CN110188319B - Method for calculating number of grounding points of TN-C grounding system based on multi-objective optimization - Google Patents

Method for calculating number of grounding points of TN-C grounding system based on multi-objective optimization Download PDF

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CN110188319B
CN110188319B CN201910467715.0A CN201910467715A CN110188319B CN 110188319 B CN110188319 B CN 110188319B CN 201910467715 A CN201910467715 A CN 201910467715A CN 110188319 B CN110188319 B CN 110188319B
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郑荣进
邓慧琼
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Fujian University of Technology
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Abstract

The invention discloses a method for calculating the number of grounding points of a TN-C grounding system based on multi-objective optimization, which aims at the grounding configuration of the TN-C grounding system, provides a multi-objective optimization model which simultaneously meets the requirements of the number of grounding points with the lowest contact voltage, the largest possible fault phase zero-sequence current and the lowest grounding cost under the condition of considering the uniform distribution of the grounding points, and further calculates the number of the grounding configurations by utilizing a given solving model. The calculation method provided by the invention gives the optimal number of the grounding electrodes of the TN-C grounding system on the basis of the comprehensive consideration of the goals of lowest contact voltage, highest fault phase zero-sequence current and lowest grounding cost, and is convenient for field personnel to reasonably select the number of the grounding electrodes of the TN-C grounding system.

Description

Method for calculating grounding point number of TN-C grounding system based on multi-objective optimization
Technical Field
The invention relates to the field of electrical systems, in particular to a method for calculating the number of grounding points of a TN-C grounding system based on multi-objective optimization.
Background
The low-voltage distribution network is a terminal system for supplying power to thousands of households and also relates to a power supply system which has the widest scope and can cause damage to user equipment and personal casualty accidents. Because the grounding selection is improper or the personnel or equipment accidents caused by improper handling after the grounding fault occurs in the low-voltage system, the deep analysis and the solution of the grounding-related problem of the low-voltage system have very important significance.
The grounding types of the low-voltage system are mainly three, namely a TN system, a TT system and an IT system. Wherein TN can be divided into TN-C, TN-C-S and TN-S systems according to the configuration mode of working neutral wire (N) and protective neutral wire (PE) [1]
In the middle of the 20 th century, the grounding mode of the soviet union low-voltage distribution system basically adopts a TN-C system. Although the TN-C system can save one PE wire compared with the TN-S system, when the PEN wire is broken, because the over-current protection can not be operated, the leakage equipment has very high contact voltage for a long time, which is easy to cause electric shock hazard. In recent years, foreign countries have also studied the possible damage of low-voltage networks with residual current protectors installed, and document [2] mentions that when a fault occurs after a leakage protector is installed, the device still generates a contact voltage.
While adopting TN-S system abroad [3] Also for TN-C systemsThe improvement is that after entering the building, a TN-C-S system is adopted, and in order to reduce the contact voltage when the PEN line is broken, the PEN line is repeatedly grounded at the entrance of the building. The united states has adopted a repeatedly grounded TN-C-S system. Such a repeated-ground TN-C-S system, also referred to as a multipoint protection grounding system, is now more and more commonly used in the uk for new building power supply. Documents [4 to 6]The application of a TN-C-S system in recent years abroad is introduced, and although the TN-C-S system can effectively reduce the contact voltage generated when the PEN wire is broken, the investment of one conducting wire needs to be increased, and the cost is increased.
In order to meet the IEC standard and to increase the electrical safety, at the end of the last 90 s.a.russia proposed to change the low-voltage distribution network before 1995 from a TN-C system to a TN-S system, but with millions of kilometers of wires and cables, and therefore suggested to modify the soviet union code, the TN-C system had to be repeatedly earthed at the user access, whether it was supplied by an overhead line or a cable line [7] . When the potential of the protective conductor is not close to the ground potential as much as possible in large buildings such as high-rise buildings and the like, the underground conductor which is connected with the total equipotential in the building can be used as a repeated grounding body [8] The electrical safety level of the repeatedly grounded TN-C system is not inferior to that of the TN-S system, so the repeatedly grounded TN-C system is generally adopted abroad [9] However, the IEC standard does not clearly specify the grounding resistance value and grounding position of the repetitive grounding, and there is still a lack of research on the rational arrangement of the repetitive grounding for safety and economy.
In China, because the poor power supply and utilization equipment in the 70 s and the backward management level cause the accidents of personal electric shock and casualty to happen, the national protection of low-voltage lines is to firstly popularize and use the voltage type protector in rural areas [10] The protector is suitable for the operation mode that the neutral point of a distribution transformer is not grounded, so that the rural low-voltage power grid is changed into the operation mode that the neutral point of the low-voltage side is grounded through high resistance from the end of 70 to the beginning of 80 years, namely an IT system indicated by rural low-voltage power technical code. Documents [11 to 13]Some applications of IT systems are presented.
Over the years of operation, neutral ungrounded systemsCannot limit high voltage to ground caused by some reason of low-voltage network, such as induced overvoltage caused by lightning strike, operation overvoltage, erection of high-low voltage lines on same pole, etc [14] . In the neutral point high-resistance grounding system, the phase line grounding voltage is increased to the line voltage due to the leakage of one phase line to the ground, the voltage of the zero line to the ground is measured in maintenance, and the phenomenon that one phase line has no voltage to the ground [15] . Although the voltage-type protector plays a small role in protecting the electric shock casualty accidents at that time, the voltage-type protector is rapidly replaced by the current-type protector in the 80 s due to the defects of low commissioning rate, poor protection reliability, incapability of installing shunt protection, power grid operation and the like [16-17]
It can be seen from the above that the operation mode of the low-voltage power grid in China is changed in 80 s to adapt to the operation requirement of the leakage protector [18] . At present, after rural power grid engineering transformation, most electric power facilities reach a certain level, the health condition of rural power supply facilities is not lower than that of a city, and a grounding mode of a TN-C system can be adopted as in the urban power grid.
The TN-C system has the advantages that the PEN line has the functions of the PE line and the N line, one conducting wire can be saved, and meanwhile, overcurrent protection can be used as insulation fault protection of electric equipment. The fault current can form a loop through a person touching the leakage equipment and the working ground of the transformer if the system has a ground short circuit fault, thereby causing direct use threat to the human body.
In order to solve the above problem, the main solution at present is to repeatedly ground. From the present research situation, most of the articles mention and analyze the role and importance of the repeated grounding [19-21] Reference [22]]The approximate location of repeated grounding and resistance values are given, document [23]]Demonstrating the importance of repeated grounding and equipotential bonding combinations for reducing faulty contact voltages [24]It is proposed that in order to ensure that the safety voltage is below 50V during fault, the resistance value of the repeated grounding should not be simply set to 10 Ω, but the article only analyzes whether the repeated grounding is effective by using an equivalent circuit, and does not give a specific repeated grounding position and resistance value. Document [25]]Analyze the low-voltage distribution network systemThe limitation of grounding and zero-crossing protection in the system proposes a solution of repeated grounding, but does not propose a specific solution. Therefore, repeated grounding configuration research of grounding patterns of the TN-C system is started, but a specific optimization configuration scheme is not mentioned yet. That is, the main disadvantage of the prior art is that it is not possible to provide the optimal number of grounding points based on the multiple objectives of simultaneously keeping the contact voltage as low as possible, the zero-sequence current of the fault phase as large as possible, and the grounding cost as low as possible, and therefore, how many grounding points? This is entirely empirical or heuristic in practice and does not give quantitative analysis and comparison.
Disclosure of Invention
The invention aims to provide a method for calculating the number of grounding points of a TN-C grounding system based on multi-objective optimization.
The technical scheme adopted by the invention is as follows:
the method for calculating the number of grounding points of the TN-C grounding system based on multi-objective optimization comprises the following steps:
step 1, constructing a multi-objective optimization model for calculating the number of grounding points of the TN-C grounding system;
step 1-1, constructing an objective function, wherein a specific formula is as follows:
minf(n)=[f 1 (n),f 2 (n),f 3 (n)] (1)
wherein f is 1 (n) is the total grounding cost of the TN-C grounding system; f. of 2 (n) is the reciprocal of a fault phase zero sequence current modulus value when a single-phase earth fault occurs in the TN-C grounding system; f. of 3 (n) is the device contact voltage;
step 1-2, constructing a multi-objective optimization model based on constraint conditions: a multi-objective optimization model for calculating the grounding point number of the TN-C grounding system is constructed based on equality constraint and inequality constraint conditions of the TN-C grounding system, and the method comprises the following specific steps:
Figure GDA0003741696280000031
wherein f is 1 (n) is total of TN-C grounding systemThe cost of grounding; f. of 2 (n) is the reciprocal of a fault phase zero sequence current modulus value when a single-phase earth fault occurs in the TN-C grounding system; f. of 3 (n) is the device contact voltage; h (n) represents a mapping relation, U, which is satisfied when the power grid complies with kirchhoff law constraints safe Indicating a safety voltage, I, specified for the TN-C grounded system set The action setting value of zero sequence protection on the line in the TN-C grounding system is represented;
step 2, obtaining the optimal grounding number based on the multi-objective optimization model;
step 2-1, constructing an unconstrained weighting function based on the multi-objective optimization model, wherein the formula is as follows:
Figure GDA0003741696280000032
wherein, mu 1 ,μ 2 ,μ 3 As weighting coefficients, α, β, λ k Are penalty coefficients, N is the total number of the equation represented by h (N) =0 in the formula (6), h k (n) is the kth element of the h (n) vector;
and 2-2, solving the optimal grounding number n based on the weighting function of the formula (7).
Further, in step 1-1 f 1 (n) is expressed as the following equation:
f 1 (n)=cn (2)
n is the number of grounding points at the TN-C grounding system, and the n grounding points are uniformly distributed; c is the comprehensive investment of each set of grounding device.
Further, in step 1-1 f 2 (n) is expressed as the following formula:
f 2 (n)=1/I 0 (3)
wherein, I 0 Indicating fault phase zero sequence current phasor when single-phase earth fault occurs in TN-C grounding system
Figure GDA0003741696280000041
A modulus value of (d);
further, in step 1-1 f 3 (n) is expressed as the following formula:
f 3 (n)=U T (4)
Wherein, U T Indicating device contact voltage
Figure GDA0003741696280000042
The modulus value of (a).
Further, in the step 2-2, the optimal grounding number n is solved by adopting a particle swarm optimization algorithm based on the weighting function of the formula (7).
By adopting the technical scheme, aiming at the TN-C grounding system, the optimization function for calculating the number of grounding points with the lowest contact voltage, the largest fault phase zero-sequence current and the lowest grounding cost is simultaneously met, and the grounding configuration number is further calculated by utilizing a given solving model. The calculation method provided by the invention gives the optimal number of the grounding electrodes of the TN-C grounding system on the basis of the comprehensive consideration of the goals of lowest contact voltage, highest fault phase zero-sequence current and lowest grounding cost, and is convenient for field personnel to reasonably select the number of the grounding electrodes of the TN-C system.
Drawings
The invention is described in further detail below with reference to the accompanying drawings and the detailed description;
FIG. 1 is a schematic diagram of a typical distribution network TN-C grounding system;
FIG. 2 is a flow diagram of the method for calculating the number of grounding points of the TN-C grounding system based on multi-objective optimization.
Detailed Description
Interpretation of terms:
an IT grounding system: the power supply neutral point is not grounded or grounded through high impedance, and the exposed conductive part of the load side electric equipment is directly grounded through respective protective zero line and is mutually independent from the grounding of the power supply side.
TT grounding system: the power supply neutral is connected directly to ground, while the exposed conductive portion of the load side electrical device is connected to a grounding system on a separate grounding device independent of the power system grounding point.
TN grounding system: the neutral point of the power supply is grounded, a neutral line is led out, and the exposed conductive part of the electrical equipment is directly connected with the neutral line.
TN-C grounding System: and the working neutral wire N and the protection neutral wire PE are integrated into a grounding system.
TN-S ground system: a grounding system in which the working neutral wire N and the protection neutral wire PE are separated.
TN-C-S grounding system: the protection zero line (PE) and the working zero line (N) of the trunk line part of the whole system are integrated, and the protection zero line (PE) and the working zero line (N) of the branch line part are separated grounding systems.
The invention mainly aims at a typical distribution network TN-C grounding system shown in figure 1, and optimally configures the number of grounding poles according to an optimization method. In figure 1 f indicates a single-phase earth fault in one phase,
Figure GDA0003741696280000056
for the zero sequence current flowing through the fault phase,
Figure GDA0003741696280000057
contact voltage of the user equipment housing.
As shown in FIG. 2, the invention discloses a method for calculating the number of grounding points of a TN-C grounding system based on multi-objective optimization,
step 1, constructing a multi-objective optimization model for calculating the number of grounding points of the TN-C grounding system;
step 1-1, constructing an objective function, wherein a specific formula is as follows:
minf(n)=[f 1 (n),f 2 (n),f 3 (n)] (1)
wherein f is 1 (n) is the total grounding cost of the TN-C grounding system; f. of 2 (n) is the reciprocal of a fault phase zero sequence current modulus when a single-phase earth fault occurs in the TN-C grounding system; f. of 3 (n) is the device contact voltage;
further, in step 1-1 f 1 (n) is expressed as the following formula:
f 1 (n)=cn (2)
n is the number of grounding points of the TN-C grounding system, and the n grounding points are uniformly distributed; c is the comprehensive investment of each set of grounding device.
Further, in the TN-C grounding system shown in FIG. 1, when a single-phase ground fault occurs, the phase current is failed due to the fault
Figure GDA0003741696280000052
Modulus value of 0 Is a function of n, so 1/I 0 Also a function of n, i.e. f in step 1-1 2 (n) is expressed as the following equation:
f 2 (n)=1/I 0 (3)
wherein, I 0 Indicating fault phase zero sequence current phasor when single-phase earth fault occurs in TN-C grounding system
Figure GDA0003741696280000053
A modulus value of (d);
further, in the TN-C grounding system shown in FIG. 1, when a single-phase ground fault occurs, the equipment contacts the voltage
Figure GDA0003741696280000054
Is also a function of n, then f in step 1-1 3 (n) is expressed as the following formula:
f 3 (n)=U T (4)
wherein, U T Indicating device contact voltage
Figure GDA0003741696280000055
The modulus value of (a).
Step 1-2, constructing a multi-objective optimization model based on constraint conditions: the method comprises the following steps of constructing a multi-objective optimization model for calculating the number of grounding points of the TN-C grounding system based on equality constraints and inequality constraints of the TN-C grounding system, and specifically comprising the following steps:
Figure GDA0003741696280000051
wherein f is 1 (n) is the total grounding cost of the TN-C grounding system; f. of 2 (n) is the reciprocal of a fault phase zero sequence current modulus when a single-phase earth fault occurs in the TN-C grounding system; f. of 3 (n) is a mapping relation which is satisfied when the equipment contact voltage h (n) represents the power grid obeys kirchhoff's law constraint, U safe Indicating the safety voltage, I, prescribed by the TN-C grounding system set The action setting value of zero sequence protection on a circuit in the TN-C grounding system is represented;
specifically, the derivation process of the constraint condition-based multi-objective optimization model is as follows:
considering that when the grounding point is configured, the total grounding cost is as small as possible, the contact voltage of the equipment is as small as possible, and the fault phase current modulus I is simultaneously enabled 0 As large as possible to ensure the zero sequence protection can operate smoothly, therefore, when configuring the grounding point, the objective function shown in formula (1) should be considered comprehensively:
minf(n)=[f 1 (n),f 2 (n),f 3 (n)] (1)
for the typical TN-C grounding system shown in fig. 1, when a single-phase ground fault occurs, the system should also satisfy the following constraint relationship:
Figure GDA0003741696280000061
in the formula (5), x is a voltage vector and a current vector in the system, is a state variable of the system and is a function of n; g (x) =0 represents the circuit constraint relationship that the power grid should follow kirchhoff's law after the single-phase earth fault occurs, and since x is a function of n, g (x) =0 can be further expressed as g (x) = h (n) =0. In the formula (5), U safe Represents the safety voltage, I, prescribed for TN-C earthed systems set The method is an action setting value of zero sequence protection on a line in the TN-C grounding system.
By combining formula (1) and formula (5), the optimization model shown in formula (6) can be formed.
Figure GDA0003741696280000062
Wherein f is 1 (n) is the total grounding cost of the TN-C grounding system; f. of 2 (n) is single-phase connection of TN-C grounding systemThe reciprocal of the fault phase zero sequence current modulus at the time of ground fault; f. of 3 (n) is the device contact voltage; h (n) represents a mapping relation, U, satisfied when the power grid complies with kirchhoff's law constraint safe Indicating the safety voltage, I, prescribed by the TN-C grounding system set The action setting value of zero sequence protection on a circuit in the TN-C grounding system is represented;
step 2, obtaining the optimal grounding quantity based on the multi-objective optimization model;
step 2-1, constructing an unconstrained weighting function based on the multi-objective optimization model, and modifying the objective function shown in the formula (6) into each objective weighted sum shown in the formula (7) in an unconstrained form, wherein the specific formula is as follows:
Figure GDA0003741696280000071
wherein u is 1 、u 2 And u 3 Are all weighting coefficients, α, β, λ k Are penalty coefficients, N is the total number of the equation represented by h (N) =0 in the formula (6), h k (n) is the kth element of the h (n) vector;
and 2-2, solving the optimal grounding number n based on the weighting function of the formula (7). Specifically, in this step, the existing mature algorithm may be selected to solve the formula (7), and as a feasible implementation, the particle swarm optimization algorithm is adopted to solve the weighting function of the formula (7) in step 2-2 to obtain the optimal ground number n.
The specific calculation process of the present invention is described below with respect to a specific embodiment:
taking the system shown in fig. 1 as an example, for simplicity, the resistance R on the horizontal ground in the actual grid is taken into account 1 Relatively small, this example takes R approximately 1 =0, the equivalent resistance to the earth system as seen from point O is R, according to fig. 1 O =n×R 2 Wherein R is 2 Is the ground resistance of each ground electrode.
In this example, the system to the left of the bus B is assumed to be an infinite power system, i.e. the second transient supply potential
Figure GDA0003741696280000072
When short circuit occurs, the impedance is zero, and the impedance formed by winding resistance and leakage reactance of transformer is Z T And the equivalent ground impedance of the parallel device is Z D And mutual inductance between the effective conductive part of the device and the housing is jX M
According to fig. 1, assuming that the cost of laying each grounding electrode is C, and n grounding electrodes are laid in total, according to the above steps, the following steps can be obtained: f. of 1 (n)=cn。
In fig. 1, when a single-phase ground fault occurs at point f, the equivalent positive sequence impedance viewed from point f is:
Z 1∑ =(Z T +Z L(1) )//Z D +Z′ L(1) (e1)
z in the formula (e 1) L(1) 、Z′ L(1) Are positive sequence impedances of the supply lines, the former to the left of the device in fig. 1 and the latter to the right of the device in fig. 1.
The equivalent negative sequence impedance as seen from point f is:
Z 1∑ =(Z T +Z L(2) )//Z D +Z′ L(2) (e2)
z in the formula (e 2) L(2) 、Z′ L(2) Are positive sequence impedances of the supply lines, the former to the left of the device in fig. 1 and the latter to the right of the device in fig. 1.
The equivalent zero-sequence impedance seen from point f is:
Z 0∑ =(Z T +Z L(0) +3nR 2 )//Z D +Z′ L(0) (e3)
when a single-phase earth fault occurs at point f, the constraint that the corresponding circuit in fig. 1 should satisfy according to kirchhoff's law is as follows:
Figure GDA0003741696280000081
in the formula (e 4), the reaction mixture,
Figure GDA0003741696280000082
positive, negative and zero sequence voltages of respective fault points
Figure GDA0003741696280000083
Figure GDA0003741696280000084
The positive sequence current, the negative sequence current and the zero sequence current flowing through the fault point respectively, and the six quantities form a state vector x of the system, namely:
Figure GDA0003741696280000085
the abbreviation is written for equation (e 4) as:
g(x)=0 (e6)
given the parameters of the system, it can be seen from the previous analysis that Z is a factor 0∑ Is a function of n, so x in equation (e 6) is necessarily a function of n, and therefore equation (e 6) can be written in the abbreviated form shown in equation (e 7):
h(n)=0 (e7)
the result shown in formula (e 8) can be obtained from formula (4) and FIG. 1.
Figure GDA0003741696280000086
In the formula (e 8)
Figure GDA0003741696280000087
Is a fault phase zero sequence current.
By the formula (e 8)
Figure GDA0003741696280000088
Taking the reciprocal after taking the modulus value to further obtain f 2 (n)=1/I 0
The results shown in formula (e 9) can be obtained from formula (e 8).
Figure GDA0003741696280000091
General formula (e 9)
Figure GDA0003741696280000092
Further taking the modulus value to obtain f 3 (n)=U T
From the above, a multi-objective optimization model for calculating the number of grounding points of the system shown in FIG. 1 can be written, in this example, U safe Is taken as 36V set When 0.1A is taken, the model shown by the formula (e 10) can be obtained.
Figure GDA0003741696280000093
Next, this example will solve the model given by equation (e 10) in the form of equation (7) described in the aforementioned application. The weighting factor for each term in equation (7) can be given based on the importance of each term, in this case μ 1 Is taken as 0.2, mu 2 And mu 3 Are all taken to be 0.4, in order to guarantee constraint, in this example α, β, λ k Take larger values, all taken as 100.
Next, the model shown in formula (7) is solved by using the basic particle swarm optimization. The basic form of iteration is shown as equation (e 11).
Figure GDA0003741696280000094
In the formula (e 11), the reaction mixture,
Figure GDA0003741696280000095
is the position of the particle i at the k iteration;
Figure GDA0003741696280000096
the speed of the k-th iteration of the particle i is generally required to be satisfied
Figure GDA0003741696280000097
P best·i Is the optimal solution experienced by the particle i itself; g best An optimal solution experienced for the entire population of particles; w is the coefficient of inertia, in this example decreasing in a linear manner from 0.9 to 0.1; c. C 1 、c 2 For the acceleration constant, the value is taken to be 2 in this example; r is 1 、r 2 Is [0,1]Random numbers are uniformly distributed in the interval. In a specific iteration, x is taken as the number n of the grounding electrodes to be solved in this example.
In this example, the parameters R in FIG. 1 2 Taken as 5 omega, Z T Is taken as 0.02+j0.3 omega, Z D Is taken as 0.4+ j1 omega, jX M Taken as 0.2 omega, Z L(1) Is taken as 0.6 j0.8 omega, Z L(2) Is taken as 0.6 j0.8 omega, Z L(0) Taken as 0.8+j2.4 omega, Z' L(1) Taken as 0.3+ j0.4 omega, Z' L(2) Taken as 0.3+ j0.4 omega, Z' L(0) Take as 0.4+ j1.2 omega. And (4) iteratively calculating according to the formula (e 11) by using the programmed program, wherein the calculation result of the number n of the grounding electrodes is 11, namely the target shown in the formula (e 10) is achieved, and 11 grounding electrodes are needed in total.
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Claims (5)

1. The method for calculating the number of grounding points of the TN-C grounding system based on multi-objective optimization is characterized by comprising the following steps: which comprises the following steps:
step 1, constructing a multi-objective optimization model for calculating the number of grounding points of the TN-C grounding system;
step 1-1, constructing an objective function, wherein a specific formula is as follows:
minf(n)=[f 1 (n),f 2 (n),f 3 (n)] (1)
wherein f is 1 (n) is the total grounding cost of the TN-C grounding system; f. of 2 (n) is the reciprocal of a fault phase zero sequence current modulus value when a single-phase earth fault occurs in the TN-C grounding system; f. of 3 (n) is the device contact voltage; n is the number of grounding points at the TN-C grounding system, and the n grounding points are uniformly distributed;
f 1 (n) is expressed as the following formula:
f 1 (n)=cn (2)
Wherein, c is the comprehensive investment of each set of grounding device;
f 2 (n) is expressed as the following formula:
f 2 (n)=1/I 0 (3)
wherein, I 0 Indicating fault phase zero sequence current phasor when single-phase earth fault occurs in TN-C grounding system
Figure FDA0003741696270000013
A modulus value of (d);
f 3 (n) is expressed as the following equation:
f 3 (n)=U T (4)
wherein, U T Indicating device contact voltage
Figure FDA0003741696270000011
A modulus value of (d);
step 1-2, constructing a multi-objective optimization model based on constraint conditions: the method comprises the following steps of constructing a multi-objective optimization model for calculating the number of grounding points of the TN-C grounding system based on equality constraints and inequality constraints of the TN-C grounding system, and specifically comprising the following steps:
Figure FDA0003741696270000012
wherein h (n) represents a mapping relation which is satisfied when the power grid complies with kirchhoff law constraints, and U safe Indicating the safety voltage, I, prescribed by the TN-C grounding system set The action setting value of zero sequence protection on the line in the TN-C grounding system is represented;
step 2, calculating and obtaining the optimal grounding number based on the multi-objective optimization model;
step 2-1, constructing an unconstrained weighting function based on the multi-objective optimization model, wherein the formula is as follows:
Figure FDA0003741696270000021
wherein, mu 1 、μ 2 And mu 3 Are all weighting coefficients, α, β, λ k N is the total number of the equation represented by h (N) =0 in the formula (6), h is a penalty coefficient k (n) is the kth element of the h (n) vector;
and 2-2, solving the optimal grounding number n based on the weighting function of the formula (7).
2. The method for calculating the number of grounding points of the TN-C grounding system based on multi-objective optimization according to claim 1, wherein: mu in step 2-1 1 Is taken to be 0.2 mu 2 And mu 3 Are all taken as 0.4; alpha, beta, lambda k Are all taken as 100.
3. The method for calculating the number of grounding points of the TN-C grounding system based on multi-objective optimization according to claim 1, wherein: and 2-2, solving the optimal grounding number n by adopting a particle swarm optimization algorithm based on the weighting function of the formula (7).
4. The method for calculating the grounding point number of the TN-C grounding system based on multi-objective optimization according to claim 3, wherein: the iteration basic form of the particle swarm optimization algorithm is as follows:
Figure FDA0003741696270000022
wherein the content of the first and second substances,
Figure FDA0003741696270000023
the iteration position of the particle i at the kth time is taken;
Figure FDA0003741696270000024
the iteration speed of the particle i at the k time is satisfied
Figure FDA0003741696270000025
Figure FDA0003741696270000026
P best·i Is the optimal solution experienced by the particle i itself; g is a radical of formula best An optimal solution experienced for the entire population of particles; w is an inertia coefficient which decreases in a linear manner from 0.9 to 0.1; c. C 1 、c 2 Is an acceleration constant, r 1 、r 2 Is [0,1]And uniformly distributing random numbers in the interval, and taking x as the number n of the grounding electrodes to be solved during iteration.
5. The method for calculating the number of grounding points of the TN-C grounding system based on multi-objective optimization according to claim 4, wherein: c. C 1 、c 2 The values of (c) were all taken to be 2.
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