CN103474989A - Network reconstruction method based on sensitivity analysis - Google Patents

Abstract

The invention relates to a network reconstruction method based on sensitivity analysis. The method includes the following steps: (1) establishing a network topology with n nodes according to a network to be reconstructed, (2) establishing a network reconstruction model with the smallest transmission loss as an objective function, (3) calculating the change rate of the sensitivity and the objective function, (4) carrying out selection sorting, specifically, sorting transmission loss increments from small to large and sequentially disconnecting operating switches corresponding to the transmission loss increments to complete the local optimum unlinking process, and (5) obtaining the optimum network structure under the intended objective function. According to the reconstruction technology, the optimum operating switch can be found out quickly and accurately through sensitivity calculation, the number of load flow calculation times is small, besides, the optimum objective is approached step by step, the defects that a traditional method consumes a long time and is low in efficiency can be well overcome, great practical significance is achieved, corresponding sensitivity analysis models are established according to different problems needing to be solved in power distribution network reconstruction, and all the problems can be solved through the method.

Description

A kind of network reconfiguration method based on sensitivity analysis

Technical field

The invention belongs to the Distribution Automation Technology field, especially a kind of network reconfiguration method based on sensitivity analysis.

Background technology

The development of modern power systems has changed the development pattern of traditional electrical network: the expanding day of electrical network scale, and the variation gradually of power supply type and the sharply increase of quantity, and power consumer supplies with to electric power require more strict.Distribution network is generally the closed loop construction, open loop operation and requirement are without the islet operation phenomenon, due to these characteristics, the network reconfiguration technology is utilized optimized algorithm, and under the prerequisite that does not increase network investment, choose reasonable changes the assembled state of block switch, interconnection switch, select the supply path of load bus, form the network configuration of an optimum, heavy load can be transferred on the underloading feeder line on the one hand, thereby reach the purpose that balanced load improves quality of voltage; Can improve on the other hand the operational mode of electrical network and then reduce network loss, improving the economy of system; Simultaneously, when system breaks down, by isolation and recovery operation, can reduce to greatest extent power supply interrupted district and restore electricity in time, therefore the network reconfiguration method both can have been avoided the waste caused because of blind investment, again fail safe and the economy of the operation of fully raising system.

The network reconfiguration method has usually: the branch exchange method, optimum stream method, expert system approach, the intelligent heuristics optimized algorithm of artificial neural network method and rise in recent years etc., these methods emphasize particularly on different fields, its unique advantage is arranged, but also have separately its deficiency, the network reconfiguration method that further research and development are more optimized is the direction that those skilled in the art make great efforts all the time.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of network reconfiguration method based on sensitivity analysis is provided.

The present invention solves its technical problem and takes following technical scheme to realize:

A kind of network reconfiguration method based on sensitivity analysis comprises that step is as follows:

(1) according to treating that reconstructed network sets up n meshed network topology;

(2) take loss minimization sets up the network reconfiguration model as target function;

Polar form by power flow equation active power:

$\mathrm{\Δ}{P}_i=P_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\∈i}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})=0,(i=\mathrm{1,2},...,n)$

Each node power deviation is added and, derive take network reconfiguration model description that loss minimization is target as:

$\min F=f(p,x)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{V}_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})$ Formula A,

The power flow equation w (p, x) that constraints is network=0 and to the requirement of system voltage, electric current, load balancing.

Wherein, △ P _ifor power error; P _gifor the meritorious injection rate of the generating of node i; P _difor the meritorious numerical value of the load of node i; During i ≠ j, G _ij=-g _ij; B _ij=-b _ij; During i=j,

s is the node set directly be connected with the i node; G, B are the element in network admittance matrix, and n is the network node number, and x is the state vector x=[V be comprised of node voltage V and phase angle theta _i, θ _ij] ^t, p is branch of a network admittance parameter p=[g _ij, b _ij] ^t;

(3) sensitivity and target function rate of change calculate;

Computing network branch road admittance parameter to the sensitivity of system losses is:

$s=\frac{\∂F}{\∂p}=\frac{\∂f}{\∂p}+\frac{\∂f}{\∂x}\·\frac{\∂x}{\∂p}$

Power flow equation asks local derviation to obtain to the branch of a network admittance parameter:

wherein

for Jacobian matrix, therefore

entering the sensitivity calculations formula can obtain:

$s=\frac{\∂F}{\∂p}=\frac{\∂f}{\∂p}+\frac{\∂f}{\∂x}\·J^{-1}\·(-\frac{\∂w}{\∂p})$ Formula B,

Therefore, in the time of can obtaining disconnecting a certain console switch, the variation of branch of a network parameter causes the increment of system losses to be:

△ F=s* △ p formula C,

Interconnection switch is numbered, closed a certain interconnection switch according to the order of sequence, carry out trend and calculate the system mode value, utilize sensitivity model formula B to calculate in the looped network that the interconnection switch closure generates afterwards the sensitivity of corresponding network loss while disconnecting each console switch separately, and then calculate network impedance while disconnecting in ring each console switch and change the increment on the network loss impact;

(4) select sequence, the network loss increment, by sequence from small to large, is disconnected to the console switch that each network loss increment is corresponding successively, complete the local optimum process of unlinking;

(5) obtain the optimum network structure under the intended target function.

And, described step (4) is selected sequence, completing the unlink concrete grammar of process of local optimum is: the network loss increment is changed to minimum corresponding console switch and disconnect, then carry out trend calculating, verify whether the rear structure of unlinking meets the constraintss such as voltage, electric current, load balancing, if meet, carry out next step, if do not meet, abandon first solution, the console switch of sequence second is disconnected, again carry out trend calculating, whether checking constraints meets, the like, until be met the solution of requirement, complete the local optimum process of unlinking.

And, the concrete grammar step that described step (5) obtains the optimum network structure under the intended target function is: closed next interconnection switch according to the order of sequence after completing steps (4), utilize the described sensitivity computing method of step (3), the variable quantity of network impedance on network loss impact when in ring, each console switch disconnects, utilize step (4) to select sequence, and find out in this looped network situation the console switch that can optimum unlink, the like, until traveled through all interconnection switches, obtain optimum network structure.

Advantage of the present invention and good effect are:

1, the present invention proposes a kind of network reconfiguration method based on sensitivity analysis, Sensitivity Analysis Method is a kind of linearizing analytical method from mathematics, by the problem by the actual complicated higher-dimension run into, the simple question that utilizes the method linearity of mathematics to change into the linearity of one dimension is processed, under the prerequisite that guarantees certain precision, speed and the efficiency of dealing with problems have greatly been improved.

2, the reconfiguration technique that the present invention proposes can utilize sensitivity calculations, find fast and accurately best console switch, the trend calculation times is less, and progressively approach optimal objective, can overcome well conventional method length consuming time, the shortcoming such as efficiency is low, there is very high realistic meaning, the problem that will solve for different power distribution network reconfiguration, set up corresponding Sensitivity Analysis, all can be solved by the method simultaneously.

The accompanying drawing explanation

Figure 1 shows that the inventive method flow chart of steps;

Figure 2 shows that the procedure schematic diagram of 7 node instance systems.

Embodiment

Below in conjunction with accompanying drawing, the embodiment of the present invention is further described, it is emphasized that following execution mode is illustrative, rather than determinate, can not using this execution mode as limitation of the invention.

A kind of network reconfiguration method based on sensitivity analysis as shown in Figure 1, comprises that step is as follows:

(1) according to treating that reconstructed network sets up n meshed network topology;

(2) take loss minimization sets up the network reconfiguration model as target function;

Polar form by power flow equation active power:

$\mathrm{\Δ}{P}_i=P_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\∈i}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})=0,(i=\mathrm{1,2},...,n)$

Each node power deviation is added and, derive take network reconfiguration model description that loss minimization is target as:

$\min F=f(p,x)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{V}_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})$ Formula A,

The power flow equation w (p, x) that constraints is network=0 and to the requirement of system voltage, electric current, load balancing.

Wherein, △ P _ifor power error; P _gifor the meritorious injection rate of the generating of node i; P _difor the meritorious numerical value of the load of node i; During i ≠ j, G _ij=-g _ij; B _ij=-b _ij; During i=j,

s is the node set directly be connected with the i node; G, B are the element in network admittance matrix, and n is the network node number, and x is the state vector x=[V be comprised of node voltage V and phase angle theta _i, θ _ij] ^t, p is branch of a network admittance parameter p=[g _ij, b _ij] ^t.

(3) sensitivity and target function rate of change calculate;

Computing network branch road admittance parameter to the sensitivity of system losses is:

$s=\frac{\∂F}{\∂p}=\frac{\∂f}{\∂p}+\frac{\∂f}{\∂x}\·\frac{\∂x}{\∂p}$

Power flow equation asks local derviation to obtain to the branch of a network admittance parameter: wherein

jacobian matrix, therefore

entering the sensitivity calculations formula can obtain:

$s=\frac{\∂F}{\∂p}=\frac{\∂f}{\∂p}+\frac{\∂f}{\∂x}\·J^{-1}\·(-\frac{\∂w}{\∂p})$ Formula B,

Therefore, in the time of can obtaining disconnecting a certain console switch, the variation of branch of a network parameter causes the increment of system losses to be:

△ F=s* △ p formula C,

Interconnection switch is numbered, closed a certain interconnection switch according to the order of sequence, carry out trend and calculate the system mode value, utilize sensitivity model formula B to calculate in the looped network that the interconnection switch closure generates afterwards the sensitivity of corresponding network loss while disconnecting each console switch separately, and then calculate network impedance while disconnecting in ring each console switch and change the increment on the network loss impact;

(4) select sequence, the network loss increment, by sequence from small to large, is disconnected to the console switch that each network loss increment is corresponding successively, complete the local optimum process of unlinking; The network loss increment is changed to minimum corresponding console switch and disconnect, then carry out trend calculating, verify whether the rear structure of unlinking meets the constraintss such as voltage, electric current, load balancing, if meet, carry out next step, if do not meet, abandon first solution, the console switch of sequence second is disconnected, again carry out trend calculating, whether checking constraints meets, the like, until be met the solution of requirement, complete the local optimum process of unlinking;

(5) obtain the optimum network structure under the intended target function: closed next interconnection switch according to the order of sequence after completing steps (4), utilize the described sensitivity computing method of step (3), the variable quantity of network impedance on network loss impact when in ring, each console switch disconnects, utilize step (4) to select sequence, and find out in this looped network situation the console switch that can optimum unlink, the like, until traveled through all interconnection switches, obtain optimum network structure.

Example

In order to describe clearly content of the present invention, choose a simple distribution network system (7 node example system) and describe in detail, as shown in Figure 2, system has 7 of buses, numbers respectively 1 to 7,6 of block switches, number respectively s1 to s6), two of interconnection switches are numbered respectively s7 and s8.

As shown in Figure 2, system initial network topology is all block switch closures, and all interconnection switches disconnect.

The network reconfiguration first step, first closed first interconnection switch s7, now generate a loop in system, the radial of recovery system, needs to disconnect a block switch on this loop.

Trend calculates the value of each node voltage of network, phase angle quantity of state, corresponding target function variable quantity while adopting formula A, B and C to calculate respectively to disconnect on this loop each block switch, then by the variable quantity size, sorted, after supposing to calculate, sequence is as shown in c part in Fig. 2

According to sequencing table, select to disconnect block switch s3, make system recover radial, as shown in d part in Fig. 2, again carry out trend calculating, whether the network topology that checking disconnects after s3 meets the constraintss such as voltage, electric current, if do not meet the demands, the switch of with reference to sequencing table, selecting successively the next one to disconnect, trend is calculated again, until meet the demands; If meet the demands, enter d part in Fig. 2.

Closed second interconnection switch s8, now in system, again generate a loop, want the radial of recovery system, need equally to disconnect a block switch on this loop, a same step is identical, again calculate sequence, obtain target function variable quantity sequencing table, according to sequencing table, select to disconnect block switch s1, make system recover radial, as f part in Fig. 2, according to constraints, in proof diagram 2, whether the network topology shown in the f part meets the demands, if do not meet the demands, with reference to sequencing table, re-start the switch that selection need to disconnect, until meet the demands.Suppose that topological structure shown in the f part in Fig. 2 meets the requirement of practical problem, this topological structure is exactly the network configuration of the optimum that obtains after network reconfiguration.

Claims (3)

1. the network reconfiguration method based on sensitivity analysis is characterized in that comprising that step is as follows:

(1) according to treating that reconstructed network sets up n meshed network topology;

(2) take loss minimization sets up the network reconfiguration model as target function;

Polar form by power flow equation active power:

$\mathrm{\Δ}{P}_i=P_{\mathrm{Gi}}-P_{\mathrm{Di}}-V_i\underset{j\∈i}{\mathrm{\Σ}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})=0,(i=\mathrm{1,2},...,n)$

Each node power deviation is added and, derive take network reconfiguration model description that loss minimization is target as:

$\min F=f(p,x)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{V}_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}})$ Formula A,

The power flow equation w (p, x) that constraints is network=0 and to the requirement of system voltage, electric current, load balancing.

Wherein, △ P _ifor power error; P _gifor the meritorious injection rate of the generating of node i; P _difor the meritorious numerical value of the load of node i; During i ≠ j, G _ij=-g _ij; B _ij=-b _ij; During i=j,

s is the node set directly be connected with the i node; G, B are the element in network admittance matrix, and n is the network node number, and x is the state vector x=[V be comprised of node voltage V and phase angle theta _i, θ _ij] ^t, p is branch of a network admittance parameter p=[g _ij, b _ij] ^t;

(3) sensitivity and target function rate of change calculate;

Computing network branch road admittance parameter to the sensitivity of system losses is:

$s=\frac{\∂F}{\∂p}=\frac{\∂f}{\∂p}+\frac{\∂f}{\∂x}\·\frac{\∂x}{\∂p}$

Power flow equation asks local derviation to obtain to the branch of a network admittance parameter:

wherein

for Jacobian matrix, therefore entering the sensitivity calculations formula can obtain:

$s=\frac{\∂F}{\∂p}=\frac{\∂f}{\∂p}+\frac{\∂f}{\∂x}\·J^{-1}\·(-\frac{\∂w}{\∂p})$ Formula B,

Therefore, in the time of can obtaining disconnecting a certain console switch, the variation of branch of a network parameter causes the increment of system losses to be:

△ F=s* △ p formula C,

Interconnection switch is numbered, closed a certain interconnection switch according to the order of sequence, carry out trend and calculate the system mode value, utilize sensitivity model formula B to calculate in the looped network that the interconnection switch closure generates afterwards the sensitivity of corresponding network loss while disconnecting each console switch separately, and then calculate network impedance while disconnecting in ring each console switch and change the increment on the network loss impact;

(4) select sequence, the network loss increment, by sequence from small to large, is disconnected to the console switch that each network loss increment is corresponding successively, complete the local optimum process of unlinking;

(5) obtain the optimum network structure under the intended target function.

2. the network reconfiguration method based on sensitivity analysis according to claim 1, it is characterized in that: described step (4) is selected sequence, completing the unlink concrete grammar of process of local optimum is: the network loss increment is changed to minimum corresponding console switch and disconnect, then carry out trend calculating, verify whether the rear structure of unlinking meets voltage, electric current, the constraintss such as load balancing, if meet, carry out next step, if do not meet, abandon first solution, the console switch of sequence second is disconnected, again carry out trend calculating, whether checking constraints meets, the like, until be met the solution of requirement, complete the local optimum process of unlinking.

3. the network reconfiguration method based on sensitivity analysis according to claim 1, it is characterized in that: the concrete grammar step that described step (5) obtains the optimum network structure under the intended target function is: closed next interconnection switch according to the order of sequence after completing steps (4), utilize the described sensitivity computing method of step (3), the variable quantity of network impedance on network loss impact when in ring, each console switch disconnects, utilize step (4) to select sequence, and find out in this looped network situation the console switch that can optimum unlink, the like, until traveled through all interconnection switches, obtain optimum network structure.

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