CN104901316A - Emergency load shedding control method based on trace sensitivity - Google Patents

Abstract

The present invention discloses an emergency load shedding control method based on trace sensitivity. The method comprises obtaining traces of post-accident state variables through power system transient numerical simulation, so as to solve transient security and stability allowance indicator vectors, and judging if solving emergency load shedding measures need to be carried out through transient security and stability constraint conditions; solving a trace sensitivity matrix of transient security and stability allowance indicators through power system transient numerical simulation and a numerical perturbation method, and linearizing the transient security and stability constraint conditions. The transient security and stability, including transient power angle stability, transient frequency security and transient voltage security of a post-accident system may be ensured, the load shedding cost is reduced, and economical efficiency of the measures is raised. Through trace sensitivity, the transient security and stability conditions are linearized, the original problem is converted into a linear programming problem, iteration solving is realized, and the rate of convergence is fast.

Description

A kind of urgent load shedding control method based on trace sensitivity

Technical field

The present invention relates to a kind of urgent load shedding control method based on trace sensitivity.

Background technology

Along with electricity needs increases, for meeting electricity needs, the Large Copacity power supply of electric power system increases gradually, as the construction, extra-high voltage alternating current-direct current access etc. of Large Copacity fired power generating unit, when formulating POWER SYSTEM EMERGENCY cutting load control measure, just need the Large Copacity power supply vacancy accident considering to cause because these Large Copacity power supplys are out of service.

Large Copacity power supply vacancy accident belongs in the short time the extreme accident that can cause system transient modelling security and stability severe exacerbation.Transient safe and stable comprises Transient angle stability, transient frequency fail safe and Transient Voltage Security three aspects.When this kind of extreme accident occurs, because system power amount of unbalance is very large, system transient modelling security and stability severe exacerbation, transient state merit angle instability may be caused, transient frequency is dangerous and transient voltage is dangerous, and bring out the serious consequences such as merit angle unstability, frequency collapse and voltage collapse, electric power system cannot ensure the reliability to customer power supply.The urgent cutting load control measure of the Track fusion type such as UFLS were when defending this kind of extreme accident in the past, some quantity of state of system is needed to depart from normal operation range, and when reaching the threshold value of setting, just meeting trigger action, this can delay control opportunity, cause cutting load cost very large, less economical, even control effects cannot meet the requirement that power system safety and stability runs; Or do not take into account the Transient angle stability of system, transient frequency fail safe and Transient Voltage Security, be difficult to the transient safe and stable ensureing POST FAULT POWER SYSTEMS.

Visible, after proposing a kind of defence Large Copacity power supply vacancy accident, ensure that the urgent load shedding control method of Transient Security for Power Systems stability and economy is extremely necessary.The method should ensure that Transient angle stability, transient frequency fail safe and Transient Voltage Security meet the demands, and suppresses system unstability, form urgent cutting load control measure with the least possible cutting load cost.These control measure should be event drivens, namely after detecting that accident occurs, according to measure cut-out load immediately, improve the transient safe and stable of system.

Summary of the invention

The present invention is in order to solve the problem, propose a kind of urgent load shedding control method based on trace sensitivity, it is excessive that the method effectively solves conventional emergency cutting load control measure cutting load amount when defending Large Copacity power supply vacancy accident, less economical, do not consider to ensure the problem of the Transient angle stability of system, transient frequency fail safe and Transient Voltage Security simultaneously, based on trace sensitivity, under the prerequisite ensureing Transient Security for Power Systems stability, formulate the control measure making cutting load Least-cost, improve the economy of measure.

To achieve these goals, the present invention adopts following technical scheme:

Based on a urgent load shedding control method for trace sensitivity, comprise the following steps:

(1) gather electric power system data, determine the number of cutting load node, form cutting load dominant vector; That determines each cutting load node can the maximum of cutting load amount, forms maximum cutting load amount vector;

(2) supervision track, transient safe and stable discriminant parameter and transient state numerical simulation parameter are set, for judging whether safety and stability;

(3) for forecast accident, after obtaining accident by electrical power system transient numerical simulation, monitor track, calculate transient safe and stable margin index vector, judge whether to meet transient safe and stable constraints, if meet, then do not need to take urgent cutting load measure, solve end; Otherwise enter step (4);

(4) the urgent cutting load Mathematical Modeling of iterative is started, obtain cutting load dominant vector, the trace sensitivity matrix of transient safe and stable margin index is calculated, by the linearisation of transient safe and stable constraints by electrical power system transient numerical simulation and numerical perturbation method;

(5) solve and transform by urgent cutting load Mathematical Modeling the linear programming problem obtained, calculate knots modification and the cutting load dominant vector of the cutting load dominant vector of iteration;

(6) judge whether the cutting load dominant vector that iteration is tried to achieve meets the condition of convergence, if meet, then using this cutting load dominant vector as optimal solution, and terminate solve; Otherwise perform step (4), continue iterative;

(7) according to the cutting load dominant vector obtained, formulate urgent cutting load control measure prediction scheme, entry condition is set to detect that fault occurs then to perform immediately.

In described step (1), electric power system data comprises node parameter, line parameter circuit value, generator and load parameter.

In described step (1), determine the number of cutting load node, form cutting load dominant vector P; That determines each cutting load node can the maximum of cutting load amount, forms maximum cutting load amount vector the selection of cutting load node and each cutting load node can the maximum of cutting load amount by User Defined:

P＝[p ₁,p ₂,...,p _N]

$\stackrel{\‾}{P}=\[{\stackrel{\‾}{p}}_1,{\stackrel{\‾}{p}}_2,...,{\stackrel{\‾}{p}}_N\]$

Wherein, N represents the number of cutting load node.

In described step (2), arrange and monitor track, transient safe and stable discriminant parameter and transient state numerical simulation parameter, monitor that track comprises generator's power and angle track and frequency locus, and busbar voltage track; Transient safe and stable discriminant parameter comprises frequency two-element list and voltage two-element list; Transient state numerical simulation parameter comprises electrical power system transient numerical simulation duration T and simulation step length Δ t.

In described step (2), the form of frequency two-element list is (f _cr, t _cr), for judging transient frequency fail safe, wherein f _crfor frequency shift (FS) threshold value, t _crfor the frequency shift (FS) maximum allowed time, when transient state numerical simulation process medium frequency track is continued above f _crtime be greater than t _crtime, then think that transient frequency is dangerous, frequency two-element list has several;

The form of voltage two-element list is (V _cr, t _cr), for judging Transient Voltage Security, wherein V _crfor variation threshold value, t _crfor the variation maximum allowed time, when in transient state numerical simulation process, voltage trace is continued above V _crtime be greater than t _crtime, then think that transient voltage is dangerous, voltage two-element list has several;

Electrical power system transient numerical simulation duration T is the duration that fault generation initial time experiences to transient process end time.

In described step (3), for forecast accident, after obtaining accident by electrical power system transient numerical simulation, monitor track; Calculate transient safe and stable margin index vector η, judge whether to meet transient safe and stable constraints:

η＞ε

Wherein, ε is transient safe and stable critical value vector;

If meet, then do not need to take urgent cutting load measure, solve end; Otherwise enter step (4), start the following urgent cutting load Mathematical Modeling of iterative, obtain cutting load dominant vector P:

$\min F\left(P\right)=\underset{i}{\Σ}{C}_i{p}_i$

s.t.

$\left\{\begin{array}{c}\mathrm{\η}>\mathrm{\ϵ}\\ 0\≤P\≤\stackrel{\‾}{P}\end{array}\right.$

Wherein, for cutting load cost target function, C _ibe i-th cutting load amount p _icost; η > ε is transient safe and stable constraints; for cutting load amount constraints.

In described step (3), transient safe and stable margin index vector η and transient safe and stable critical value vector ε is expressed as follows:

$\mathrm{\η}=\left[\begin{array}{c}{\mathrm{\η}}_{\mathrm{\δ}}\\ {\mathrm{\η}}_f\\ {\mathrm{\η}}_V\end{array}\right],\mathrm{\ϵ}=\left[\begin{array}{c}{\mathrm{\ϵ}}_{\mathrm{\δ}}\\ {\mathrm{\ϵ}}_f\\ {\mathrm{\ϵ}}_V\end{array}\right]$

Wherein, η _δfor Transient angle stability margin index, η _ffor transient frequency fail safe margin index, η _vfor Transient Voltage Security margin index; ε _δtransient angle stability critical value, ε _ftransient frequency security critical value, ε _vit is Transient Voltage Security critical value;

Transient safe and stable constraints η > ε is by Transient angle stability constraints η _δ> ε _δ, transient frequency safety constraint η _f> ε _fwith Transient Voltage Security constraints η _v> ε _vthe unified compact form write as:

$\left.\begin{array}{c}{\mathrm{\η}}_{\mathrm{\δ}}>{\mathrm{\ϵ}}_{\mathrm{\δ}}\\ {\mathrm{\η}}_f>{\mathrm{\ϵ}}_f\\ {\mathrm{\η}}_V>{\mathrm{\ϵ}}_V\end{array}\right\}\⇒\mathrm{\η}>\mathrm{\ϵ}$

Transient angle stability margin index η _δcalculate based on EEAC (Extended Equal Area Criterion).

Transient frequency fail safe margin index η _fby considering that the frequency shift (FS) security margin index of cumulative effect is weighed, calculate transient frequency fail safe margin index η by following formula _f:

η _f＝min(η _f,i,j),0≤i≤N _f,0≤j≤M _f

${\mathrm{\η}}_{f,i,j}=min\left(\frac{{\∫}_t^{t+t_{cr,j}}(f_i-f_{cr,j})dt}{(f_N-f_{cr,j})t_{cr,j}}\right),0\≤t\≤T-t_{cr,j}$

Wherein, N _ffor the number of monitored generator frequency track, M _ffor the number of the frequency two-element list of setting; η _{f, i, j}represent i-th monitored frequency locus f _iat a jth frequency two-element list (f _{cr, j}, t _{cr, j}) weigh under transient frequency fail safe margin index, t is integration initial time, f _nfor electric power system rated frequency;

Transient Voltage Security margin index η _vby considering that the variation security margin index of cumulative effect is weighed, calculate Transient Voltage Security margin index η by following formula _v:

η _V＝min(η _V,i,j),0≤i≤N _V,0≤j≤M _V

${\mathrm{\η}}_{V,i,j}=min\left(\frac{{\∫}_t^{t+t_{cr,j}}(V_i-V_{cr,j})dt}{(V_N-V_{cr,j})t_{cr,j}}\right),0\≤t\≤T-t_{cr,j}$

Wherein, N _vfor the number of monitored busbar voltage track, M _vfor the number of the voltage two-element list of setting; η _{v, i, j}represent i-th monitored voltage trace V _iat a jth voltage two-element list (V _{cr, j}, t _{cr, j}) weigh under Transient Voltage Security margin index, t is integration initial time, V _nfor electric power system rated voltage.

In described step (4), calculated the trace sensitivity matrix A of transient safe and stable margin index by electrical power system transient numerical simulation and numerical perturbation method, transient safe and stable constraints linearly turned to following form:

η＝η(P ^(k))+AΔP ^(k+1)＞ε

Wherein, k represents the current iterative number of times solving process, η (P ^(k)) represent the cutting load dominant vector P tried to achieve in kth time iteration ^(k)effect under transient safe and stable nargin, Δ P ^(k+1)for the knots modification of the cutting load dominant vector that current iteration solves, there is following form:

ΔP＝[Δp ₁,Δp ₂,...,Δp _N]

In described step (4), trace sensitivity matrix A has the expression formula of following form:

$A=\left[\begin{array}{cccccc}{a}_{\mathrm{\δ}1}& a_{\mathrm{\δ}2}& ...& a_{\mathrm{\δ}i}& ...& a_{\mathrm{\δ}N}\\ a_{f1}& a_{f2}& ...& a_{fi}& ...& a_{jN}\\ a_{V1}& a_{V2}& ...& a_{Vi}& ...& a_{VN}\end{array}\right]$

Wherein, a _{δ i}that Transient angle stability margin index is to i-th cutting load amount p _itrace sensitivity, a _fithat transient frequency fail safe margin index is to i-th cutting load amount p _itrace sensitivity, a _vithat Transient Voltage Security margin index is to i-th cutting load amount p _itrace sensitivity, trace sensitivity by electrical power system transient numerical simulation and numerical perturbation method, is tried to achieve with following formula:

$a_{\mathrm{\δ}i}=\frac{{\mathrm{\η}}_{\mathrm{\δ}}\left(P^{\left(k\right)}\right)-{\mathrm{\η}}_{\mathrm{\δ}}(P^{\left(k\right)},{\mathrm{\τ}}_i)}{{\mathrm{\τ}}_i}$

$a_{fi}=\frac{{\mathrm{\η}}_f\left(P^{\left(k\right)}\right)-{\mathrm{\η}}_f(P^{\left(k\right)},{\mathrm{\τ}}_i)}{{\mathrm{\τ}}_i}$

$a_{Vi}=\frac{{\mathrm{\η}}_V\left(P^{\left(k\right)}\right)-{\mathrm{\η}}_V(P^{\left(k\right)},{\mathrm{\τ}}_i)}{{\mathrm{\τ}}_i}$

Wherein, η _δ(P ^(k)), η _f(P ^(k)) and η _v(P ^(k)) be respectively at cutting load dominant vector P ^(k)under Transient angle stability margin index, transient frequency fail safe margin index and the Transient Voltage Security margin index of trying to achieve; η _δ(P ^(k), τ _i), η _f(P ^(k), τ _i) and η _v(P ^(k), τ _i) be respectively at cutting load dominant vector P ^(k)under, to i-th cutting load amount p _iapply Perturbation τ _iafter Transient angle stability margin index, transient frequency fail safe margin index and the Transient Voltage Security margin index of trying to achieve; Perturbation value τ _ibeing a positive number, when calculating each margin index, needing first to obtain phase-swing curves, frequency locus and the voltage trace under corresponding cutting load scheme by transient state numerical simulation, and then obtain the value of each margin index.

In described step (5), by the linearizing transient safe and stable constraints obtained in step (4), urgent cutting load Mathematical Modeling is converted into linear programming problem:

$\min F\left(P\right)=\underset{i}{\Σ}{C}_i({p_i}^{\left(k\right)}+{{\mathrm{\Δp}}_i}^{(k+1)})$

s.t.

$\left\{\begin{array}{c}\mathrm{\η}\left(P^{\left(k\right)}\right)+A\mathrm{\Δ}{P}^{(k+1)}>\mathrm{\ϵ}\\ 0\≤P^{\left(k\right)}+\mathrm{\Δ}{P}^{(k+1)}\≤\stackrel{\‾}{P}\end{array}\right.$

The knots modification Δ P of the cutting load dominant vector of current iteration is obtained by linear programming for solution ^(k+1), this cutting load dominant vector P ^(k+1)try to achieve by following formula:

P ^(k+1)＝P ^(k)+ΔP ^(k+1)

In described step (6), the condition of convergence comprises following 3 aspects:

1) have at least a transient stability margin index to be in critical condition, namely meet following formula:

η _δ-ε _δ< Δ ε or η _f-ε _f< Δ ε or η _v-ε _v< Δ ε

Wherein, critical condition threshold value Δ ε is a positive number;

2) change of total cutting load amount is less than threshold value ε _load, namely meet following formula:

$\underset{i}{\&Sigma;}{\mathrm{\&Delta;p}}_i^{(k+1)}<{\mathrm{\&epsiv;}}_{load}$

3) each cutting load amount change be less than threshold value ε _p, namely meet following formula:

${\mathrm{\&Delta;p}}_i^{(k+1)}<{\mathrm{\&epsiv;}}_p$

Beneficial effect of the present invention is:

(1) the urgent cutting load measure that this method for solving obtains is event driven, and the event that namely detects occurs just to perform at once, in time the trend of containment Transient Instability, improves the ability of electric power system defence risk;

(2) this method for solving account for Transient angle stability, transient frequency fail safe and Transient Voltage Security simultaneously, the transient safe and stable of system after guarantee accident;

(3) method of iteration convergence is adopted, in each iteration, make use of trace sensitivity and quantize the impact of cutting load amount on transient safe and stable, former problem is converted into linear programming problem, by existing linear programming for solution method rapid solving, solving speed can be accelerated, through little iteration, just can converge to an optimal solution, convergence rate is very fast;

(4) electric power enterprise can be on the defensive to serious accident by less cutting load cost;

(5) power failure range that minimizing accident causes, reduces the impact on the normal productive life of the people.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

Based on a urgent load shedding control method for trace sensitivity, comprise the following steps:

Step 1: read in electric power system data by computer, comprises node parameter, line parameter circuit value, generator, load parameter etc.

Step 2: the number determining cutting load node, forms cutting load dominant vector P; That determines each cutting load node can the maximum of cutting load amount, forms maximum cutting load amount vector the selection of cutting load node and each cutting load node can the maximum of cutting load amount can by User Defined:

P＝[p ₁,p ₂,...,p _N]

$\stackrel{\&OverBar;}{P}=\&lsqb;{\stackrel{\&OverBar;}{p}}_1,{\stackrel{\&OverBar;}{p}}_2,...,{\stackrel{\&OverBar;}{p}}_N\&rsqb;$

Wherein, N represents the number of cutting load node.

Step 3: arrange and monitor track, transient safe and stable discriminant parameter and transient state numerical simulation parameter.Monitor that track comprises generator's power and angle track and frequency locus, and busbar voltage track.Transient safe and stable discriminant parameter comprises frequency two-element list and voltage two-element list.Transient state numerical simulation parameter comprises electrical power system transient numerical simulation duration T and simulation step length Δ t etc.

Step 4: for forecast accident, the track of each quantity of state after obtaining accident by electrical power system transient numerical simulation.Calculate transient safe and stable margin index vector η, judge whether to meet transient safe and stable constraints:

η＞ε

Wherein, ε is transient safe and stable critical value vector.

If meet, then do not need to take urgent cutting load measure, solve end; Otherwise enter step 5, start the following urgent cutting load Mathematical Modeling of iterative, obtain cutting load dominant vector P:

$\min F\left(P\right)=\underset{i}{\&Sigma;}{C}_i{p}_i$

s.t.

$\left\{\begin{array}{c}\mathrm{\&eta;}>\mathrm{\&epsiv;}\\ 0\&le;P\&le;\stackrel{\&OverBar;}{P}\end{array}\right.$

Wherein, for cutting load cost target function, C _ibe i-th cutting load amount p _icost; η > ε is transient safe and stable constraints; for cutting load amount constraints.

Step 5: the trace sensitivity matrix A being calculated transient safe and stable margin index by electrical power system transient numerical simulation and numerical perturbation method, linearly turns to following form by transient safe and stable constraints:

η＝η(P ^(k))+AΔP ^(k+1)＞ε

Wherein, k represents the current iterative number of times solving process, η (P ^(k)) represent the cutting load dominant vector P tried to achieve in kth time iteration ^(k)effect under transient safe and stable nargin, Δ P ^(k+1)for the knots modification of the cutting load dominant vector that current iteration solves, there is following form:

ΔP＝[Δp ₁,Δp ₂,...,Δp _N]

By the linearisation of transient safe and stable constraints, urgent cutting load Mathematical Modeling is converted into linear programming problem:

$\min F\left(P\right)=\underset{i}{\&Sigma;}{C}_i({p_i}^{\left(k\right)}+{{\mathrm{\&Delta;p}}_i}^{(k+1)})$

s.t.

$\left\{\begin{array}{c}\mathrm{\&eta;}\left(P^{\left(k\right)}\right)+A\mathrm{\&Delta;}{P}^{(k+1)}>\mathrm{\&epsiv;}\\ 0\&le;P^{\left(k\right)}+\mathrm{\&Delta;}{P}^{(k+1)}\&le;\stackrel{\&OverBar;}{P}\end{array}\right.$

The knots modification Δ P of the cutting load dominant vector obtaining current iteration can be solved by linear programming ^(k+1).This cutting load dominant vector P ^(k+1)try to achieve by following formula:

P ^(k+1)＝P ^(k)+ΔP ^(k+1)

Step 6: solve and transform by former problem the linear programming problem obtained.

Step 7: judge whether the cutting load dominant vector that iteration is tried to achieve meets the condition of convergence, if meet, then using this cutting load dominant vector as optimal solution, and terminate solve; Otherwise perform step 5, continue iterative.

Step 8: the cutting load dominant vector obtained according to step 7, formulates urgent cutting load control measure prediction scheme, and entry condition is set to detect that fault occurs then to perform immediately.

In step 3, the form of frequency two-element list is (f _cr, t _cr), for judging transient frequency fail safe.Wherein f _crfor frequency shift (FS) threshold value, t _crfor the frequency shift (FS) maximum allowed time.When transient state numerical simulation process medium frequency track is continued above f _crtime be greater than t _crtime, then think that transient frequency is dangerous.Frequency two-element list can have multiple.

The form of voltage two-element list is (V _cr, t _cr), for judging Transient Voltage Security.Wherein V _crfor variation threshold value, t _crfor the variation maximum allowed time.When in transient state numerical simulation process, voltage trace is continued above V _crtime be greater than t _crtime, then think that transient voltage is dangerous.Voltage two-element list can have multiple.

Electrical power system transient numerical simulation duration T is the duration that fault generation initial time experiences to transient process end time.

In described step 4, transient safe and stable margin index vector η and transient safe and stable critical value vector ε is expressed as follows:

$\mathrm{\&eta;}=\left[\begin{array}{c}{\mathrm{\&eta;}}_{\mathrm{\&delta;}}\\ {\mathrm{\&eta;}}_f\\ {\mathrm{\&eta;}}_V\end{array}\right],\mathrm{\&epsiv;}=\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{\&delta;}}\\ {\mathrm{\&epsiv;}}_f\\ {\mathrm{\&epsiv;}}_V\end{array}\right]$

Wherein, η _δfor Transient angle stability margin index, η _ffor transient frequency fail safe margin index, η _vfor Transient Voltage Security margin index; ε _δtransient angle stability critical value, ε _ftransient frequency security critical value, ε _vit is Transient Voltage Security critical value.

Transient safe and stable constraints η > ε is by Transient angle stability constraints η _δ> ε _δ, transient frequency safety constraint η _f> ε _fwith Transient Voltage Security constraints η _v> ε _vthe unified compact form write as:

$\left.\begin{array}{c}{\mathrm{\&eta;}}_{\mathrm{\&delta;}}>{\mathrm{\&epsiv;}}_{\mathrm{\&delta;}}\\ {\mathrm{\&eta;}}_f>{\mathrm{\&epsiv;}}_f\\ {\mathrm{\&eta;}}_V>{\mathrm{\&epsiv;}}_V\end{array}\right\}\&DoubleRightArrow;\mathrm{\&eta;}>\mathrm{\&epsiv;}$

Transient angle stability margin index η _δcalculate based on EEAC (Extended Equal Area Criterion).

Transient frequency fail safe margin index η _fby considering that the frequency shift (FS) security margin index of cumulative effect is weighed.Transient frequency fail safe margin index η is calculated by following formula _f:

η _f＝min(η _f,i,j),0≤i≤N _f,0≤j≤M _f

${\mathrm{\&eta;}}_{f,i,j}=min\left(\frac{{\&Integral;}_t^{t+t_{cr,j}}(f-f_{cr,j})dt}{(f_N-f_{cr,j})t_{cr,j}}\right),0\&le;t\&le;T-t_{cr,j}$

Wherein, N _ffor the number of monitored generator frequency track, M _ffor the number of the frequency two-element list of setting; η _{f, i, j}represent i-th monitored frequency locus f _iat a jth frequency two-element list (f _{cr, j}, t _{cr, j}) weigh under transient frequency fail safe margin index, t is integration initial time, f _nfor electric power system rated frequency.

Transient Voltage Security margin index η _vby considering that the variation security margin index of cumulative effect is weighed.Transient Voltage Security margin index η is calculated by following formula _v:

η _V＝min(η _V,i,j),0≤i≤N _V,0≤j≤M _V

${\mathrm{\&eta;}}_{V,i,j}=min\left(\frac{{\&Integral;}_t^{t+t_{cr,j}}(V-V_{cr,j})dt}{(V_N-V_{cr,j})t_{cr,j}}\right),0\&le;t\&le;T-t_{cr,j}$

Wherein, N _vfor the number of monitored busbar voltage track, M _vfor the number of the voltage two-element list of setting; η _{v, i, j}represent i-th monitored voltage trace V _iat a jth voltage two-element list (V _{cr, j}, t _{cr, j}) weigh under Transient Voltage Security margin index, t is integration initial time, V _nfor electric power system rated voltage.

In described step 5, trace sensitivity matrix A has the expression formula of following form:

$A=\left[\begin{array}{cccccc}{a}_{\mathrm{\&delta;}1}& a_{\mathrm{\&delta;}2}& ...& a_{\mathrm{\&delta;}i}& ...& a_{\mathrm{\&delta;}N}\\ a_{f1}& a_{f2}& ...& a_{fi}& ...& a_{fN}\\ a_{V1}& a_{V2}& ...& a_{Vi}& ...& a_{VN}\end{array}\right]$

Wherein, a _{δ i}that Transient angle stability margin index is to i-th cutting load amount p _itrace sensitivity, a _fithat transient frequency fail safe margin index is to i-th cutting load amount p _itrace sensitivity, a _vithat Transient Voltage Security margin index is to i-th cutting load amount p _itrace sensitivity.Trace sensitivity can pass through electrical power system transient numerical simulation and numerical perturbation method, tries to achieve with following formula:

$a_{\mathrm{\&delta;}i}=\frac{{\mathrm{\&eta;}}_{\mathrm{\&delta;}}\left(P^{\left(k\right)}\right)-{\mathrm{\&eta;}}_{\mathrm{\&delta;}}(P^{\left(k\right)},{\mathrm{\&tau;}}_i)}{{\mathrm{\&tau;}}_i}$

$a_{fi}=\frac{{\mathrm{\&eta;}}_f\left(P^{\left(k\right)}\right)-{\mathrm{\&eta;}}_f(P^{\left(k\right)},{\mathrm{\&tau;}}_i)}{{\mathrm{\&tau;}}_i}$

$a_{Vi}=\frac{{\mathrm{\&eta;}}_V\left(P^{\left(k\right)}\right)-{\mathrm{\&eta;}}_V(P^{\left(k\right)},{\mathrm{\&tau;}}_i)}{{\mathrm{\&tau;}}_i}$

Wherein, η _δ(P ^(k)), η _f(P ^(k)) and η _v(P ^(k)) be respectively at cutting load dominant vector P ^(k)under Transient angle stability margin index, transient frequency fail safe margin index and the Transient Voltage Security margin index of trying to achieve; η _δ(P ^(k), τ _i), η _f(P ^(k), τ _i) and η _v(P ^(k), τ _i) be respectively at cutting load dominant vector P ^(k)under, to i-th cutting load amount p _iapply Perturbation τ _iafter Transient angle stability margin index, transient frequency fail safe margin index and the Transient Voltage Security margin index of trying to achieve; Perturbation value τ _iit is a very little positive number.When calculating each margin index, need first to obtain phase-swing curves, frequency locus and the voltage trace under corresponding cutting load scheme by transient state numerical simulation, and then obtain the value of each margin index.

In described step 7, the condition of convergence comprises following 3 aspects:

1) have at least a transient stability margin index to be in critical condition, namely meet following formula:

η _δ-ε _δ< Δ ε or η _f-ε _f< Δ ε or η _v-ε _v< Δ ε

Wherein, critical condition threshold value Δ ε is a very little positive number.

2) change of total cutting load amount is less than threshold value ε _load, namely meet following formula:

$\underset{i}{\&Sigma;}{\mathrm{\&Delta;p}}_i^{(k+1)}<{\mathrm{\&epsiv;}}_{load}$

3) each cutting load amount change be less than threshold value ε _p, namely meet following formula:

${\mathrm{\&Delta;p}}_i^{(k+1)}<{\mathrm{\&epsiv;}}_p$

The inventive method considers the electric power system of 148 nodes, includes 44 generators, 57 loads, and system gross generation is 5155MW.

Utilize computer to read in electric power system data by the first step, comprise the parameter of 222 circuits, the parameter of 44 generators, the parameter etc. of 57 loads, the generator model of system all adopts high-order dynamic model, and has excitation system and governing system.There are 4 generator excision faults in initial time, excise 1810MW energy output altogether, cutting load controls moment 0.2s.The rated frequency of system is 50Hz, and the rated voltage of perunit value form is 1.0.

By second step, choosing can maximum 15 load of cutting load amount, forms cutting load dominant vector and maximum cutting load amount vector.The maximum cutting load amount of each load is as shown in table 1:

The maximum cutting load amount of each load of table 1

Load is numbered	Maximum cutting load amount/MW
		A	265
B	230
		C	192
D	190
		E	190
F	180
		G	180
H	180
		I	170
J	165
		K	164
L	145
		M	140
N	140
		O	130

By the 3rd step, monitor phase-swing curves and the frequency locus of all 40 generators do not excised, monitor the voltage trace of all 57 on-load buses.A frequency two-element list (49.0,1.0) is set, a voltage two-element list (0.75,1.0) is set.Electrical power system transient numerical simulation duration T is set to 10s.

By the 4th step, carry out transient state numerical simulation by calling BPA to system, simulation step length is 0.01s, obtains phase-swing curves, frequency locus and voltage trace.The transient rotor angle stability nargin critical value ε of system _δ, transient frequency security critical value ε _fwith Transient Voltage Security critical value ε _vall be set to 0.Calculate transient safe and stable margin index, obtain Transient angle stability margin index η _δbe 0.90994, transient frequency fail safe margin index η _ffor-0.92998, Transient Voltage Security margin index η _vfor-0.28726.Obviously cannot meet transient safe and stable constraints, occur that transient frequency is dangerous and transient voltage is dangerous, needed to formulate urgent cutting load measure.

By the 5th step to the 7th step, the initial cutting load dominant vector P of iterative is set ⁽⁰⁾=0 (namely not taking any control measure), iterates and solves.When solving trace sensitivity, perturbation value is set to 30MW.In the condition of convergence, each threshold value is set to:

Δε＝0.0001,ε _load＝0.2MW,ε _p＝0.1MW

In the 8th step, cutting load dominant vector will be tried to achieve as POWER SYSTEM EMERGENCY cutting load control measure, and control the resection of each load, and the excision correspondence of equal proportion is idle.Under ensureing the prerequisite of Transient Security for Power Systems stability, improve the economy of measure.The solving result of the cutting load amount of each load as

Shown in table 2.

The cutting load amount of each load of table 2

Load is numbered	Cutting load amount/MW
		A	0
B	230
		C	0
D	190
		E	0
F	9.72
		G	180
H	0
		I	0
J	0
		K	0
L	0
		M	140
N	0
		O	128.09

Only need to converge to optimal solution for 8 times and need excise 877.81MW load altogether.After implementing urgent cutting load control measure, the Transient angle stability margin index of electric power system is 0.96263, transient frequency fail safe margin index is 0.00008, Transient Voltage Security margin index is 0.00001, illustrates that the measure of trying to achieve can ensure the transient safe and stable of electric power system after fault.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1., based on a urgent load shedding control method for trace sensitivity, it is characterized in that: comprise the following steps:

(1) gather electric power system data, determine the number of cutting load node, form cutting load dominant vector; That determines each cutting load node can the maximum of cutting load amount, forms maximum cutting load amount vector; The selection of cutting load node and each cutting load node can the maximum of cutting load amount can by User Defined;

(2) supervision track, transient safe and stable discriminant parameter and transient state numerical simulation parameter are set, for judging whether safety and stability;

(3) for forecast accident, after obtaining accident by electrical power system transient numerical simulation, monitor track, calculate transient safe and stable margin index vector, judge whether to meet transient safe and stable constraints, if meet, then do not need to take urgent cutting load measure, solve end; Otherwise enter step (4), start the urgent cutting load Mathematical Modeling of iterative, obtain cutting load dominant vector;

(4) the trace sensitivity matrix of transient safe and stable margin index is calculated by electrical power system transient numerical simulation and numerical perturbation method, by the linearisation of transient safe and stable constraints;

(5) solve and transform by urgent cutting load Mathematical Modeling the linear programming problem obtained, calculate knots modification and the cutting load dominant vector of the cutting load dominant vector of iteration;

(6) judge whether the cutting load dominant vector that iteration is tried to achieve meets the condition of convergence, if meet, then using this cutting load dominant vector as optimal solution, and terminate solve; Otherwise perform step (4), continue iterative;

(7) according to the cutting load dominant vector obtained, formulate urgent cutting load control measure prediction scheme, entry condition is set to detect that fault occurs then to perform immediately.

2. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, is characterized in that: in described step (1), electric power system data comprises node parameter, line parameter circuit value, generator and load parameter,

Determine the number of cutting load node, form cutting load dominant vector P; That determines each cutting load node can the maximum of cutting load amount, forms maximum cutting load amount vector the selection of cutting load node and each cutting load node can the maximum of cutting load amount by User Defined:

P＝[p ₁,p ₂,...,p _N]

$\stackrel{\&OverBar;}{P}=\&lsqb;{\stackrel{\&OverBar;}{p}}_1,{\stackrel{\&OverBar;}{p}}_2,...,{\stackrel{\&OverBar;}{p}}_N\&rsqb;$

Wherein, N represents the number of cutting load node.

3. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, it is characterized in that: in described step (2), arrange and monitor track, transient safe and stable discriminant parameter and transient state numerical simulation parameter, monitor that track comprises generator's power and angle track and frequency locus, and busbar voltage track; Transient safe and stable discriminant parameter comprises frequency two-element list and voltage two-element list; Transient state numerical simulation parameter comprises electrical power system transient numerical simulation duration T and simulation step length Δ t.

4. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, it is characterized in that: in described step (2), the form of frequency two-element list is (f _cr, t _cr), for judging transient frequency fail safe, wherein f _crfor frequency shift (FS) threshold value, t _crfor the frequency shift (FS) maximum allowed time, when transient state numerical simulation process medium frequency track is continued above f _crtime be greater than t _crtime, then think that transient frequency is dangerous, frequency two-element list has several;

The form of voltage two-element list is (V _cr, t _cr), for judging Transient Voltage Security, wherein V _crfor variation threshold value, t _crfor the variation maximum allowed time, when in transient state numerical simulation process, voltage trace is continued above V _crtime be greater than t _crtime, then think that transient voltage is dangerous, voltage two-element list has several;

Electrical power system transient numerical simulation duration T is the duration that fault generation initial time experiences to transient process end time.

5. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, is characterized in that: in described step (3), for forecast accident, the track of each quantity of state after obtaining accident by electrical power system transient numerical simulation; Calculate transient safe and stable margin index vector η, judge whether to meet transient safe and stable constraints:

η＞ε

Wherein, ε is transient safe and stable critical value vector;

If meet, then do not need to take urgent cutting load measure, solve end; Otherwise enter step (4), start the following urgent cutting load Mathematical Modeling of iterative, obtain cutting load dominant vector P:

$minF\left(P\right)=\underset{i}{\&Sigma;}{C}_i{p}_i$

s.t.

$\left\{\begin{array}{c}\mathrm{\&eta;}>\mathrm{\&epsiv;}\\ 0\&le;P\&le;\stackrel{\&OverBar;}{P}\end{array}\right.$

Wherein, for cutting load cost target function, C _ibe i-th cutting load amount p _icost; η > ε is transient safe and stable constraints; for cutting load amount constraints.

6. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, is characterized in that: in described step (3), and transient safe and stable margin index vector η and transient safe and stable critical value vector ε is expressed as follows:

$\mathrm{\&eta;}=\left[\begin{array}{c}{\mathrm{\&eta;}}_{\mathrm{\&delta;}}\\ {\mathrm{\&eta;}}_f\\ {\mathrm{\&eta;}}_V\end{array}\right],\mathrm{\&epsiv;}=\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{\&delta;}}\\ {\mathrm{\&epsiv;}}_f\\ {\mathrm{\&epsiv;}}_V\end{array}\right]$

Wherein, η _δfor Transient angle stability margin index, η _ffor transient frequency fail safe margin index, η _vfor Transient Voltage Security margin index; ε _δtransient angle stability critical value, ε _ftransient frequency security critical value, ε _vtransient Voltage Security critical value,

Transient safe and stable constraints η > ε is by Transient angle stability constraints η _δ> ε _δ, transient frequency safety constraint η _f> ε _fwith Transient Voltage Security constraints η _v> ε _vthe unified compact form write as:

$\left.\begin{array}{c}{\mathrm{\&eta;}}_{\mathrm{\&delta;}}>{\mathrm{\&epsiv;}}_{\mathrm{\&delta;}}\\ {\mathrm{\&eta;}}_f>{\mathrm{\&epsiv;}}_f\\ {\mathrm{\&eta;}}_V>{\mathrm{\&epsiv;}}_V\end{array}\right\}\&DoubleRightArrow;\mathrm{\&eta;}>\mathrm{\&epsiv;}$

Transient angle stability margin index η _δcalculate based on EEAC (Extended Equal Area Criterion),

Transient frequency fail safe margin index η _fby considering that the frequency shift (FS) security margin index of cumulative effect is weighed, calculate transient frequency fail safe margin index η by following formula _f:

η _f＝min(η _f,i,j),0≤i≤N _f,0≤j≤M _f

${\mathrm{\&eta;}}_{f,i,j}=min\left(\frac{{\&Integral;}_t^{t+t_{cr,j}}(f_i-f_{cr,j})dt}{(f_N-f_{cr,j})t_{cr,j}}\right),0\&le;t\&le;T-t_{cr,j}$

Wherein, N _ffor the number of monitored generator frequency track, M _ffor the number of the frequency two-element list of setting; η _{f, i, j}represent i-th monitored frequency locus f _iat a jth frequency two-element list (f _{cr, j}, t _{cr, j}) weigh under transient frequency fail safe margin index, t is integration initial time, f _nfor electric power system rated frequency;

Transient Voltage Security margin index η _vby considering that the variation security margin index of cumulative effect is weighed, calculate Transient Voltage Security margin index η by following formula _v:

η _V＝min(η _V,i,j),0≤i≤N _V,0≤j≤M _V

${\mathrm{\&eta;}}_{V,i,j}=min\left(\frac{{\&Integral;}_t^{t+t_{cr,j}}(V_i-V_{cr,j})dt}{(V_N-V_{cr,j})t_{cr,j}}\right),0\&le;t\&le;T-t_{cr,j}$

Wherein, N _vfor the number of monitored busbar voltage track, M _vfor the number of the voltage two-element list of setting; η _{v, i, j}represent i-th monitored voltage trace V _iat a jth voltage two-element list (V _{cr, j}, t _{cr, j}) weigh under Transient Voltage Security margin index, t is integration initial time, V _nfor electric power system rated voltage.

7. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, it is characterized in that: in described step (4), calculated the trace sensitivity matrix A of transient safe and stable margin index by electrical power system transient numerical simulation and numerical perturbation method, transient safe and stable constraints linearly turned to following form:

η＝η(P ^(k))+AΔP ^(k+1)＞ε

Wherein, k represents the current iterative number of times solving process, η (P ^(k)) represent the cutting load dominant vector P tried to achieve in kth time iteration ^(k)effect under transient safe and stable nargin, Δ P ^(k+1)for the knots modification of the cutting load dominant vector that current iteration solves, there is following form:

ΔP＝[Δp ₁,Δp ₂,...,Δp _N]。

8. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, is characterized in that: in described step (4), trace sensitivity matrix A has the expression formula of following form:

$A=\left[\begin{array}{cccccc}{a}_{\mathrm{\&delta;}1}& a_{\mathrm{\&delta;}2}& ...& a_{\mathrm{\&delta;}i}& ...& a_{\mathrm{\&delta;}N}\\ a_{f1}& a_{f2}& ...& a_{fi}& ...& a_{fN}\\ a_{V1}& a_{V2}& ...& a_{Vi}& ...& a_{VN}\end{array}\right]$

Wherein, a _{δ i}that Transient angle stability margin index is to i-th cutting load amount p _itrace sensitivity, a _fithat transient frequency fail safe margin index is to i-th cutting load amount p _itrace sensitivity, a _vithat Transient Voltage Security margin index is to i-th cutting load amount p _itrace sensitivity, trace sensitivity by electrical power system transient numerical simulation and numerical perturbation method, is tried to achieve with following formula:

$a_{\mathrm{\&delta;}i}=\frac{{\mathrm{\&eta;}}_{\mathrm{\&delta;}}\left(P^{\left(k\right)}\right)-{\mathrm{\&eta;}}_{\mathrm{\&delta;}}(P^{\left(k\right)},{\mathrm{\&tau;}}_i)}{{\mathrm{\&tau;}}_i}$

$a_{fi}=\frac{{\mathrm{\&eta;}}_f\left(P^{\left(k\right)}\right)-{\mathrm{\&eta;}}_f(P^{\left(k\right)},{\mathrm{\&tau;}}_i)}{{\mathrm{\&tau;}}_i}$

$a_{Vi}=\frac{{\mathrm{\&eta;}}_V\left(P^{\left(k\right)}\right)-{\mathrm{\&eta;}}_V(P^{\left(k\right)},{\mathrm{\&tau;}}_i)}{{\mathrm{\&tau;}}_i}$

Wherein, η _δ(P ^(k)), η _f(P ^(k)) and η _v(P ^(k)) be respectively at cutting load dominant vector P ^(k)under Transient angle stability margin index, transient frequency fail safe margin index and the Transient Voltage Security margin index of trying to achieve; η _δ(P ^(k), τ _i), η _f(P ^(k), τ _i) and η _v(P ^(k), τ _i) be respectively at cutting load dominant vector P ^(k)under, to i-th cutting load amount p _iapply Perturbation τ _iafter Transient angle stability margin index, transient frequency fail safe margin index and the Transient Voltage Security margin index of trying to achieve; Perturbation value τ _ibeing a positive number, when calculating each margin index, needing first to obtain phase-swing curves, frequency locus and the voltage trace under corresponding cutting load scheme by transient state numerical simulation, and then obtain the value of each margin index.

9. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, it is characterized in that: in described step (5), by the linearizing transient safe and stable constraints obtained in step (4), urgent cutting load Mathematical Modeling is converted into linear programming problem:

$minF\left(P\right)=\underset{i}{\&Sigma;}{C}_i({p_i}^{\left(k\right)}+{{\mathrm{\&Delta;p}}_i}^{\left(k+1\right)})$

s.t.

$\left\{\begin{array}{c}\mathrm{\&eta;}\left(P^{\left(k\right)}\right)+A\mathrm{\&Delta;}{P}^{(k+1)}>\mathrm{\&epsiv;}\\ 0\&le;P^{\left(k\right)}+\mathrm{\&Delta;}{P}^{(k+1)}\&le;\stackrel{\&OverBar;}{P}\end{array}\right.$

The knots modification Δ P of the cutting load dominant vector of current iteration is obtained by linear programming for solution ^(k+1), this cutting load dominant vector P ^(k+1)try to achieve by following formula:

P ^(k+1)＝P ^(k)+ΔP ^(k+1)。

10. a kind of urgent load shedding control method based on trace sensitivity as claimed in claim 1, it is characterized in that: in described step (6), the condition of convergence comprises following 3 aspects:

1) have at least a transient stability margin index to be in critical condition, namely meet following formula:

η _δ-ε _δ< Δ ε or η _f-ε _f< Δ ε or η _v-ε _v< Δ ε

Wherein, critical condition threshold value Δ ε is a positive number;

2) change of total cutting load amount is less than threshold value ε _load, namely meet following formula:

$\underset{i}{\&Sigma;}{\mathrm{\&Delta;p}}_i^{(k+1)}<{\mathrm{\&epsiv;}}_{load}$

3) each cutting load amount change be less than threshold value ε _p, namely meet following formula:

${\mathrm{\&Delta;p}}_i^{(k+1)}<{\mathrm{\&epsiv;}}_p.$