CN101387679B - Method for weighting dynamic voltage stability margin index - Google Patents

Abstract

The invention provides a method for measuring dynamic voltage stability margin index, while the dynamic voltage stability margin index is the margin to the voltage collapse point of a power system which load increase slowly in a certain speed; the dynamic voltage stability margin index considers that the system is affected by the dynamic components such as the on-load tap changer (ULTC) and the over excitation limit of engines. The method can calculate the dynamic margins of the system which load increases in various types such as single node, regional or full-network type, to provide a visual measurement presenting the distance between the prior operation point of the system and the voltage collapse point, while the distance and the dynamic margin have linear relationship. Therefore, the dynamic margin index has high practical values.

Description

A kind of method of weighting dynamic voltage stability margin index

Technical field

The present invention relates to a kind of method of weighting dynamic voltage stability margin index, belong to the simulation and the computing field of electric system.

Background technology

Stablize the progress of research work along with voltage; Emulation tool and modeling work are progressively perfect; China's operation of power networks and planning department are paid special attention to the stable simulation study work of medium-term and long-term voltage, and the important content of in-depth stability Calculation is classified in also clearly that dynamic electric voltage is stable check research as in " power system safety and stability guide rule ".

Weigh system stability and adopt the nargin index more; So-called nargin index is meant the given running status from system; According to certain pattern; Growth through load growth or through-put power progressively approaches the collapse of voltage point, and the current operating point of system can be used as the index of voltage degree of stability to the distance of collapse of voltage point.Traditional static load nargin is based on the continuous tide method, from present operating point, constantly increases with load, finds the solution trend successively, up to through critical point, tries to achieve load margin thereby obtain node PU curve.But the quiescent voltage analytical approach is based on stable state power flow equation or expansion power flow equation; Ignore Electrical Power System Dynamic and regulated effect of factors; With the behavior of algebraic equation descriptive system, the judgement system keeps the stable ability of voltage under microvariations, and the result who therefore obtains is relatively conservative.

The nargin index has the following advantages: can provide one to represent the current operating point of system measuring to collapse of voltage point distance more intuitively to the operations staff; System's operating point is big or small linear to the distance of collapse of voltage point and nargin index; Can take into account the influence that the distribution of work, load growth mode etc. are arranged of various factors in the transient process such as constraint condition, generator more easily.

When calculating the nargin index, the power of each load bus can increase according to any-mode in the network, to approach collapse point, in order to simplify calculating, often supposes that load power increases with following four kinds of modes:

(1) active power of single load bus and/or reactive power increase, and the power of other load buses remains unchanged;

(2) the meritorious and/or reactive power of the load bus of selection area increases, and other some power of load remain unchanged;

(3) the meritorious and/or reactive power of the load bus of a certain selection area increases, and the active power of the load bus of another selection area and/or reactive power reduce, and other load bus power remain unchanged;

(4) all the active power and/or the reactive power of load bus increase simultaneously.

Dynamic voltage stability margin index is to find the solution electric system when load slowly increases with given pace, and system is apart from the nargin of collapse of voltage point; Dynamic voltage stability margin has been considered the influence of dynamic element such as ULTC (ULTC), the restriction of generator overexcitation in the system; Can calculate the dynamic nargin of system under the multiple load growth modes such as single node, subregion and the whole network; For the operations staff provides one to represent the current operating point of system more intuitively to the measuring of collapse of voltage point distance, system's operating point apart from collapse point with dynamically nargin is linear.Therefore, dynamic voltage stability margin index has actual preferably directive significance.

Electric power system full dynamic simulation is meant electric system electromechanical transient, medium and long term process organically united and carries out Digital Simulation.It described electric system be disturbed after whole continuous dynamic process.The differential algebraic equations algorithm use of full dynamic simulation program becomes GEAR method, network equation and the differential equation simultaneous solution of rank variable step.

The main calculation procedure of GEAR method is following:

For the 1 rank differential equation,

$\left\{\begin{array}{c}\frac{\mathrm{dy}}{\mathrm{dt}}=f(y,t)\\ y\left(t_0\right)=y_0\end{array}\right.$

(1) definition Nordsieck vector z _m, it is higher derivative y ', y with back " ... wait the y or f (y, t) data that replace former steps.Promptly

$z_m={[y_m,{\mathrm{hy}}_m^{\′},\frac{h^2}{2!}{y}_m^{\′\′},...,\frac{h^k}{K!}{y_m}^{\left(k\right)}]}^T$

(2) prediction

z _M+1 ⁽⁰⁾=Pz _mP is a Pascal triangle battle array,

(3) proofread and correct

z _m+1 ⁽ⁱ⁺¹⁾＝z _m+1 ⁽ⁱ⁾+LG _m+1 ⁽ⁱ⁾

Wherein: L is a K dimension constant vector, $G_{m+1}^{\left(i\right)}=\mathrm{Hf}\left(y_{m+1}^{\left(i\right)}\right)-\mathrm{Hf}\left(y_{m+1}^{(i-1)}\right),$

(4) truncation error

The truncation error in K rank method m step is:

$E_m\≅C_{k+1}K!\▿Z_m^K$

Wherein: C _K+1The constant relevant with rank.

Be the Z that the m step calculates gained _mZ with back _M-1The value that last component of these two vectors subtracts each other.

The normal relative error of using in the emulation, the relative error that promptly requires per step is less than a value ε who stipulates in advance ₀:

$C_{k+1}K!\left|\frac{{\▿Z}_m^K}{y_{\max }}\right|\≤{\mathrm{\ϵ}}_0$

Y wherein _MaxThe maximal value of the y that had occurred when being integrated to this step, but when the beginning integration, if y=0 then should get y _Max=1.

Under the situation of differential equation group, more than one of y supposes total N variable y (1), y (2) ... Y (N), then relative error is defined as:

$\mathrm{\ϵ}=\sqrt{\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left[\frac{C_{k+1}K!Z_{\left(j\right)m}^K}{y_{\left(j\right)\max }}\right]}^2}$

ε≤ε ₀, think that then this step is effective, change down the step over to, and consider to become rank, variable step.

ε>=ε ₀, think that then this step is invalid, become rank, variable step, recomputate.

(5) become rank, variable step control

After per step integration was accomplished, program was estimated current rank respectively, is risen the truncation error of rank and depression of order variable afterwards.Through certain strategy, determine order and step-length when next step calculates.The constant rank only formula during variable step are following:

New step-length is: h _s=R _k* h.Wherein: $R_k=\frac{1}{1.2}\sqrt[k+1]{\frac{{\mathrm{\ϵ}}_0}{C_{k+1}K!\left|\frac{{\▿Z}_m^K}{y_{\mathrm{Max}}}\right|}}$

Summary of the invention

The present invention based on institute of system of China Electric Power Research Institute power system analysis software-electric power system full dynamic simulation program, has proposed dynamic voltage stability margin index through after researching and analysing.This index has obtained application in the stable research of Chongqing electricity grid voltage, obtained effect preferably.

The method for solving of existing power system voltage stability margin mostly can not taking into account system in the influence of dynamic element; Particularly actuation times such as ULTC (ULTC), generator excitation restriction are than long protection link; Therefore; Based on the dynamic voltage stability margin index that the electric power system full dynamic simulation program is calculated, this index is the ruuning situation of closing to reality system more.

With reference to Fig. 1, dynamic voltage stability margin index is following in the implementation method of electric power system full dynamic simulation program:

(1) builds network topology structure according to computation requirement, set up the load model that system-computed needs, comprise static load model and induction motor model;

Setting up system's static load model is:

$\left\{\begin{array}{c}P=P_0[P_1{\left(\frac{V}{V_0}\right)}^2+P_2\left(\frac{V}{V_0}\right)+P_3+P_4(1+\mathrm{\Δf}*L_{\mathrm{DP}})+P_5*V^{N_p}]\\ Q=Q_0[Q_1{\left(\frac{V}{V_0}\right)}^2+Q_2\left(\frac{V}{V_0}\right)+Q_3+Q_4(1+\mathrm{\Δf}*L_{\mathrm{DQ}})+Q_5*V^{N_Q}]\end{array}\right.$

Wherein: P ₀Be burden with power, P ₁, P ₂, P ₃, P ₄, P ₅Be respectively constant impedance burden with power ratio, steady current burden with power ratio, firm power burden with power ratio, relevant burden with power ratio with frequency, the relevant burden with power ratio of voltage index, V is system's virtual voltage, V ₀Be system reference voltage, Δ f is a frequency variation, L _DPBe the meritorious percent change that change of frequency 1% causes, N _PBe the active voltage index, load or burden without work model formation parameter is named in like manner, in the following formula: P ₁+ P ₂+ P ₃+ P ₄+ P ₅=1, Q ₁+ Q ₂+ Q ₃+ Q ₄+ Q ₅=1.

Set up system's motor load model:

According to known motor stator resistance R _S, motor stator reactance X _S, excitatory reactance X _M, rotor resistance R _R, rotor reactance X _R, motor slippage S, calculating machine moment coefficient: A, B, C;

(2) calculate preparation

Confirm fault type, fault-time, fill in corresponding fault card,, fill in cards such as corresponding ULTC (ULTC) card, generator overexcitation restriction card, relay protection action according to system's actual conditions; Accomplish data preliminary work;

(3) import according to calculation requirement: the zone of the speed of load growth, the time of load growth, load growth or bus title,

$P=\frac{\mathrm{\ΔP}}{\mathrm{\Δt}}*T_{\mathrm{END}}$

Wherein: P is the load growth total amount, and Δ P is a unit interval internal loading increment, and Δ t is the unit interval, T _ENDBe the load growth duration,

According to above-mentioned formula construction load sustainable growth model, get final product through the proportionate relationship of controlling Δ P and Δ t;

(4) simulation calculation

A. read in data and network parameter, inspection Rational Parameters property, the model corresponding relation of formation state variable, intermediate variable and parameter constant and each element carries out initialization process to state variable;

B. form admittance matrix and Jacobi matrix, differentiate the rationality of starting condition;

C. revise the Jacobi matrix element of network equation according to the fault card of having filled in, confirm system state;

D. the GEAR method in the application background technology, calculate the prediction term of GEAR method:

z _M+1 ⁽⁰⁾=Pz _m(P is a Pascal triangle battle array)

Calculate the correction term in the GEAR method:

z _m+1 ⁽ⁱ⁺¹⁾＝z _m+1 ⁽ⁱ⁾+LG _m+1 ⁽ⁱ⁾

Wherein: L is a K dimension constant vector, and m, i are positive integer, $G_{m+1}^{\left(i\right)}=\mathrm{Hf}\left(y_{m+1}^{\left(i\right)}\right)-\mathrm{Hf}\left(y_{m+1}^{(i-1)}\right);$

According to the correction term that obtains, with the differential equation and algebraic equation simultaneous solution;

E. carry out the variable step processing based on calculating actual conditions;

F. simulation calculation finishes, and exports required result;

(5) interpretation of result

Obtain the laggard line data analysis of simulation result, confirm the system power limits to growth,,, obtain by the computes dynamic voltage stability margin index according to the node power limit that calculates and system's normal condition lower node initial power from the node power growth chart:

$K_p=\frac{P_1-P_0}{P_1}$

K _p-dynamic voltage stability margin index (%)

P ₀-system initial power (MW)

P ₁-system limits power (MW)

P ₀Can obtain P by system's normal operating mode statistics ₁Result by simulation analysis obtains by whole process simulation calculating back.

Three, dynamic voltage stability margin index characteristics

1. dynamic voltage stability margin index has considered that dynamic element is to factors such as the influence of voltage stability, particularly ULTC (ULTC), generator excitation limiting elements in the system, and the result who obtains more presses close to system's actual conditions.

2. but the different modes of load growth in the computing system, like modes such as single busbar, zone and the whole networks, load growth speed also can be set arbitrarily, can the multiple method of operation of simulation system.

3. assumed load initial, the concluding time that increase arbitrarily during the system loading growth pattern after simulated failure.

Advantage of the present invention:

Dynamically nargin index clear physics conception has good calculability and suit property, can calculate the voltage stability margin of system under the sustainable growth of loading in the various electrical networks easily.

Description of drawings

Fig. 1 is the full dynamic simulation program flow diagram;

Fig. 2 is 3 machines, 9 node system wiring diagrams;

Fig. 3 is a bus A load variations curve map.

Embodiment

With 3 machines, 9 node single systems (wiring diagram such as accompanying drawing 2) is simulation example, calculates the performing step that dynamic nargin further specifies this method:

1. set up the data of 3 machines, 9 node systems, confirm that the load model that system-computed needs is 100% constant-impedance model;

2. calculate and prepare

Confirm that system loading is the constant-impedance load, load growth requires to fill in exciter current of generator protection card and ULTC (ULTC) action card based on reality under system's non-failure conditions.

3. selective system median generatrix A is the load growth zone, and growth rate is that per second increases by 1% under the normal mode, and be 800 seconds rise time.

4. simulation calculation

Through the whole process simulation calculation procedure, 3 machines, 9 node systems obtain the whole network node load and change in voltage curve when calculating non-fault under bus A load sustainable growth situation.(as shown in Figure 3)

5. analytical calculation

As can beappreciated from fig. 3, normal condition Down Highway A load is 125MW (P ₀), under load sustainable growth situation, power limit is 355MW (P ₁), through formula Calculate dynamic electric voltage nargin index:

K _p＝64.8％。

Dynamically the calculating of nargin index is more convenient, and clear concept has obtained using in actual electric network and checking.

The present invention has been described according to the preferred example of implementing.Obviously, reading and understanding above-mentioned detailed description postscript and can make multiple correction and replacement.What this invention is intended to is that the application is built into all these corrections and the replacement that has comprised within the scope that falls into appended claims book or its equivalent.

Claims (1)

1. the appraisal procedure of a weighting dynamic voltage stability margin index, it mainly may further comprise the steps:

(1) builds network topology structure according to computation requirement, set up the load model that system-computed needs, comprise static load model and induction motor model;

Setting up system's static load model is:

$\left\{\begin{array}{c}P=P_0[P_1{\left(\frac{V}{V_0}\right)}^2+P_2\left(\frac{V}{V_0}\right)+P_3+P_4(1+\mathrm{\Δf}*L_{\mathrm{DP}})+P_5*V^{N_p}]\\ Q=Q_0[Q_1{\left(\frac{V}{V_0}\right)}^2+Q_2\left(\frac{V}{V_0}\right)+Q_3+Q_4(1+\mathrm{\Δf}*L_{\mathrm{DQ}})+Q_5*V^{N_Q}]\end{array}\right.$

Wherein: P ₀Be burden with power, P ₁, P ₂, P ₃, P ₄, P ₅Be respectively constant impedance burden with power ratio, steady current burden with power ratio, firm power burden with power ratio, relevant burden with power ratio with frequency, the relevant burden with power ratio of voltage index, V is system's virtual voltage, V ₀Be system reference voltage, Δ f is a frequency variation, L _DPBe the meritorious percent change that change of frequency 1% causes, N _PBe the active voltage index, load or burden without work model formation parameter is named in like manner, in the following formula: P ₁+ P ₂+ P ₃+ P ₄+ P ₅=1, Q ₁+ Q ₂+ Q ₃+ Q ₄+ Q ₅=1;

Set up system's motor load model:

According to known motor stator resistance R _S, motor stator reactance X _S, excitatory reactance X _M, rotor resistance R _R, rotor reactance X _R, motor slippage S, calculating machine moment coefficient: A, B, C;

(2) calculate preparation

Confirm fault type, fault-time, fill in corresponding fault card; According to system's actual conditions, fill in corresponding ULTC (ULTC) card, generator overexcitation restriction card and relay protection action card, accomplish data preliminary work;

(3) import according to calculation requirement: the zone of the speed of load growth, the time of load growth, load growth or bus title obtain:

$P=\frac{\mathrm{\ΔP}}{\mathrm{\Δt}}*T_{\mathrm{END}}$

Wherein: P is the load growth total amount, and Δ P is a unit interval internal loading increment, and Δ t is the unit interval, T _ENDBe the load growth duration,

According to above-mentioned formula construction load sustainable growth model, get final product through the proportionate relationship of controlling Δ P and Δ t;

(4) simulation calculation

A. read in data and network parameter, inspection Rational Parameters property, the model corresponding relation of formation state variable, intermediate variable and parameter constant and each element carries out initialization process to state variable;

B. form admittance matrix and Jacobi matrix, differentiate the rationality of starting condition;

C. revise the Jacobi matrix element of network equation according to the fault card of having filled in, confirm system state;

D. the GEAR method in the application background technology, calculate the prediction term of GEAR method:

z _m+1 ⁽⁰⁾＝Pz _m，

Wherein, P is a Pascal triangle battle array;

Calculate the correction term in the GEAR method:

z _m+1 ⁽ⁱ⁺¹⁾＝z _m+1 ⁽ⁱ⁾+LG _m+1 ⁽ⁱ⁾

Wherein: L is a K dimension constant vector, and m, i are positive integer, $G_{m+1}^{\left(i\right)}=\mathrm{Hf}\left(y_{m+1}^{\left(i\right)}\right)-\mathrm{Hf}\left(y_{m+1}^{(i-1)}\right);$

According to the correction term that obtains, with the differential equation and algebraic equation simultaneous solution;

E. carry out the variable step processing based on calculating actual conditions;

F. simulation calculation finishes, and exports required result;

(5) interpretation of result

Obtain the laggard line data analysis of simulation result, confirm the system power limits to growth from the node power growth chart, according to the node power limit that calculates and system's normal condition lower node initial power, by the computes dynamic voltage stability margin index:

$K_p=\frac{P_1-P_0}{P_1}$

K _p-dynamic voltage stability margin index (%)

P ₀-system initial power (MW)

P ₁-system limits power (MW)

P ₀Can obtain P by system's normal operating mode statistics ₁Result by simulation analysis obtains by whole process simulation calculating back.

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