closed-loop network system0And Jacobian matrix J0(ii) a Then at X0Calculating the loop closing current according to a formula (8) to obtain a loop closing current variable Z0And a coefficient matrix G0(ii) a Finally, a conversion matrix T is obtained0。
Step D, calculating each-order semi-invariant of closed-loop current;
in step D, each order semi-invariant of the loop closing current is calculated from each order semi-invariant of the input variables obtained in step B and the transformation matrix obtained in step C.
Specifically, in step B, the semi-invariants of each order of the input variables have been found, setting Δ K(v)A v-order semi-invariant representing an input variable,
Figure BDA0001685051310000104
represents T0A coefficient matrix formed by v powers of the elements in (A), may be formed by the nature of the semi-invariant in this step D
Figure BDA0001685051310000105
Obtaining v-order semi-invariant of closed-loop current variableΔZ(v)。
Step E, solving the probability distribution of each loop closing current;
in the step E, a Cornish-Fisher series expansion method is adopted, and the cumulative probability distribution of the closed-loop current is obtained through each-stage semi-invariant of the closed-loop current.
Specifically, the method for calculating the cumulative probability distribution of the closed-loop current by using the Cornish-Fisher series in the step E is as follows:
let the cumulative distribution function of a loop current variable Z be F (Z), and the α quantiles of the standard normal distribution function phi (Z), F (Z) and phi (Z) be respectively expressed as Z (α) and phi (Z)
Figure BDA0001685051310000111
I.e. z (α) ═ F-1(α)，
Figure BDA0001685051310000112
Then z (α) and
Figure BDA0001685051310000113
the following relationship is satisfied:
Figure BDA0001685051310000114
wherein, gvNormalizing the semi-invariants for the v-order of the closed-loop current variable Z, i.e. if the v-order semi-invariants of the random variable Z is gammavWith a standard deviation of σ, then
Figure BDA0001685051310000115
The cumulative probability distribution function can be obtained from the semi-invariant of each step of the closed loop current according to the formula (11).
F, evaluating the out-of-limit probability of each loop closing current;
in step F, according to the safe loop closing condition, the maximum allowable current-carrying capacity of the feeder line and the current protection setting value are respectively used as limit values, the out-of-limit probability of each loop closing current is calculated, and the safety of the loop closing operation is evaluated.
In particular, areThe loop current variable Z includes: steady-state current effective value I of two-side feeder line head ends after loop closing1'and I'2And the maximum impact current effective value I which can appear at the head ends of the feeder lines at two sides1MAnd I2M. Set variable I1'、I'2、I1M、I2MRespectively, is F1(x)、F2(x)、F3(x)、F4(x) The maximum allowable current-carrying capacity of the feeder lines on both sides of the loop closing point is Imax,1And Imax,2The protection setting values of the current I sections at two sides are respectively IsetI,1And IsetI,2Then, the out-of-limit probability of each loop closing current is respectively:
P1＝P(I1'≥Imax,1)＝1-F1(Imax,1)
P2＝P(I'2≥Imax,2)＝1-F2(Imax,2)
P3＝P(I1M≥IsetI,1)＝1-F3(IsetI,1)
P4＝P(I2M≥IsetI,2)＝1-F4(IsetI,2)
finally, the safety of the medium-voltage distribution network closed-loop operation can be quantitatively evaluated according to the four out-of-limit probabilities: if the out-of-limit probabilities are all less than 5%, the safety of the loop closing operation can be considered to be high, otherwise, the safety of the loop closing operation cannot be guaranteed, and the loop closing is considered after the corresponding operation mode is adjusted.
In summary, the invention provides a method for evaluating the safety of the closed-loop operation of the medium-voltage distribution network, which quantitatively evaluates the safety of the closed-loop operation by calculating the out-of-limit probability of the closed-loop steady-state current and the transient impact current, and solves the problem that real-time load data of each load point cannot be obtained in practice. The method is applied to actual production, can quickly and effectively evaluate the safety of the loop closing operation before loop closing, and provides support for operators to make loop closing decisions.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (9)

1. A method for evaluating the safety of closed-loop operation of a medium-voltage distribution network is characterized in that the method takes load point loads on a closed-loop feeder line as random variables, obtains the out-of-limit probability of closed-loop steady-state current and transient impact current based on a probability load flow theory and evaluates the safety of the closed-loop operation, and comprises the following steps:
s1, acquiring a topological structure, equipment parameters and real-time operation data before loop closing of the loop closing network, and performing state estimation on the high-voltage distribution network to obtain the voltage amplitude and phase angle of 10kV buses at the head ends of two loop closing feeders;
s2, selecting the ratio of the active load of each load point on the loop closing feed line to the active power of the head end of the feed line and the ratio of the reactive load of each load point on the loop closing feed line to the reactive power of the head end of the feed line as input variables, and calculating each-order semiinvariant of each input variable in the season and time period of the loop closing time based on the historical load data of each load point;
s3, performing deterministic load flow calculation and closed-loop current calculation at the reference operating point to obtain a closed-loop network system state variable reference value, a closed-loop current reference value and a conversion matrix;
s4, calculating each-order semi-invariant of the loop closing current according to each-order semi-invariant of the input variables and the conversion matrix;
s5, calculating the cumulative probability distribution of the loop closing current according to each-order semi-invariant of the loop closing current;
and S6, taking the maximum allowable current-carrying capacity of the feeder line and the current protection setting value as limit values, calculating the out-of-limit probability of each loop closing current, and evaluating the safety of the loop closing operation.
2. The method for evaluating the safety of closed-loop operation of medium voltage distribution network as claimed in claim 1,
the step S1 further includes:
and performing state estimation on the high-voltage distribution network by adopting a weighted least square criterion to obtain the voltage amplitude and phase angle of 10kV buses at the head ends of the two closed-loop feeders, and identifying and correcting bad measurement data.
3. The method for evaluating the safety of closed-loop operation of medium voltage distribution network as claimed in claim 1,
the step S2 further includes:
and selecting the ratio of the active load of each load point to the active power of the head end of the feeder line and the ratio of the reactive load of each load point on the closed-loop feeder line to the reactive power of the head end of the feeder line as input variables to perform probability load flow calculation, and solving each-order semi-invariant of the input variables based on historical load data.
4. A method for evaluating the safety of closed-loop operations of medium voltage distribution networks according to claim 3,
the method for solving each-order semi-invariant of the input variable based on the historical load data comprises the following processes:
setting an input variable kPIs the ratio of the active load of any load point to the active power of the head end of the feeder line; sorting the load point and the daily load historical data of 96 points all year around of the corresponding outgoing line to obtain the discrete actual measurement data all year around of the input variable, and constructing the daily load historical data for solving the input variable kPThe sample set S of each order of semi-invariant;
dividing a sample set S into a plurality of sub-sample sets according to seasons and time periods, and solving an input variable k through analysis of any one sub-sample setPSemi-invariants of each step in seasons and time periods of loop closing time;
if the sub-sample set corresponding to the loop closing time has N discrete historical data { k }P1,kP2,kP3,…,kPNAt first, calculate its origin moment of each order αv：
Figure FDA0002364441420000021
Then, the relationship between the semi-invariant and the origin moment is used to calculate the semi-invariant gamma of each orderv：
Figure FDA0002364441420000022
Wherein, α1And αjThe origin moments when v is 1 and v is j respectively;
Figure FDA0002364441420000023
is the number of different combinations of j elements out of v elements.
5. The method for evaluating the safety of the closed-loop operation of the medium voltage distribution network according to claim 4,
the step S3 further includes:
the voltage difference between two sides of the fracture of the interconnection switch is set to
Figure FDA0002364441420000024
Total impedance of closed loop is Z∑Then loop-closing steady-state circulation
Figure FDA0002364441420000031
Comprises the following steps:
Figure FDA0002364441420000032
is provided with
Figure FDA0002364441420000033
And
Figure FDA0002364441420000034
the initial current of the head ends of the two side feed lines before loop closing is respectively, X ═ theta1,V1,θ2,V2,…,θn,Vn]TFor the state variable of the loop closing network system, according to the superposition theorem, the steady state current effective values I 'of the head ends of the feeder lines on two sides after loop closing'1And l'2Respectively as follows:
Figure FDA0002364441420000035
Figure FDA0002364441420000036
let I1And I2Are respectively as
Figure FDA0002364441420000037
And
Figure FDA0002364441420000038
effective value of (1), maximum impact current effective value I appearing at the head ends of the feeder lines at two sides in the transient process of loop closing1MAnd I2MRespectively as follows:
I1M＝I1+1.51Ic＝g3(X) (6)
I2M＝I2+1.51Ic＝g4(X) (7)
if Z ═ I'1,I′2,I1M,I2M]TIf the loop closing current is a variable, the loop closing current equation is as follows:
Z＝g(X) (8)
setting K as an input variable of probability load flow calculation; w represents the injection power of each node in the closed loop network system, and W is AK, wherein A is a diagonal matrix formed by active power and reactive power at the head ends of two feeders; the closed loop network system power flow equation is expressed as:
W＝f(X) (9)
the input variable K is a random variable, denoted K0+ Δ K, where K0Is the expectation of a random variable KThe value is a reference operation point of the closed loop network system; delta K is random disturbance; the state variable X of the closed-loop network system is represented as X0+ΔX，X0The state variable is an expected value of a closed loop network system state variable, and delta X is random disturbance; the injection power W of each node is represented as W0+ΔW，W0Injecting a power expected value for the node, wherein delta W is random disturbance corresponding to delta X; the variable Z of the closed-loop current is represented as Z0+ΔZ，Z0The variable expectation value of the closed-loop current is shown, and the delta Z is random disturbance corresponding to the delta X;
performing Taylor series expansion on a power flow equation (9) and a closed loop current equation (8) of the closed loop network system and omitting high-order terms to obtain a linear relation between delta Z and delta K:
Figure FDA0002364441420000041
wherein, Jacobian matrix
Figure FDA0002364441420000042
Coefficient matrix
Figure FDA0002364441420000043
6. The method for evaluating the safety of the closed-loop operation of the medium voltage distribution network according to claim 5,
the step S3 further includes: firstly, at a reference operating point K0Performing deterministic load flow calculation according to a formula (9) to obtain a state variable X of the closed-loop network system0And Jacobian matrix J0Wherein W is0＝AK0(ii) a Then at X0Calculating the loop closing current according to a formula (8) to obtain a loop closing current variable Z0And a coefficient matrix G0(ii) a Finally, a conversion matrix T is obtained0。
7. The method for evaluating the safety of the closed-loop operation of the medium voltage distribution network according to claim 6,
said step (c) isS4 further comprises: let Δ K(v)A v-order semi-invariant representing an input variable,
Figure FDA0002364441420000044
represents T0The coefficient matrix formed by v powers of the elements in (1) is composed of the property of semi-invariants
Figure FDA0002364441420000045
Determining v-order semi-invariants Delta Z of closed-loop current variables(v)。
8. The method for evaluating the safety of the closed-loop operation of the medium voltage distribution network according to claim 7,
the step S5 further includes: the cumulative probability distribution of the closed-loop current is solved by adopting a Cornish-Fisher series, and the method comprises the following steps:
the cumulative distribution function of the loop current variable Z is represented as F (Z), the standard normal distribution function is represented as phi (Z), and the α quantiles of F (Z) and phi (Z) are represented as Z (α) and phi (Z), respectively
Figure FDA0002364441420000046
I.e. z (α) ═ F-1(α)，
Figure FDA0002364441420000047
Then z (α) and
Figure FDA0002364441420000048
the following relationship is satisfied:
Figure FDA0002364441420000049
wherein, gvNormalizing the v-order semi-invariant of the closed-loop current variable Z if the v-order semi-invariant of the random variable Z is gammavWith a standard deviation of σ, then
Figure FDA0002364441420000051
By the formula(11) The cumulative probability distribution function can be obtained from the semi-invariant of each step of the closed loop current.
9. The method of claim 8, wherein the method for evaluating the safety of closed-loop operation of medium voltage distribution network,
the step S6 further includes:
the loop closing current variable Z comprises steady-state current effective values I 'of the head ends of the feeder lines on two sides after loop closing'1And l'2And the maximum impact current effective value I appearing at the head ends of the feeder lines at two sides1MAnd I2M；
Is provided with a variable I'1、I′2、I1M、I2MRespectively, is F1(x)、F2(x)、F3(x)、F4(x) The maximum allowable current-carrying capacity of the feeder lines on both sides of the loop closing point is Imax,1And Imax,2The protection setting values of the current I sections at two sides are respectively IsetI,1And IsetI,2Then, the out-of-limit probability of each loop closing current is respectively:
P1＝P(I′1≥Imax,1)＝1-F1(Imax,1)
P2＝P(I′2≥Imax,2)＝1-F2(Imax,2)
P3＝P(I1M≥IsetI,1)＝1-F3(IsetI,1)
P4＝P(I2M≥IsetI,2)＝1-F4(IsetI,2)
quantitatively evaluating the safety of the medium-voltage distribution network loop closing operation according to the out-of-limit probability of each loop closing current: if the out-of-limit probabilities are all less than 5%, the safety of the loop closing operation is determined to be high, otherwise, the safety of the loop closing operation is determined not to be guaranteed.
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