CN102570493A - Optimal control method for reducing parallel initial fault current angles of looped network in power system restoration - Google Patents

Abstract

The invention discloses an optimal control method for reducing parallel initial fault current angles of a looped network in power system restoration, which comprises the following steps of: 1) building a mixed integer programming model for reducing parallel initial fault current angles of the looped network through taking an operation of increasing the active power outputs and inputted to-be-recovered loads of generators as a control means; 2) judging whether the number of the generators participating in the adjustment and controlling on initial fault current angles is minimized, if so, turning to a step 7), and otherwise, turning to the next step; 3) to the generators that the active power output is increased and the active power output does not reach the upper power-output limit, calculating the sensitivities of the increased active power output on the reduction of initial fault current angles, and sequencing the sensitivities from high to low; 4) by using a dichotomy principle, selecting the generators with a high sensitivity in the sequence to participate in the adjustment and controlling on the initial fault current angles; 5) by using the model built in the step 1), calculating the active power output increasing amounts and restored load amounts of the generators; 6) according to the active power output adjusting conditions of the generators, judging whether the number of the generators is minimized, if so, turning to the step 7), and otherwise, turning to the step 4); and 7) completing the adjustment and controlling on the initial fault current angles.

Description

Reduce the method for optimally controlling of looped network switching angle arranged side by side in the power system recovery

Technical field

The present invention relates to reduce in a kind of power system recovery the method for optimally controlling of looped network switching angle arranged side by side.

Background technology

Power system recovery after having a power failure on a large scale is the control and the decision problem of a complicacy; And there is a series of relevant issues [document 1; ADIBI M M.Power system restoration:methodologies&implementation strategies [M] .New York:IEEE Press, 2000.].During the looped network parallel operation, treat and the excessive phase difference of voltage in column line two ends (standing phase angle, SPA); It is switching angle; Be exactly one of them major issue [document 2, ADIBI M M, KAFKAR J.Power system restoration issues [J] .IEEE Computer Applications in Power; 1991,4 (2): 19-24.].If when switching angle is excessive, carry out parallel operation, then can cause damage, even once more power outage take place near system equipment.Therefore, before carrying out the looped network parallel operation, need switching angle be reduced in the scope of permission.

For the looped network parallel operation between convalescence, usually by the dispatcher according to prediction scheme and the experience of in the past handling similar accident handle.Yet there is very big difference in the scene of having a power failure on a large scale with normal operating condition, and existing recovery prediction scheme can not contain all power failure scenes of electrical network.Complexity [document 3, Xue Yusheng, Wang Haohao in view of the switching angle adjustment; DONG Zhaoyang; Deng. interconnected network recovers the commentary [J] of control under the Power Market. Automation of Electric Systems, 2007,31 (21): 110-115.]; No matter during recovering prediction scheme and formulating still during restoration, all need the decision-making assistant information of looped network parallel operation.

At present, existing multiple looped network switching angle control method arranged side by side realizes the looped network parallel operation apace in order to instruct scheduling and operations staff.In these methods, be adjusted into main control device, be aided with a small amount of load of excision with meritorious the exerting oneself of generator; With system's safety in operation and switching angle limit value is constraints.Wherein, safety in operation constraint comprises that generator is meritorious exerts oneself and the idle upper lower limit value of exerting oneself, node voltage upper lower limit value and circuit maximum transmission power, etc.Target function mainly is that the meritorious adjustment amount quadratic sum of exerting oneself of generator is minimum, the also additional requirement of participating in adjustment unit minimum number that has.[document 4, WUNDERLICHS, ADIBI M M; FISCHL R, et al.An approach to standing phase angle reduction [J] .IEEE Trans on Power Systems, 1994; 9 (1): 470-478.], [document 5, MARTINS N, OLIVEIRA E J de; PEREIRA J L R, et al.Reducing standing phase angle via interior point optimum power flow for improved system restoration [C] //Proceedings of IEEE PES Power System Conference and Exposition, 2004; New York; USA:404-408.] and [document 6, YUAN R, LING J; ZHANG Z; Et al.A genetic algorithm method for standing phase angle reduction in power system restoration [C] //Proceedings of 2010 IEEE Power and Energy Society General Meeting Minneapolis, 2010, USA:1-6.] adopt Mathematical Planning and genetic algorithm respectively; Through finding the solution the optimization problem that comprises system's safety in operation and switching angle constraint, obtain reducing the switching angle control strategy.[document 7, HAZARIKA D, SINHA A K.Standing phase angle reduction for power system restoration [J] .IEEE Proceedings-Generation; Transmission and Distribution; 1998,145 (1): 82-88.], [document 8, HAZARIKAD; SINHA A K.An algorithm for standing phase angle reduction for power system restoration [J] .IEEE Trans on Power Systems; 1999,14 (4): 1213-1218.], [document 9, KETABI A; RANJBAR A M; FEUILLETR.New approach to standing phase angle reduction for power system restoration [J] .European Transactions on Electric Power, 2002,12 (4): 301-307.] based on sensitivity analysis; With treating that also the variation approximate representation of column line two ends switching angle is the linear combination of the meritorious adjustment amount of exerting oneself of generator, obtain participating in the minimum number generator and the meritorious adjustment amount of exerting oneself thereof of adjustment through heuristic search.

Above-mentionedly reduce the method for switching angle with the meritorious adjustment of exerting oneself of generator as control variables, the control of switching angle suits in the conventional looped network parallel operation of zero load loss for the stoppage in transit circuit is only arranged.In the back system restoration process of having a power failure on a large scale, because load recovery fully as yet, if when increasing generator output; Optionally drop into and have big sensitivity, load that importance is high, realize the coordination of switching angle regulation and control and load restoration, when reaching looped network condition arranged side by side within a short period of time reducing switching angle; Also realized recovery to the part important load; This obviously can improve recovery efficient, accelerates recovering process, reduces loss of outage.

As everyone knows, active power is transmitted on the line and can be produced the voltage landing, makes the phase angle that receives terminal voltage greater than sending end.Move towards clear and definite system for simple in structure, trend; Based on the assurance that the analysis of electric network composition and trend are distributed; The thinking of switching angle regulation and control is: at first, according to the phase angle size of node voltage, treating and the column line both sides are divided into electrical network and are held and send end; Receive the terminal voltage phase angle little, send the terminal voltage phase angle big; Then, utilize to reduce and send the method for being held active power, can reduce to treat the also switching angle at column line two ends.Particularly, sending end can drop into, selected reducing the effective unit of switching angle and increasing meritorious exerting oneself by end to reducing the switching angle load that effectively has a power failure.

Because during restoration can not there be abundant power backup in system; For larger, baroque electrical network; How to select reducing switching angle the most effectively unit, the most effective and high load of importance; And accomplish the regulation and control of switching angle with minimum regulation and control object and adjustment amount, be above-mentioned regulation and control Application of thought difficult point.

In addition, in the system restoration process after having a power failure on a large scale, automatic electricity generation control system often unavailable [document 4], the meritorious adjustment of generator needs the repeatedly mutual of scheduling and operations staff and accomplishes through manual operation.Therefore, in reducing the process of switching angle,, should make the generator minimum number of participating in adjustment for alleviating scheduling and operations staff's burden as far as possible.

Document [7-9] increases the generator quantity of participating in adjustment according to the meritorious adjustment amount of generator to the level of sensitivity that reduces switching angle one by one, is reduced to set point until switching angle.Document [4] is at first supposed the regulation process of whole generators participation reducing switching angles, obtains the generator adjustment amount; Preferentially participate in the principle adjusted according to the big generator of adjustment amount then, increase generator quantity one by one, until reaching goal of regulation and control.Confirm that more than there is certain deficiency in the method for participating in adjustment minimum number generator: 1. in the process that increases generator one by one, need recomputate the meritorious adjustment amount of generator; 2. in document [4] method, it is less but to reducing the generator that switching angle has higher sensitivity, can not preferentially participate in situation about adjusting the meritorious adjustable range of exerting oneself to occur.

Summary of the invention

The object of the invention is exactly for addressing the above problem; The method for optimally controlling that reduces looped network switching angle arranged side by side in a kind of power system recovery is provided; Generator is meritorious exerts oneself and drops into load as control variables to increase for it, takes into account and waits the importance recovering to load, through finding the solution mixed-integer programming model; Obtain reducing the optimal control amount of looped network and column line two ends excessive voltage phase angle difference, utilize the dichotomy principle to confirm to participate in the generator of adjustment minimum number.

For realizing above-mentioned purpose, the present invention adopts following technical scheme:

Reduce the method for optimally controlling of looped network switching angle arranged side by side in a kind of power system recovery, step is:

Step 1; Selection is held the whole generators in the electrical network to increase and is meritoriously exerted oneself and drop into and send load to be recovered in the end electrical network as control variables; Take into account and wait the importance recovering to load, set up the mixed-integer programming model that reduces looped network and column line two ends excessive voltage phase angle difference;

Step 2 by the meritorious adjustment situation of exerting oneself of the generator that calculates, judges whether the generator quantity of participating in regulation and control reaches minimum; If reach, then change step 7; Otherwise, change next step;

Step 3 increases meritorious exerting oneself to reducing the sensitivity of switching angle for increasing meritorious exert oneself and meritorious exerting oneself do not reach the generator of the upper limit of exerting oneself, calculating, and ordering from high to low;

Step 4 is utilized two fens principles, selects the higher part generator of sensitivity in the sequence to participate in the switching angle regulation and control, changes next step;

Step 5 is utilized the Optimization Model of step 1 once more, obtains meritorious adjustment situation of exerting oneself of this part generator and the situation that drops into load;

Step 6 by the meritorious adjustment situation of exerting oneself of the generator that calculates, judges whether generator quantity reaches minimum; If reach, then change step 7; Otherwise, change step 4;

Step 7, the switching angle regulation and control finish.

In the said step 1, mixed-integer programming model is following:

$\underset{P_{\mathrm{gi}},Q_{\mathrm{gi}},{\mathrm{\ΔP}}_{\mathrm{dis}},{\mathrm{\ΔQ}}_{\mathrm{dis}}}{\min }\underset{i}{\mathrm{\Σ}}\mathrm{\α}(P_{\mathrm{gi}}-P_{\mathrm{gi}0})+\underset{i}{\mathrm{\Σ}}\underset{s}{\mathrm{\Σ}}\frac{x_{\mathrm{is}}{\mathrm{\ΔP}}_{\mathrm{dis}}}{w_{\mathrm{is}}}---\left(1\right)$

$P_{\mathrm{gi}}-P_{\mathrm{di}}-\underset{s}{\mathrm{\Σ}}{x}_{\mathrm{is}}{\mathrm{\ΔP}}_{\mathrm{dis}}$

(2)

$=U_i\underset{j\∈i}{\mathrm{\Σ}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}),i\∈S_B$

$Q_{\mathrm{gi}}-Q_{\mathrm{di}}-\underset{s}{\mathrm{\Σ}}{x}_{\mathrm{is}}{\mathrm{\ΔQ}}_{\mathrm{dis}}$

(3)

$=U_i\underset{j\∈i}{\mathrm{\Σ}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}),i\∈S_B$

$P_{\mathrm{ij}}=-U_i^2{G}_{\mathrm{ij}}+U_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}),i\∈S_L---\left(4\right)$

$P_{\mathrm{gi}0}\≤P_{\mathrm{gi}}\≤P_{\mathrm{gi}}^{\max },i\∈---\left(5\right)$

$Q_{\mathrm{gi}}^{\min }\≤Q_{\mathrm{gi}}\≤Q_{\mathrm{gi}}^{\max },i\∈S_R---\left(6\right)$

$U_i^{\min }\≤U_i\≤U_i^{\max },i\∈S_B---\left(7\right)$

$\left|P_{\mathrm{ij}}\right|\≤P_{\mathrm{ij}}^{\max },i,j\∈S_L---\left(8\right)$

θ _mn≤θ _set (9)

In the formula: P _GiAnd Q _GiBe respectively meritorious, idle the exerting oneself of generator i; P _Gi0For the meritorious of generator i under the initial condition exerted oneself; Definition Δ P _Gi=P _Gi-P _Gi0Δ P _DisWith Δ Q _DisBe respectively meritorious and load or burden without work amount to be recovered in the outlet of s load of node i; x _IsWhether the outlet of s load of expression node i is resumed, and is 1 if be resumed, otherwise is 0; w _IsWeight for the outlet of s load of node i; α is that meritorious the exerting oneself of generator increases the weight of total amount with respect to weighting load restoration total amount.U _iAnd θ _iBe respectively the voltage magnitude and the phase angle of node i; θ _Ij=θ _i-θ _jP _DiAnd Q _DiBe respectively the meritorious and load or burden without work that has been resumed on the node i; G _IjAnd B _IjThe electricity that is respectively circuit i-j is led and susceptance; P _IjBe the active power on the circuit i-j;

The meritorious higher limit of exerting oneself for generator i;

With

Be respectively the idle upper limit value and lower limit value of exerting oneself of generator i;

With

Be respectively the upper limit value and lower limit value of node i voltage magnitude;

For circuit i-j goes up meritorious through-put power limit value; θ _MnAnd θ _SetBe respectively and treat and the switching angle at column line m-n two ends and detect relay switching angle set point the same period.S _G, S _R, S _B, S _LBe respectively adjustable meritorious generator set, the set of adjustable reactive power generation machine, all node set of system and all set of fingers.

Operation principle of the present invention:

1. generator is meritorious exerts oneself and drops into load as control device to increase, and is constraint with system's safety in operation and switching angle higher limit, and the importance and the discreteness characteristics [document 10 that recover to load waited in consideration; Zhou Yunhai, Min Yong. the fast restoration algorithm research [J] of load. Proceedings of the CSEE, 2003; 23 (3): 74-79.], [document 11; Qu Hanbing, Liu Yutian. the load restoration optimization [J] in the unit starting process. Automation of Electric Systems, 2010; 33 (8): 16-21.] it is following, to set up the mixed integer nonlinear programming model reduce switching angle:

$\underset{P_{\mathrm{gi}},Q_{\mathrm{gi}},{\mathrm{\ΔP}}_{\mathrm{dis}},{\mathrm{\ΔQ}}_{\mathrm{dis}}}{\min }\underset{i}{\mathrm{\Σ}}\mathrm{\α}(P_{\mathrm{gi}}-P_{\mathrm{gi}0})+\underset{i}{\mathrm{\Σ}}\underset{s}{\mathrm{\Σ}}\frac{x_{\mathrm{is}}{\mathrm{\ΔP}}_{\mathrm{dis}}}{w_{\mathrm{is}}}---\left(10\right)$

$P_{\mathrm{gi}}-P_{\mathrm{di}}-\underset{s}{\mathrm{\Σ}}{x}_{\mathrm{is}}{\mathrm{\ΔP}}_{\mathrm{dis}}$

(11)

$=U_i\underset{j\∈i}{\mathrm{\Σ}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}),i\∈S_B$

$Q_{\mathrm{gi}}-Q_{\mathrm{di}}-\underset{s}{\mathrm{\Σ}}{x}_{\mathrm{is}}{\mathrm{\ΔQ}}_{\mathrm{dis}}$

(12)

$=U_i\underset{j\∈i}{\mathrm{\Σ}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\θ}}_{\mathrm{ij}}),i\∈S_B$

$P_{\mathrm{ij}}=-U_i^2{G}_{\mathrm{ij}}+U_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\θ}}_{\mathrm{ij}}),i\∈S_L---\left(13\right)$

${\mathrm{<figure-callout\; id="0"\; label="P\; gi"\; filenames="HDA0000106605250000031.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{gi}}\&le;P_{\mathrm{gi}}\&le;P_{\mathrm{gi}}^{\max },i\&Element;---\left(14\right)$

$Q_{\mathrm{gi}}^{\min }\&le;Q_{\mathrm{gi}}\&le;Q_{\mathrm{gi}}^{\max },i\&Element;S_R---\left(15\right)$

$U_i^{\min }\&le;U_i\&le;U_i^{\max },i\&Element;S_B---\left(16\right)$

$\left|P_{\mathrm{ij}}\right|\&le;P_{\mathrm{ij}}^{\max },i,j\&Element;S_L---\left(17\right)$

θ _mn≤θ _set (18)

In the formula: P _GiAnd Q _GiBe respectively meritorious, idle the exerting oneself of generator i; P _Gi0For the meritorious of generator i under the initial condition exerted oneself; Definition Δ P _Gi=P _Gi-P _Gi0Δ P _DisWith Δ Q _DisBe respectively meritorious and load or burden without work amount to be recovered in the outlet of s load of node i; x _IsWhether the outlet of s load of expression node i is resumed, and is 1 if be resumed, otherwise is 0; w _IsWeight for the outlet of s load of node i; α is that meritorious the exerting oneself of generator increases the weight of total amount with respect to weighting load restoration total amount.U _iAnd θ _iBe respectively the voltage magnitude and the phase angle of node i; θ _Ij=θ _i-θ _jP _DiAnd Q _DiBe respectively the meritorious and load or burden without work that has been resumed on the node i; G _IjAnd B _IjThe electricity that is respectively circuit i-j is led and susceptance; P _IjBe the active power on the circuit i-j;

The meritorious higher limit of exerting oneself for generator i; With Be respectively the idle upper limit value and lower limit value of exerting oneself of generator i;

With

Be respectively the upper limit value and lower limit value of node i voltage magnitude;

For circuit i-j goes up meritorious through-put power limit value; θ _MnAnd θ _SetBe respectively and treat and the switching angle at column line m-n two ends and detect relay switching angle set point the same period.S _G, S _R, S _B, S _LBe respectively adjustable meritorious generator set, the set of adjustable reactive power generation machine, all node set of system and all set of fingers.

2. the switching angle optimum is regulated and control flow process

The present invention proposes a kind of definite method of adjusting the minimum number generator based on the participation of two fens principles.Based on this method and combine to reduce the new model of switching angle, provide the flow process of the optimum regulation and control of looped network switching angle arranged side by side in the system restoration, as shown in Figure 1.

Among Fig. 1, at first select to be held the generator in the electrical network to participate in regulation and control, gaining merit exerts oneself and exert oneself does not reach the generator of the upper limit for increasing, and according to increasing meritorious exerting oneself the sensitivity that reduces switching angle is sorted from high to low; Adopt the dichotomy iteration then, obtain increasing the generator set and the corresponding recruitment of the meritorious minimum number of exerting oneself.Like this, satisfying scheduling and operations staff to participating in adjusting under the prerequisite of generator quantitative requirement the total computation amount that makes optimum regulation and control.

3 model solutions and performance evaluation

Branch-bound algorithm combine with Nonlinear Programming Algorithm be the effective ways of finding the solution the mixed integer nonlinear programming problem [document 13, HILLIER F S, LIEBERMAN G J. operational research introduction (the 9th edition) [M]. Beijing: publishing house of Tsing-Hua University, 2010.].At universal algebra modeling software (General Algebraic Modeling System; GAMS) set up the model shown in formula (1)-Shi (9) in; Adopt branch-and-bound solver (Standard Branch and Bound; SBB) find the solution, wherein adopt MINOS (Modular In-core Non-linear Optimization System) solver to find the solution with the corresponding nonlinear programming problem of model.

The invention has the beneficial effects as follows: the model that reduces switching angle with routine is compared, and the optimum regulate and control method that reduces switching angle that the present invention proposes has following advantage.

1) routine reduces switching angle model [document 5; MARTINS N, OLIVEIRA E J de, PEREIRA J L R; Et al.Reducing standing phase angle via interior point optimum power flow for improved system restoration [C] //Proceed ings of IEEE PES Power System Conference and Exposition; 2004, New York, USA:404-408.] be target function with the meritorious adjustment amount quadratic sum minimum of exerting oneself of generator; If do not consider to participate in adjusting the minimum requirement of generator quantity, then nearly all unit will be participated in adjustment.And in reducing the new model of switching angle, be sub-goal with the meritorious recruitment sum minimum of exerting oneself of generator, the generator quantity of participating in adjustment is few.And then when utilizing dichotomy to confirm to participate in the generator of adjustment minimum number, required iterations is few.

2) meritorious to exert oneself and recover load be control device to the new model that reduces switching angle to increase generator, and under same switching angle limit value, required controlled quentity controlled variable is little, requires low to system reserve.See that from another kind of angle it has stronger ability of regulation and control to switching angle.

3) reduce in the model [document 5] of switching angle in routine, have at least a generator to reduce meritorious exerting oneself, other has a generator to increase meritorious exerting oneself.Thereby, based on increase meritorious exert oneself be control variables reduce the switching angle new model, the minimum number of the participation that obtains adjustment unit lacks more than one than conventional model.

4) new model that reduces switching angle has recovered partly to demand urgently the load that recovers when reducing the meritorious adjustment amount (promptly reducing the adjustment time) of exerting oneself of generator, meet the target [document 14 of power system recovery more; ADIBI M M; FINK L H.Power system restoration planning [J] .IEEE Trans on Power Systems, 1994,9 (1): 22-28.]; Improve the efficient of recovering, accelerated the system restoration process.

Description of drawings

Fig. 1 is a flow chart of the present invention.

Fig. 2 is New England 10 machines, 39 node system figure.

Fig. 3 is the system load flow under the initial condition.

Fig. 4 is θ _SetIn the time of=20 °, optimum regulation and control finish the trend of back system.

Fig. 5 is θ _SetIn the time of=10 °, optimum regulation and control finish the trend of back system.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is further specified.

The present invention is directed to New England 10 machines, 39 node example systems and carry out emulation, reduce the characteristics and the performance of the optimum regulate and control method of switching angle with explanation.System's line chart is as shown in Figure 2.Wherein, circuit 3～18 is stopped transport owing to overhauling with circuit 4～14.

Among Fig. 2, catastrophe failure takes place in the lower right side subregion that assumed curve is surrounded, and through breaking off section { 15-16, circuit that 17-16} is last and upper left side major network off-the-line.After the off-the-line, generator is meritorious exerts oneself major network through reducing, and finally keeps stable operation; And the lower right side subregion finally develops into and has a power failure on a large scale.After having a power failure on a large scale, major network provides power to support through circuit 15-16 to the lower right side subregion, successfully realizes black the startup, and finally recovers the load about main grid structure and 50%.In order to reduce the recovery risk, before carrying out large-scale load restoration, plan is through combined floodgate circuit 16-17, and promptly the looped network parallel operation strengthens getting in touch between bottom right subregion and the major network, the fail safe of raising system operation.

Have 10,22,8,8 respectively on the lower right side subregion internal loading node 16,20,21,23,24, the outlet of 10 loads waits to recover (seeing Table A 1 for details).Load in each outlet and weights all are the positive numbers that generates at random, and obtain [document 10] through normalization.System's reference capacity is 100MVA.Suppose that the power factor in the load outlet is identical with the total load power factor of its place node; Load adopts 40% constant-impedance, 60% permanent power module; The upper and lower limit perunit value of node voltage is respectively 11 and 0.95; Circuit 4～5,5～6,6～31,10～32,25～37,29～38 meritorious through-put power upper limit perunit value is respectively 9.0,10.5,11.5,7.5,7.0,8.0, and the upper limit perunit value of all the other circuits is 6.5; Switching angle set point θ _Set=20 ° [document 4].Under the initial condition; Generator initial launch state and parameter thereof [document 15; Lin Shunjiang, Liu Mingbo. the trace sensitivity method [J] of transient voltage safety precautions Control and Optimization. Automation of Electric Systems, 2010; 34 (4): 12-17.] as shown in table 1, the trend result of system sees Fig. 3 phase difference of voltage θ of circuit both sides that waits to close a floodgate _16-17=23 °.

Table 1 generator initial launch state and parameter thereof

Tab.1Generators?initial?parameters

Wait to recover load outlet and load in the Table A 1 New England system

Generator 33,34,35,36 among Fig. 2 in the subregion of lower right side is in the back that has a power failure on a large scale and is restarted, recovers gradually the unit of exerting oneself.In order to obtain practicable looped network control strategy arranged side by side, when the calculating that reduces switching angle, meritorious the exerting oneself of generator in the subregion of lower right side limited, do not allow them to reduce meritorious exerting oneself.

Through analyzing starter system tidal current chart (Fig. 3), with section 8-9,4-3} upper left side subregion is as being held electrical network, the lower right side subregion of section right side and curve encirclement send the end electrical network as 2.To be held generator 30,37,38 in the electrical network; 39 meritorious recruitment and the lower right side subregion internal loading node 16,20,21 of exerting oneself; Treating on 23,24 recovered the load outlet as control variables, and getting weight is 50; Through finding the solution formula (1)～formula (9), the load outlet and the load that obtain being resumed, as shown in table 2; The meritorious recruitment of exerting oneself of corresponding generator is shown in table 3 the 2nd row.

Table 2 θ _SetBe resumed the load outlet in the time of=20 °

Tab.2Restored?load?switches?for?θ _set＝20°

In the table 2,

The burden with power of expression node i is to reducing θ _16-17Sensitivity.The load outlet that is resumed is according to weight w _IsWith a _iThe product descending.

Table 3 θ _SetMeritorious adjustment amount (the Δ P that exerts oneself of generator in the time of=20 ° _Gi)

Tab.3Adjustment?of?active?generation?for?θ _set＝20°(ΔP _gi)

In the table 3, " not considering " and " consideration " refers to consider to participate in minimum whether the requirement under two kinds of situation of adjustment generator quantity, the result of switching angle regulation and control respectively; ∑ | Δ P _Gi| the meritorious adjustment amount absolute value sum of exerting oneself of expression generator.

Can know that by table 3 in reducing the process of switching angle, generator 37,38 all increases meritorious exerting oneself, and does not all reach the upper limit.Therefore, need to analyze whether have the possibility that further reduces to participate in adjusting generator quantity.Through sensitivity analysis, generate electricity to reducing θ according to meritorious _16-17The size of sensitivity sorts to generator, obtains sequence: 38,37.Because current meritorious subsequent use of generator 38 is 0.0654,, only increase that gaining merit exerts oneself can't make switching angle be reduced to set point by generator 38 less than the meritorious recruitment 0.215 7 of generator 37.Therefore, when realizing the switching angle regulation and control by generator 38,37, it is minimum that unit quantity has reached.Also promptly, it is identical consider to participate in the minimum switching angle regulation and control result calculated that whether requires under two kinds of situation of adjustment generator quantity, and the meritorious increase total amount of exerting oneself is 0.450 3.Under above-mentioned control strategy, the trend result of system sees Fig. 4.Comparison diagram 4 can know with Fig. 3, send to be held section { 8-9, the last meritorious trend of 4-3} is reduced to 4.689 by 5.139.This makes the phase angle of node 17 increase by 1.647 °, and the phase angle of node 16 reduces 1.354 °, θ _16-17Be reduced to 20 ° by 23 °.On Intel Pentium Dual2.0GHz CPU and 2.24GB RAM computer, accomplish and calculate 16.219s consuming time altogether.

For the optimum regulate and control method with the present invention's proposition compares, the method that adopts document [5] to propose below reduces the calculating of switching angle.Do not considering and considering that generator quantity minimum requires under these 2 kinds of situation, the meritorious adjustment amount of exerting oneself of the generator that calculates is shown in table 3 the 4th～5 row.For preceding a kind of situation, the unit in the subregion of bottom right, all units are all participated in adjustment; For latter event, after 2 iteration of dichotomy, the generator quantity of participating in adjustment is reduced to 3 by 6.Gaining merit exerts oneself increase and reduce total amount is respectively 0.7342 and 0.7302, and both add up to total amount is 1.4644.Meritorious the exerting oneself of generator can be adjusted as unique control device continuously, after regulation and control finish, and θ _16-17Equal 20 °.The calculating difference consuming time 0.703 and the 1.875s of two kinds of situation.

The result of calculation of 2 kinds of methods can be known in the contrast table 3; The inventive method adopts the increase generator to gain merit simultaneously and exerts oneself and drop into these 2 kinds of control devices of load and reduces switching angle; The unit quantity that needs is few, and generator is meritorious exerts oneself adjustment amount also much smaller than document [5] institute extracting method.But the inventive method is when obtaining optimal control policy, and required computing time is much larger than document [5] institute extracting method, but still satisfies the actual requirement of engineering.

In order to reduce unsafe factor, avoid taking place once more power outage, for the system restoration after having a power failure on a large scale, can suitably improve the established standards of switching angle limit value.For this reason, the present invention resets the limit value θ of switching angle _Set=10 °, utilize above-mentioned 2 kinds of methods to reduce the calculating of switching angle once more.The meritorious adjustment amount of exerting oneself of the generator that calculates is as shown in table 4, accomplishes calculate consuming time and is followed successively by 3.313,6.362,0.656 and 1.281s.Utilize that the inventive method obtains be resumed the load outlet and load as shown in table 5.After regulation and control finished, the trend result of system saw Fig. 5.

Table 4 θ _SetMeritorious adjustment amount (the Δ P that exerts oneself of generator in the time of=10 ° _Gi)

Tab.4Adjustment?of?active?generation?for?θ _set＝10°(ΔP _gi)

Table 5 θ _SetBe resumed the load outlet in the time of=10 °

Tab.5Restored?load?switches?for?θ _set＝10°

Result of calculation by document in the table 4 [5] method is known under new switching angle limit value, no matter consider to participate in minimum whether requirement of adjustment generator quantity, generator 30,37, and 38,39 meritorious exerting oneself all reached higher limit separately.And in the methods of the invention, only meritorious the exerting oneself of generator 38 reaches higher limit, generator 30,37, and 39 still have bigger available adjusting range.Therefore, no matter the inventive method exerts oneself adjustment amount all less than document [5] institute extracting method in that the generator quantity of participating in adjustment is still meritorious.This explains that on the one hand the inventive method is strong to the ability of regulation and control of switching angle; Explain that on the other hand the inventive method is low to the system reserve requirement, it can be used in the switching angle regulation and control under the meritorious subsequent use not abundant situation of system between convalescence.

In the process of reality adjustment, constantly keep watch on the variation of differential seat angle, frequency and voltage difference, after the satisfied requirement of being incorporated into the power networks, assign reclosing command.

Claims (2)

1. reduce the method for optimally controlling of looped network switching angle arranged side by side in the power system recovery, it is characterized in that step is:

Step 1; Selection is held the whole generators in the electrical network to increase and is meritoriously exerted oneself and drop into and send load to be recovered in the end electrical network as control variables; Take into account and wait the importance recovering to load, set up the mixed-integer programming model that reduces looped network and column line two ends excessive voltage phase angle difference;

Step 2 by the meritorious adjustment situation of exerting oneself of the generator that calculates, judges whether the generator quantity of participating in regulation and control reaches minimum; If reach, then change step 7; Otherwise, change next step;

Step 3 increases meritorious exerting oneself to reducing the sensitivity of switching angle for increasing meritorious exert oneself and meritorious exerting oneself do not reach the generator of the upper limit of exerting oneself, calculating, and ordering from high to low;

Step 4 is utilized two fens principles, selects the higher part generator of sensitivity in the sequence to participate in the switching angle regulation and control, changes next step;

Step 5 is utilized the Optimization Model of step 1 once more, obtains meritorious adjustment situation of exerting oneself of this part generator and the situation that drops into load;

Step 6 by the meritorious adjustment situation of exerting oneself of the generator that calculates, judges whether generator quantity reaches minimum; If reach, then change step 7; Otherwise, change step 4;

Step 7, the switching angle regulation and control finish.

2. reduce the method for optimally controlling of looped network switching angle arranged side by side in the power system recovery as claimed in claim 1, it is characterized in that, in the said step 1, mixed-integer programming model is following:

$\underset{P_{\mathrm{gi}},Q_{\mathrm{gi}},{\mathrm{\&Delta;P}}_{\mathrm{dis}},{\mathrm{\&Delta;Q}}_{\mathrm{dis}}}{\min }\underset{i}{\mathrm{\&Sigma;}}\mathrm{\&alpha;}(P_{\mathrm{gi}}-P_{\mathrm{gi}0})+\underset{i}{\mathrm{\&Sigma;}}\underset{s}{\mathrm{\&Sigma;}}\frac{x_{\mathrm{is}}{\mathrm{\&Delta;P}}_{\mathrm{dis}}}{w_{\mathrm{is}}}---\left(19\right)$

$P_{\mathrm{gi}}-P_{\mathrm{di}}-\underset{s}{\mathrm{\&Sigma;}}{x}_{\mathrm{is}}{\mathrm{\&Delta;P}}_{\mathrm{dis}}$

(20)

$=U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\&theta;}}_{\mathrm{ij}}),i\&Element;S_B$

$Q_{\mathrm{gi}}-Q_{\mathrm{di}}-\underset{s}{\mathrm{\&Sigma;}}{x}_{\mathrm{is}}{\mathrm{\&Delta;Q}}_{\mathrm{dis}}$

(21)

$=U_i\underset{j\&Element;i}{\mathrm{\&Sigma;}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\&theta;}}_{\mathrm{ij}}),i\&Element;S_B$

$P_{\mathrm{ij}}=-U_i^2{G}_{\mathrm{ij}}+U_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}{\sin \mathrm{\&theta;}}_{\mathrm{ij}}),i\&Element;S_L---\left(22\right)$

$P_{\mathrm{gi}0}\&le;P_{\mathrm{gi}}\&le;P_{\mathrm{gi}}^{\max },i\&Element;---\left(23\right)$

$Q_{\mathrm{gi}}^{\min }\&le;Q_{\mathrm{gi}}\&le;Q_{\mathrm{gi}}^{\max },i\&Element;S_R---\left(24\right)$

$U_i^{\min }\&le;U_i\&le;U_i^{\max },i\&Element;S_B---\left(25\right)$

$\left|P_{\mathrm{ij}}\right|\&le;P_{\mathrm{ij}}^{\max },i,j\&Element;S_L---\left(26\right)$

θ _mn≤θ _set (27)

In the formula: P _GiAnd Q _GiBe respectively meritorious, idle the exerting oneself of generator i; P _Gi0For the meritorious of generator i under the initial condition exerted oneself; Definition Δ P _Gi=P _Gi-P _Gi0Δ P _DisWith Δ Q _DisBe respectively meritorious and load or burden without work amount to be recovered in the outlet of s load of node i; x _IsWhether the outlet of s load of expression node i is resumed, and is 1 if be resumed, otherwise is 0; w _IsWeight for the outlet of s load of node i; α is that meritorious the exerting oneself of generator increases the weight of total amount with respect to weighting load restoration total amount.U _iAnd θ _iBe respectively the voltage magnitude and the phase angle of node i; θ _Ij=θ _i-θ _jP _DiAnd Q _DiBe respectively the meritorious and load or burden without work that has been resumed on the node i; G _IjAnd B _IjThe electricity that is respectively circuit i-j is led and susceptance; P _IjBe the active power on the circuit i-j;

The meritorious higher limit of exerting oneself for generator i;

With

Be respectively the idle upper limit value and lower limit value of exerting oneself of generator i;

With

Be respectively the upper limit value and lower limit value of node i voltage magnitude;

For circuit i-j goes up meritorious through-put power limit value; θ _MnAnd θ _SetBe respectively and treat and the switching angle at column line m-n two ends and detect relay switching angle set point the same period.S _G, S _R, S _B, S _LBe respectively adjustable meritorious generator set, the set of adjustable reactive power generation machine, all node set of system and all set of fingers.

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