CN104484832A - Method for evaluating total supplying capability of 220KV Lashou net - Google Patents
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Abstract
The invention provides a method for evaluating the total supplying capability of a 220KV Lashou net. The method comprises the following steps of obtaining a space truss structure of the 220KV Lashou net, determining the network node number and the branch number of the space truss structure, and numbering the nodes and the branches of the space truss structure; reading the parameter and the load parameter of the space truss structure as well as the voltage amplitude and the phase angle of a balance node for the numbered space truss structure of the 220KV Lashou net; according to the constraint of the preset node voltage Vi and the phase angle difference deltaij as well as a PQnode and a balance node, obtaining an initialized Newton-Ralfson's method; obtaining an initialized self-adaptive differential evolutionary algorithm; according to the Newton-Ralfson's method, solving the tidal current of the 220KV Lashou net, and processing the tidal current by the self-adaptive differential evolutionary algorithm to obtain the total supplying capability of 220KV Lashou net under a N-1 constraint. According to the method, a district can be taken as a minimum unit to evaluate the total supplying capability, and the total supplying capability of the 220KV Lashou net can be quickly and accurately obtained when the N-1 condition is satisfied.
Description
Technical Field
The invention relates to the technical field of power supply capacity of a power grid, in particular to a method for evaluating the maximum power supply capacity of a 220KV handhold network.
Background
With the development of economy in China, the living standard of people is continuously improved, and the demand for electric energy is continuously increased. The increase of the power load is obviously accelerated, so that the power quality, the power supply capacity and the power supply reliability cannot meet the power demand of users, and a plurality of power supply bottlenecks are formed. However, the urban power grid is basically built at present, and it is very difficult to obtain the site of a new substation and the underground passage of a new feeder from the planning and reconstruction of the system. Therefore, it becomes important to study the maximum power supply capacity of the grid without constructing underground tunnels for new power stations and feeders.
The TSC (Total supply Capacity) refers to the condition that a power grid in a certain power supply area meets the N-1 safety criterion and the maximum load supply Capacity under the actual operation condition of the network is considered. Common methods for solving the maximum power supply capacity of the power grid include a linear programming method, an interior point method, an attempt method, a maximum load multiple method and the like. The Available Transmission Capacity (ATC) refers to the transmission Capacity remaining in the actual physical transmission network for commercial use on the basis of the existing transmission contract, compared to the maximum power supply Capacity. The TSC emphasizes the maximum load that the grid can carry under certain constraints, and the ATC focuses on the maximum power that can be transmitted in the transmission network after subtracting the basic power flow and a suitable margin on the basis of the maximum transmission capacity.
At present, the common methods for determining the maximum power supply capacity of the power grid include a linear programming method, an attempt method, a maximum load multiple method and the like.
The linear programming method is based on a direct current power flow model, and influence of reactive power and voltage is not considered, so that accuracy and effectiveness of results are influenced; the trial method solution process is time-consuming, and the accuracy of the result is difficult to guarantee; the maximum load multiple method is high in solving speed, but the load of each node is supposed to increase in the same proportion, so that the accuracy is reduced.
Disclosure of Invention
Based on the above, the invention provides a method for evaluating the maximum power supply capacity of the 220KV handhold network, which can evaluate the maximum power supply capacity by taking a parcel as a minimum unit and quickly and accurately determine the maximum power supply capacity of the 220KV handhold network under the condition of meeting N-1.
A method for evaluating the maximum power supply capacity of a 220KV handhold network comprises the following steps:
acquiring a grid structure of a 220KV handhold network, determining the number of network nodes and the number of branches of the grid structure, and numbering the nodes and the branches of the grid structure; the balance node of the 220kV handle net is the 220kV side of a main transformer of a 500kV transformer substation, and the PQ node is a load node in the 220kV handle net;
reading the parameters of the space truss structure, the load parameters and the voltage amplitude V of the balance node for the space truss structure of the numbered 220KV handhold netnAnd phase angle thetan；
According to a preset node voltage ViPhase angle differenceijConstraining, and obtaining an initialized Newton-Raphson method by the PQ node and the balance node;
according to initialization of loads of all nodes, population X obtained by carrying out population expansion processing on a preset initial population, maximum iteration times Gm of a preset differential evolution algorithm and minimum value F0 of a self-adaptive scaling factorminAnd maximum value F0maxSelf-adaptive traffic controlMinimum value CR of cross probability factorminAnd maximum value CRmaxObtaining an initialized self-adaptive differential evolution algorithm; the initialization of the node load is carried out according to the following formula, and the average value of the upper limit value and the lower limit value of each load is taken to generate an initial population:in the formula S i Respectively the maximum value and the minimum value of the rated load of the node i;
and solving the power flow of the 220KV handle network according to the Newton-Raphson method, and processing the power flow through the self-adaptive differential evolution algorithm to obtain the maximum power supply capacity of the 220KV handle network under the constraint of N-1.
According to the method for evaluating the maximum power supply capacity of the 220KV handhold network, the Newton-Raphson method is embedded in the self-adaptive differential evolution method, the embedded Newton-Raphson method is used for accurately solving the power flow of the handhold network, and the self-adaptive differential evolution algorithm is used for rapidly processing the power flow solved by the Newton-Raphson method so as to rapidly and accurately solve the maximum power supply capacity of the handhold network under the constraint of N-1; the method can calculate the maximum power supply capacity by taking the parcel as the minimum unit, and has the characteristics of good stability, high precision, strong global search capacity and the like.
Drawings
Fig. 1 is a schematic flow chart of a method for evaluating the maximum power supply capacity of a 220KV trolley network according to an embodiment of the present invention.
Fig. 2 is a schematic view of a typical pull tab net.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
As shown in fig. 1, a method for evaluating the maximum power supply capacity of a 220KV hand-held network of the present invention comprises the following steps:
s11, acquiring a grid structure of the 220KV handhold net, determining the number of network nodes and the number of branches of the grid structure, and numbering the nodes and the branches of the grid structure; the balance node of the 220kV handle net is the 220kV side of a main transformer of a 500kV transformer substation, and the PQ node is a load node in the 220kV handle net;
s12, reading the grid structure parameters, the load parameters and the voltage amplitude V of the balance nodes of the numbered grid structure of the 220KV handhold netnAnd phase angle thetan；
S13, according to the preset node voltage ViPhase angle differenceijConstraining, and obtaining an initialized Newton-Raphson method by the PQ node and the balance node;
s14, carrying out group expanding processing on a preset initial group according to initialization of each node load to obtain a group X, a preset maximum iteration number Gm of a differential evolution algorithm and a minimum value F0 of a self-adaptive scaling factorminAnd maximum value F0maxAdaptive crossover probability factor minimum CRminAnd maximum value CRmaxObtaining an initialized self-adaptive differential evolution algorithm; the initialization of the node load is carried out according to the following formula, and the average value of the upper limit value and the lower limit value of each load is taken to generate an initial population:in the formula S i Respectively the maximum value and the minimum value of the rated load of the node i;
s15, solving the power flow of the 220KV Laplacian network according to the Newton-Raphson method, and processing the power flow through the self-adaptive differential evolution algorithm to obtain the maximum power supply capacity of the 220KV Laplacian network under the constraint of N-1;
the maximum power supply capacity refers to the maximum load supply capacity of a power grid in a certain power supply area, which meets the N-1 safety criterion and takes the actual operation condition of the network into consideration. The method for calculating the maximum power supply capacity of the 220KV handhold network is an adaptive differential evolution method embedded with a Newton Raphson method, the embedded Newton Raphson method is used for accurately solving the power flow of the handhold network, and the adaptive differential evolution method is used for rapidly processing the power flow solved by the Newton Raphson method so as to rapidly and accurately solve the maximum power supply capacity of the handhold network under the constraint of N-1.
Specifically, the method comprises the following steps:
firstly, a typical pull net structure of 220kV is extracted. In a 220kV handle network, the number of power supply points of an upper-level power grid is generally two, the power supply points are generally on the 220kV side of a main transformer of a 500kV transformer substation, and the power supply points are generally regarded as balance nodes; the other load nodes are generally referred to as PQ nodes. Determining the number of network nodes and the number of branches in the net rack, and numbering from left to right in sequence;
the pull net refers to a topological structure of a power grid formed in a manner of pulling a hand, and as shown in fig. 2, a typical pull net schematic diagram is shown.
And secondly, inputting simplified net rack data. Reading 220kV handle net rack structure parameters (namely, each branch resistance R)iReactance XiAnd a ground susceptance value BiAnd maximum ampacity Imax) Load parameter (maximum load value at each load point)And minimum load valueSd i ) And a voltage amplitude V given by the balancing nodenAnd phase angle thetan。
And initializing the Newton Raphson method. The main steps include the voltage V of the nodeiAngle of sumDifference (D)ijThe setting of constraints, the identification of PQ nodes and balancing nodes, etc.
Because the pull net has two balance nodes, the Newton-Raphson method is adopted to calculate the load flow in order to ensure the accuracy of calculation. In the calculation process, 3 load iterations of 220KV can converge with the calculation error being almost zero. The steps of calculating the power flow by using the Newton Raphson method are as follows:
step 21, inputting original data: if the voltage Vn and the phase angle theta n of the 220kV side of the main transformer of the two 500KV transformer substations, the parameters of the net rack, the voltage constraint and the phase angle difference constraint are input;
step 22, forming a node admittance matrix, and modifying the node admittance matrix according to the N-1 fault criterion;
step 23, calculating the power unbalance amount of each node <math>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>ΔP</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>ΔQ</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
</math> (in the formula, delta P and delta Q respectively refer to active power deviation and reactive power deviation of the nodes), and whether the maximum power flow deviation meets the convergence condition is judged; if yes, jumping to step 26, and if not, performing step 24; the calculation formula of the power flow deviation is as follows:
step 24, generating a load flow calculation Jacobian matrix J by the input variables and the existing node admittance matrix:
wherein H is a (n-1) -order square matrix having elements ofN is an (N-1) x m-order matrix of elementsK is a matrix of order mx (n-1) having elements ofL is an m-th order square matrix having elements of <math>
<mrow>
<msub>
<mi>L</mi>
<mi>ij</mi>
</msub>
<mo>=</mo>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mfrac>
<mrow>
<mo>∂</mo>
<mi>Δ</mi>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<mo>∂</mo>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
</math>
Step 25, solving the linear correction equation set <math>
<mrow>
<mo>-</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>ΔP</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>ΔQ</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>H</mi>
</mtd>
<mtd>
<mi>N</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>K</mi>
</mtd>
<mtd>
<mi>L</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>Δθ</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>V</mi>
<mi>D</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mi>ΔV</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
</math> WhereinObtaining the correction quantities delta theta and delta V of the voltage amplitude and the phase angle of each node, updating the node voltage, and jumping to the step 23;
step 26, calculating the power of all branches according to the following formula:
wherein, i is the first node of the branch, j is the last node of the branch, and the wave number represents the conjugate value of the complex number.
And fourthly, initializing the adaptive differential algorithm (DE). The method mainly comprises the steps of initializing loads of all nodes, carrying out population expansion processing on an initial population to obtain a population X, setting the maximum iteration number Gm of a differential evolution algorithm, and setting the minimum value F0 of a self-adaptive scaling factorminAnd maximum value F0maxSetting of (2), adaptive crossover probability factor minimum value CRminAnd maximum value CRmaxAnd the like. The initialization of the node load is obtained by taking the average value of the upper limit value and the lower limit value of each load to generate an initial population, and the specific formula is as follows:in the formula S i Respectively the maximum value and the minimum value of the rated load of the node i;
for the preset population individual Xi＝{Si1,Si2,…,SimPerforming group expansion operation to obtain an initialized group omega ═ X1,X2,…,Xnp}; wherein np is a preset population expansion parameter, and each individual X in the populationiThe generation rule of each variable in (1) is as follows: <math>
<mrow>
<msubsup>
<mi>S</mi>
<mi>ij</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>S</mi>
<mi>ij</mi>
<mi>min</mi>
</msubsup>
<mo>+</mo>
<mi>rand</mi>
<mrow>
<mo>(</mo>
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<mo>)</mo>
</mrow>
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<mrow>
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<mi>ij</mi>
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</msubsup>
<mo>-</mo>
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<mi>S</mi>
<mi>ij</mi>
<mi>min</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</math> in the formula,andare each XiThe minimum value and the maximum value of the jth component in the sequence, and rand (0,1) is a uniformly distributed random number between (0, 1);
the key steps of the self-adaptive differential evolution algorithm comprise:
1. cross-handling
Two individual vectors are randomly selected to generate a difference vector, and the generated difference vector is added to another vector randomly selected to generate a variation vector. The concrete formula is as follows:in the formula xr1、xr2、xr3Representing 3 different individuals in the population. t represents the current state and t +1 represents the next generation state.
Wherein, the scaling factor of the mutation operation adopts a self-adaptive strategy, and the specific formula is as follows:
wherein F0l、F0uUpper and lower limits, F, of F0, respectivelyt1、ft2、ft3Are respectively asThe fitness of (2);
2. mutation treatment
The variation vectorCrossing the target vectorGenerating cross vectorsThe concrete formula is as follows: <math>
<mrow>
<msubsup>
<mi>ui</mi>
<mi>j</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<mfenced open='{' close=''>
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>v</mi>
<mi>ij</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>,</mo>
<mi>rand</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>≤</mo>
<mi>CR</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>x</mi>
<mi>ij</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>,</mo>
<mi>otherwise</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
</math> wherein rand (j) is epsilon [0, 1-]CR is a cross probability factor for a uniformly distributed random function.
The cross probability factor adopts a self-adaptive strategy, and the specific formula is as follows:
in the formula, CRmin and CRmax are respectively a minimum cross probability factor and a maximum cross probability factor, and T is the maximum iteration number;
3. selection process
If it is notIs adapted toIs superior toIs adapted toThen useInstead of the formerAnd is selected as the next generation; otherwiseAs the next generation. And selecting by using a preset greedy search strategy and taking the maximum load level as an objective function.
And fifthly, optimizing and realizing.
Step 31, judging whether the current iteration number reaches the maximum value, if not, performing step 32, and if the iteration number reaches the set iteration number or the calculated precision meets the requirement, skipping to step 39;
and 32, carrying out variation treatment on the population X after population expansion to obtain a variation population XVar: randomly selecting two individual vectors to generate a differential vector, and adding the generated differential vector and another randomly selected vector to generate a variation vector; wherein, the scaling factor of the mutation operation adopts a self-adaptive strategy, and the specific formula is as follows:wherein F0min、F0maxRespectively, a predetermined upper and lower limit, F, of F0t1、ft2、ft3Are respectively asThe fitness of (2);
and step 33, performing cross processing on the variant population XVar to obtain a cross population Xcross: crossing the variation vector and the target vector to generate a cross vector; the cross probability factor adopts a self-adaptive strategy, and the specific formula is as follows:in the formula, CRmin and CRmax are respectively a minimum cross probability factor and a maximum cross probability factor, and T is the maximum iteration number;
step 34, judging whether population traversal is completed, if not, performing step 35, otherwise, performing 1 addition processing on the iteration times, and jumping to step 31;
step 35, calculating the initial population X and the cross population Xcross at the same time, namely respectively substituting the population X and the population Xcross into the Newton Raphson method according to the dimension (each dimension represents the load value of each node), and performing load flow calculation when the ground state and the N-1 are in fault; wherein each of the dimensions represents a load value of a respective node;
step 36, checking the power flow when the ground state and the N-1 are in fault, if all the checks are passed, performing step 37, otherwise, adding 1 to the number of traversed variables, and skipping to step 34;
step 37, taking a preset maximum power supply capacity mathematical model as a self-adaptive function, wherein a calculation formula is as follows:whereinRepresenting the active load of the node i, namely the ith number in one dimension in the population X or Xcross; the value with larger fitness is saved, which is possible to obtain the maximum power supply capacity;
step 38, updating the population X: updating the dimension value with the fitness larger than the preset value to the same dimension of the population X;
and step 39, exiting iteration and outputting the numerical value of the maximum power supply capacity.
Wherein the maximum power supply capability mathematical model may be described as: and taking the maximum power supply capacity as an objective function, taking the N-1 safety criterion into consideration according to the definition of the maximum power supply capacity, and taking the actual conditions of network operation into consideration, including the constraints of main transformer capacity, network topology structure, line overload capacity and the like, so as to obtain the maximum power supply capacity. The specific mathematical model is as follows:
the state variables are as follows: including apparent power S of each load pointdiAnd power factor angle (impedance angle)Voltage amplitude V of nodeiPhase angle differenceij. Considering the actual operation condition of a 220kV power grid, the power factors of all load points are consideredAre all set to 0.98.
An objective function: taking the maximum power supply capacity as an objective function, namely taking the sum of the active power of each load node as the objective function
The constraint conditions include:
1) load restraint
2) Line transmission power constraint
3) Upper and lower limit constraints of node voltage
4) Upper and lower constraint of phase angle
|i-j|＜|i-j|max (5)
In the formula,S di、respectively, a lower limit value and an upper limit value of the apparent power of the node i;S ij、respectively is the lower limit value and the upper limit value of the transmission power of the line from the node i to the node j branch;V i、respectively, the lower and upper limit values of the voltage at node i.
The invention relates to a method for evaluating the maximum power supply capacity of a 220KV handhold network, wherein a Newton-Raphson method is embedded in an adaptive differential evolution method, the embedded Newton-Raphson method is used for accurately solving the power flow of the handhold network, and the adaptive differential evolution method is used for rapidly processing the power flow solved by the Newton-Raphson method so as to rapidly and accurately solve the maximum power supply capacity of the handhold network under the constraint of N-1; the method can calculate the maximum power supply capacity by taking the parcel as the minimum unit, and has the characteristics of good stability, high precision, strong global search capacity and the like.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (6)
1. A method for evaluating the maximum power supply capacity of a 220KV handhold network is characterized by comprising the following steps:
acquiring a grid structure of a 220KV handhold network, determining the number of network nodes and the number of branches of the grid structure, and numbering the nodes and the branches of the grid structure; the balance node of the 220kV handle net is the 220kV side of a main transformer of a 500kV transformer substation, and the PQ node is a load node in the 220kV handle net;
reading grid structure parameters, load parameters and balance nodes of the numbered grid structure of the 220KV handhold netAmplitude of voltage VnAnd phase angle thetan；
According to a preset node voltage ViPhase angle differenceijConstraining, and obtaining an initialized Newton-Raphson method by the PQ node and the balance node;
according to initialization of loads of all nodes, population X obtained by carrying out population expansion processing on a preset initial population, maximum iteration times Gm of a preset differential evolution algorithm and minimum value F0 of a self-adaptive scaling factorminAnd maximum value F0maxAdaptive crossover probability factor minimum CRminAnd maximum value CRmaxObtaining an initialized self-adaptive differential evolution algorithm; the initialization of the node load is carried out according to the following formula, and the average value of the upper limit value and the lower limit value of each load is taken to generate an initial population:in the formulaRespectively the maximum value and the minimum value of the rated load of the node i;
and solving the power flow of the 220KV handle network according to the Newton-Raphson method, and processing the power flow through the self-adaptive differential evolution algorithm to obtain the maximum power supply capacity of the 220KV handle network under the constraint of N-1.
2. The method for evaluating the maximum power supply capacity of a 220KV handhold network as recited in claim 1, wherein the step of solving the power flow of the 220KV handhold network according to the newton-raphson method comprises:
step 21, inputting original data: voltage Vn and phase angle theta n at 220kV side of main transformers of two 500KV transformer substations, parameters of a net rack, voltage constraint and constraint of phase angle difference;
step 22, forming a node admittance matrix, and modifying the node admittance matrix according to the N-1 fault;
step 23, calculating the power unbalance amount of each node <math>
<mrow>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>ΔP</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>ΔQ</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
</math> Judging whether the maximum power flow deviation meets a convergence condition or not; if yes, jumping to step 26, and if not, performing step 24; the calculation formula of the power flow deviation is as follows:
wherein, the delta P and the delta Q are respectively the active power deviation and the reactive power deviation of the node, Pis、QisThe active power and the reactive power are given to the ith node; vi、VjThe voltages of the ith node and the jth node respectively; gij、BijAre respectively asConductance and susceptance of the branch from node i to node j; thetaijIs the phase angle difference between the node i and the node j;
step 24, generating a load flow by the input variables and the existing node admittance matrix, and calculating a Jacobian matrix J:
wherein H is a (n-1) -order square matrix having elements ofN is an (N-1) x m-order matrix of elementsK is a matrix of order mx (n-1) having elements ofL is an m-th order square matrix having elements of <math>
<mrow>
<msub>
<mi>L</mi>
<mi>ij</mi>
</msub>
<mo>=</mo>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mfrac>
<msub>
<mrow>
<mo>∂</mo>
<mi>ΔQ</mi>
</mrow>
<mi>i</mi>
</msub>
<msub>
<mrow>
<mo>∂</mo>
<mi>V</mi>
</mrow>
<mi>j</mi>
</msub>
</mfrac>
<mo>;</mo>
</mrow>
</math>
Step 25, solving the linear correction equation set <math>
<mrow>
<mo>-</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>ΔP</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>ΔQ</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>H</mi>
</mtd>
<mtd>
<mi>N</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>K</mi>
</mtd>
<mtd>
<mi>L</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mi>Δθ</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>V</mi>
<mi>D</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mi>ΔV</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
</math> WhereinObtaining the correction quantities delta theta and delta V of the voltage amplitude and the phase angle of each node, updating the node voltage, and jumping to the step 23;
step 26, calculating the power of all branches according to the following formula:
wherein, i is the first node of the branch, j is the last node of the branch, and the wave number represents the conjugate value of the complex number.
3. The method for calculating the maximum power supply capacity of the 220KV handhold network according to claim 2, wherein the step of processing the power flow through the adaptive differential evolution algorithm to obtain the maximum power supply capacity of the 220KV handhold network under the N-1 constraint comprises the following steps:
step 31, judging whether the current iteration number reaches the maximum value, if not, performing step 32, and if the iteration number reaches the set iteration number or the calculated precision meets the requirement, skipping to step 39;
and 32, carrying out variation treatment on the population X after population expansion to obtain a variation population XVar: randomly selecting two individual vectors to generate a differential vector, and adding the generated differential vector and another randomly selected vector to generate a variation vector;
and step 33, performing cross processing on the variant population XVar to obtain a cross population Xcross: crossing the variation vector and the target vector to generate a cross vector;
step 34, judging whether population traversal is completed, if not, performing step 35, otherwise, performing 1 addition processing on the iteration times, and jumping to step 31;
step 35, calculating the initial population X and the cross population Xcross simultaneously, namely substituting the population X and the population Xcross into the Newton Raphson method according to the dimensions respectively to calculate the power flow when the ground state and the N-1 are in fault; wherein each of the dimensions represents a load value of a respective node;
step 36, checking the power flow when the ground state and the N-1 are in fault, if all the checks are passed, performing step 37, otherwise, adding 1 to the number of traversed variables, and skipping to step 34;
step 37, taking a preset maximum power supply capacity mathematical model as a self-adaptive function, wherein a calculation formula is as follows:whereinRepresenting the active load of the node i, namely the ith number in one dimension in the population X or Xcross;
step 38, updating the population X: updating the dimension value which is properly larger than the preset value to the same dimension of the population X;
and step 39, outputting the value of the maximum power supply capacity.
4. The method for calculating the maximum power supply capacity of the 220KV shaking net according to claim 3, wherein the state variables of the mathematical model of the maximum power supply capacity comprise: apparent power S of each load pointdiAngle of power factorVoltage amplitude V of nodeiAnd phase angle differenceij；
The objective function of the mathematical model of the maximum power supply capacity is the maximum power supply capacity, and the sum of the active powers of the load nodes is calculated as the objective function according to the following formula:
the constraint conditions of the maximum power supply capacity mathematical model are as follows: and (3) load restraint:constraint of line transmission power:and (3) limiting the upper and lower limits of the node voltage:and phase angle upper and lower constraints: non-viable cellsi-j|＜|i-j|max；
Wherein,respectively, a lower limit value and an upper limit value of the apparent power of the node i;respectively is the lower limit value and the upper limit value of the transmission power of the line from the node i to the node j branch;respectively, the lower and upper limit values of the voltage at node i.
5. The method for evaluating the maximum power supply capacity of a 220KV hand-held network according to claim 3, wherein the cross-over process is: randomly selecting two individual vectors to generate a difference vector, and adding the generated difference vector to another vector randomly selected to generate a variation vector according to the following formula:
in the formula xr1、xr2、xr3Representing 3 different individuals in the population.
6. The method for evaluating the maximum power supply capacity of a 220KV hand-held network according to claim 3, wherein the mutation process comprises:
the variation vector is calculated according to the following formulaCrossing the target vectorGenerating cross vectors
the cross probability factor adopts a self-adaptive strategy:in the formula, CRmin and CRmax are respectively a minimum cross probability factor and a maximum cross probability factor, and T is the maximum iteration number.
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