CN101534010B - Method for solving the local boundary of cut-set voltage stability regions on the basis of perturbation - Google Patents

Abstract

The invention belongs to the technical field of power systems and relates to a method for solving the local boundary of cut-set voltage stability regions on the basis of perturbation. The method comprises the following steps: firstly, determining the generator-load node pair most influencing each branch power flow in the cut-set by tracing the power flow, and realizing the bidirectional perturbation increasing and decreasing each branch power flow through controlling the generator-load node pair; further, determining the voltage stability critical points of the system in the cut-set power space by perturbed operating points, and acquiring local boundary approximation hyper-planes of the security region boundary in the two symmetrical perturbation directions of increasing and decreasing respectively by utilizing the critical points; and finally, acquiring the accurate results of the local boundary of the voltage stability region through the translational and weighted processing of the two local boundary approximation hyper-planes. The invention not only has higher computational efficiency, but also ensures that the acquired boundary hyper-plane contains the limit point corresponding to the current operating point, the error is relatively small, therefore, the invention has great practical value in engineering.

Description

Cut set voltage stability domain solution method of local boundary based on perturbation

Technical field

The invention belongs to technical field of power systems, relate to a kind of voltage stability domain solution method of local boundary.

Background technology

The accident of having a power failure on a large scale of the interior frequent appearance of world wide in recent years ^[1-2]How relevant with the voltage stable problem, make the voltage stable problem more outstanding.The method in territory is applied to Voltage Stability Analysis, can overcomes the some shortcomings of tradition " point by point method ", so the method in territory has become a kind of important means of safety on line assessment, supervision and optimization ^[3-7]

No matter electric power system is in normal operation catastrophe failure still occurs, and the dispatcher often needs to realize improving by the trend of monitoring some crucial cut set sections the purpose of system stability ^[8,9]At this moment, cut set voltage stability domain (CVSR) just becomes the useful tool that they implement to monitor ^[9-12]CVSR is defined on the cut set trend space, is made of whole voltage stable operating points.Traditional CVSR method for solving generally by random perturbation, forms a large amount of voltages and stablizes critical point, adopts least square to fit process then, is similar to the border of CVSR with a hyperplane (HP).The precision of this method gained hyperplane depends on the number of the limit point of asking, and the many more precision of limit point are high more, therefore fits precision for obtaining higher border, need carry out a large amount of computings; In addition, when CVSR border curvature was big, this method only adopted a hyperplane to come the border is similar to, and may cause than mistake.

Summary of the invention

For remedying the deficiency of existing method, the present invention provides a kind of by operating point being implemented perturbation to obtain the new method of CVSR local boundary, not only has higher computational efficiency, simultaneously can guarantee that the bounding hyperplane of asking comprises the pairing limit point of current operating point, have less error, therefore have the excellent engineering practical value.

For this reason, the present invention adopts following technical scheme:

A kind of cut set voltage stability domain solution method of local boundary based on perturbation comprises the following steps:

(1) for any branch road B _i∈ I _Tf, utilize current trend result, by power flow tracing, obtain contributive generator of this branch road trend and load bus set: G _Bi={ G _{I, 1}, G _{I, 2}..., G _{I, n}, L _Bi={ L _{I, 1}, L _{I, 2}..., L _{I, m}Wherein: n, m are respectively the number with this branch road relevant generator and load bus;

(2) establish G _BiAnd L _BiIn each node to branch road B _iTrend P _{I, i}Contribution amount be respectively: P _GBi={ P _{Gi, 1}, P _{Gi, 2}..., P _{Gi, n}And P _LBi={ P _{Li, 1}, P _{Li, 2}..., P _{Li, m}, above-mentioned generator and load are to the contribution factor of this branch road trend: α respectively _Bi={ α _{I, 1}, α _{I, 2}..., α _{I, n}And β _Bi={ β _{I, 1}, β _{I, 2}..., β _{I, m}Wherein: α _{I, k}=P _{Gi, k}/ P _{I, i}* 100%, G _{I, k}∈ G _Bi, β _{I, j}=P _{Li, j}/ P _{I, i}* 100%, L _{I, j}∈ L _Bi

(3) note GL _iFor with B _iOne group of generator-load bus that branch road is relevant is right, is used for branch road B _iTrend implement perturbation control: GL _i={ G _{I, p}, L _{I, q}, G _{I, p}∈ G _Bi, L _{I, q}∈ L _Bi, and note GL _ItfFor implement the whole generators-right set of load: the GL of perturbation control at cut set _Itf={ GL ₁, GL ₂..., GL _N, determine set GL by following cyclic process _Itf, and ensure GL _ItfIn do not have that identical two generators-load is right:

The first step is established i=1 and GL _ItfBe sky, starting algorithm;

In second step, obtain GL by following formula _iPRELIMINARY RESULTS: GL _i={ G _{I, p}, L _{I, q}, wherein: G _{I, p}∈ G _Bi, α _{I, p}=max (α _Bi), L _{I, q}∈ L _Bi, β _{I, q}=max (β _Bi);

In the 3rd step, check GL _ItfWhether existed and GL _iIdentical generator-load is right, if not, changes for the 4th step and continues; If, then as follows to GL _iRevised:

1) makes β _BiIn α _{I, p}Be zero, and by α _{I, p}=max (α _Bi) definite once more G _{I, p}With new GL _i, and judge GL _iWhether at GL _ItfThe middle existence is if continue; Otherwise changeed for the 4th step;

2) make β _BiIn β _{I, q}Be zero, by β _{I, q}=max (β _Bi) redefine L _{I, q}GL with correspondence _i, and judge GL _iWhether at GL _ItfExist, if then repeated for the 3rd step; Otherwise changeed for the 4th step;

The 4th step is with GL _iAdd GL _ItfWhether set with seasonal i=i+1, checks i＞N, if continue; Otherwise changeed for second step;

In the 5th step, algorithm finishes, GL _ItfBe the objective for implementation of the perturbation of asking control;

(4) note perturbation controlled quentity controlled variable is Δ P＞0, by formula $P_{\mathrm{Gi},p}^{+}=P_{\mathrm{Gi},p}+\mathrm{\ΔP},$ $P_{\mathrm{Li},q}^{+}=P_{\mathrm{Li},q}+\mathrm{\ΔP}$ Successively to GL _ItfIn generator-load to implementing perturbation, obtain the critical point set X of forward perturbation correspondence _C ⁺: $X_C^{+}=\{x_{C,1}^{\′+},x_{C,2}^{\′+},\·\·\·,x_{C,N}^{\′+}\};$ Press $P_{\mathrm{Gi},p}^{-}=P_{\mathrm{Gi},p}-\mathrm{\ΔP},$ $P_{\mathrm{Li},q}^{-}=P_{\mathrm{Li},q}-\mathrm{\ΔP},$ Successively to GL _ItfIn all generator-loads to implementing perturbation, can get the critical point set X after the negative sense perturbation _C ^-: $X_C^{-}=\{x_{C,1}^{\′-},x_{C,2}^{\′-},\·\·\·,x_{C,N}^{\′-}\};$

(5) utilize limit point set X after the forward perturbation _C ⁺, obtain the hyperplane HP on CVSR border ⁺: $\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i^{+}\·P_{I,i}=1.0,$ Utilize the limit point set X after the reverse perturbation _C ^-, can get corresponding bounding hyperplane HP ^-: $\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i^{-}\·P_{I,i}=1.0;$

(6) adopt following formula to be revised: a _i=a ' _i/ K, wherein: $a_i^{\′}=(a_i^{-}+a_i^{+})/2,$ $K=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i^{\′}\·P_{\mathrm{IC},i}^0,$ $x_{C0}=\{P_{\mathrm{IC},1}^0,P_{\mathrm{IC},2}^0,...,P_{\mathrm{IC},N}^0\},$ Obtain revised bounding hyperplane HP: $\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i\·P_{I,i}=1.0.$

The present invention provides a kind of according to the current operating point of system, realize the new method of cut set voltage stability domain local boundary rapid solving by accurate perturbation, the cut set voltage stability domain local boundary that obtains has higher computational efficiency [9-11] by the traditional C VSR border method for solving of finding the solution a large amount of limit points and adopt LSM to fit process, utilize [10,11] definition of error in, can get error of the present invention only is 0.88%, and the error of [9-11] method is 2.40%, when the radius of neighbourhood of limit point disturbance is got 8MW and 2MW, error of the present invention will become 0.44% and 0.091%, and the error of [9-11] changes not quite, so computational accuracy also is improved.In a word, utilize the checking of systems such as New England-39 and IEEE-118 node to show, the inventive method explicit physical meaning, can effectively reduce the error of fitting on voltage stability domain border, can accurately find the solution the CVSR bounding hyperplane of the current limit point of system, and have the quick advantage of arithmetic speed, have favorable engineering application prospect.

Description of drawings

Fig. 1 the inventive method schematic diagram.

Fig. 2 New England 39 node systems and cut set.

Embodiment

Below the present invention is further described.

1. cut set voltage stability domain (CVSR) and boundary property thereof

The cut set of electric power system is defined as one group of set that is made of following branch road, and it is divided into mutual disconnected two parts with system:

I _tf＝{B ₁，B ₂，...，B _N} (1)

Wherein, B _i={ F _i, T _iBe the i bar branch road of cut set, F _i, T _iBe respectively the initial sum terminal node of branch road; N is for constituting a way of this cut set.Use P _ItfThe power space of expression cut set:

P _Itf＝[P _I，1，P _I，2，...，P _I，N] (2)

P wherein _{I, i}Be i bar branch road active power.Use S _GL=S _G∪ S _LExpression system injecting power vector; S _G=P _G∪ Q _G, S _L=P _L∪ Q _LRepresent generator and load injecting power vector respectively.Work as S _GLAfter given, can be by the running status x of the unique definite system of power flow equation:

f(x，S _GL)＝0 (3)

Wherein, f () is the system load flow equation.Further, when x satisfied following formula (4), the title system was that voltage is stable; Otherwise if x satisfies formula (5), then the title system is in voltage and stablizes critical condition ^[5,6]F wherein _xBe the power flow equation Jacobian matrix, det () is its determinant.

det(f _x)≠0 (4)

det(f _x)＝0 (5)

Further, use X ^sFormula (3) is satisfied in expression simultaneously, and X is used in the set of whole steady operational status of (4) ^cFormula (3), the set of whole critical stable states of (5) are satisfied in expression simultaneously.We know in addition, appoint and inject vectorial S for a system power _GL, it is a running status x of unique decision systems not only, at P _ItfOn the space, also unique definite operating point x of system _Itf, this process can be with following mapping T _IRepresent:

x _Itf＝T _I(S _GL)

＝[P _I，1(S _GL)，P _I，2(S _GL)，...，P _I，N(S _GL)] (6)

Then cut set static voltage stability territory (CVSR) and border thereof can be provided by following formula:

Ω _CVSR：＝{x _Itf|x∈X ^s，x _Itf＝T _I(S _GL)} (7)

$\∂{\mathrm{\Ω}}_{\mathrm{CVSR}}:=\left\{x_{\mathrm{Itf}}\right|x\∈X^c,x_{\mathrm{Itf}}=T_I\left(S_{\mathrm{GL}}\right)\}---\left(8\right)$

And power injection space voltage stability region (IVSR) ^[13-15]Can be expressed as:

Ω _IVSR：＝{S _GL|x∈X ^s} (9)

$\∂{\mathrm{\Ω}}_{\mathrm{IVSR}}:=\left\{S_{\mathrm{GL}}\right|x\∈X^c\}---\left(10\right)$

Be not difficult to find out that by above-mentioned definition CVSR has comprised P _ItfWhole voltage stable operating points on the space.Work as x _ItfWhen being positioned at CVSR inside (or on its border), corresponding S _GLVector must be positioned at IVSR (or on its border), so CVSR can see that rate of doing work injection space voltage stability domain IVSR is at P _ItfA mapping on the space ^[15]Numerous researchs show that the border of IVSR is the curved surface that higher-dimension power injects the space.Be not difficult to find out that by above-mentioned analysis the CVSR border also should be P as a mapping on IVSR border in theory _ItfA higher-dimension curved surface on the space.Although more existing studies show that can be come the border of approximate representation CVSR with a hyperplane, and approximate error can accept, and when CVSR border curvature is big, adopts a hyperplane to be similar to the CVSR border and will have greater risk.

2, the CVSR border approximation method principle based on the initial point perturbation of the present invention

With situation shown in Figure 1 is example, supposes that curved surface is the CVSR border of waiting to ask system.Existing method only adopts a hyperplane to come approximate evaluation CVSR border, as HP among the figure _∑Shown in, be not difficult to find out, when CVSR border curvature is big, can produce very big error.If can utilize the space distribution information of the limit point of current operating point of system and correspondence, adopt different local hyperplane to come the CVSR border is similar to, then can reduce consequent error greatly.With Fig. 1 is example, by definite respectively three the local hyperplane HP1～HP3 of the operating point P1～P3 of three systems, is used for approximate corresponding limit point CP1～CP3 CVSR local boundary on every side, is not difficult to find out that the latter's approximate error will reduce greatly.Institute of the present invention extracting method promptly passes through P _ItfThe initial point of system applies small sample perturbations on the space, is similar to the part on the CVSR border that obtains to represent with the hyperplane form.The inventive method principle is as follows: at first to the initial point x of system _Itf0Carry out accurately perturbation with obtain N disturbance point x ' _{Itf, 1}, x ' _{Itf, 2}..., x ' _{Itf, N}, find the solution then each disturbance point correspondence limit point x ' _{C, 1}, x ' _{C, 2}..., x ' _{C, N}, the last approximate hyperplane that obtains the CVSR local boundary by the limit point after the disturbance.Suppose that the CVSR border is a sphere, then the border of determining by this method is the surface of similar football, each facet approximate representation one little block boundary all on it.For reaching good propinquity effect, need to guarantee following 2 points:

1) the initial disturbance point x ' _{Itf, 1}, x ' _{Itf, 2}..., x ' _{Itf, N}Should be strict uncorrelated, with guarantee by limit point x ' _{C, 1}, x ' _{C, 2}..., x ' _{C, N}Can obtain the local approximation of CVSR bounding hyperplane, need initial point x for this reason _Itf0Carry out accurate perturbation.Because cut set branch road trend does not have controllability, therefore to x _Itf0Perturbation need be converted into injecting power S by certain mode to system _GL0Disturbance;

2) should guarantee that the gained hyperplane is accurate as far as possible to being similar to of CVSR border, need utilize x for this reason _Itf0Corresponding limit point x _C0The gained hyperplane is implemented to revise.

3, algorithm concrete steps

CVSR border derivation algorithm based on the initial point perturbation is divided into the accurate perturbation of initial point, two steps are found the solution and revised on the hyperplane border:

CVSR border derivation algorithm based on the initial point perturbation is divided into the accurate perturbation of initial point, two steps are found the solution and revised on the hyperplane border:

● initial point is carried out accurate perturbation

As previously mentioned, when initial point is carried out perturbation, should guarantee disturbance point x ' _{Itf, 1}, x ' _{Itf, 2}..., x ' _{Itf, N}Strict uncorrelated, the present invention adopts following steps to realize:

1, determine with cut set in every generator and the load bus collection that branch road is relevant

The purpose in this step is to determine under current state, with bigger generator and the load bus of branch road trend relation.The sensitivity information of branch road trend is realized that because of need are inverted to the power flow equation Jacobian matrix, computing is comparatively complicated although can be injected by node, the present invention adopts the method for power flow tracing to realize ^[8,16], to improve operation efficiency, its process is as follows:

For any branch road B _i∈ I _Tf, utilize current trend result, pass through power flow tracing ^[8,16]Can gather contributive generator of this branch road trend and load bus:

G _Bi＝{G _i，1，G _i，2，...，G _i，n} (11)

L _Bi＝{L _i，1，L _i，2，...，L _i，m} (12)

Wherein: n, m are respectively the number with this branch road relevant generator and load bus.If G _BiAnd L _BiIn each node to branch road B _iTrend P _{I, i}Contribution amount be respectively:

P _GBi＝{P _Gi，1，P _Gi，2，...，P _Gi，n}(13)

P _LBi＝{P _Li，1，P _Li，2，...，P _Li，m}(14)

With network loss approximate share and system be converted into lossless network after, formula (13) and (14) gained result satisfy following relation ^[8,16]:

$\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{P}_{\mathrm{Gi},k}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{P}_{\mathrm{Li},j}=P_{I,i}---\left(15\right)$

Further can get above-mentioned generator is respectively with the contribution factor of load to this branch road trend:

α _Bi＝{α _i，1，α _i，2，...，α _i，n}(16)

β _Bi＝{β _i，1，β _i，2，...，β _i，m}(17)

Wherein:

α _i，k＝P _Gi，k/P _I，i×100％，G _i，k∈G _Bi?(18)

β _i，j＝P _Li，j/P _I，i×100％，L _i，j∈L _Bi?(19)

2, definite controlled generator-load bus to every branch road enforcement perturbation is right

For ease of describing note GL _iFor with B _iOne group of generator-load bus that branch road is relevant is right, is used for branch road B _iTrend implement perturbation control:

GL _i＝{G _i，p，L _i，q}，G _i，p∈G _Bi，L _i，q∈L _Bi (20)

And note GL _ItfFor implement the whole generators-right set of load of perturbation control at cut set:

GL _itf＝{GL ₁，GL ₂，…，GL _N} (21)

The purpose in this step is exactly to determine set GL fast _Itf, and ensure GL _ItfIn do not have that identical two generators-load is right, uncorrelated to guarantee the operating point strictness after the disturbance.Realize by following cyclic process:

The first step is established i=1 and GL _ItfBe sky, starting algorithm;

In second step, obtain GL by following formula _iPRELIMINARY RESULTS:

GL _i＝{G _i，p，L _i，q} (22)

Wherein: G _{I, p}∈ G _Bi, α _{I, p}=max (α _Bi) (23)

I _i，q∈L _Bi，β _i，q＝max(β _Bi) (24)

In the 3rd step, check GL _ItfWhether existed and GL _iIdentical generator-is load right? if not, changeing for the 4th step continues; If, then as follows to GL _iRevised:

1) makes α _BiIn α _{I, p}Be zero, and by α _{I, p}=max (α _Bi) definite once more G _{I, p}With new GL _i, and judge GL _iWhether at GL _ItfThe middle existence? if continue; Otherwise changeed for the 4th step;

2) make β _BiIn β _{I, q}Be zero, by β _{I, q}=max (β _Bi) redefine L _{I, q}GL with correspondence _i, and judge GL _iWhether at GL _ItfExist? if then repeated for the 3rd step; Otherwise changeed for the 4th step.

The 4th step is with GL _iAdd GL _ItfWhether set with seasonal i=i+1, checks i＞N, if continue; Otherwise changeed for second step.

In the 5th step, algorithm finishes, GL _ItfBe the objective for implementation of the perturbation of asking control.

3, utilize GL _ItfCut set branch road trend is carried out accurate perturbation

Note perturbation controlled quentity controlled variable is Δ P＞0, passes through GL as follows _ItfTrend to the cut set branch road is implemented perturbation:

The forward perturbation: $P_{\mathrm{Gi},p}^{+}=P_{\mathrm{Gi},p}+\mathrm{\ΔP}---\left(25\right)$

$P_{\mathrm{Li},q}^{+}=P_{\mathrm{Li},q}+\mathrm{\ΔP}---\left(26\right)$

Oppositely perturbation: $P_{\mathrm{Gi},p}^{-}=P_{\mathrm{Gi},p}-\mathrm{\ΔP}---\left(27\right)$

$P_{\mathrm{Li},q}^{-}=P_{\mathrm{Li},q}-\mathrm{\ΔP}---\left(28\right)$

Press formula (25) (26) to GL _i∈ GL _ItfSystem's operating point of implementing to obtain after the perturbation is designated as S _{GL, i} ⁺(operating point in the cut set power space after the disturbance is designated as x ' _{Itf, i}).With it is system's initial point, and by default load growth and power generation dispatching mode, the voltage of solving system is stablized critical point and is designated as X ' _{C, i} ⁺Press formula (25) (26) successively to GL _ItfIn generator-load to implementing perturbation, can get the critical point set X of forward perturbation correspondence _C ⁺:

$X_C^{+}=\{x_{C,1}^{\′+},x_{C,2}^{\′+},\·\·\·,x_{C,N}^{\′+}\}---\left(29\right)$

Equally, by formula (27) (28), successively to GL _ItfIn all generator-loads to implementing perturbation, can get the critical point set X after the negative sense perturbation _C ^-:

$X_C^{-}=\{x_{C,1}^{\′-},x_{C,2}^{\′-},\·\·\·,x_{C,N}^{\′-}\}---\left(30\right)$

By top solution procedure as can be known, the element during two groups of limit points are gathered is uncorrelated with strictness.

● bounding hyperplane is found the solution and is revised

At first, utilize limit point set X after the forward perturbation _C ⁺, by finding the solution N system of linear equations, can obtain the hyperplane on CVSR border, be designated as HP ⁺:

${\mathrm{HP}}^{+}:\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i^{+}\·P_{I,i}=1.0---\left(31\right)$

Equally, utilize limit point set X after the reverse perturbation _C ^-, can get corresponding bounding hyperplane, be designated as HP ^-:

${\mathrm{HP}}^{-}:\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i^{-}\·P_{I,i}=1.0---\left(32\right)$

Since the existence of disturbance quantity, HP ⁺And HP ^-Usually do not comprise cut set initial point x in two planes _Itf0Corresponding limit point x _C0, adopt following method to be revised for this reason:

a _i＝a′ _i/K (33)

Wherein: $a_i^{\′}=(a_i^{-}+a_i^{+})/2---\left(34\right)$

$K=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i^{\′}\·P_{\mathrm{IC},i}^0---\left(35\right)$

$x_{C0}=\{P_{\mathrm{IC},1}^0,P_{\mathrm{IC},2}^0,...,P_{\mathrm{IC},N}^0\}---\left(36\right)$

Can get revised bounding hyperplane thus is:

$\mathrm{HP}:\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i\·P_{I,i}=1.0---\left(37\right)$

Be not difficult to find out that above-mentioned correction is actual to be to HP ⁺And HP ^-The coefficient on two planes is weighted on average, and revised hyperplane HP is carried out translation, guarantees that it crosses x _C0Point, therefore satisfy:

$\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i\·P_{\mathrm{IC},i}=1.0---\left(38\right)$

4, algorithmic descriptions

1) the present invention adopts the meritorious trend of cut set branch road to represent the CVSR border, and does not adopt complex power, and mainly consider following reasons: on the one hand, actual power department more is concerned about the power component of branch road trend when carrying out the section tidal current monitoring ^[17,18]On the other hand, when closing on the voltage unstability, the charging of high pressure branch road (idle) power is very big, even the situation of branch road idle " only can not going into " occurs, it is idle to be that branch road two end systems are supplied with branch road simultaneously, and will be difficult to adopt the branch road reactive power that the CVSR border is represented this moment; Its three, the present invention institute was x to HP _C0The part on CVSR border is approximate, is distributed in x _C0Limit point on every side, corresponding branch road reactive power numerical value change is little, when adopting complex power to represent the CVSR bounding hyperplane, the contribution of reactive component can be thought of as a constant that approximately constant is constant, thereby but dimensionality reduction to branch road active power space.

2) [9-11] etc. with hyperplane to the CVSR border when approximate, adopting least square to fit method (LSM) realizes, there are 2 deficiencies in this method: one, the precision of gained hyperplane depends on the number of the limit point number that fits, the big more precision of limit point number is high more, therefore fit precision for obtaining higher border, this method need be calculated in a large number; Its two, the gained bounding hyperplane often can not guarantee necessarily to cross initial threshold point x _C0With Fig. 1 is example, supposes that the CP2 point is current x among the figure _C0, this method is to find the solution a large amount of critical points at random around the CP2 point, fits out hyperplane HP by the LSM algorithm then _∑, be not difficult to find out HP _∑Must not comprise the CP2 point.The inventive method guarantees that then by initial point is carried out accurate perturbation the disturbance point strictness is uncorrelated, obtains the coefficient of bounding hyperplane by directly finding the solution system of linear equations, and guarantees the strict x of mistake of hyperplane through revising _C0, reduced limit point greatly simultaneously and found the solution number.Therefore, the inventive method has improved the efficient of finding the solution when improving the border precision.

5, New England 39 node system examples

New England 39 node systems as shown in Figure 2, the branch road arrow has been indicated direction of tide among the figure, power reference is got 100MW.

Table 1.New England 39 node system cut set A

The initial threshold point x of table 2. cut set A _C0, X _C ⁺And X _C ^-Set

Table 3. hyperplane HP ⁺, HP ^-With revised hyperplane HP

The hyperplane coefficient	a 1	a 2	a 3
				HP +	-0.0004969	0.0005980	-0.0005727
HP -	-0.0005072	0.0006078	-0.0005824
				HP	-0.0005020	0.0006028	-0.0005775

Table 4.HP reaches only by HP ⁺And HP ^-The bounding hyperplane of determining

The hyperplane coefficient of the different perturbation quantity correspondences of table 5.

A, cut set A numerical results

Get that cut set A is a research object among the figure, the branch road that table 1 has provided cut set constitutes and initial trend.Adopt joint 3 methods to find the solution its generator-load pair set GL _Itf, gained the results are shown in table 1.Get perturbation quantity Δ P=10MW, table 2 has provided the x of system's this moment _C0With the forward and reverse perturbation control of enforcement back gained limit point set X _C ⁺, X _C ^-, can get HP in view of the above ⁺, HP ^-Further, utilize x _C0The result revises to gained, and final gained hyperplane HP is shown in table 3.

1) approximate calculation: as shown in Table 3, HP ⁺With HP ^-Approximate parallel, its angle only is 0.103 °.The present invention adopts two-way perturbation to obtain accurate CVSR border, but because HP ⁺And HP ^-Approximate parallel, if only utilize x _C0To HP ⁺Carry out translation, can be similar to the hyperplane coefficient: (0.0005013,0.0006033 ,-0.0005778), the HP angle that asked in it and the table 3 this moment only is 0.053 °; Equally, if only adopt HP ^-Bounding hyperplane of finding the solution and the angle between the HP only are 0.050 °, and be as shown in table 4.Consider that from the engineering application point of view such error is an acceptable, therefore, can directly utilize HP fully ⁺Or HP ^-Find the solution CVSR bounding hyperplane---approximate calculation, at this moment the amount of calculation of algorithm will reduce approximately half.Adopt two-way perturbation demand to separate 2N+1 limit point, an employing approximation method then demand is separated N+1 limit point.But no matter adopt which kind of method, all have higher computational efficiency by the traditional C VSR border method for solving of finding the solution a large amount of limit points and adopt LSM to fit process ^[9-11]

2) error ratio: with x _C0Be the center, in radius is the neighborhood of 16MW, generate 200 limit points at random, substitution table 3 gained hyperplane, and compare with [9-11] gained result, utilize the definition of error in [10,11], can get error of the present invention only is 0.88%, and the error of [9-11] method is 2.40%.When the radius of neighbourhood of limit point disturbance is got 8MW and 2MW, error of the present invention will become 0.44% and 0.091%, and the error of [9-11] changes not quite.Being not difficult to find out thus, was exactly x owing to hyperplane that the present invention gives is actual _C0The section on some CVSR border, when the initial point of system changed little (so the limit point change is also little), the approximation on gained border was very accurate.When initial point has than cataclysm, can utilize the inventive method to calculate advantage efficiently, find the solution hyperplane again to guarantee the approximation quality on border.

3) relation of result of calculation and perturbation quantity: P gets 1MW respectively with the perturbation quantity Δ, and 5MW and 10MW utilize joint 3 methods to calculate the hyperplane of cut set A correspondence then, and gained the results are shown in table 5.With 1MW perturbation gained hyperplane is benchmark, and 5MW and 10MW gained result angle with it only are 0.279 ° and 0.362 °, and three hyperplane almost completely overlap, so the inventive method gained result is subjected to perturbation quantity value size to influence less.But consider the nonlinear characteristic of electric power system, the perturbation quantity value is unsuitable excessive in the practical application.

Table 6.New England 39 node system cut set B, C

The result of calculation of table 7. cut set B, C

Cut set	a 1	a 2	a 3	[9-11] error	This paper error
						B	-0.00110 5	0.001896	0.001574	3.14％	1.23％
C	0.003029	0.004212	-0.00495 9	2.84％	0.72％

Table 8.IEEE-118 system cut set

Circuit number	Initial female wire size	Stop female wire size
			1	15	19
2	17	16
			3	8	30
4	15	33
			5	17	15

B, cut set B, the numerical results of C

The branch road that table 6 provides cut set B and cut set C among Fig. 2 constitutes situation.As Δ P=10MW, the radius of checking neighborhood is when getting 16MW, table 7 provided two cut set hyperplane result of calculation and with the error comparative result of [9-11].Be not difficult to find out that the error of the inventive method gained result of calculation is much smaller than [9-11].

6, IEEE-118 node system example

IEEE-118 node system parameter and initial scene are that example is verified with [9] with cut set shown in the table 8.Get Δ P=10MW, can get the hyperplane coefficient and be: [0.000936,0.003585 ,-0.001264 ,-0.000476,0.003310], the disturbance radius of neighbourhood is taken as 25MW during checking, and the error of result of calculation only is 1.30%.

Further adopt EPRI-1000 node system, domestic a plurality of real system examples to verify, the inventive method all can accurately be found the solution the CVSR border around the initial threshold point, while the inventive method computational efficiency height, can satisfy the needs of safety on line monitoring fully, have good practical values.

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Claims (1)

1. the cut set voltage stability domain solution method of local boundary based on perturbation comprises the following steps:

(1) cut set of definition electric power system is one group of set that is made of following branch road, and it is divided into mutual disconnected two parts: I with system _Tf={ B ₁, B ₂..., B _N, wherein, B _i={ F _i, T _iBe the i bar branch road of cut set, F _i, T _iBe respectively the initial sum terminal node of branch road; N is for constituting a way of this cut set, for any branch road B _i∈ I _Tf, utilize current trend result, by power flow tracing, obtain contributive generator of this branch road trend and load bus set: G _Bi={ G _{I, 1}, G _{I, 2}..., G _{I, n}, L _Bi={ L _{I, 1}, L _{I, 2}..., L _{I, m}Wherein: n, m are respectively the number with this branch road relevant generator and load bus;

(2) establish G _BiAnd L _BiIn each node to branch road B _iTrend P _{I, i}Contribution amount be respectively: P _GBi={ P _{Gi, 1}, P _{Gi, 2}..., P _{Gi, n}And P _LBi={ P _{Li, 1}, P _{Li, 2}..., P _{Li, m}, calculate above-mentioned generator and load contribution factor: α respectively to this branch road trend _Bi={ α _{I, 1}, α _{I, 2}..., α _{I, n}And β _Bi={ β _{I, 1}, β _{I, 2}..., β _{I, m}Wherein: α _{I, k}=P _{Gi, k}/ P _{I, i}* 100%, G _{I, k}∈ G _Bi, β _{I, j}=P _{Li, j}/ P _{I, i}* 100%, L _{I, j}∈ L _Bi

(3) note G _LiFor with B _iOne group of generator-load bus that branch road is relevant is right, is used for branch road B _iTrend implement perturbation control: GL _i={ G _{I, p}, L _{I, q}, G _{I, p}∈ G _Bi, L _{I, q}∈ L _Bi, and note GL _ItfFor implement the whole generators-right set of load: the GL of perturbation control at cut set _Itf={ GL ₁, GL ₂..., GL _N, determine set GL by following cyclic process _Itf, and ensure GL _ItfIn do not have that identical two generators-load is right:

The first step is established i=1 and GL _ItfBe sky, starting algorithm;

In second step, obtain GL by following formula _iPRELIMINARY RESULTS: GL _i={ G _{I, p}, L _{I, q}, wherein:

G _i，p∈G _Bi，α _i，p＝max(α _Bi)，L _i，q∈L _Bi，β _i，q＝max(β _Bi)；

In the 3rd step, check GL _ItfWhether existed and GL _iIdentical generator-load is right, if not, changes for the 4th step and continues; If, then as follows to GL _iRevised:

1) makes α _BiIn α _{I, p}Be zero, and by α _{I, p}=max (α _Bi) definite once more G _{I, p}With new GL _i, and judge GL _iWhether at GL _ItfThe middle existence is if continue; Otherwise changeed for the 4th step;

2) make β _BiIn β _{I, q}Be zero, by β _{I, q}=max (β _Bi) redefine L _{I, q}GL with correspondence _i, and judge GL _iWhether at GL _ItfExist, if then repeated for the 3rd step; Otherwise changeed for the 4th step;

The 4th step is with GL _iAdd GL _ItfWhether set with seasonal i=i+1, checks i＞N, if continue; Otherwise changeed for second step;

In the 5th step, algorithm finishes, GL _ItfBe the objective for implementation of the perturbation of asking control;

(4) note perturbation controlled quentity controlled variable is Δ P＞0, by formula

Successively to GL _ItfIn generator-load to implementing perturbation, obtain the critical point set of forward perturbation correspondence

Press

Successively to GL _ItfIn all generator-loads to implementing perturbation, can get the critical point set after the negative sense perturbation

(5) utilize limit point set after the forward perturbation Obtain the hyperplane HP on CVSR border ⁺:

Utilize the limit point set after the reverse perturbation

Can get corresponding bounding hyperplane HP ^-:

(6) adopt following formula to be revised: a _i=a ' _i/ K, wherein:

Obtain revised bounding hyperplane HP:

Wherein

The voltage of representing current system operating point correspondence is stablized the active power value on the i bar circuit of critical operation point.

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