CN111934320B - Active power distribution network rapid reconstruction method based on linear tide equation and improved firework algorithm - Google Patents

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

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CN111934320B
CN111934320B CN202010843843.3A CN202010843843A CN111934320B CN 111934320 B CN111934320 B CN 111934320B CN 202010843843 A CN202010843843 A CN 202010843843A CN 111934320 B CN111934320 B CN 111934320B
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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
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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    • H—ELECTRICITY
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Abstract

A quick reconfiguration method of an active power distribution network based on a linear tide equation and an improved firework algorithm comprises the following steps: combining typical characteristics of the power distribution network, quantitatively analyzing simplified conditions suitable for the power distribution network; 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 a simplifying condition of a power distribution network to obtain a group of linear power flow equations; in order to increase the convergence rate of the firework algorithm, the firework algorithm is improved according to the reconstruction characteristics of the power distribution network; 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 tide equation and an improved firework algorithm. The invention provides a quick reconstruction method of an active power distribution network based on a linear tide equation and an improved firework algorithm.

Description

Active power distribution network rapid reconstruction method based on linear tide equation and improved firework algorithm
Technical Field
The invention relates to the technical field of active power distribution network reconstruction, in particular to a method for rapidly reconstructing an active power distribution network based on a linear tide equation and an improved firework algorithm.
Background
In recent years, with the increasing serious problems of insufficient energy sources, environmental pollution and the like, distributed power generation is becoming an emerging energy utilization mode, and is getting more attention. Compared with a large power grid with centralized power supply, the unique environmental protection property, economy and higher energy conversion rate become important measures for adjusting the energy structure, and are important directions for future development of a power distribution system. The distributed power sources (Distribution Generation, DG) are connected to the power distribution network, which will affect the power supply reliability of the power distribution network, so the influence of DG needs to be considered when the power distribution network is reconstructed.
At present, certain achievements are achieved on the reconstruction of a distribution network containing DGs. The current calculation method adopted by the commonly used power distribution network reconstruction model mainly comprises a forward-push back substitution method, an improved Newton method, a loop impedance method and the like. However, the tide equations of the methods are nonlinear and involve an iterative process, so that the calculation efficiency is low, and the requirement of rapid reconstruction of the power distribution network is difficult to meet.
In order to improve the efficiency of a power flow calculation method, a plurality of documents have developed and related researches are carried out, a typical processing method at present uses a loop analysis method as a power flow calculation theory according to the structure of a tree network of a power distribution system, typical characteristics of a power distribution network are utilized to carry out linearization processing on a loop voltage equation, the loop voltage equation is simplified into a linear algebraic equation set, and finally a voltage distribution result can be obtained through substitution of a formula. Or polynomial fitting is carried out on trigonometric function items in the basic flow equation, and then the voltage amplitude and the phase angle are decoupled by utilizing the operation characteristics of the system, so as to obtain a full-linear flow equation. However, none of the above methods is suitable for a power distribution network including PV nodes, and is difficult to directly apply to an active power distribution network reconstruction model. In addition, power distribution network reconstruction often requires the use of intelligent algorithms for solution. However, the traditional intelligent algorithm has the problems of low convergence speed and low efficiency in solving. The firework algorithm is a novel group intelligent optimization algorithm provided in 2010, has good convergence and robustness in solving the high complexity problem, and is focused by a plurality of students. However, the firework algorithm is applied to the field of power distribution network reconstruction in the prior art.
In view of the above, it is of great significance to research an active power distribution network rapid reconstruction method based on a linear tide equation and an improved firework algorithm.
Disclosure of Invention
The method aims at solving the problems of low calculation efficiency and low universality of the existing active power distribution network reconstruction model. The invention provides a quick reconstruction method of an active power distribution network based on a linear tide 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 tide equation and an improved firework algorithm,
step 1: combining typical characteristics of an active power distribution network, quantitatively analyzing simplified conditions suitable for the active power distribution network;
step 2: based on the consideration of a distributed power supply model and a ZIP load model, carrying out Taylor series expansion and voltage amplitude and phase angle decoupling on a power flow equation according to the simplified condition of an active power distribution network to obtain a group of linear power flow equations;
step 3: in order to increase the convergence rate of the firework algorithm, the firework algorithm is improved according to the reconstruction characteristics of the active power distribution network;
step 4: establishing a comprehensive objective function of the active power distribution network, and constructing an active power distribution network reconstruction model;
step 5: and solving the active power distribution network reconstruction model by combining a linear tide equation and an improved firework algorithm.
The invention discloses a quick reconstruction method of an active power distribution network based on a linear tide equation and an improved firework algorithm, which has the following technical effects:
1) The linear tide equation of the invention is pure numerical operation, has simple model, small calculated amount and high calculation speed, does not have convergence problem,
2) The linear power flow disclosed by the invention not only overcomes the defect that most of linear power flow methods cannot process the PV type DG, but also has higher calculation accuracy.
3) The invention improves the firework algorithm, accelerates the convergence rate of the algorithm and improves the stability of the algorithm.
4) The invention provides a quick reconstruction method of an active power distribution network based on a linear tide equation and an improved firework algorithm. The method not only can improve the network loss, voltage offset and load balance of the power distribution system, but also can meet the requirement of quick reconstruction of the distribution network containing DGs.
Drawings
Fig. 1 is a schematic diagram of an IEEE33 node system architecture.
FIG. 2 is a graph of voltage amplitude distribution at each node of the system
Fig. 3 is a graph of voltage offset before and after reconstruction of a power distribution network.
FIG. 4 is a time-consuming graph of an algorithm stability analysis and reconstruction model.
Detailed Description
An active power distribution network rapid reconstruction method based on a linear tide equation and an improved firework algorithm,
step 1: combining typical characteristics of an active power distribution network, quantitatively analyzing simplified conditions suitable for the active power distribution network;
step 2: based on the consideration of a distributed power supply model and a ZIP load model, carrying out Taylor series expansion and voltage amplitude and phase angle decoupling on a power flow equation according to the simplified condition of an active power distribution network to obtain a group of linear power flow equations;
step 3: in order to increase the convergence rate of the firework algorithm, the firework algorithm is improved according to the reconstruction characteristics of the active power distribution network;
step 4: establishing a comprehensive objective function of the active power distribution network, and constructing an active power distribution network reconstruction model;
step 5: and solving the active power distribution network reconstruction model by combining a linear tide equation and an improved firework algorithm.
The preferred examples are described in detail below with reference to the attached drawing figures:
1. the simplifying conditions suitable for the power distribution network are as follows:
first, the typical characteristics of the distribution network are summarized, mainly including: (1) the node voltage amplitude approaches 1.0p.u.; (2) the phase angles at the two ends of the line are very small, so that the phase angles of the voltages of all nodes in the power distribution network are not greatly different from the phase angles of the voltages of the balance nodes; (3) the ratio of resistance to reactance is large, approaching or greater than 1.
From typical characteristics of the distribution network, simplified conditions of the distribution network can be deduced, as shown in formula (1):
wherein i and j represent the numbers of the nodes; delta i ，δ j The phase angles of the nodes i and j are respectively; delta ij For the phase angle difference of nodes i, j, V j The voltage amplitude at node j; sin delta ij Representing delta ij Is a sinusoidal function of (c).
2. According to different modes of distributed power grid connection, the distributed power models can be divided into the following three types:
(1) pQ type DG:
the direction of the output power of the PQ type DG is opposite to the direction of the load power flow, and the load flow calculation is shown in the formula (2):
wherein P, Q is the active power and the reactive power of the load respectively; p (P) G 、Q G Active power and reactive power respectively given for DG;
(2) PV type DG:
the active power and the voltage of the PV type DG are known, and the load flow calculation model is shown as a formula (3):
wherein P is the active power of the load; p (P) G 、Q G Respectively isDG, given active power and reactive power; v is the voltage amplitude of the node; v (V) G Node voltage for DG; q (Q) Gmax And Q Gmin The reactive power upper and lower limits of DG, respectively.
(3) PI type DG:
the active power and the current of the DG are constant values, and the load flow calculation model is shown as a formula (4):
wherein P, Q is the active power and the reactive power of the load respectively; p (P) G Active power given for DG; i G Constant current output for DG; v is the voltage amplitude of the node; f (V) represents a function related to V.
3. Considering the variation of the load size with voltage, a ZIP load model of the node can be established, as shown in equation (5):
wherein P (V), Q (V) represent node load active power and reactive power respectively. V, V N The actual voltage and the rated voltage of the node are respectively; p (P) N ,Q N Active power and reactive power at rated voltage are shown, respectively. C (C) Z ,C I ,C P The proportional coefficients of the node active constant impedance, constant current and constant power load are respectively represented; c'. Z ,C' I ,C' P The proportional coefficients of the reactive constant impedance, constant current and constant power load of the node are respectively represented; the constraint condition satisfied by each parameter is C Z +C I +C P ＝1,C' Z +C' I +C' P ＝1。
4. The expression of the tide equation is shown in a formula (6):
wherein i and j represent the numbers of the nodes; p (P) Li 、Q Li Respectively loading active power and reactive power for the node i; p (P) Gi 、Q Gi Active power and reactive power for DG; v (V) i 、V j The voltage amplitudes at node i and node j, respectively. G ij 、B ij The real and imaginary parts of the admittance matrix, respectively. Delta ij Is the voltage phase angle difference between node i and node j. sin delta ij 、cosδ ij Delta respectively ij Sine and cosine functions of (a).
5. According to typical characteristics of the power distribution network, the linearization processing method is as shown in formula (7):
wherein y (V) is a function related to the voltage amplitude; k represents an order; y is k Represents the power of y to the k; deltaV 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 Δv of each node of the power distribution system is actually small. When the voltage amplitude V approaches to 1p.u., taylor series expansion can be performed on the nonlinear term related to the voltage amplitude V.
6. The expression of the linear tide equation is shown in a formula (8):
wherein h is 1 ＝2，h 2 =1; s, W and R are respectively sets of balance nodes, PQ nodes and PV nodes in the power distribution network; p (P) PS ，P PW ，Q PW Respectively balancing constant power coefficients of node active power, PQ node active power and PQ node reactive power; p (P) IS ，P IW ，Q IW Constant current coefficients of the active power of the balance node, the active power of the PQ node and the reactive power of the PQ node are respectively obtained; v (V) S 、δ S Respectively the voltage amplitudes of the balance nodesValues and phase angles; v (V) W 、δ W The voltage amplitude and the phase angle of the PQ node are respectively; v (V) R 、δ R The voltage amplitude and the phase angle of the PV node are respectively; diag (P) PR )、diag(P PW )、diag(Q PW ) The constant power load factor diagonal matrix of the active power of the PV node, the constant power load factor diagonal matrix of the active power of the PQ node and the constant power load factor diagonal matrix of the reactive power of the PV node are respectively adopted; g RS And B RS Real and imaginary parts of the transadmittance matrix of the PV node and the balance node, respectively; g WS And B WS The real part and the imaginary part of the transadmittance matrix of the PQ node and the balance node are respectively; g WR And B WR Real and imaginary parts of the transadmittance matrix of the PQ node and the PV node, respectively; g RR And B RR Real and imaginary parts of the PV node self-admittance matrix; b (B) RW And G RW Real and imaginary parts of the transadmittance matrix of the PQ node and the PV node, respectively; g WW And B WW The real and imaginary parts of the PQ node self-admittance matrix, 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 x i Represents a feasible solution for each firework x i Explosion radius A of (2) i And number of sparks S i As shown in the formula (9) and the formula (10):
wherein: a is that i Is fireworks x i Is a radius of explosion; s is S i The number of sparks; m, A the constants for adjusting the total number of explosion sparks and the explosion radius, respectively; y is max 、y min The adaptation degree of fireworks is maximum and minimum respectively; i represents the number of fireworks; n represents the total number of fireworks; f (x) i ) Is x i Is used for the adaptation value of the (c). Epsilon 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, which shows that the better the fitness function is.
Solving the reconstruction model through a firework algorithm, and combining the characteristics of the reconstruction model of the power distribution network. I.e. each dimension of the feasible solution must be a continuous integer. The convergence speed of the firework algorithm refers to the iteration number reaching the global optimal solution.
8. The firework algorithm is improved according to the characteristics of the power distribution network as follows:
since the switch combination of the power distribution network reconstruction must be an integer, and the firework explosion radius is required not to be too small. Therefore, a minimum explosion radius adjustment mechanism is employed as shown in equation (11):
wherein A is i,k Is fireworks x i The explosion radius of the k-th dimension; a is that min,k A minimum explosion radius of the kth dimension; [ A ] i,k ]Representation of pair A i,k And (5) rounding.
In order to balance global searching capability and local searching capability of a firework algorithm, the invention makes the firework minimum explosion radius A min,k The size of (2) is adjusted as follows, as shown in formula (12):
wherein A is min,k (t) represents the minimum burst radius of the k dimension of the firework for the t-th iteration; a is that init 、A final The initial value and the final value of the explosion radius are respectively; t is the iteration number, t max Is the maximum number of iterations.Representing an exponential function as a function of t.
In order to ensure timeliness of power distribution network reconstruction, the firework algorithm should reduce the number of distance and tide calculation in terms of selection strategy. Thus, the present invention employs elite selection strategy as shown in formula (13):
wherein p (x) i ) Representing fireworks x i Probability of being selected as the next generation; f (x) i ) Representing fireworks x i Is a fitness value of (a); f (f) max 、f min Respectively represent fireworks x i Adaptation maximum and minimum.
From equation (13), if the fitness value corresponding to the spark is minimized, the spark will be selected to the next generation with 100% probability.
9. The integrated objective function established by the invention is shown as a formula (14):
in which f loss (x)、f sv (x)、f lb (x) F respectively represents a network loss function, a voltage offset function, a load balancing function and a comprehensive objective function of the power distribution network; beta 1 、β 2 、β 3 Random weights of three objective functions respectively; f (F) loss 、F sv 、F lb Respectively 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; c (C) i A state variable of the bypass switch, wherein 0 represents opening and 1 represents closing; r is R i The resistance of branch i; p (P) i 、Q i The total injected active power and reactive power of node i are respectively. V (V) i Is the voltage magnitude at node i. n is the number of system nodes; v (V) i,N Is the rated value of the node voltage. S is S i The complex power amplitude of branch i;the maximum allowed transmission capacity for leg i. min is the mostSmall value symbols.
10. The active power distribution network reconstruction model established by the invention is as follows:
an objective function of the active distribution network reconstruction model is shown in formula (15):
wherein f loss (x)、f sv (x)、f lb (x) F respectively represents a network loss function, a voltage offset function, a load balancing function and a comprehensive objective function of the power distribution network; beta 1 、β 2 、β 3 Random weights of three objective functions respectively; f (F) loss 、F sv 、F lb The minimum value of each iteration of the three objective functions is respectively.
The constraint function of the active distribution network reconstruction model is as follows:
(1) The flow balance constraint is as shown in formula (16):
wherein i and j represent the numbers of the nodes; p (P) Li 、Q Li Respectively loading active power and reactive power for the node i; p (P) Gi 、Q Gi Active power and reactive power for DG; v (V) i 、V j The voltage amplitudes at node i and node j, respectively. G ij 、B ij The real and imaginary parts of the admittance matrix, respectively. Delta ij Is the voltage phase angle difference between node i and node j. sin delta ij 、cosδ ij Delta respectively ij Sine and cosine functions of (a).
(2) The branch current constraint is shown in formula (17):
I l ≤I lmax (17)
wherein I is l ,I lmax The current through branch l and the maximum allowed current, respectively.
(3) The node voltage constraint is shown in equation (18):
V i min ≤V i ≤V i max (18)
wherein V is i The voltage amplitude of the node i; v (V) i min 、V i max The lower limit and the upper limit of the voltage amplitude are respectively defined.
(4) Network topology constraints: the distribution network must maintain a radial topology after reconstruction and no ring network exists.
Taking an IEEE33 node system as a case, the simplification condition of the power distribution system and the effectiveness of the invention are analyzed: the IEEE33 node system is shown in FIG. 1, and the reference voltage and reference power of the system are respectively 12.66kV and 10MVA. Assuming that the head end is a balanced node, the voltage amplitude is 1.0p.u., and the voltage phase angle is 0. Considering the static characteristics of load voltage, nodes 2-6, 19-22 represent commercial loads, nodes 7-18 represent municipal living loads, and nodes 23-33 represent industrial loads. Node 27 and node 33 access DG, respectively, for specific parameters, see tables 1 and 2.
TABLE 1 scaling factor reference values for static load Voltage characteristics
Table 2 distributed power access scenario
FIG. 2 is a plot of voltage amplitude for an IEEE33 node system using the NR method and linear flow equation. It can be found that the invention is highly consistent with the calculation result of the Newton Lapherson method, and the rationality of the simplified condition of the invention is proved.
Fig. 3 is a voltage amplitude deviation diagram of the IEEE33 node system after power distribution network reconfiguration according to 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 reconfigured.
Fig. 4 shows the structure of three different models after 50 reconfigurations of the IEEE33 node system. The model A represents a self-adaptive particle swarm algorithm, the model B represents an improved firework algorithm, and the load flow calculation methods of the two models adopt an NR method. As can be seen from the graph, the stability of the invention is better than that of the model A, and the calculation efficiency is better than that of the models A and B
The NR method and the linear power flow method are respectively used for solving an IEEE69 node system, an IEEE141 node system and an IEEE874 node system, and the maximum relative error and the running time of two power flow equations in different test systems are shown in a table 3:
TABLE 3 errors and runtime for different test systems
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 tide equation is also applicable to other test systems. Meanwhile, compared with an NR method, the load flow calculation method does not need iteration, the calculation efficiency is higher, and in an IEEE874 node test system, the load flow calculation method is 100 times faster than the NR method in operation.
Table 4 is data after the present invention has performed power distribution network reconfiguration for an IEEE33 node test system.
Table 4 comparison of results before and after network reconstruction
As can be seen from table 4, after the power distribution network is optimally reconstructed, the power distribution network loss, voltage offset and load balance degree can be further reduced. When the power distribution network is reconfigured, the reasonable access DG can also effectively improve various indexes of the system.

Claims (9)

1. The active power distribution network rapid reconstruction method based on the linear tide equation and the improved firework algorithm is characterized by comprising the following steps of:
step 1: combining typical characteristics of an active power distribution network, quantitatively analyzing simplified conditions suitable for the active power distribution network;
step 2: based on the consideration of a distributed power supply model and a ZIP load model, carrying out Taylor series expansion and voltage amplitude and phase angle decoupling on a power flow equation according to the simplified condition of an active power distribution network to obtain a group of linear power flow equations;
step 3: in order to increase the convergence rate of the firework algorithm, the firework algorithm is improved according to the reconstruction characteristics of the active power distribution network;
in the step 3, the principle of the firework algorithm is as follows:
in the firework algorithm, each firework x z Represents a feasible solution for each firework x z Explosion radius A of (2) z And number of sparks S z As shown in the formula (9) and the formula (10):
wherein: a is that z Is fireworks x z Is a radius of explosion; s is S z The number of sparks; m, A the constants for adjusting the total number of explosion sparks and the explosion radius, respectively; y is max 、y min The adaptation degree of fireworks is maximum and minimum respectively; z represents the number of fireworks; n represents the total number of fireworks; f (x) z ) Is x z Is a fitness value of (a); epsilon is a minimum value;
the reconstructed characteristic of the active distribution network means that each dimension of the feasible solution must be a continuous integer;
the convergence speed of the firework algorithm refers to the iteration number reaching the global optimal solution;
the firework algorithm is improved as follows:
because the switch combination of the power distribution network reconstruction must be an integer, and the firework explosion radius is required not to be too small; therefore, a minimum explosion radius adjustment mechanism is employed as shown in equation (11):
wherein A is z,k Is fireworks x z The explosion radius of the k-th dimension; a is that min,k A minimum explosion radius of the kth dimension; [ A ] z,k ]Representation of pair A z,k Rounding;
in order to balance the global searching capability and the local searching capability of the firework algorithm, the minimum explosion radius A of the firework is calculated min,k The size of (2) is adjusted as follows, as shown in formula (12):
wherein A is min,k (t) represents the minimum burst radius of the k dimension of the firework for the t-th iteration; a is that init 、A final The initial value and the final value of the explosion radius are respectively; t is the iteration number, t max The maximum iteration number;an exponential function representing variation with t;
in order to ensure timeliness of power distribution network reconstruction, the firework algorithm should reduce the distance and the times of tide calculation in terms of a selection strategy; thus, an elite selection strategy is employed, as shown in equation (13):
wherein p (x) z ) Representing fireworks x z Probability of being selected as the next generation; f (x) z ) Representing fireworks x z Is a fitness value of (a); f (f) max 、f min Respectively represent fireworks x z Maximum and minimum fitness values;
step 4: establishing a comprehensive objective function of the active power distribution network, and constructing an active power distribution network reconstruction model;
step 5: and solving the active power distribution network reconstruction model by combining a linear tide equation and an improved firework algorithm.
2. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 1, typical characteristics of the active power distribution network include:
(1) the method comprises the following steps The node voltage amplitude approaches 1.0p.u.;
(2) the method comprises the following steps The phase angles at the two ends of the line are very small, so that the phase angles of the voltages of all nodes in the power distribution network are not greatly different from the phase angles of the voltages of the balance nodes;
(3) the method comprises the following steps The ratio of resistance to reactance is large, approaching or greater than 1.
3. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 1, the simplified condition of the active power distribution network is as shown in formula (1):
wherein i and j represent the numbers of the nodes; delta i ，δ j The phase angles of the nodes i and j are respectively; delta ij For the phase angle difference of nodes i, j, V j The voltage amplitude at node j; sin delta ij Representing delta ij Is a sinusoidal function of (c).
4. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 2, the distributed power model is of the following three types:
(1) pQ type DG:
the direction of the output power of the PQ type DG is opposite to the direction of the load power flow, and the load flow calculation is shown in the formula (2):
wherein P, Q is the active power and the reactive power of the load respectively; p (P) G 、Q G Active power and reactive power respectively given for DG;
(2) PV type DG:
the active power and the voltage of the PV type DG are known, and the load flow calculation model is shown as a formula (3):
wherein P is the active power of the load; p (P) G 、Q G Active power and reactive power respectively given for DG; v is the voltage amplitude of the node; v (V) G Node voltage for DG; q (Q) Gmax And Q Gmin The reactive power upper limit and the reactive power lower limit of DG are respectively;
(3) PI type DG:
the active power and the current of the DG are constant values, and the load flow calculation model is shown as a formula (4):
wherein P, Q is the active power and the reactive power of the load respectively; p (P) G Active power given for DG; i G Constant current output for DG; v is the voltage amplitude of the node; f (V) represents a function related to V.
5. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 2, the ZIP load model is shown in formula (5):
wherein P (V), Q (V) represent node load active power and reactive power respectively; v, V N The actual voltage and the rated voltage of the node are respectively; p (P) N ,Q N Respectively representing active power and reactive power at rated voltage; c (C) Z ,C I ,C P The proportional coefficients of the node active constant impedance, constant current and constant power load are respectively represented; c'. Z ,C' I ,C' P The proportional coefficients of the reactive constant impedance, constant current and constant power load of the node are respectively represented; the constraint condition satisfied by each parameter is C Z +C I +C P ＝1,C' Z +C' I +C' P ＝1。
6. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 2, the tide equation is shown in formula (6):
wherein i and j represent the numbers of the nodes; p (P) Li 、Q Li Respectively loading active power and reactive power for the node i; p (P) Gi 、Q Gi Active power and reactive power for DG; v (V) i 、V j The voltage amplitudes of the node i and the node j are respectively; g ij 、B ij The real part and the imaginary part of the admittance matrix are respectively; delta ij Is the voltage phase angle difference between node i and node j; sin delta ij 、cosδ ij Delta respectively ij Sine and cosine functions of (a);
the linearization method is as shown in formula (7):
wherein y (V) is a function related to the voltage amplitude; k represents an order; y is k Represents the power of y to the k; deltaV 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 delta V of each node of the power distribution system is small in practice; when the voltage amplitude V approaches to 1p.u., performing Taylor series expansion on a nonlinear term related to the voltage amplitude V;
the linear power flow equation is shown in formula (8):
wherein h is 1 ＝2，h 2 =1; s, W and R are respectively sets of balance nodes, PQ nodes and PV nodes in the power distribution network; p (P) PS ，P PW ，Q PW Respectively balancing constant power coefficients of node active power, PQ node active power and PQ node reactive power; p (P) IS ，P IW ，Q IW Constant current coefficients of the active power of the balance node, the active power of the PQ node and the reactive power of the PQ node are respectively obtained; v (V) S 、δ S Respectively balancing node voltage amplitude and phase angle; v (V) W 、δ W The voltage amplitude and the phase angle of the PQ node are respectively; v (V) R 、δ R The voltage amplitude and the phase angle of the PV node are respectively; diag (P) PR )、diag(P PW )、diag(Q PW ) The constant power load factor diagonal matrix of the active power of the PV node, the constant power load factor diagonal matrix of the active power of the PQ node and the constant power load factor diagonal matrix of the reactive power of the PQ node are respectively; g RS And B RS Real and imaginary parts of the transadmittance matrix of the PV node and the balance node, respectively; g WS And B WS The real part and the imaginary part of the transadmittance matrix of the PQ node and the balance node are respectively; g WR And B WR Real and imaginary parts of the transadmittance matrix of the PQ node and the PV node, respectively; g RR And B RR Real and imaginary parts of the PV node self-admittance matrix; b (B) RW And G RW Transadmittance matrix of PQ node and PV node respectivelyReal and imaginary parts of (a); g WW And B WW The real and imaginary parts of the PQ node self-admittance matrix, respectively.
7. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 4, the comprehensive objective function of the power distribution network is shown in formula (14):
in which f loss (x)、f sv (x)、f lb (x) F respectively represents a network loss function, a voltage offset function, a load balancing function and a comprehensive objective function of the power distribution network; beta 1 、β 2 、β 3 Random weights of three objective functions respectively; f (F) loss 、F sv 、F lb Respectively 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; c (C) i A state variable of the bypass switch, wherein 0 represents opening and 1 represents closing; r is R i The resistance of branch i; p (P) i 、Q i Respectively injecting active power and reactive power into the total of the node i; v (V) i The voltage amplitude of the node i; n is the number of system nodes; v (V) i,N Is the rated value of the node voltage; s is S i The complex power amplitude of branch i;the maximum allowable transmission capacity of the branch i is set; min is the minimum sign.
8. The method for rapidly reconstructing the active power distribution network based on the linear tide equation and the improved firework algorithm according to claim 1 is characterized in that: in the step 4, the active power distribution network reconstruction model is as follows:
and establishing a comprehensive objective function of the active power distribution network reconstruction model, wherein the comprehensive objective function is shown in a formula (15):
wherein f loss (x)、f sv (x)、f lb (x) F respectively represents a network loss function, a voltage offset function, a load balancing function and a comprehensive objective function of the power distribution network; beta 1 、β 2 、β 3 Random weights of three objective functions respectively; f (F) loss 、F sv 、F lb The minimum value of each iteration of the three objective functions is respectively.
9. The method for rapidly reconstructing the active power distribution network based on the linear power flow equation and the improved firework algorithm according to claim 8, wherein the method comprises the following steps: in the step 4, the 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 distribution network reconstruction model is as follows:
(1) The flow balance constraint is as shown in formula (16):
wherein i and j represent the numbers of the nodes; p (P) Li 、Q Li Respectively loading active power and reactive power for the node i; p (P) Gi 、Q Gi Active power and reactive power for DG; v (V) i 、V j The voltage amplitudes of the node i and the node j are respectively; g ij 、B ij The real part and the imaginary part of the admittance matrix are respectively; delta ij Is the voltage phase angle difference between node i and node j; sin delta ij 、cosδ ij Delta respectively ij Sine and cosine functions of (a);
(2) The branch current constraint is shown in formula (17):
I l ≤I lmax (17)
in the middle of，I l ,I lmax The current flowing through the branch l and the maximum allowable current respectively;
(3) The node voltage constraint is shown in equation (18):
V i min ≤V i ≤V i max (18)
wherein V is i The voltage amplitude of the node i; v (V) i min 、V i max The lower limit and the upper limit of the voltage amplitude are respectively set;
(4) Network topology constraints: the distribution network must maintain a radial topology after reconstruction and no ring network exists.
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Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105740970A (en) * 2016-01-22 2016-07-06 中国电力科学研究院 Power distribution network reconstruction method based on fireworks algorithm
CN107658840A (en) * 2017-09-30 2018-02-02 山东科技大学 Distribution network failure restoration methods based on A* algorithms Yu fireworks algorithm
CN107887908A (en) * 2017-11-20 2018-04-06 四川大学 Power transmission network based on VSC and high voltage distribution network topology reconstruction blocks management-control method
CN108183502A (en) * 2017-12-21 2018-06-19 上海电机学院 Promote the active distribution network reconstructing method of distributed energy consumption
CN110021966A (en) * 2019-03-07 2019-07-16 华中科技大学 A kind of active distribution network Optimization Scheduling considering dynamic network reconfiguration
CN110518590A (en) * 2019-08-05 2019-11-29 三峡大学 Consider the linear tidal current computing method of power distribution network of static load characteristics
CN110932320A (en) * 2019-12-09 2020-03-27 华北电力大学 Design method of distributed model predictive controller of automatic power generation control system
CN111463778A (en) * 2020-04-20 2020-07-28 南昌大学 Active power distribution network optimization reconstruction method based on improved suburb optimization algorithm

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8086355B1 (en) * 2007-02-28 2011-12-27 Global Embedded Technologies, Inc. Method, a system, a computer-readable medium, and a power controlling apparatus for applying and distributing power

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105740970A (en) * 2016-01-22 2016-07-06 中国电力科学研究院 Power distribution network reconstruction method based on fireworks algorithm
CN107658840A (en) * 2017-09-30 2018-02-02 山东科技大学 Distribution network failure restoration methods based on A* algorithms Yu fireworks algorithm
CN107887908A (en) * 2017-11-20 2018-04-06 四川大学 Power transmission network based on VSC and high voltage distribution network topology reconstruction blocks management-control method
CN108183502A (en) * 2017-12-21 2018-06-19 上海电机学院 Promote the active distribution network reconstructing method of distributed energy consumption
CN110021966A (en) * 2019-03-07 2019-07-16 华中科技大学 A kind of active distribution network Optimization Scheduling considering dynamic network reconfiguration
CN110518590A (en) * 2019-08-05 2019-11-29 三峡大学 Consider the linear tidal current computing method of power distribution network of static load characteristics
CN110932320A (en) * 2019-12-09 2020-03-27 华北电力大学 Design method of distributed model predictive controller of automatic power generation control system
CN111463778A (en) * 2020-04-20 2020-07-28 南昌大学 Active power distribution network optimization reconstruction method based on improved suburb optimization algorithm

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
含分布式电源的配电网快速前推回代算法;刘会家;李奔;廖小兵;李;;水电能源科学;第34卷(第06期);213-216 *
基于改进烟花算法的矿用配电网重构;徐嘉斌;张鑫;张玉振;张晶;;工矿自动化;第44卷(第09期);32-36 *
计及分布式电源输出特性的有源配电网重构方法;徐嘉斌;吉兴全;公茂法;;电测与仪表;第55卷(第13期);53-73 *

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