CN111934320A - Active power distribution network rapid reconstruction method based on linear power flow equation and improved firework algorithm - Google Patents

Active power distribution network rapid reconstruction method based on linear power flow equation and improved firework algorithm Download PDF

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CN111934320A
CN111934320A CN202010843843.3A CN202010843843A CN111934320A CN 111934320 A CN111934320 A CN 111934320A CN 202010843843 A CN202010843843 A CN 202010843843A CN 111934320 A CN111934320 A CN 111934320A
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徐艳春
罗凯
汪平
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China Three Gorges University CTGU
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    • H—ELECTRICITY
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Abstract

The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm comprises the following steps: the typical characteristics of the power distribution network are combined, and the simplified conditions suitable for the power distribution network are quantitatively analyzed; on the basis of considering a distributed power supply and a ZIP load model, carrying out linearization processing on a nonlinear high-dimensional power flow equation according to simplified conditions of a power distribution network to obtain a group of linear power flow equations; in order to improve the convergence rate of the firework algorithm, the firework algorithm is improved according to the characteristics of power distribution network reconstruction; establishing a comprehensive objective function of the power distribution network, and constructing an active power distribution network reconstruction model; and solving the active power distribution network reconstruction model by combining a linear power flow equation and an improved firework algorithm. The invention provides a rapid active power distribution network reconstruction method based on a linear power flow equation and an improved firework algorithm.

Description

Active power distribution network rapid reconstruction method based on linear power flow equation and improved firework algorithm
Technical Field
The invention relates to the technical field of active power distribution network reconstruction, in particular to a rapid active power distribution network reconstruction method based on a linear power flow equation and an improved firework algorithm.
Background
In recent years, with the problems of insufficient energy, environmental pollution and the like becoming more serious, distributed power generation has attracted more and more attention as a new energy utilization mode. Compared with a large power grid with centralized power supply, the unique environmental protection and economy and the higher energy conversion rate of the power grid become important measures for adjusting energy structures, and the power grid is an important direction for future development of power distribution systems. When a Distributed Generation (DG) is connected to a power Distribution network, the DG affects the reliability of power supply to the power Distribution network, and therefore, the DG needs to be considered when reconstructing the power Distribution network.
At present, certain achievements are obtained for reconstructing a power distribution network containing DGs. The commonly used power distribution network reconstruction model adopts a power flow calculation method which mainly comprises a forward-backward substitution method, an improved Newton method, a loop impedance method and the like. However, the power flow equations of the methods are nonlinear and involve an iterative process, so that the calculation efficiency is not high, and the requirement of rapid reconstruction of the power distribution network is difficult to meet.
In order to improve the efficiency of the power flow calculation method, many documents have developed relevant researches, and a typical processing method at present is to take a loop analysis method as the theory of power flow calculation according to the structure of a power distribution system tree network, utilize the typical characteristics of a power distribution network to carry out linearization processing on a loop voltage equation, simplify the loop voltage equation into a linear algebraic equation set, and finally obtain a voltage distribution result through one-time formula substitution. Or polynomial fitting is carried out on a trigonometric function item in the basic load flow equation, and the voltage amplitude and the phase angle are decoupled by utilizing the operation characteristics of the system, so that a full-linear load flow equation is obtained. However, the method is not suitable for the power distribution network containing the PV nodes, and is difficult to be directly applied to the active power distribution network reconstruction model. In addition, the power distribution network reconstruction often needs to be solved by adopting an intelligent algorithm. However, the traditional intelligent algorithm has the problems of low solution convergence speed and low efficiency. The firework algorithm is a novel group intelligent optimization algorithm proposed in 2010, has good convergence and robustness in the aspect of solving the problem of high complexity, and is concerned by numerous scholars. But the application of the firework algorithm in the field of power distribution network reconstruction is small at present.
In view of the above, it is of great significance to research a fast active power distribution network reconstruction method based on a linear power flow equation and an improved firework algorithm.
Disclosure of Invention
The method aims at the problems of low calculation efficiency and low universality of the existing active power distribution network reconstruction model. The invention provides a rapid active power distribution network reconstruction method based on a linear power flow equation and an improved firework algorithm.
The technical scheme adopted by the invention is as follows:
an active power distribution network rapid reconstruction method based on a linear power flow equation and an improved firework algorithm,
step 1: the typical characteristics of the active power distribution network are combined, and the simplified conditions suitable for the active power distribution network are quantitatively analyzed;
step 2: performing Taylor series expansion and voltage amplitude and phase angle decoupling on a power flow equation according to the simplified condition of the active power distribution network on the basis of considering a distributed power supply model and a ZIP load model to obtain a group of linear power flow equations;
and step 3: in order to improve the convergence rate of the firework algorithm, the firework algorithm is improved according to the characteristics of the active power distribution network reconstruction;
and 4, step 4: establishing a comprehensive objective function of the active power distribution network, and constructing a reconstruction model of the active power distribution network;
and 5: and solving the active power distribution network reconstruction model by combining a linear power flow equation and an improved firework algorithm.
The invention relates to a rapid active power distribution network reconstruction method based on a linear power flow equation and an improved firework algorithm, which has the following technical effects:
1) the linear power flow equation of the invention is pure numerical operation, the model is simple, the calculated amount is small, the calculating speed is high, the convergence problem does not exist,
2) the linear power flow of the invention not only overcomes the defect that most linear power flow methods cannot process PV type DGs, but also has higher calculation precision.
3) The method improves the firework algorithm, accelerates the convergence speed of the algorithm and improves the stability of the algorithm.
4) The invention provides a rapid active power distribution network reconstruction method based on a linear power flow equation and an improved firework algorithm. The method can improve the network loss, the voltage deviation and the load balance of the power distribution system, and meet the requirement of quick reconstruction of the DG-containing power distribution network.
Drawings
Fig. 1 is a schematic diagram of an IEEE33 node system.
FIG. 2 is a voltage amplitude distribution diagram of each node of the system
Fig. 3 is a voltage deviation graph before and after reconstruction of the distribution network.
FIG. 4 is a graph of algorithm stability analysis and time consumption for model reconstruction.
Detailed Description
An active power distribution network rapid reconstruction method based on a linear power flow equation and an improved firework algorithm,
step 1: the typical characteristics of the active power distribution network are combined, and the simplified conditions suitable for the active power distribution network are quantitatively analyzed;
step 2: performing Taylor series expansion and voltage amplitude and phase angle decoupling on a power flow equation according to the simplified condition of the active power distribution network on the basis of considering a distributed power supply model and a ZIP load model to obtain a group of linear power flow equations;
and step 3: in order to improve the convergence rate of the firework algorithm, the firework algorithm is improved according to the characteristics of the active power distribution network reconstruction;
and 4, step 4: establishing a comprehensive objective function of the active power distribution network, and constructing a reconstruction model of the active power distribution network;
and 5: and solving the active power distribution network reconstruction model by combining a linear power flow equation and an improved firework algorithm.
Preferred embodiments are described in detail below with reference to the accompanying drawings:
1. the simplified conditions suitable for the power distribution network are as follows:
firstly, typical characteristics of the power distribution network are summarized and summarized, and the method mainly comprises the following steps: firstly, the node voltage amplitude approaches to 1.0 p.u.; the phase angles at two ends of the line are very small, so that the voltage phase angles of all nodes in the power distribution network and the voltage phase angles of the balance nodes have little difference; and the ratio of the resistance to the reactance is larger and is close to or larger than 1.
According to the typical characteristics of the power distribution network, the simplification condition of the power distribution network can be deduced, as shown in formula (1):
Figure BDA0002642363630000031
wherein i and j represent the number of the node;i，jphase angles of nodes i and j are respectively;ijis the phase angle difference, V, of the nodes i, jjIs the voltage amplitude of node j; sin for medical useijTo representijIs calculated as a sine function of (c).
2. According to different modes of grid connection of the distributed power supply, the distributed power supply models can be divided into the following three types:
(1) PQ-type DG:
the output power direction of the PQ-type DG is opposite to the load power flowing direction, and the load flow calculation is shown as the formula (2):
Figure BDA0002642363630000032
wherein P, Q are the active power and reactive power of the load, respectively; pG、QGRespectively giving active power and reactive power to DGs;
(2) PV type DG:
the active power and voltage of the PV type DG are known quantities, and the load flow calculation model is shown as the formula (3):
Figure BDA0002642363630000033
in the formula, P is the active power of the load; pG、QGRespectively giving active power and reactive power to DGs; v is the voltage amplitude of the node; vGA node voltage that is DG; qGmaxAnd QGminRespectively the upper and lower reactive power limits of DG.
(3) PI type DG:
the active power and the current of the type DG are constant values, and a load flow calculation model of the type DG is shown as a formula (4):
Figure BDA0002642363630000041
wherein P, Q are the active power and reactive power of the load, respectively; pGActive power given for DG; i isGA constant current output for DG; v is the voltage amplitude of the node; f (V) represents a function related to V.
3. Considering that the size of the load varies with the voltage, a ZIP load model of the node can be established, as shown in equation (5):
Figure BDA0002642363630000042
wherein, P (V), Q (V) respectively represent the node load active power and reactive power. V, VNThe actual voltage and the rated voltage of the node are respectively; pN,QNRespectively representing active power and reactive power at rated voltage. CZ,CI,CPRespectively representing the proportional coefficients of the active constant impedance, the constant current and the constant power load of the node; c'Z,C'I,C'PRespectively representing the proportional coefficients of node reactive constant impedance, constant current and constant power load; the constraint condition satisfied by each parameter is CZ+CI+CP＝1,C'Z+C'I+C'P＝1。
4. The expression of the trend equation is shown in formula (6):
Figure BDA0002642363630000043
wherein i and j represent the number of the node; pLi、QLiLoading active power and reactive power for the node i respectively; pGi、QGiActive power and reactive power which are DGs; vi、VjThe voltage amplitudes of node i and node j, respectively. Gij、BijThe real and imaginary parts of the admittance matrix, respectively.ijIs the voltage phase angle difference between node i and node j. sin for medical useij、cosijAre respectively asijSine function and cosine function.
5. According to the typical characteristics of the power distribution network, the linearization method is shown as the formula (7):
Figure BDA0002642363630000044
wherein y (V) is a voltage amplitude dependent function; k represents the order; y iskRepresents y to the power k; Δ V is the voltage drop; v is the voltage amplitude of the node.
In order to ensure safe and reliable operation of the power equipment, the voltage drop Δ V at each node of the power distribution system is substantially small. As the voltage magnitude V approaches 1p.u., a Taylor-series expansion may be performed on the nonlinear term associated with the voltage magnitude V.
6. The expression of the linear power flow equation is shown in formula (8):
Figure BDA0002642363630000051
wherein h is1＝2，h21 is ═ 1; s, W and R are respectively a balance node, a PQ node and a PV node in the power distribution networkA set of points; pPS，PPW，QPWRespectively balancing constant power coefficients of active power of the nodes, active power of the PQ nodes and reactive power of the PQ nodes; pIS，PIW，QIWConstant current coefficients of active power of a balance node, active power of a PQ node and reactive power of the PQ node are respectively; vS、SRespectively, the voltage amplitude and the phase angle of the balance node; vW、WThe voltage amplitude and the phase angle of the PQ node are respectively; vR、RRespectively PV node voltage amplitude and phase angle; diag (P)PR)、diag(PPW)、diag(QPW) Respectively a constant power load coefficient diagonal matrix of PV node active power, a constant power load coefficient diagonal matrix of PQ node active power and a constant power load coefficient diagonal matrix of PV node reactive power; gRSAnd BRSRespectively a real part and an imaginary part of a mutual admittance matrix of the PV node and the balance node; gWSAnd BWSRespectively a real part and an imaginary part of a mutual admittance matrix of the PQ node and the balance node; gWRAnd BWRThe real part and the imaginary part of the transadmittance matrix of the PQ node and the PV node respectively; gRRAnd BRRThe real part and the imaginary part of the PV node self-admittance matrix are taken as the reference; b isRWAnd GRWThe real part and the imaginary part of the transadmittance matrix of the PQ node and the PV node respectively; gWWAnd BWWThe real part and the imaginary part of the PQ node auto-admittance matrix are respectively.
7. The power distribution network reconstruction model can be solved by adopting a firework algorithm, and the principle of the firework algorithm is as follows:
in the Firework Algorithm, each Firework xiRepresents a feasible solution, each fireworks xiRadius of detonation AiNumber of sparks SiAs shown in formulas (9) and (10):
Figure BDA0002642363630000052
Figure BDA0002642363630000053
in the formula: a. theiFor fireworks xiThe radius of detonation of; siThe number of sparks; m, A respectively represent constants for adjusting the total number of explosion sparks and the explosion radius; y ismax、yminRespectively the maximum value and the minimum value of the fitness of the fireworks; i represents the number of fireworks; n represents the total number of fireworks; f (x)i) Is xiThe fitness value of (a). Is a minimum value.
In the firework algorithm, the smaller the explosion radius of the firework is, the larger the number of explosion sparks is, and the better the fitness function is.
And solving the reconstruction model through a firework algorithm, wherein the characteristics of the reconstruction model of the power distribution network are combined. I.e., each dimension of the feasible solution must be a continuous integer. The convergence rate of the firework algorithm in the text refers to the number of iterations to reach the global optimal solution.
8. The firework algorithm is improved according to the characteristics of the power distribution network as follows:
the switch combination of the power distribution network reconstruction must be an integer, and the explosion radius of the fireworks cannot be too small. Therefore, a minimum explosion radius adjustment mechanism is adopted, as shown in formula (11):
Figure BDA0002642363630000061
in the formula, Ai,kFor fireworks xiThe detonation radius of the kth dimension; a. themin,kMinimum explosion radius for the k-dimension; [ A ]i,k]Represents a to Ai,kAnd (6) taking the whole.
In order to balance the global searching capability and the local searching capability of the firework algorithm, the minimum explosion radius A of the fireworks is usedmin,kThe size of (c) is adjusted as follows, as shown in formula (12):
Figure BDA0002642363630000062
in the formula, Amin,k(t) represents the minimum detonation radius of the firework for the t-th iteration in the k-dimension; a. theinit、AfinalRespectively an initial value and a final value of the explosion radius; t is the number of iterations, tmaxIs the maximum number of iterations.
Figure BDA0002642363630000063
Representing an exponential function as a function of t.
In order to ensure timeliness of power distribution network reconstruction, distance and load flow calculation times of the firework algorithm should be reduced in the aspect of selection strategies. Therefore, the present invention employs an elite selection strategy, as shown in formula (13):
Figure BDA0002642363630000064
in the formula, p (x)i) Representing fireworks xiProbability of being selected as next generation; f (x)i) Representing fireworks xiA fitness value of; f. ofmax、fminRespectively representing fireworks xiFitness maximum and minimum.
As can be seen from equation (13), if the fitness value corresponding to a spark is minimized, the spark will be selected to the next generation with a probability of 100%.
9. The comprehensive objective function established by the invention is shown as the formula (14):
Figure BDA0002642363630000065
in the formula floss(x)、fsv(x)、flb(x) F represents a network loss function, a voltage deviation function, a load balancing function and a comprehensive objective function of the power distribution network respectively; beta is a1、β2、β3Random weights of the three objective functions respectively; floss、Fsv、FlbRespectively, the minimum value of each iteration of the three objective functions; i represents the number of the node; l is the total branch number of the power distribution system; ciIs the state variable of the branch switch, 0 represents open, 1 represents closed; riIs the resistance of branch i; pi、QiTotal injection of node i respectivelyActive power and reactive power. ViIs the voltage magnitude at node i. n is the number of system nodes; vi,NIs the nominal value of the node voltage. SiIs the complex power amplitude of branch i;
Figure BDA0002642363630000071
the maximum allowed transmission capacity is for branch i. min is the minimum value symbol.
10. The active power distribution network reconstruction model established by the invention is as follows:
an objective function of the active power distribution network reconstruction model is shown as formula (15):
Figure BDA0002642363630000072
in the formula (f)loss(x)、fsv(x)、flb(x) F represents a network loss function, a voltage deviation function, a load balancing function and a comprehensive objective function of the power distribution network respectively; beta is a1、β2、β3Random weights of the three objective functions respectively; floss、Fsv、FlbRespectively, the minimum value of each iteration of the three objective functions.
The constraint function of the active power distribution network reconstruction model is as follows:
(1) a power flow balance constraint, as shown in equation (16):
Figure BDA0002642363630000073
wherein i and j represent the number of the node; pLi、QLiLoading active power and reactive power for the node i respectively; pGi、QGiActive power and reactive power which are DGs; vi、VjThe voltage amplitudes of node i and node j, respectively. Gij、BijThe real and imaginary parts of the admittance matrix, respectively.ijIs the voltage phase angle difference between node i and node j. sin for medical useij、cosijAre respectively asijSine function and cosine function.
(2) The branch current constraint is as shown in equation (17):
Il≤Ilmax (17)
in the formula Il,IlmaxRespectively the current flowing through branch i and the maximum allowed current.
(3) The node voltage constraint is as shown in equation (18):
Vi min≤Vi≤Vi max (18)
in the formula, ViIs the voltage amplitude of node i; vi min、Vi maxRespectively, the lower limit and the upper limit of the voltage amplitude.
(4) And (3) network topology constraint: after the power distribution network is reconstructed, a radiation-shaped topological structure must be kept, and a ring network does not exist.
Taking an IEEE33 node system as a case, the simplification conditions of the power distribution system and the effectiveness of the invention are analyzed: an IEEE33 node system is shown in fig. 1, where the reference voltage and reference power are 12.66kV and 10MVA, respectively. Assume that the head end is a balanced node, the voltage amplitude is 1.0p.u., and the voltage phase angle is 0. Considering the voltage static characteristics of the load, 2-6 nodes, 19-22 represent commercial loads, 7-18 nodes represent municipal domestic loads, and 23-33 nodes represent industrial loads. The node 27 and the node 33 access the DG respectively, and specific parameters are shown in table 1 and table 2.
TABLE 1 reference value of proportionality coefficient of static characteristic of load voltage
Figure BDA0002642363630000081
TABLE 2 distributed Power Access scenarios
Figure BDA0002642363630000082
Fig. 2 is a distribution diagram of voltage amplitudes for solving the IEEE33 node system by the NR method and the linear power flow equation. It can be found that the calculation results of the method are highly consistent with those of the Newton Raphson method, and the rationality of the simplified conditions of the method is proved.
Fig. 3 is a voltage amplitude deviation diagram after the IEEE33 node system is reconstructed by the present invention. It can be found that the voltage amplitude of the node can be improved to a certain extent after the system is reconstructed by the method.
Fig. 4 shows a structure of an IEEE33 node system after 50 reconstructions of the system according to three different models. The model A represents an adaptive particle swarm algorithm, the model B represents an improved firework algorithm, and the load flow calculation methods of the two models both adopt an NR method. As can be seen from the figure, the stability of the method is better than that of the model A, and the computational efficiency is better than that of the model A and the model B
The NR method and the linear power flow method are respectively used to solve the IEEE69, IEEE141 and IEEE874 node systems, and the maximum relative error and the running time of the two power flow equations in different test systems are shown in table 3:
TABLE 3 errors and runtimes for different test systems
Figure BDA0002642363630000083
As can be seen from Table 3, the maximum relative error of the voltage amplitude in the large-scale power distribution network system can be always kept within 0.1%, which shows that the proposed linear power flow equation is also applicable to other test systems. Meanwhile, compared with the NR method, the power flow calculation method disclosed by the invention does not need iteration and is higher in calculation efficiency, and in an IEEE874 node test system, the operation speed of the power flow calculation method disclosed by the invention is 100 times faster than that of the NR method.
Table 4 shows data obtained by reconstructing the distribution network of the IEEE33 node test system according to the present invention.
TABLE 4 comparison of results before and after network reconstruction
Figure BDA0002642363630000091
As can be seen from table 4, after the power distribution network is optimized and reconstructed, the network loss, the voltage deviation and the load balance of the power distribution network can be further reduced. When the power distribution network is reconstructed, the reasonable access to the DG can also effectively improve various indexes of the system.

Claims (10)

1. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm is characterized in that:
step 1: the typical characteristics of the active power distribution network are combined, and the simplified conditions suitable for the active power distribution network are quantitatively analyzed;
step 2: performing Taylor series expansion and voltage amplitude and phase angle decoupling on a power flow equation according to the simplified condition of the active power distribution network on the basis of considering a distributed power supply model and a ZIP load model to obtain a group of linear power flow equations;
and step 3: in order to improve the convergence rate of the firework algorithm, the firework algorithm is improved according to the characteristics of the active power distribution network reconstruction;
and 4, step 4: establishing a comprehensive objective function of the active power distribution network, and constructing a reconstruction model of the active power distribution network;
and 5: and solving the active power distribution network reconstruction model by combining a linear power flow equation and an improved firework algorithm.
2. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in step 1, typical characteristics of the active power distribution network include:
the method comprises the following steps: the node voltage amplitude approaches 1.0 p.u.;
secondly, the step of: the phase angles at two ends of the line are very small, so that the voltage phase angles of all nodes in the power distribution network and the voltage phase angles of the balance nodes have little difference;
③: the ratio of resistance to reactance is large, close to or greater than 1.
3. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in the step 1, the simplification conditions of the active power distribution network are as shown in formula (1):
Figure RE-FDA0002715953320000011
wherein i and j represent the number of the node;i，jphase angles of nodes i and j are respectively;ijis the phase angle difference, V, of the nodes i, jjIs the voltage amplitude of node j; sin for medical useijTo representijIs calculated as a sine function of (c).
4. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in the step 2, the distributed power supply models are classified into the following three types:
(1) PQ-type DG:
the output power direction of the PQ-type DG is opposite to the load power flowing direction, and the load flow calculation is shown as the formula (2):
Figure RE-FDA0002715953320000012
wherein P, Q are the active power and reactive power of the load, respectively; pG、QGRespectively giving active power and reactive power to DGs;
(2) PV type DG:
the active power and voltage of the PV type DG are known quantities, and the load flow calculation model is shown as the formula (3):
Figure RE-FDA0002715953320000021
in the formula, P is the active power of the load; pG、QGRespectively giving active power and reactive power to DGs; v is the voltage amplitude of the node; vGA node voltage that is DG; qGmaxAnd QGminRespectively, the upper limit and the lower limit of reactive power of DG;
(3) PI type DG:
the active power and the current of the type DG are constant values, and a load flow calculation model of the type DG is shown as a formula (4):
Figure RE-FDA0002715953320000022
wherein P, Q are the active power and reactive power of the load, respectively; pGActive power given for DG; i isGA constant current output for DG; v is the voltage amplitude of the node; f (V) represents a function related to V.
5. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in the step 2, the ZIP load model is shown as the formula (5):
Figure RE-FDA0002715953320000023
wherein, P (V), Q (V) respectively represent node load active power and reactive power; v, VNThe actual voltage and the rated voltage of the node are respectively; pN,QNRespectively representing active power and reactive power under rated voltage; cZ,CI,CPRespectively representing the proportional coefficients of the active constant impedance, the constant current and the constant power load of the node; c'Z,C'I,C'PRespectively representing the proportional coefficients of node reactive constant impedance, constant current and constant power load; the constraint condition satisfied by each parameter is CZ+CI+CP＝1,C'Z+C'I+C'P＝1。
6. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in the step 2, the power flow equation is shown as a formula (6):
Figure RE-FDA0002715953320000024
wherein i and j represent the number of the node; pLi、QLiLoading active power and reactive power for the node i respectively; pGi、QGiActive power and reactive power which are DGs; vi、VjThe voltage amplitudes of the node i and the node j are respectively; gij、BijRespectively the real part and the imaginary part of the admittance matrix;ijis the voltage phase angle difference between node i and node j; sin for medical useij、cosijAre respectively asijSine and cosine functions of (1);
the method of linearization processing is shown in equation (7):
Figure RE-FDA0002715953320000031
wherein y (V) is a voltage amplitude dependent function; k represents the order; y iskRepresents y to the power k; Δ V is the voltage drop; v is the voltage amplitude of the node;
in order to ensure safe and reliable operation of power equipment, the voltage drop delta V of each node of the power distribution system is actually very small; when the voltage amplitude V approaches to 1p.u., carrying out Taylor series expansion on the nonlinear terms related to the voltage amplitude V;
the linear power flow equation is shown in equation (8):
Figure RE-FDA0002715953320000032
wherein h is1＝2，h21 is ═ 1; s, W and R are respectively a set of a balance node, a PQ node and a PV node in the power distribution network; pPS，PPW，QPWRespectively balancing constant power coefficients of active power of the nodes, active power of the PQ nodes and reactive power of the PQ nodes; pIS，PIW，QIWConstant current coefficients of active power of a balance node, active power of a PQ node and reactive power of the PQ node are respectively; vS、SRespectively, the voltage amplitude and the phase angle of the balance node; vW、WThe voltage amplitude and the phase angle of the PQ node are respectively; vR、RRespectively PV node voltage amplitude and phase angle; diag (P)PR)、diag(PPW)、diag(QPW) Respectively a constant power load coefficient diagonal matrix of PV node active power, a constant power load coefficient diagonal matrix of PQ node active power and a constant power load coefficient diagonal matrix of PV node reactive power; gRSAnd BRSRespectively a real part and an imaginary part of a mutual admittance matrix of the PV node and the balance node; gWSAnd BWSRespectively a real part and an imaginary part of a mutual admittance matrix of the PQ node and the balance node; gWRAnd BWRThe real part and the imaginary part of the transadmittance matrix of the PQ node and the PV node respectively; gRRAnd BRRThe real part and the imaginary part of the PV node self-admittance matrix are taken as the reference; b isRWAnd GRWThe real part and the imaginary part of the transadmittance matrix of the PQ node and the PV node respectively; gWWAnd BWWThe real part and the imaginary part of the PQ node auto-admittance matrix are respectively.
7. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in the step 3, the principle of the firework algorithm is as follows:
in the Firework Algorithm, each Firework xiRepresents a feasible solution, each fireworks xiRadius of detonation AiNumber of sparks SiAs shown in formulas (9) and (10):
Figure RE-FDA0002715953320000033
Figure RE-FDA0002715953320000041
in the formula: a. theiFor fireworks xiThe radius of detonation of; siThe number of sparks; m, A respectivelyA constant for adjusting the total number of explosion sparks and the explosion radius; y ismax、yminRespectively the maximum value and the minimum value of the fitness of the fireworks; i represents the number of fireworks; n represents the total number of fireworks; f (x)i) Is xiA fitness value of; is a minimum value;
the characteristic of active power distribution network reconstruction means that each dimension of a feasible solution must be a continuous integer;
the convergence rate of the firework algorithm refers to the number of iterations to reach the global optimal solution;
the firework algorithm is improved as follows:
the switch combination of the power distribution network reconstruction must be an integer, and the explosion radius of the fireworks cannot be too small; therefore, a minimum explosion radius adjustment mechanism is adopted, as shown in formula (11):
Figure RE-FDA0002715953320000042
in the formula, Ai,kFor fireworks xiThe detonation radius of the kth dimension; a. themin,kMinimum explosion radius for the k-dimension; [ A ]i,k]Represents a to Ai,kGetting the whole;
in order to balance the global searching capability and the local searching capability of the firework algorithm, the minimum explosion radius A of the fireworksmin,kThe size of (c) is adjusted as follows, as shown in formula (12):
Figure RE-FDA0002715953320000043
in the formula, Amin,k(t) represents the minimum detonation radius of the firework for the t-th iteration in the k-dimension; a. theinit、AfinalRespectively an initial value and a final value of the explosion radius; t is the number of iterations, tmaxIs the maximum iteration number;
Figure RE-FDA0002715953320000044
an exponential function representing the variation with t;
in order to ensure timeliness of power distribution network reconstruction, the distance and load flow calculation times of the firework algorithm are reduced in the aspect of selecting strategies; therefore, an elite selection strategy is employed, as shown in equation (13):
Figure RE-FDA0002715953320000045
in the formula, p (x)i) Representing fireworks xiProbability of being selected as next generation; f (x)i) Representing fireworks xiA fitness value of; f. ofmax、fminRespectively representing fireworks xiFitness maximum and minimum.
8. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in step 4, the comprehensive objective function of the power distribution network is as shown in formula (14):
Figure RE-FDA0002715953320000051
in the formula floss(x)、fsv(x)、flb(x) F represents a network loss function, a voltage deviation function, a load balancing function and a comprehensive objective function of the power distribution network respectively; beta is a1、β2、β3Random weights of the three objective functions respectively; floss、Fsv、FlbRespectively, the minimum value of each iteration of the three objective functions; i represents the number of the node; l is the total branch number of the power distribution system; ciIs the state variable of the branch switch, 0 represents open, 1 represents closed; riIs the resistance of branch i; pi、QiRespectively injecting active power and reactive power into the node i; viIs the voltage amplitude of node i; n is the number of system nodes; vi,NIs the nominal value of the node voltage; siIs the complex power amplitude of branch i; si maxMaximum allowed transmission capacity for branch i; min is the minimum value symbol.
9. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 1, wherein: in the step 4, the active power distribution network reconstruction model is as follows:
establishing a comprehensive objective function of the active power distribution network reconstruction model, as shown in formula (15):
Figure RE-FDA0002715953320000052
in the formula (f)loss(x)、fsv(x)、flb(x) F represents a network loss function, a voltage deviation function, a load balancing function and a comprehensive objective function of the power distribution network respectively; beta is a1、β2、β3Random weights of the three objective functions respectively; floss、Fsv、FlbRespectively, the minimum value of each iteration of the three objective functions.
10. The active power distribution network rapid reconstruction method based on the linear power flow equation and the improved firework algorithm as claimed in claim 9, wherein: in the step 4, a constraint function of the active power distribution network reconstruction model is to establish corresponding power flow balance constraint, branch current constraint, node voltage constraint and network topology constraint;
the constraint function of the active power distribution network reconstruction model is as follows:
(1) a power flow balance constraint, as shown in equation (16):
Figure RE-FDA0002715953320000053
wherein i and j represent the number of the node; pLi、QLiLoading active power and reactive power for the node i respectively; pGi、QGiActive power and reactive power which are DGs; vi、VjThe voltage amplitudes of the node i and the node j are respectively; gij、BijRespectively the real part and the imaginary part of the admittance matrix;ijis the voltage phase angle difference between node i and node j; sin for medical useij、cosijAre respectively asijSine and cosine functions of (1);
(2) the branch current constraint is as shown in equation (17):
Il≤Ilmax (17)
in the formula Il,IlmaxRespectively the current flowing through the branch l and the maximum allowable current;
(3) the node voltage constraint is as shown in equation (18):
Vi min≤Vi≤Vi max (18)
in the formula, ViIs the voltage amplitude of node i; vi min、Vi maxThe lower limit and the upper limit of the voltage amplitude are respectively;
(4) and (3) network topology constraint: after the power distribution network is reconstructed, a radiation-shaped topological structure must be kept, and a ring network does not exist.
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