CN104934961A - Multi-FACTS-damping-controller interaction risk analysis method - Google Patents

Abstract

The present invention provides a multi-FACTS-damping-controller interaction risk analysis method which comprises the steps of (1) optionally selecting two FACTS damping controllers in a power system and calculating the equivalent open loop transfer functions of the FACTS damping controllers respectively, (2) calculating the impact factor between the two FACTS damping controllers, (3) calculating the interaction risk factor between the two FACTS damping controllers, (4) analyzing the risk of the interaction between the two FACTS damping controllers according to the interaction risk factor, and (5) repeating steps of (1) to (4) and completing the risk analysis of the interaction between all FACTS damping controllers as the research object in the power system. The method provided by the invention has the function that the interaction risk between the FACTS damping controllers can be predicted in advance, the possible negative interaction between the multiple FACTS controllers is avoided, the system safety and stability hidden trouble is eliminated, and the system safety and stability are improved.

Description

A kind of many FACTS damping controller reciprocation risk analysis method

Technical field

The present invention relates to field of power, be specifically related to a kind of many FACTS damping controller reciprocation risk analysis method based on EOP theory.

Background technology

Appear as the safe, economic, reliable of modern power systems and the high-quality of flexible ac transmission system (flexible AC transmission system, FACTS) are run and are provided highly effective means.Increasing research in recent years shows: the reciprocal effect that may exist between multiple FACTS device, and produces significant impact by the operation and control of electric power system, the control performance of FACTS device may be made to worsen, even cause system unstability time serious.But under normal conditions, people only consider the effect of single assembly when designing FACTS controller, and do not consider the reciprocation problem between each FACTS device, therefore the interactive analysis method of many FACTS controller is studied, avoid the negative reciprocation that may occur between many FACTS controller, to ensure that the safe and stable operation of system has important practical significance.

In recent years, the research about FACTS interaction analysis method gets the attention, and current main method has model analysis, the positive rule theory of Normal Form, Relative increasing rate, odd value analysis etc.But at present about the rarely seen report of analytical method of many FACTS reciprocation risk.The present invention is research many FACTS reciprocation risk analysis method, and the stable coordination realizing multiple stage FACTS damping controller runs, and gives full play to the superperformance of multiple stage FACTS.

Summary of the invention

In order to overcome the defect of prior art, the object of the present invention is to provide a kind of many FACTS damping controller reciprocation risk analysis method based on EOP theory, the method is based on EOP theory deduction and form the mutual risks and assumptions index of many FACTS and analysis process, the reciprocation risk between many FACTS damping controller can be predicted in advance under many FACTS damping controller not yet input situation, avoid the negative reciprocation that may occur between many FACTS controller, eliminate system safety and stablize hidden danger, to ensure the safe and stable operation of bulk power grid.

In order to realize foregoing invention object, the present invention adopts following technical proposals to realize:

A kind of many FACTS damping controller reciprocation risk analysis method, its improvements are, described method comprises the steps:

(1) optional two FACTS damping controller g from electric power system _ciand g _cj, calculate two FACTS damping controller g respectively _ciand g _cjequivalent open-loop transfer function;

(2) two FACTS damping controller g are calculated _ciwith g _cjbetween factor of influence;

(3) two FACTS damping controller g are calculated _ciwith g _cjbetween reciprocation risks and assumptions;

(4) according to reciprocation risks and assumptions, the reciprocation risk between two FACTS damping controllers is analyzed;

(5) repeat step (1) to (4), complete in electric power system as the reciprocation risk analysis between all FACTS damping controllers of research object.

In described step (1), set up the FACTS damping controller g be shown below _ciequivalence open-loop transfer function:

${\hat{g}}_{\mathrm{ii}}\left(s\right)=g_{\mathrm{ii}}+{\stackrel{\‾}{g}}_{i.}^{\mathrm{ij}}{\stackrel{\‾}{G}}_C^{\mathrm{ij}}{(I-{\stackrel{\‾}{G}}^{\mathrm{ij}}{\stackrel{\‾}{G}}_C^{\mathrm{ij}})}^{-1}{\stackrel{\‾}{g}}_{.j}^{\mathrm{ij}}$

Wherein, be i-th FACTS damping controller g _ciequivalent open-loop transfer function, i=1,2 ..., N, j=1,2 ..., N, N be in electric power system as research object FACTS damping controller sum, g _iirepresent in G (s) element being positioned at the i-th row i-th and arranging, with represent respectively and remove g in G (s) _ijafter the i-th row vector and jth column vector, represent and remove G _c(s) i-th matrix of gained after row and jth row, represent the matrix removing G (s) i-th row and the rear gained of jth row, G (s), G _cs () is respectively ssystem transfer function matrix and FACTS damping controller transfer function matrix, I representation unit matrix.

In described step (1), set up the FACTS damping controller g be shown below _cjequivalence open-loop transfer function:

${\hat{g}}_{\mathrm{jj}}\left(s\right)=g_{\mathrm{jj}}+{\stackrel{\‾}{g}}_{j.}^{\mathrm{ji}}{\stackrel{\‾}{G}}_C^{\mathrm{ji}}{(I-{\stackrel{\‾}{G}}^{\mathrm{ji}}{\stackrel{\‾}{G}}_C^{\mathrm{ji}})}^{-1}{\stackrel{\‾}{g}}_{.i}^{\mathrm{ji}}$

Wherein, for jth platform FACTS damping controller g _ciequivalent open-loop transfer function, i=1,2 ..., N, j=1,2 ..., N, N be in electric power system as research object FACTS damping controller sum, g _jjrepresent the element being positioned at jth row jth row in G (s), with represent respectively and remove g in G (s) _jiafter jth row vector and the i-th column vector, represent and remove G _cthe matrix of (s) jth row and the rear gained of the i-th row, represent the matrix removing G (s) jth row and the rear gained of the i-th row, G (s), G _cs () is respectively ssystem transfer function matrix and FACTS damping controller transfer function matrix, I representation unit matrix.

In described step (2), the factor of influence method calculated between two FACTS damping controllers comprises:

2-1) according to FACTS damping controller g _ciequivalent open-loop transfer function, calculate FACTS damping controller g by following formula _cito FACTS damping controller g _cjfactor of influence:

${\mathrm{\ψ}}_{\mathrm{ij}}=\underset{\mathrm{\ω}}{\sup }{\left|\right|\left(\right[g_{\mathrm{ii}}+{\stackrel{\‾}{g}}_{i.}^{\mathrm{ij}}{\stackrel{\‾}{G}}_C^{\mathrm{ij}}{(I-{\stackrel{\‾}{G}}^{\mathrm{ij}}{\stackrel{\‾}{G}}_C^{\mathrm{ij}})}^{-1}{\stackrel{\‾}{g}}_{.j}^{\mathrm{ij}}\left]g_{\mathrm{Ci}}\right)\left(\mathrm{j\ω}\right)\left|\right|}_{\∞}$

2-2) according to FACTS damping controller g _cjequivalent open-loop transfer function, calculate FACTS damping controller g by following formula _cjto FACTS damping controller g _cifactor of influence:

${\mathrm{\ψ}}_{\mathrm{ji}}=\underset{\mathrm{\ω}}{\sup }{\left|\right|\left(\right[g_{\mathrm{jj}}+{\stackrel{\‾}{g}}_{j.}^{\mathrm{ji}}{\stackrel{\‾}{G}}_C^{\mathrm{ji}}{(I-{\stackrel{\‾}{G}}^{\mathrm{ji}}{\stackrel{\‾}{G}}_C^{\mathrm{ji}})}^{-1}{\stackrel{\‾}{g}}_{.i}^{\mathrm{ji}}\left]g_{\mathrm{Cj}}\right)\left(\mathrm{j\ω}\right)\left|\right|}_{\∞}$

Wherein, g _ci, g _cjrepresent the transfer function of i-th and jth platform FACTS damping controller respectively, j represents imaginary part, and ω represents angular frequency.

In described step (3), the maximum in selecting step (2) in all factors of influence, as FACTS damping controller g _ciwith g _cjbetween reciprocation risks and assumptions, as follows:

R _ij＝max{ψ _ij,ψ _ji}

In described step (4), the method analyzed the reciprocation risk between two FACTS damping controllers is as follows:

4-1) work as R _ijwhen=1, show that between controller, reciprocation risk is high, must consider the coordination between controller;

4-2) work as 0.8<R _ijduring <1, show that between controller, reciprocation risk is very high, need to consider the coordination between controller;

4-3) work as 0.5<R _ijwhen≤0.8, show that between controller, reciprocation risk is higher, the coordination between controller is considered in suggestion;

4-4) work as R _ijduring <0.5, show that between controller, reciprocation risk is lower, without the need to considering the coordination between controller.

Compared with the prior art, the beneficial effect that the present invention reaches is:

(1) analytical method of the present invention has the function predicting reciprocation risk between many FACTS damping controller in advance, the reciprocation risk between many FACTS damping controller can be predicted in advance under many FACTS damping controller not yet input situation, avoid the negative reciprocation that may occur between many FACTS controller, eliminate system safety and stablize hidden danger, to ensure the safe and stable operation of bulk power grid.

(2) the present invention can directly apply to electric power system on-line analysis platform, and based on the security and stability analysis field of wide area measurement system, not only there is important engineer applied be worth, for the coordinate design of many FACTS damping controller and bulk power grid vibration accident analysis, also there is important directive significance.

Accompanying drawing explanation

Fig. 1 is the flow chart of the many FACTS damping controller reciprocation risk analysis method based on EOP theory of the present invention;

Fig. 2 is two machine system models provided by the invention;

Fig. 3 is First FACTS damping controller independent operating control effects figure provided by the invention;

Fig. 4 is second FACTS damping controller independent operating control effects figure provided by the invention;

Fig. 5 is that two FACTS damping controllers provided by the invention run control effects figure simultaneously.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

Many FACTS damping controller reciprocation risk analysis method based on EOP theory provided by the invention, Fig. 1 is the flow chart of multiple stage FACTS damping controller method for designing of the present invention, and the method comprises the steps:

Step (1), optional two FACTS damping controller g from electric power system _ciand g _cj, calculate two FACTS damping controller g respectively _ciand g _cjequivalent open-loop transfer function; Concrete steps are as follows:

1-1) set up the FACTS damping controller g be shown below _cithe basic function of equivalence open-loop transfer function:

${\hat{g}}_{\mathrm{ii}}\left(s\right)=g_{\mathrm{ii}}+{\stackrel{\&OverBar;}{g}}_{i.}^{\mathrm{ij}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ij}}{(I-{\stackrel{\&OverBar;}{G}}^{\mathrm{ij}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ij}})}^{-1}{\stackrel{\&OverBar;}{g}}_{.j}^{\mathrm{ij}}$ ①

1-2) set up the FACTS damping controller g be shown below _cjthe basic function of equivalence open-loop transfer function:

${\hat{g}}_{\mathrm{jj}}\left(s\right)=g_{\mathrm{jj}}+{\stackrel{\&OverBar;}{g}}_{j.}^{\mathrm{ji}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ji}}{(I-{\stackrel{\&OverBar;}{G}}^{\mathrm{ji}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ji}})}^{-1}{\stackrel{\&OverBar;}{g}}_{.i}^{\mathrm{ji}}$ ②

Calculate electric power system transfer function matrix G used in equivalent open-loop transfer function process _c(s) and FACTS damping controller transfer function matrix G _c(s) [this matrix G _cs the transfer function in () is FACTS damping controller Transfer function in the frequency domain], can calculate in this step (1), also can precalculate electric power system transfer function matrix G before this step (1) _cas whole N platform FACTS damping controller transfer functions of research object in (s) and electric power system, then forming matrix G by then extracting directly reading electric power system transfer function values _cs (), reads FACTS damping controller transfer function composition matrix G _c(s).

In equivalence open-loop transfer function computational process, electric power system transfer function matrix G (s) and FACTS damping controller transfer function matrix G _cs the computational methods of () adopt and well known to a person skilled in the art prior art, such as:

The computational methods of electric power system transfer function matrix G (s) are:

A1, under FACTS damping controller open loop operation condition, if the output variable of i-th FACTS damping controller is U, the input variable of jth platform FACTS damping controller is Y;

B1, transfer function discrimination method is utilized to calculate electric power system transfer function

C1, repetition steps A 1-B1, also can adopt any one in other related identification, frequency domain identification method, least-squares estimation or Kalman filtering method in step bl is determined., (this element is electric power system transfer function g to calculate each element in electric power system transfer function matrix _ij), thus form electric power system transfer function matrix.

FACTS damping controller transfer function matrix G _cs the computational methods of () are:

A2, setting i-th FACTS damping controller transfer function form are

$g_{\mathrm{Ci}}\left(s\right)=K_i\frac{{\mathrm{sT}}_{\mathrm{\&omega;i}}}{1+s{T}_{\mathrm{\&omega;i}}}\frac{1+s{T}_{1i}}{1+s{T}_{2i}}\frac{s{T}_{3i}}{1+s{T}_{4i}}$ ③

By the parameter sets K that equipment sets _i, T _{ω i}, T _1i, T _2i, T _3i, T _4isubstitute into above formula 2., the transfer function of i-th FACTS damping controller can be calculated;

B2, repetition steps A 2, complete the calculating of each element in FACTS damping controller transfer function matrix (this element is FACTS damping controller transfer function), thus form damping controller transfer function matrix.

It should be noted that, 3. formula is only give a kind of conventional transfer function form as example, and in actual applications, the transfer function form of different manufacturers may difference to some extent, and producer can adopt the transfer function form consistent with equipment in different Practical Calculation.

Step (2), calculates two FACTS damping controller g _ciwith g _cjbetween factor of influence; Concrete steps are as follows:

2-1) according to FACTS damping controller g _ciequivalent open-loop transfer function, calculate FACTS damping controller gci to FACTS damping controller g by following formula _cjfactor of influence:

${\mathrm{\&psi;}}_{\mathrm{ij}}=\underset{\mathrm{\&omega;}}{\sup }{\left|\right|\left(\right[g_{\mathrm{ii}}+{\stackrel{\&OverBar;}{g}}_{i.}^{\mathrm{ij}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ij}}{(I-{\stackrel{\&OverBar;}{G}}^{\mathrm{ij}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ij}})}^{-1}{\stackrel{\&OverBar;}{g}}_{.j}^{\mathrm{ij}}\left]g_{\mathrm{Ci}}\right)\left(\mathrm{j\&omega;}\right)\left|\right|}_{\&infin;}$ ④

2-2) according to FACTS damping controller g _cjequivalent open-loop transfer function, calculate FACTS damping controller g by following formula _cjto FACTS damping controller g _cifactor of influence:

${\mathrm{\&psi;}}_{\mathrm{ji}}=\underset{\mathrm{\&omega;}}{\sup }{\left|\right|\left(\right[g_{\mathrm{jj}}+{\stackrel{\&OverBar;}{g}}_{j.}^{\mathrm{ji}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ji}}{(I-{\stackrel{\&OverBar;}{G}}^{\mathrm{ji}}{\stackrel{\&OverBar;}{G}}_C^{\mathrm{ji}})}^{-1}{\stackrel{\&OverBar;}{g}}_{.i}^{\mathrm{ji}}\left]g_{\mathrm{Cj}}\right)\left(\mathrm{j\&omega;}\right)\left|\right|}_{\&infin;}$ ⑤

Wherein, sup () represents supremum, g _ci, g _cjrepresent the transfer function of i-th and jth platform FACTS damping controller respectively, j represents imaginary part, and ω represents angular frequency.

Step (3), the maximum in selecting step (2) in all factors of influence, as FACTS damping controller g _ciwith g _cjbetween reciprocation risks and assumptions, as follows:

R _ij＝max{ψ _ij,ψ _ji} ⑥

Step (4), according to reciprocation risks and assumptions, the reciprocation risk between two FACTS damping controllers is analyzed as follows:

4-1) work as R _ijwhen=1, show that between controller, reciprocation risk is high, must consider the coordination between controller;

4-2) work as 0.8<R _ijduring <1, show that between controller, reciprocation risk is very high, need to consider the coordination between controller;

4-3) work as 0.5<R _ijwhen≤0.8, show that between controller, reciprocation risk is higher, the coordination between controller is considered in suggestion;

4-4) work as R _ijduring <0.5, show that between controller, reciprocation risk is lower, without the need to considering the coordination between controller.

Step (5), repeat step (1) to (4), complete in electric power system as the reciprocation risk analysis between all FACTS damping controllers of research object.

Embodiment

For the typical two-machine system shown in Fig. 2, the present invention is further described in detail below, but the invention is not restricted to given example.There is the underdamping low frequency oscillation mode of about 0.8Hz in minor interference analysis result display system, need by means of the dynamic stability of FACTS device elevator system.A SVC damping controller is respectively installed, the damping characteristic of elevator system area oscillation pattern at bus 1 and bus 2 place.Two SVC damping controller parameters obtain based on the controller independent design method of classical phase compensation principle.Fig. 3 and 4 sets forth control effects during two SVC damping controller independent operatings, curve chart when wherein WithoutDamping Controller is undamped controller independent operating, curve chart when With Damping Controller is damping controller independent operating, article two, the contrast of curve is to prove that separate unit SVC damping controller is can independent operating, and has excellent damping control effects.From simulation result, two SVC dampings control can normal independent operating, and damping controller has the ability of obvious elevator system damping characteristic, and FACTS controller control effects is good.

Use the reciprocation situation between methods analyst provided by the invention two SVC damping controllers, to confirm whether two SVC can run by stable coordination, and step is as follows:

Step one: optional two FACTS damping controller g _ciand g _cj, calculate the equivalent open-loop transfer function of two FACTS damping controllers respectively;

Calculate electric power system transfer function used in equivalent open-loop transfer function process and FACTS damping controller transfer function, can only two FACTS damping controller transfer functions (this transfer function is FACTS damping controller Transfer function in the frequency domain) in this step, also can whole N platform FACTS damping controller transfer functions as research object in first computing system before this step, then reading with then extracting directly.

Step 2: calculate FACTS damping controller g _cito FACTS damping controller g _cjfactor of influence;

Step 3: calculate FACTS damping controller g _cjto FACTS damping controller g _cifactor of influence;

Step 4: calculate many FACTS damping controller reciprocation risks and assumptions;

Step 5: the reciprocation situation judging many FACTS damping controller according to the characteristic of many FACTS damping controller reciprocation risks and assumptions, analysis result is as shown in table 1;

Table 1 more than FACTS damping controller reciprocation risks and assumptions result of calculation

Step 6: repeat the reciprocation risk analysis of step one ~ step 5 successively in completion system between all FACTS damping controllers: from many FACTS damping controller reciprocation risks and assumptions result of calculation, two FACTS controller reciprocation risks and assumptions are all greater than 1, therefore there is comparatively serious reciprocation between two damping controllers, two damping controllers run the stability of the system of destruction simultaneously.

For checking context of methods validity, by two FACTS damping controllers operation with closed ring simultaneously, simulation result as shown in Figure 5.Comparison diagram 3 ~ Fig. 4, Fig. 5 is known, the FACTS controller that two platform independent control effects are good, not only do not obtain the control effects being better than separate unit SVC controller after dropping at the same time, cause system unstability on the contrary, comparatively serious negative reciprocation is there is between two FACTS, consistent with methods analyst result provided by the invention, thus demonstrate correctness and the validity of the many FACTS damping controller reciprocation risk analysis method based on EOP theory provided by the invention, and method provided by the invention has the function predicting reciprocation risk between many FACTS damping controller in advance, the present invention can directly apply to electric power system on-line analysis platform, and based on the security and stability analysis field of wide area measurement system, there is important engineer applied be worth.

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit, although with reference to above-described embodiment to invention has been detailed description, those of ordinary skill in the field are to be understood that: still can modify to the specific embodiment of the present invention or equivalent replacement, and not departing from any amendment of spirit and scope of the invention or equivalent replacement, it all should be encompassed in the middle of right of the present invention.

Claims (6)

1. the damping controller of FACTS more than a reciprocation risk analysis method, it is characterized in that, described method comprises the steps:

(1) optional two FACTS damping controller g from electric power system _ciand g _cj, calculate two FACTS damping controller g respectively _ciand g _cjequivalent open-loop transfer function;

(2) two FACTS damping controller g are calculated _ciwith g _cjbetween factor of influence;

(3) two FACTS damping controller g are calculated _ciwith g _cjbetween reciprocation risks and assumptions;

(4) according to reciprocation risks and assumptions, the reciprocation risk between two FACTS damping controllers is analyzed;

(5) repeat step (1) to (4), complete in electric power system as the reciprocation risk analysis between all FACTS damping controllers of research object.

2. many FACTS damping controller reciprocation risk analysis method as claimed in claim 1, is characterized in that, in described step (1), sets up the FACTS damping controller g be shown below _ciequivalence open-loop transfer function:

Wherein, be i-th FACTS damping controller g _ciequivalent open-loop transfer function, i=1,2 ..., N, j=1,2 ..., N, N be in electric power system as research object FACTS damping controller sum, g _iirepresent in G (s) element being positioned at the i-th row i-th and arranging, with represent respectively and remove g in G (s) _ijafter the i-th row vector and jth column vector, represent and remove G _c(s) i-th matrix of gained after row and jth row, represent the matrix removing G (s) i-th row and the rear gained of jth row, G (s), G _cs () is respectively ssystem transfer function matrix and FACTS damping controller transfer function matrix, I representation unit matrix.

3. many FACTS damping controller reciprocation risk analysis method as claimed in claim 1, is characterized in that, in described step (1), sets up the FACTS damping controller g be shown below _cjequivalence open-loop transfer function:

Wherein, for jth platform FACTS damping controller g _ciequivalent open-loop transfer function, i=1,2 ..., N, j=1,2 ..., N, N be in electric power system as research object FACTS damping controller sum, g _jjrepresent the element being positioned at jth row jth row in G (s), with represent respectively and remove g in G (s) _jiafter jth row vector and the i-th column vector, represent and remove G _cthe matrix of (s) jth row and the rear gained of the i-th row, represent the matrix removing G (s) jth row and the rear gained of the i-th row, G (s), G _cs () is respectively ssystem transfer function matrix and FACTS damping controller transfer function matrix, I representation unit matrix.

4. many FACTS damping controller reciprocation risk analysis method as claimed in claim 1, is characterized in that, in described step (2), the factor of influence method calculated between two FACTS damping controllers comprises:

2-1) according to FACTS damping controller g _ciequivalent open-loop transfer function, calculate FACTS damping controller g by following formula _cito FACTS damping controller g _cjfactor of influence:

2-2) according to FACTS damping controller g _cjequivalent open-loop transfer function, calculate FACTS damping controller g by following formula _cjto FACTS damping controller g _cifactor of influence:

Wherein, g _ci, g _cjrepresent the transfer function of i-th and jth platform FACTS damping controller respectively, j represents imaginary part, and ω represents angular frequency.

5. many FACTS damping controller reciprocation risk analysis method as claimed in claim 1, is characterized in that, in described step (3), the maximum in selecting step (2) in all factors of influence, as FACTS damping controller g _ciwith g _cjbetween reciprocation risks and assumptions, as follows:

R _ij＝max{ψ _ij,ψ _ji} 。

6. many FACTS damping controller reciprocation risk analysis method as claimed in claim 1, is characterized in that, in described step (4), the method analyzed the reciprocation risk between two FACTS damping controllers is as follows:

4-1) work as R _ijwhen=1, show that between controller, reciprocation risk is high, must consider the coordination between controller;

4-2) work as 0.8<R _ijduring <1, show that between controller, reciprocation risk is very high, need to consider the coordination between controller;

4-3) work as 0.5<R _ijwhen≤0.8, show that between controller, reciprocation risk is higher, the coordination between controller is considered in suggestion;

4-4) work as R _ijduring <0.5, show that between controller, reciprocation risk is lower, without the need to considering the coordination between controller.