CN103746376A - Power distribution network dynamic power restoration method based on load curve - Google Patents

Abstract

The invention provides a power distribution network dynamic power restoration method based on a load curve, which belongs to the technical field of power distribution system automation. The method utilizes a computer, realizes computing through programs and comprises the steps of inputting basic parameters; computing active load and reactive load of each node in each hour and determining a grid structure in normal operation; determining a fault section, a power supply path of the power side of the fault section and a grid structure after failure isolation; applying a traditional genetic algorithm to determine a candidate grid structure set of the least loss load in each hour during fault restoration; finally determining the optimum dynamic power restoration scheme during fault restoration. The method fully utilizes the load curve, and the dynamic restoration scheme is formulated by hour, so that the grid structure changes along with the change of the load during fault restoration, and accordingly, the method has the characteristics of being capable of effectively reducing power failure areas caused by fault, shortening power failure time for users, reducing the power failure loss of the users, and the like. The method can be widely applied to power distribution network power restoration.

Description

A kind of power distribution network dynamic power restoration methods based on load curve

Technical field

The invention belongs to distribution system automation technical field, be specifically related to a kind of power distribution network dynamic power restoration methods based on load curve.

Background technology

Electric energy and people's production and live closely relatedly, reliable continued power is one of basic demand to power system operation.The power distribution network that is connecting power transmission network and user is the important step of distributing electric energy, is the important component part of electric power system.The power distribution network having a large capacity and a wide range is difficult to avoid the generation of fault in actual motion, fault outage will cause economic loss to user, have influence on people's quality of life, so power distribution network often adopts closed loop design and open loop operation, to can effectively recover the power supply that has a power failure and load when fault occurs.Power distribution network service restoration refers to, the power distribution network breaking down is in definite abort situation and carry out after isolated fault, recovers the load of power supply interrupted district power by the block switch on reasonable operation distribution feeder and the interconnection switch between feeder line.By power distribution network service restoration, the power supply interrupted district causing because of fault and the interruption duration that shortens user be can reduce, thereby user's loss of outage and the electricity sales amount of increase power supply department reduced.Therefore, study effective power distribution network service restoration method, to improving the fail safe of power distribution network operation and the reliability tool of power supply, be of great significance.

The service restoration method of existing power distribution network, as 2008 the 23rd the 1st phase of volume IEEE < < electric power system > > proceedings (IEEE Transactions on Power Systems) in " considering the exploitation of the object-oriented service restoration expert system of load variations " (Development of an Object-Oriented Service Restoration Expert System With Load Variations) literary composition, disclosed method is to consider the expert system service restoration method of load variations.The concrete steps of described method are: fault is caused to the situation that user has a power failure progressively analyzes and recover, first, the available current surplus of the main standby feeder line that calculating is connected with the interconnection switch of each power failure section, according to abort situation, the merger of interconnective power failure section is become to some groups, when the load current of each power failure section group surpasses the available current-carrying surplus of the main standby feeder line being connected by interconnection switch in set period, this interconnection switch can not be for the service restoration of this section group that has a power failure, otherwise this interconnection switch is for the service restoration of this power failure section group.Secondly, when the section that has a power failure in addition does not restore electricity, power failure section between breakout place section in this power supply interrupted district and this section and fault section is formed to main power failure section group, remaining interconnective power failure section forms power failure section group, also, other power failure section groups are as power failure section group recovery separately in the power failure section combination that main power failure section group is connected with the main standby feeder line with maximum available ampacity.Again, when the section that has a power failure in addition does not restore electricity, from making the interconnection switch of ampacity maximum of main standby feeder line, at every turn by a sector transfer of this main standby feeder line to the less important standby feeder line that connects this interconnection switch and moving, until the load power supply of the section that can as often as possible recover to have a power failure; When not obtaining suitable recovery scheme, select another less important standby feeder line to repeat this step.Then, when having searched for all less important standby feeder lines, have a power failure in addition section while not restoring electricity, more logical overladen continuous transfer realizes the service restoration of maximum power failure sections.Finally, by trend, calculate and guarantee that service restoration scheme meets the requirement of voltage constraint and the constraint of feeder line ampacity.In this service restoration method, consider that the principle of the termination service restoration process that load variations adopts is, the current-carrying surplus of accepting the feeder line of power failure section load is less than the load current of power failure section in set period.Therefore the major defect of the method is: 1. in fact the set period in the method refers to fault correction time, can only consider by fault correction time the variation of load, the rule over time of can not considering by the hour to load during fault restoration; The principle of the termination service restoration process 2. adopting can cause abandoning can't making in certain period in fault correction time accepting the service restoration scheme of the feeder line overload of power failure section load, thereby causes the increase of sub-load interruption duration; 3. during fault restoration, can only obtain a grid structure, can not adjust the interruption duration that grid structure reduces user according to load variations; 4. after obtaining final service restoration scheme, just by trend, calculate to judge whether scheme meets voltage and retrain, when the discontented afc voltage constraint of this scheme, can not formulate rational service restoration scheme.Therefore by the method, can not make full use of the rule over time of loading formulates effective service restoration scheme, can not reduce the power supply interrupted district causing because of fault and the interruption duration that shortens user, thereby can not reduce user's loss of outage.

Summary of the invention

The object of the invention is the deficiency for the service restoration method of existing power distribution network, a kind of power distribution network dynamic power restoration methods based on load curve is proposed, have in service restoration process, based on load curve, consider by the hour the variation of payload, take that to lose load minimum be target, branch current and node voltage security constraint are that during the preferred distribution network failure of condition is repaired, the grid structure of each hour forms the set of candidate's rack, and then obtain changing with load variations during fault restoration, make the features such as dynamic power recovery scheme of switch motion least number of times, thereby provide scientific basis for formulating rational service restoration scheme, can effectively reduce the power supply interrupted district causing because of fault, shorten user's interruption duration and the loss of outage that reduces user.

The technical scheme that realizes the object of the invention is: a kind of power distribution network dynamic power restoration methods based on load curve, utilize computer, pass through program, first input basic parameter, grid structure, the supply path of determining fault section and upstream and the grid structure after Fault Isolation when calculating the meritorious load or burden without work of each hour and determining normal operation according to load curve again, then use traditional genetic algorithm to determine candidate's grid structure set of each hour minimum mistake load during fault restoration, finally determine the optimum dynamic power recovery scheme during fault restoration.The concrete steps of described method are as follows:

(1) input basic parameter

First, required basic parameter is calculated in input, comprises the parameter of basic parameter and the traditional genetic algorithm of power distribution network.The basic parameter of power distribution network comprises circuit sum (M), circuit number, circuit first and last end node numbering, line resistance (R), line reactance (X), line energizing flow amount, line switching type (not installing switch, installing block switch, installing interconnection switch), circuit place feeder line numbering; Node sum (N), power supply node sum (K _s), power supply node numbering, node burden with power (P _l), node load or burden without work (Q _l), the meritorious daily load rate curve of node load type, various load types; The node voltage upper limit (U _max), node voltage lower limit (U _min); Faulty line numbering, time of failure (t ₁), fault end time (t ₂); Reference voltage (U _b), reference power (S _b).The parameter of traditional genetic algorithm comprises population scale (P _p), maximum evolutionary generation (K _max), generation gap (P _g), crossing-over rate (p _c), aberration rate (p _m).

(2) grid structure while calculating meritorious, the load or burden without work of each node each hour and determining normal operation

After (1) step completes, first according to the burden with power (P of each node of (1) step input _l), load or burden without work (Q _l) and the meritorious daily load curve of various load types, according to the constant principle of power factor, calculate each node burden with power and the load or burden without work of each hour.According to the position of the interconnection switch of installing in power distribution network, determine the grid structure while normally moving again.

(3) determine the supply path of fault section and mains side and the grid structure after Fault Isolation

After (2) step completes, in (2) step, determine normal operation time grid structure in, for ease of optimizing, calculate and reduce computing time, first failure definition section is centered by fault point and take the line set that nearest switch is border from fault point; The supply path of failure definition section mains side is the line set between from power supply node to fault section.Use again conventional Depth Priority Algorithm, according to faulty line head end, whether install switch and determine fault section; From the power supply node of faulty line place feeder line, start to determine the supply path of fault section mains side.The boundary switch isolated fault of fault section for grid structure while finally normally moving according to the definite power distribution network of (2) step, determines the grid structure after Fault Isolation.

(4) use traditional genetic algorithm to determine candidate's grid structure set of each hour minimum mistake load during fault restoration

After (3) step completes, in grid structure after the definite Fault Isolation of (3) step, for obtaining the grid structure of power distribution network each hour minimum mistake load during fault restoration after Fault Isolation, to determine candidate's grid structure set of dynamic power recovery scheme, during the fault restoration that utilization obtains based on load curve, each hour loads and solves the optimal models of corresponding power distribution network service restoration.The target function of this model is minimum mistake load, and constraints is the constraints such as branch current, node voltage and Radiation Network shelf structure.Concrete formula is as follows:

$\min P_{t,c}\left(X_{t,r}\right)=\underset{n\&Element;{\mathrm{\&Omega;}}_N}{\mathrm{\&Sigma;}}{P}_{t,n}-\underset{k\&Element;{\mathrm{\&Omega;}}_K}{\mathrm{\&Sigma;}}{P}_{t,k}---\left(1\right)$

s.t.I _t,b≤I _b.max (2)

U _min≤U _t,k≤U _max (3)

g _t,i∈G (4)

In formula: t is the period, the time of one day being divided into 24 hours, every 1 hour is 1 period; P _t,cmistake load for period t; X _t,rfor the line switching state vector of the service restoration power distribution network of period t, X _t,r=[W _{t, r1}..., W _{t, rm}... W _{t, rM}]; M is circuit sum; W _{t, rm}for X _t,rthe on off state of m bar circuit, the switch of not installing switch or installing when circuit is taken as 1 during in closure state, when the switch of installing is taken as 0 during in off-state; Ω _nand P _t,nbe respectively the node set of the power distribution network before service restoration and node n in the burden with power of period t; Ω _kand P _t,kbe respectively the node set of service restoration power distribution network and node k in the burden with power of period t; N and K are respectively the node sum of service restoration front and back power distribution network; I _t,b, U _t,kand g _t,ibe respectively in the service restoration power distribution network of period t and flow through the electric current of circuit b, voltage and the grid structure of node k; I _b.maxampacity for circuit b; U _maxand U _minbe respectively the bound of node voltage; G is the set of Radiation Network shelf structure.

The concrete steps of grid structure that solve during fault restoration the minimum mistake load that each hour load is corresponding by traditional genetic algorithm are as follows:

1) form initial population

After (3) step completes, according to the population scale (P of (1) step input _p), with { 0,1} binary code, the individuality that is population scale to the number of random generation is encoded, and forms initial population.In initial population, each individual code length is circuit sum, and each coding represents the circuit head end on off state of power distribution network.When being encoded to 0, represent that this line switching is in off-state; When being encoded to 1, represent that this line switching is in closure state.

2) calculate target function value individual in population

The (4)-1) after step completes, for evaluating the (4)-1) quality of individual performance in the initial population that forms of step, each individual target function value in this population is calculated.The individual target function value more performance of the bright individuality of novel is more excellent.Concrete steps to each individual calculating target function value in described population are as follows:

1. revise individual coding

The (4)-1) after step completes, to the (4)-1) correction of encode of individuality in the initial population that produces of step, in first individuality being encoded, do not install the circuit of switch and the line switching state of fault section mains side supply path is set to 1; Again the on off state of fault section border circuit in individuality coding is set to 0, realizes Fault Isolation.

2. individuality is decoded

The (4)-2)-after 1. having walked, according to the (4)-2)-1. step correction individuality coding is later decoded, according to the track data of revised individual coding and input, determine that in individual coding, on off state is the track data of 1 correspondence, realize individual decoding.

3. form the Radiation distribution network that individual different electrical power node connects

The (4)-2)-after 2. having walked, the Radiation Network shelf structure connecting for obtaining each power supply node, to the (4)-2)-2. walk the Depth Priority Algorithm of decoded individual line data application routine, first from different power supply nodes, start take interconnection switch place circuit and as border, search for the formation prompt radiation shape grid structure that each power supply node was connected; In prompt radiation shape grid structure, search for successively respectively again two end nodes of the circuit that interconnection switch is housed.When interconnection two end nodes all searched out-of-date, disconnect this interconnection switch and in this individuality coding, on off state corresponding to this interconnector is set to 0 to meet the requirement of Radiation Network shelf structure constraints formula (4), otherwise the prompt radiation shape grid structure that search interconnection headend node or endpoint node connect and the not decoded individual line data of searched mistake, form individual final Radiation Network shelf structure.

4. calculate the trend of the Radiation distribution network of individual different electrical power node connection

The (4)-2)-after 3. having walked, first by the (4)-2) the line set of-Radiation network structure that 3. step is tried to achieve, according to the power distribution network basic parameter of input and the meritorious load or burden without work of each node during fault restoration of trying to achieve, determine each line impedance and the meritorious load or burden without work of each node of the Radiation network that this period different electrical power node connects; Use again and push back node voltage and the branch current that power flow algorithm is calculated the Radiation distribution network that each power supply node connects before traditional.In calculating, when the trend of the Radiation power distribution network connecting when certain power supply node does not restrain, finish whole trends and calculate.

5. calculate individual target function value

The (4)-2)-after 4. having walked, when the (4)-2)-4. calculate the Radiation distribution network trend that different electrical power node connects in step to have while not restraining situation, individual target function value is composed to a larger value, 10 ⁹.When the trend of the Radiation power distribution network connecting when all power supply nodes all restrains, calculate individual total out-of-limit value, concrete formula is:

$F_{t,\mathrm{pen}}=\underset{i-1}{\overset{K_S}{\mathrm{\&Sigma;}}}(\underset{k\&Element;{\mathrm{\&alpha;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{U_{\min }-U_{t,k}}{U_B}+\underset{k\&Element;{\mathrm{\&beta;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{U_{t,k}-U_{\max }}{U_B}+\underset{b\&Element;{\mathrm{\&gamma;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{I_{t,b}}{I_{b.\max }})---\left(5\right)$

In formula: F _{t, pen}out-of-limit value for t period service restoration power distribution network; K _sfor power supply node sum; α _t,i, β _t,iand γ _t,ithe node voltage that is respectively the Radiation power distribution network that t period power supply node i connects is node set, the node voltage more node set of the upper limit and the set of fingers of line current overload of lower limit more; U _maxand U _minbe respectively node voltage bound; U _bfor reference voltage; I _b.maxampacity for circuit b; I _t,b, U _t,kbe respectively in the service restoration power distribution network of period t and flow through the electric current of circuit b, the voltage of node k.

When the out-of-limit value of individuality is not 0, individual goal functional value is composed to a higher value, 10 ⁹; When the out-of-limit value of individuality is 0, according to formula (1), calculate individual target function value.

3) Evolution of Population calculates

The (4)-2)-after 5. having walked, use traditional genetic algorithm to be optimized calculating.First, defining current population is parent population, according to the (4)-2) the individual target function value of trying to achieve in step calculates fitness value individual in parent population; Secondly, to parent population, select operation, interlace operation and mutation operation to obtain progeny population; Again, employing the (4)-2) step is calculated whole individual goal functional values of described progeny population; Then, described progeny population is inserted into parent population and obtains new population; Finally judge whether Evolution of Population calculating finishes, when Evolution of Population algebraically does not reach maximum evolutionary generation, evolutionary generation is added to 1, and using new population as current population, repeat the calculating of this step, until Evolution of Population algebraically reaches the maximum evolutionary generation (K inputting in (1) step _max) till, just obtain coding and the target function value of each individuality in population; Otherwise finishing Evolution of Population calculates.

4) determine the rack set of minimum mistake load

The (4)-3) after step completes, from the (4)-3) select the individuality that minimum mistake load is different with coding the Evolution of Population result of calculation that obtains of step and form the set of candidate's rack.

(5) determine the optimum dynamic power recovery scheme during fault restoration

After (4) step completes, in the rack set of the minimum mistake load of determining in (4) step, first define dynamic power recovery scheme by fault restoration during the set that service restoration scheme forms of each hour.According to each network selection frame number and lasting hourage of fault as a child during fault restoration, enumerate the whole dynamic power recovery schemes of combination again.Then calculate the switch motion number of times of whole dynamic power recovery schemes.Minimum first assembled scheme of last selector switch action frequency is as optimum dynamic power recovery scheme.

The present invention adopts after technique scheme, mainly contains following effect:

1. the present invention is when considering load variations, for the payload of each hour during fault restoration, formulate and recover rack, compare with the method for existing consideration load variations, consider more carefully, can take into account more accurately the rule over time of loading during fault restoration, utilize more fully load curve.

2. dynamic power recovery scheme of the present invention, for payload hourly during fault restoration, consider, therefore during fault restoration, have a plurality of different racks, can adjust grid structure according to the needs of load variations in good time, scheme has time and space dynamic.The present invention compared with the conventional method, can reduce customer outage hours, recovers more electric weight.Meanwhile, thus the present invention can also reduce user because of power failure bring suddenly loss by prior notice customer outage hours.

3. in the process of the present invention's each hour minimum mistake load candidate rack set during determining fault restoration, considered the security constraint of branch current and node voltage, therefore definite dynamic power recovery scheme can avoid occurring that final recovery scheme becomes the situation of invalid scheme owing to not meeting security constraint.

The present invention can be widely used in the service restoration of power distribution network, can effectively shorten user's interruption duration, reduces the power failure area of power distribution network, improves the power supply reliability of power distribution network, for the formulation of power distribution network service restoration scheme provides effective scientific basis.

Accompanying drawing explanation

Fig. 1 is program flow chart of the present invention;

Fig. 2 is the schematic diagram of the 70 node power distribution network wiring of embodiment.

In figure,

for node serial number, 1～72 is circuit number, and #1～#4 is feeder line numbering,

for block switch or interconnection switch,

for interconnection,

for distribution line.

Embodiment

Below in conjunction with embodiment, further illustrate the present invention.

Embodiment

As shown in Figure 1, 2, a kind of concrete steps of the power distribution network dynamic power restoration methods based on load curve are as follows:

(1) input basic parameter

First, required basic parameter is calculated in input, comprises the parameter of basic parameter and the traditional genetic algorithm of power distribution network.The basic parameter of power distribution network comprises circuit sum (M=72), circuit number (1,2,, 72), circuit first and last end node numbering, line resistance (R), line reactance (X), line energizing flow amount, line switching type (not installing switch, installing block switch, installing interconnection switch), circuit place feeder line numbering; Node sum (N=70), power supply node sum (K _s=2), power supply node is numbered (1,70), node burden with power (P _l), node load or burden without work (Q _l), the meritorious daily load rate curve of node load type, various load types; The node voltage upper limit (U _max=1.1p.u.), node voltage lower limit (U _min=0.9p.u.); Faulty line numbering (55), time of failure (t ₁=18), fault end time (t ₂=22); Reference voltage (U _b=11kV), reference power (S _b=100MVA).The parameter of traditional genetic algorithm comprises population scale (P _p=100), maximum evolutionary generation (K _max=300), generation gap (P _g=0.95), crossing-over rate (p _c=0.9), aberration rate (p _m=0.01).

(2) grid structure while calculating meritorious, the load or burden without work of each node each hour and determining normal operation

After (1) step completes, first according to the burden with power (P of each node of (1) step input _l), load or burden without work (Q _l) and the meritorious daily load curve of various load types, according to the constant principle of power factor, calculate each node burden with power and the load or burden without work of each hour.According to the position of the interconnection switch of installing in power distribution network, determine the grid structure while normally moving again.

The power distribution network of Fig. 2 of take is example, and the grid structure when calculating the meritorious load or burden without work of each node each hour and determining normal operation is described.According to the meritorious daily load curve of the meritorious load or burden without work of each node and various load types, according to the constant principle of power factor, obtain at period t=18(18:00 to 19:00) time part of nodes load as shown in table 1.

Table 1 at period t=18(18:00 to 19:00) time part of nodes load

As seen from Figure 2, the circuit of installing interconnection switch has { 69,70,71,72}.Grid structure according to the interconnection switch position of installing during using the circuit of not installing interconnection switch as normal operation.

(3) determine the supply path of fault section and mains side and the grid structure after Fault Isolation

After (2) step completes, in (2) step, determine normal operation time grid structure in, for ease of optimizing, calculate and reduce computing time, first failure definition section is centered by fault point and take the line set that nearest switch is border from fault point; The supply path of failure definition section mains side is the line set between from power supply node to fault section.Use again conventional Depth Priority Algorithm, according to faulty line head end, whether install switch and determine fault section; From the power supply node of faulty line place feeder line, start to determine the supply path of fault section mains side.The boundary switch isolated fault of fault section for grid structure while finally normally moving according to the definite power distribution network of (2) step, determines the grid structure after Fault Isolation.

The power distribution network of Fig. 2 of take is example, illustrates and determines fault section and the supply path of upstream and the grid structure after Fault Isolation.When circuit 55 fault, use fault section that conventional Depth Priority Algorithm searches for 54,55,56}, fault section boundary switch circuit is { 54,56}; The supply path of fault section upstream is { 52,53,58,59,60,61}.After the switch 54,56 of the grid structure open failure section boundaries circuit during to normal operation, can obtain the grid structure after isolated fault.

(4) use traditional genetic algorithm to determine candidate's grid structure set of each hour minimum mistake load during fault restoration

After (3) step completes, in grid structure after the definite Fault Isolation of (3) step, for obtaining the grid structure of power distribution network each hour minimum mistake load during fault restoration after Fault Isolation, to determine candidate's grid structure set of dynamic power recovery scheme, during the fault restoration that utilization obtains based on load curve, each hour loads and solves the optimal models of corresponding power distribution network service restoration.The target function of this model is minimum mistake load, and constraints is the constraints such as branch current, node voltage and Radiation Network shelf structure.Concrete formula is as follows:

$\min P_{t,c}\left(X_{t,r}\right)=\underset{n\&Element;{\mathrm{\&Omega;}}_N}{\mathrm{\&Sigma;}}{P}_{t,n}-\underset{k\&Element;{\mathrm{\&Omega;}}_K}{\mathrm{\&Sigma;}}{P}_{t,k}---\left(1\right)$

s.t.I _t,b≤I _b.max (2)

U _min≤U _t,k≤U _max (3)

g _t,i∈G (4)

In formula: t is the period, the time of one day being divided into 24 hours, every 1 hour is 1 period; P _t,cmistake load for period t; X _t,rfor the line switching state vector of the service restoration power distribution network of period t, X _t,r=[W _{t, r1}..., W _{t, rm}... W _{t, rM}]; M is circuit sum; W _{t, rm}for X _t,rthe on off state of m bar circuit, the switch of not installing switch or installing when circuit is taken as 1 during in closure state, when the switch of installing is taken as 0 during in off-state; Ω _nand P _t,nbe respectively the node set of the power distribution network before service restoration and node n in the burden with power of period t; Ω _kand P _t,kbe respectively the node set of service restoration power distribution network and node k in the burden with power of period t; N and K are respectively the node sum of service restoration front and back power distribution network; I _t,b, U _t,kand g _t,ibe respectively in the service restoration power distribution network of period t and flow through the electric current of circuit b, voltage and the grid structure of node k; I _b.maxampacity for circuit b; U _maxand U _minbe respectively the bound of node voltage; G is the set of Radiation Network shelf structure.

The concrete steps of grid structure that solve during fault restoration the minimum mistake load that each hour load is corresponding by traditional genetic algorithm are as follows:

1) form initial population

After (3) step completes, according to the population scale (P of (1) step input _p), with { 0,1} binary code, the individuality that is population scale to the number of random generation is encoded, and forms initial population.In initial population, each individual code length is circuit sum, and each coding represents the circuit head end on off state of power distribution network.When being encoded to 0, represent that this line switching is in off-state; When being encoded to 1, represent that this line switching is in closure state.

The power distribution network of Fig. 2 of take is example, illustrates in the initial population forming with { the individuality of 0,1} binary code coding.Being encoded to of body one by one when period t=18 in the random initial population producing:

[1111110110 1110011101 1001111111 1111010111 1000111101 0001110100 1111111101 11]

This individual code length is 72; Position 7,10,14,15,19,22,23,35,37 in coding, 42-44,49,51-53,57,59,60 and 69 element are 0, represent that corresponding line switching is off-state, and the switch of all the other circuits is closure state.

2) calculate target function value individual in population

The (4)-1) after step completes, for evaluating the (4)-1) quality of individual performance in the initial population that forms of step, each individual target function value in this population is calculated.The individual target function value more performance of the bright individuality of novel is more excellent.Concrete steps to each individual calculating target function value in described population are as follows:

1. revise individual coding

The (4)-1) after step completes, to the (4)-1) correction of encode of individuality in the initial population that produces of step, in first individuality being encoded, do not install the circuit of switch and the line switching state of fault section mains side supply path is set to 1; Again the on off state of fault section border circuit in individuality coding is set to 0, realizes Fault Isolation.

Take Fig. 2 power distribution network as example, illustrate the (4)-1) correction carried out of the individuality coding that obtains in step.As seen from Figure 2, the line set of not installing switch is { 3,5,8,10,14,16,19,21,23,25,27,30,33,35,38,39,41,44,45,46,47,50,55,57,59,61,65,67,68}; To in individuality coding, not install the circuit of switch and the circuit { 52,53,58 of fault section mains side supply path, the corresponding line switching state of 59,60,61} is set to 1, the circuit of fault section boundary switch the on off state that 54,56} is corresponding is set to 0, obtains revised individuality and is encoded to:

[1111110111 1111011111 1011111111 1111110111 1001111101 0110101111 1111111101 11]，

Corresponding line 10,14,19,23,35,44,52,53 in revised individual coding, the element of 57,59 and 60 the position of the switch is modified to 1 by 0, and the element of corresponding line 54 and 56 the position of the switch is modified to 0 by 1, and the element of corresponding all the other line switching positions is constant.

2. individuality is decoded

The (4)-2)-after 1. having walked, according to the (4)-2)-1. step correction individuality coding is later decoded, according to the track data of revised individual coding and input, determine that in individual coding, on off state is the track data of 1 correspondence, realize individual decoding.

Take Fig. 2 power distribution network as example, the decoding to individuality coding is described.To the (4)-1)-individuality the coding that 1. obtains in step, the circuit that is 1 by its on off state propose to obtain corresponding line set be:

{1，2，3，4，5，6，8，9，10，11，12，13，14，16，17，18，19，20，21，23，24，25，26，27，28，29，30，31，32，33，34，35，36，38，39，40，41，44，45，46，47，48，50，52，53，55，57，58，59，60，61，62，63，64，65，66，67，68，70，71，72}

The line set that is 1 according on off state can obtain first and last end node and the switchtype information of each circuit.

3. form the Radiation distribution network that individual different electrical power node connects

The (4)-2)-after 2. having walked, the Radiation Network shelf structure connecting for obtaining each power supply node, to the (4)-2)-2. walk the Depth Priority Algorithm of decoded individual line data application routine, first from different power supply nodes, start take interconnection switch place circuit and as border, search for the formation prompt radiation shape grid structure that each power supply node was connected; In prompt radiation shape grid structure, search for successively respectively again two end nodes of the circuit that interconnection switch is housed.When interconnection two end nodes all searched out-of-date, disconnect this interconnection switch and in this individuality coding, on off state corresponding to this interconnector is set to 0 to meet the requirement of Radiation Network shelf structure constraints formula (4), otherwise the prompt radiation shape grid structure that search interconnection headend node or endpoint node connect and the not decoded individual line data of searched mistake, form individual final Radiation Network shelf structure.

Take Fig. 2 power distribution network as example, illustrate and form the Radiation distribution network that individual different electrical power node connects.To the (4)-1)-the line set that 2. obtains in step, first with conventional Depth Priority Algorithm, starting take interconnection switch place circuit respectively from power supply node 1 and 70 searches for as border, form the prompt radiation shape grid structure that two power supply nodes connect, its line set is as follows:

The line set of the prompt radiation shape grid structure that power supply node 1 connects is { 1,2,3,4,5,6,9,10,11,12,13,14,17,18,19,20,21,24,25,26,27,28,29,30};

The line set of the prompt radiation shape grid structure that power supply node 70 connects is { 31,32,33,34,35,36,48,40,41,45,46,52,53,58,59,60,61}

To the interconnection switch circuit in decoded line set, { 70,71,72} searches for its two end node with conventional Depth Priority Algorithm successively respectively in prompt radiation shape grid structure again.First search for interconnection 70, because this circuit headend node is connected in the prompt radiation l network of power supply node 1, and therefore the not searched mistake of end node not can search for the not circuit of searched mistake in decoded line set.The line set searching is accordingly { 70,65,64,63,62,57,66,67,68}; This line set is merged in the prompt radiation l network of power supply node 1.Then the step of repeat search interconnection 70, searches for interconnection 71 and 72 respectively successively.Due to the equal searched mistake of two end nodes of interconnection 71 and 72, therefore disconnect the switch of interconnection 71 and 72, and the corresponding on off state of interconnection 71 in this individuality coding and 72 is set to 0.The line set of the final Radiation Network network of individuality obtaining after search finishes is:

The line set of the prompt radiation shape grid structure that power supply node 1 connects is:

{1，2，3，4，5，6，9，10，11，12，13，14，17，18，19，20，21，24，25，26，27，28，29，30，70，65，64，63，62，57，66，67，68}

The line set of the prompt radiation shape grid structure that power supply node 70 connects is:

{31，32，33，34，35，36，48，40，41，45，46，52，53，58，59，60，61}

4. calculate the trend of the Radiation distribution network of individual different electrical power node connection

The (4)-2)-after 3. having walked, first by the (4)-2) the line set of-Radiation network structure that 3. step is tried to achieve, according to the power distribution network basic parameter of input and the meritorious load or burden without work of each node during fault restoration of trying to achieve, determine each line impedance and the meritorious load or burden without work of each node of the Radiation network that this period different electrical power node connects; Use again and push back node voltage and the branch current that power flow algorithm is calculated the Radiation distribution network that each power supply node connects before traditional.In calculating, when the trend of the Radiation power distribution network connecting when certain power supply node does not restrain, finish whole trends and calculate.

Take Fig. 2 power distribution network as example, the trend of the Radiation distribution network that calculates individual different electrical power node connection is described.To the (4)-2)-the line set that 3. obtains in step, each line impedance of the Radiation network that while first determining period t=18, power supply node 1 is connected with 70 and each node load or burden without work (as shown in table 1) of gaining merit; Use and push back node voltage and the branch current that power flow algorithm is calculated the Radiation distribution network that each power supply node connects before traditional, result is as shown in table 2.

Each node voltage that table 2 trend calculates, each branch current

5. calculate individual target function value

The (4)-2)-after 4. having walked, when the (4)-2)-4. calculate the Radiation distribution network trend that different electrical power node connects in step to have while not restraining situation, individual target function value is composed to a larger value, 10 ⁹.When the trend of the Radiation power distribution network connecting when all power supply nodes all restrains, calculate individual total out-of-limit value, concrete formula is:

$F_{t,\mathrm{pen}}=\underset{i-1}{\overset{K_S}{\mathrm{\&Sigma;}}}(\underset{k\&Element;{\mathrm{\&alpha;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{U_{\min }-U_{t,k}}{U_B}+\underset{k\&Element;{\mathrm{\&beta;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{U_{t,k}-U_{\max }}{U_B}+\underset{b\&Element;{\mathrm{\&gamma;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{I_{t,b}}{I_{b.\max }})---\left(5\right)$

In formula: F _{t, pen}out-of-limit value for t period service restoration power distribution network; K _sfor power supply node sum; α _t,i, β _t,iand γ _t,ithe node voltage that is respectively the Radiation power distribution network that t period power supply node i connects is node set, the node voltage more node set of the upper limit and the set of fingers of line current overload of lower limit more; U _maxand U _minbe respectively node voltage bound; U _bfor reference voltage; I _b.maxampacity for circuit b; I _t,b, U _t,kbe respectively in the service restoration power distribution network of period t and flow through the electric current of circuit b, the voltage of node k.

When the out-of-limit value of individuality is not 0, individual goal functional value is composed to a higher value, 10 ⁹; When the out-of-limit value of individuality is 0, according to formula (1), calculate individual target function value.

Take Fig. 2 power distribution network as example, illustrate and calculate individual target function value.From table 2, the voltage of node 24-29,55,56,61-67 is got over lower limit, branch road 17,18,24,25 overload, thereby according to formula (5), to calculate individual total out-of-limit value be F _{18, pen}=5.0828.Because the out-of-limit value of individuality is not 0, by individual target function value assignment, be therefore 10 ⁹.

3) Evolution of Population calculates

The (4)-2)-after 5. having walked, use traditional genetic algorithm to be optimized calculating.First, defining current population is parent population, according to the (4)-2) the individual target function value of trying to achieve in step calculates fitness value individual in parent population; Secondly, to parent population, select operation, interlace operation and mutation operation to obtain progeny population; Again, employing the (4)-2) step is calculated whole individual goal functional values of described progeny population; Then, described progeny population is inserted into parent population and obtains new population; Finally judge whether Evolution of Population calculating finishes, when Evolution of Population algebraically does not reach maximum evolutionary generation, evolutionary generation is added to 1, and using new population as current population, repeat the calculating of this step, until Evolution of Population algebraically reaches the maximum evolutionary generation (K inputting in (1) step _max) till, just obtain coding and the target function value of each individuality in population; Otherwise finishing Evolution of Population calculates.

Take Fig. 2 power distribution network as example, the evolutionary computation of population is described.Individuality is encoded to the (4)-2 before evolutionary computation)-individuality correction the coding that 1. obtains in step, wherein position 7,15, and 22,37,42,43,49,51,54,56,69 element is 0, and the element of all the other positions is 1, individual out-of-limit value be 5.0828 and target function value be 10 ⁹.After fitness value calculation by traditional genetic algorithm, selection, cross and variation and the Evolution of Population that the operation such as heavily inserts calculate, this individual coding evolution is:

[1111111111 1111111111 1111111111 1111111111 1111111111 1110101111 1110101101 01]

In individuality coding after evolution, position 54,56,64,66,69,71 element is 0, the element of all the other positions is 1.With the (4)-2) the individual out-of-limit value that calculates of step be 0 and target function value be 843.18.

4) determine the rack set of minimum mistake load

The (4)-3) after step completes, from the (4)-3) select the individuality that minimum mistake load is different with coding the Evolution of Population result of calculation that obtains of step and form the set of candidate's rack.

Take Fig. 2 power distribution network as example, the rack set of determining minimum mistake load is described.Candidate's rack set that Evolution of Population calculate to finish to obtain when period t=18 is by target function value, to be 8 Different Individual of 843.18 to form.In these 8 individualities, the element of coding site 7 be respectively 0 and 1 respectively have 4 individualities.In addition, 8 front 61 elements of individuality are all identical with rear 3 elements, and different is the element of position 61-69.The set consisting of the element of 8 individuality 1-61 of putting in place and the element of 70-72 is respectively { 1,1,1,1,1,1,0/1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} and { 1,0,1}; 8 set that form at the element of position 61-69 are respectively { 0,0,0,1,0,1,1,1}, { 0,1,0,1,0,1,1,1}, { 1,0,0,1,0,1,1,1}, { 1,1,0,1,0,1,1,1}, { 0,0,0,1,0,1,1,0}, { 0,1,0,1,0,1,1,0}, { 1,0,0,1,0,1,1,0}, { 1,1,0,1,0,1,1,0}.

(5) determine the optimum dynamic power recovery scheme during fault restoration

After (4) step completes, in the rack set of the minimum mistake load of determining in (4) step, first define dynamic power recovery scheme by fault restoration during the set that service restoration scheme forms of each hour.According to each network selection frame number and lasting hourage of fault as a child during fault restoration, enumerate the whole dynamic power recovery schemes of combination again.Then calculate the switch motion number of times of whole dynamic power recovery schemes.Minimum first assembled scheme of last selector switch action frequency is as optimum dynamic power recovery scheme.

Take Fig. 2 power distribution network as example, the optimum dynamic power recovery scheme of determining during fault restoration is described.Use (4) step can obtain period t=18 during fault restoration, candidate's rack set of 19,20,21 o'clock, each candidate's rack set comprises respectively 8,8,16 and 8 kind of different rack.According to these candidate's rack numbers and the lasting hourage of fault, enumerate the whole dynamic power recovery schemes of combination, and be combined in the switch motion number of times that grid structure after the Fault Isolation obtaining in (3) step is calculated each dynamic power recovery scheme.First assembled scheme of switch motion least number of times is chosen as to final scheme.The final scheme switch motion number of times of trying to achieve is 9 times; Period t=18, the set that 19,20,21 individuality is coded in the element formation of position 1-61 is { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,1,1}, the line sectionalizing switch that wherein position 54 and 56 0 element representation isolated fault disconnect; The set forming at the element of position 65-72 is { 1,0,1,1,0,1,0,1}, wherein position 65,67 and 68 element 1 represent that circuit do not install switch, the element 0 of position 66 represents the block switch of open-circuit line 66, and position 69 and 71 element 0 represent the interconnection 69 that disconnects and 71 interconnection switch, and position 70 and 72 element 1 represent closed interconnection 70 and 72 interconnection switch; 4 set that form at the element of position 62-64 are respectively { 1,1,0}, { 1,0,1}, { 0,1,1} and { 1,1,1}.The on off state corresponding with the element of position 62-64 in optimum dynamic power recovery scheme and 66 and the load of recovery are as shown in table 3,

Circuit 62-64 and 66 on off state and the load of recovery in the optimum dynamic power recovery scheme of table 3

From Fig. 2 and table 3, while normally moving, the switch of interconnection 69-72 all disconnects, and all block switch is all closed.When circuit 55 faults, after the block switch isolated fault by open-circuit line 54 and 56, node 55,56, the load of 61-67 is in fault outage state.In 4 periods of optimum dynamic power recovery scheme, the switch of interconnection 69,71 and the block switch of circuit 66 all disconnect, and the switch of interconnection 70 and 72 is all closed.Because the block switch of 4 period circuits 66 all disconnects, avoided forming looped network in service restoration process; The switch of interconnection 72 is all closed, and the load of node 65-67 restores electricity by interconnection 72.In 4 periods, the switch of interconnection 70 is all closed, node 55,56, and the load of 61-64 can restore electricity by interconnection 70.But because the load of period 18 is maximum, can not recover whole loads of these nodes, the block switch of this period open-circuit line 64, the only load of recovery nodes 63,64 power supply.Along with constantly reducing of load, in the period 19, the block switch of open-circuit line 63, the block switch of closed circuit 64, the load power supply of node 62 is also restored; In the period 20, the block switch of open-circuit line 62, the block switch of closed circuit 63, the further power supply of the load of recovery nodes 61; In 21 periods, the block switch of closed circuit 62, the load power supply of recovery nodes 55,56.

Experimental result

Take Fig. 2 electric power system as example, with the service restoration expert system method (method 2) of method of the present invention (method 1) and existing consideration load variations, carry out the comparison of service restoration effect.While carrying out service restoration by method 2, require the service restoration scheme of formulating during whole fault restoration, can not occur that line current is out-of-limit.During the fault restoration in period 18 to the period 21, the load of period 18 is maximum, thus the decision of the load of period 18 grid structure of service restoration scheme.The service restoration scheme obtaining by method 2 is, closed interconnection 70 and 72 switch, open-circuit line 64 and 66 block switch; The load point restoring electricity has 63,64,65,66,67, and grid structure is constant within the recovery scheme enforcement time.In period 19 to the period 21, the load of the feeder line 2 in Fig. 2 reduces to make the main feeder of feeder line 2 or branch feeder head end current-carrying surplus to increase gradually gradually, increased the possibility that further recovery has a power failure and loads, yet method 2 can not adapt to this variation.By method 1, can take into full account load variations, be the rational grid structure of selection per hour during fault restoration.From table 3, load while reducing gradually during fault restoration, the characteristic that rack changes flexibly can progressively be recovered node 62,61,55 in Fig. 2 and 56 power supply ladderingly.Therefore, by adjusting grid structure, can shorten the interruption duration of sub-load.

When fault occurs in load, increase, and can not cause that the main feeder that restores electricity or branch feeder head end occur that electric current is out-of-limit, while there is voltage out-of-limit in end, method 1 is better than method 2 equally.For example, at based model for load duration, between the rise period, there are circuit 55 faults in the period 7, and the period 10 is repaired fault.Because requiring the service restoration scheme of formulating, method 2 during whole fault restoration, can not occur that line current is out-of-limit, therefore the service restoration rack obtaining only can recover the power supply of load bus 63-67 during whole fault restoration, load bus 55,56,61,62 will continue to have a power failure to the period 10 from the period 7.The individuality of the optimum dynamic power recovery scheme that employing method 1 obtains is identical with 8 coding in the period 7, and the period 9 is identical with 10 coding.The difference of two codings is only, in position, 64 element is 1 for the former, and in position, 64 element is 0 to the latter.The set that element forms is { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1/0, 1, 0, 1, 1, 0, 1, 0, 1}, wherein position 54 and 56 element 0 represent the line switching that isolated fault disconnects, position 69 and 71 element 0 represent the interconnection switch disconnecting, position 70 and 72 element 1 represent closed interconnection switch, switch motion number of times is 4 times.The on off state corresponding with the element of position 64 in optimum dynamic power recovery scheme and 66 and the load of recovery are as shown in table 4,

Circuit 64 and 66 on off state and the load of recovery in the optimum dynamic power recovery scheme of table 4

From table 4, method 1 can be recovered the load power supply of all power failure nodes 55,56 and 61-67 in the period 7 and 8.Because the growth of load in period 9 and 10 will cause the overload of circuit, therefore the block switch on periods 9 open-circuit line 64, the user on excision load bus 55,56,61,62, avoids occurring line current overload.At fault early period of origination, according to load curve, can expect in the period 9 block switch on open-circuit line 64 is caused to load bus 55,56,61,62 user has a power failure, thereby these users that can notify early, reduces loss of outage.Visible, method 1 ratio method 2 can be recovered customer power supply as much as possible, and can before there is circuit overload, limit user power utilization, thereby by early reducing the unnecessary loss of user because having a power failure and bring suddenly to user notification power failure information.

Table 5 has provided the mistake load bus interruption duration between two kinds of method age at failures.In table 5, the interruption duration that recovery scheme is implemented the node 62 of 18～period of period 21 shortened to 1 hour from 4 hours, and the interruption duration of node 61 shortened to 2 hours from 4 hours, and node 55 and 56 interruption duration shortened to 3 hours from 4 hours.At recovery scheme, implement in 7～period of period 11, node 55,56,61,62 interruption duration all shortened to 2 hours from 4 hours.Because the method 1 ratio method 2 more can shorten the interruption duration of certain customers.

Mistake load point interruption duration (h) between two kinds of method age at failures of table 5

Table 6 has provided the electric weight recovering between two kinds of method age at failures.From table 6, the electric weight that the electricity ratio method 2 that method 1 is recovered is recovered is many, shows that method 1 is reducing the electricity sales amount that has increased Utilities Electric Co. when user has a power failure.

The electric weight recovering between two kinds of method age at failures of table 6

Method 1 can also be avoided occurring becoming the situation of invalid scheme owing to not meeting the final recovery scheme of security constraint.For example, at periods 18 circuit 25, break down, fault ends up being the period 20.As seen from Figure 2, load point 25,26, therefore 27,28,29 can have a power failure.By method 2, can formulate switch on closed circuit 70 load point 25,26 that makes to have a power failure, 27,28,29 schemes that restore electricity.While carrying out its security constraint of trend calculation check after making service restoration scheme, discovery system is the lower voltage limit lower than system requirements at the minimum voltage of period 18, and the recovery scheme of therefore formulating by method 2 is invalid, load point 25,26,27,28,29 all will have a power failure 4 hours.The optimal power recovery scheme of formulating by method 1 is as shown in table 7.In process due to candidate's rack set of each hour minimum mistake load during determining fault restoration, consider the security constraint of branch current and node voltage, therefore the final optimum dynamic power recovery scheme of determining can not disobeyed limit because of security constraint, become invalid scheme.

Table 7 faulty line is the optimum dynamic power recovery scheme of 25 o'clock

From above-mentioned experimental result and analysis, relatively know:

(1) the present invention, when considering load variations, can formulate service restoration rack for payload hourly during fault restoration, can utilize more careful and fully load curve.

(2) dynamic power restoration methods of the present invention can be adjusted grid structure according to the needs of load variations in good time, and scheme has time and space dynamic.

(3) the present invention compared with the conventional method, can further reduce customer outage hours, recovers more electric weight.Meanwhile, thus the present invention can also reduce user because of power failure bring suddenly loss by prior notice customer outage hours.

(4) the present invention compared with the conventional method, during determining fault restoration in the process of each hour minimum mistake load candidate rack set, considered the security constraint of branch current and node voltage, therefore definite dynamic power recovery scheme can avoid occurring that final recovery scheme becomes the situation of invalid scheme owing to not meeting security constraint.

Claims (1)

1. the power distribution network dynamic power restoration methods based on load curve, utilizes computer, by program, calculates, and effectively formulates the concrete steps that the optimum dynamic power recovery scheme during fault restoration is characterized in that described method as follows:

(1) input basic parameter

First, required basic parameter is calculated in input, the parameter that comprises basic parameter and the traditional genetic algorithm of power distribution network, the basic parameter of power distribution network comprises circuit sum (M), circuit number, circuit first and last end node numbering, line resistance (R), line reactance (X), line energizing flow amount, line switching type (not installing switch, installing block switch, installing interconnection switch), circuit place feeder line numbering; Node sum (N), power supply node sum (K _s), power supply node numbering, node burden with power (P _l), node load or burden without work (Q _l), the meritorious daily load rate curve of node load type, various load types; The node voltage upper limit (U _max), node voltage lower limit (U _min); Faulty line numbering, time of failure (t ₁), fault end time (t ₂); Reference voltage (U _b), reference power (S _b), the parameter of traditional genetic algorithm comprises population scale (P _p), maximum evolutionary generation (K _max), generation gap (P _g), crossing-over rate (p _c), aberration rate (p _m);

(2) grid structure while calculating meritorious, the load or burden without work of each node each hour and determining normal operation

After (1) step completes, first according to the burden with power (P of each node of (1) step input _l), load or burden without work (Q _l) and the meritorious daily load curve of various load types, according to the constant principle of power factor, calculate each node burden with power and the load or burden without work of each hour, then according to the position of the interconnection switch of installing in power distribution network, the grid structure while determining normal operation;

(3) determine the supply path of fault section and mains side and the grid structure after Fault Isolation

After (2) step completes, in (2) step, determine normal operation time grid structure in, for ease of optimizing, calculate and reduce computing time, first failure definition section is centered by fault point and take the line set that nearest switch is border from fault point; The supply path of failure definition section mains side is the line set between from power supply node to fault section, then uses conventional Depth Priority Algorithm, whether installs switch determine fault section according to faulty line head end; From the power supply node of faulty line place feeder line, start to determine the supply path of fault section mains side, the boundary switch isolated fault of fault section for grid structure while finally normally moving according to the definite power distribution network of (2) step, determines the grid structure after Fault Isolation;

(4) use traditional genetic algorithm to determine candidate's grid structure set of each hour minimum mistake load during fault restoration

After (3) step completes, in grid structure after the definite Fault Isolation of (3) step, for obtaining the grid structure of power distribution network each hour minimum mistake load during fault restoration after Fault Isolation, to determine candidate's grid structure set of dynamic power recovery scheme, during the fault restoration that utilization obtains based on load curve, each hour loads and solves the optimal models of corresponding power distribution network service restoration, the target function of this model is minimum mistake load, constraints is the constraints such as branch current, node voltage and Radiation Network shelf structure, and concrete formula is as follows:

$\min P_{t,c}\left(X_{t,r}\right)=\underset{n\&Element;{\mathrm{\&Omega;}}_N}{\mathrm{\&Sigma;}}{P}_{t,n}-\underset{k\&Element;{\mathrm{\&Omega;}}_K}{\mathrm{\&Sigma;}}{P}_{t,k}---\left(1\right)$

s.t.I _t,b≤I _b.max (2)

U _min≤U _t,k≤U _max (3)

g _t,i∈G(4)

In formula: t is the period, the time of one day being divided into 24 hours, every 1 hour is 1 period; P _t,cmistake load for period t; X _t,rfor the line switching state vector of the service restoration power distribution network of period t, X _t,r=[W _{t, r1}..., W _{t, rm}... W _{t, rM}]; M is circuit sum; W _{t, rm}for X _t,rthe on off state of m bar circuit, the switch of not installing switch or installing when circuit is taken as 1 during in closure state, when the switch of installing is taken as 0 during in off-state; Ω _nand P _t,nbe respectively the node set of the power distribution network before service restoration and node n in the burden with power of period t; Ω _kand P _t,kbe respectively the node set of service restoration power distribution network and node k in the burden with power of period t; N and K are respectively the node sum of service restoration front and back power distribution network; I _t,b, U _t,kand g _t,ibe respectively in the service restoration power distribution network of period t and flow through the electric current of circuit b, voltage and the grid structure of node k; I _b.maxampacity for circuit b; U _maxand U _minbe respectively the bound of node voltage; G is the set of Radiation Network shelf structure;

The concrete steps of grid structure that solve during fault restoration the minimum mistake load that each hour load is corresponding by traditional genetic algorithm are as follows:

1) form initial population

After (3) step completes, according to the population scale (P of (1) step input _p), with { 0,1} binary code, the individuality that is population scale to the number of random generation is encoded, form initial population, in initial population, each individual code length is circuit sum, and each coding represents the circuit head end on off state of power distribution network, when being encoded to 0, represent that this line switching is in off-state; When being encoded to 1, represent that this line switching is in closure state;

2) calculate target function value individual in population

The (4)-1) after step completes, for evaluating the (4)-1) quality of individual performance in the initial population that forms of step, each individual target function value in this population is calculated, the individual target function value more performance of the bright individuality of novel is more excellent, as follows to the concrete steps of each individual calculating target function value in described population:

1. revise individual coding

The (4)-1) after step completes, to the (4)-1) correction of encode of individuality in the initial population that produces of step, in first individuality being encoded, do not install the circuit of switch and the line switching state of fault section mains side supply path is set to 1; Again the on off state of fault section border circuit in individuality coding is set to 0, realizes Fault Isolation;

2. individuality is decoded

The (4)-2)-after 1. having walked, according to the (4)-2)-1. step correction individuality coding is later decoded, according to the track data of revised individual coding and input, determine that in individual coding, on off state is the track data of 1 correspondence, realize individual decoding;

3. form the Radiation distribution network that individual different electrical power node connects

The (4)-2)-after 2. having walked, the Radiation Network shelf structure connecting for obtaining each power supply node, to the (4)-2)-2. walk the Depth Priority Algorithm of decoded individual line data application routine, first from different power supply nodes, start take interconnection switch place circuit and as border, search for the formation prompt radiation shape grid structure that each power supply node was connected; In prompt radiation shape grid structure, search for successively respectively again two end nodes of the circuit that interconnection switch is housed, when interconnection two end nodes all searched out-of-date, disconnect this interconnection switch and in this individuality coding, on off state corresponding to this interconnector is set to 0 to meet the requirement of Radiation Network shelf structure constraints formula (4), otherwise the prompt radiation shape grid structure that search interconnection headend node or endpoint node connect and the not decoded individual line data of searched mistake, form individual final Radiation Network shelf structure;

4. calculate the trend of the Radiation distribution network of individual different electrical power node connection

The (4)-2)-after 3. having walked, first by the (4)-2) the line set of-Radiation network structure that 3. step is tried to achieve, according to the power distribution network basic parameter of input and the meritorious load or burden without work of each node during fault restoration of trying to achieve, determine each line impedance and the meritorious load or burden without work of each node of the Radiation network that this period different electrical power node connects; Use again and push back node voltage and the branch current that power flow algorithm is calculated the Radiation distribution network that each power supply node connects before traditional, in calculating, when the trend of the Radiation power distribution network connecting when certain power supply node does not restrain, finish whole trends and calculate;

5. calculate individual target function value

The (4)-2)-after 4. having walked, when the (4)-2)-4. calculate the Radiation distribution network trend that different electrical power node connects in step to have while not restraining situation, individual target function value is composed to a larger value, 10 ⁹, when the trend of the Radiation power distribution network connecting when all power supply nodes all restrains, calculating individual total out-of-limit value, concrete formula is:

$F_{t,\mathrm{pen}}=\underset{i-1}{\overset{K_S}{\mathrm{\&Sigma;}}}(\underset{k\&Element;{\mathrm{\&alpha;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{U_{\min }-U_{t,k}}{U_B}+\underset{k\&Element;{\mathrm{\&beta;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{U_{t,k}-U_{\max }}{U_B}+\underset{b\&Element;{\mathrm{\&gamma;}}_{t,i}}{\mathrm{\&Sigma;}}\frac{I_{t,b}}{I_{b.\max }})---\left(5\right)$

In formula: F _{t, pen}out-of-limit value for t period service restoration power distribution network; K _sfor power supply node sum; α _t,i, β _t,iwith _{γ t, i}the node voltage that is respectively the Radiation power distribution network that t period power supply node i connects is node set, the node voltage more node set of the upper limit and the set of fingers of line current overload of lower limit more; U _maxand U _minbe respectively node voltage bound; U _bfor reference voltage; I _b.maxampacity for circuit b; I _t,b, U _t,kbe respectively in the service restoration power distribution network of period t and flow through the electric current of circuit b, the voltage of node k;

When the out-of-limit value of individuality is not 0, individual goal functional value is composed to a higher value, 10 ⁹; When the out-of-limit value of individuality is 0, according to formula (1), calculate individual target function value;

3) Evolution of Population calculates

The (4)-2)-after 5. having walked, use traditional genetic algorithm to be optimized calculating, first, defining current population is parent population, according to the (4)-2) the individual target function value of trying to achieve in step calculates fitness value individual in parent population; Secondly, to parent population, select operation, interlace operation and mutation operation to obtain progeny population; Again, employing the (4)-2) step is calculated whole individual goal functional values of described progeny population; Then, described progeny population is inserted into parent population and obtains new population; Finally judge whether Evolution of Population calculating finishes, when Evolution of Population algebraically does not reach maximum evolutionary generation, evolutionary generation is added to 1, and using new population as current population, repeat the calculating of this step, until Evolution of Population algebraically reaches the maximum evolutionary generation (K inputting in (1) step _max) till, just obtain coding and the target function value of each individuality in population; Otherwise finishing Evolution of Population calculates;

4) determine the rack set of minimum mistake load

The (4)-3) after step completes, from the (4)-3) select the individuality that minimum mistake load is different with coding the Evolution of Population result of calculation that obtains of step and form the set of candidate's rack;

(5) determine the optimum dynamic power recovery scheme during fault restoration

After (4) step completes, in the rack set of the minimum mistake load of determining in (4) step, first define dynamic power recovery scheme by fault restoration during the set that service restoration scheme forms of each hour, again according to each network selection frame number and lasting hourage of fault as a child during fault restoration, enumerate the whole dynamic power recovery schemes of combination, then calculate the switch motion number of times of whole dynamic power recovery schemes, minimum first assembled scheme of last selector switch action frequency is as optimum dynamic power recovery scheme.

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