AU2020101603A4 - A Method of Constructing Wide-area Damping Controller with Iterative Identification for Improving Power System Stability - Google Patents
A Method of Constructing Wide-area Damping Controller with Iterative Identification for Improving Power System Stability Download PDFInfo
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Abstract
The invention relates to a method of constructing an iterative identification Wide-area
Damping Controller(WADC) for improving the stability of a power system, and belongs to the
technical field of power system identification and control. The method described by this
invention includes: Selecting a low-order power system initial model and a corresponding
initial wide-area damping control model, using a recursive least-squares method for identifying
the low order power system initial models, obtaining a set of power system identification
models, using a v-gap formula to acquire a v-gap distance between the power system model
and the set of power system identification model, and obtaining the maximum distance based
on the power system model; further obtaining the stability margin of power system model and
WADC. According to the v-gap distance and stability margin, selecting a few sets of power
system identification models and satisfying the conditions which the optimal power systems
identification models can obtain the corresponding wide-area damping controller models are
put forward. In this method, a power system optimal identification model and a wide-area
damping optimal control model can be obtained, so that the control stability of the power
system is further improved.
1/4
e(q)
r() + u(t) Gq0) +u y(t)
K(q, 0)
FIG, 1
Description
1/4
e(q)
r() + u(t) Gq0) +u y(t)
K(q, 0)
FIG, 1
A Method of Constructing Wide-area Damping Controller with Iterative Identification for Improving Power System Stability
[01] The invention belongs to the technical field of power system identification and control, in particular to a method of constructing an iterative identification damping controller for improving the stability of a power system.
[02] Advertising and promotion is a complex process business. There are all kinds of different advertisement and promotion campaigns all around and it is difficult to keep the consumer interested and engaged in an advertisement and promotion for a substantial period of time.
[03] With the continuous expansion of the scale of the power system and the rapid development of China's power industry, the stability of daily operation of the interconnected power system and the construction and operation management of various control and protection devices pose a high demand on the accuracy of the power system simulation. At present, the power system under multi-disturbance environment is formed due to the insufficient damping caused by factors, such as power grid structure, load flow and generator excitation control, etc. These factors may lead to negative interactions among the dominant oscillation modes of the power system, which may deteriorate the damping control effect.
[04] The construction of power system WADC in multi-disturbance environment is based on the power system identification model, and the real power system model needs to be identified in order to get this model. Therefore, the accuracy of power system identification model is very important during the process of building the WADC based on the identification model of power system. However, in the actual control process of the WADC, due to the influence of various interference factors, the mismatch between the power system identification model and the real power system model inevitably does exist. Identification error factor exists between that two, and the identification error has the randomness and it is difficult to define a priori robustness condition.Hence, the WADC constructed by the traditional method cannot guarantee that the control of real power system is stable, and at the same time, under the premise of guaranteeing the stability of power system, it has become a main current problem for concerning how to ensure control performance of the WADC to be improved continuously and suppress the low frequency oscillation of the power system better.
[05] The power system identification model in the multi-disturbance environment shown in FIG. 1 is constructed according to the actual operation of the power system which is used to study the identification problem of power system. In order to simulate the small-scale interference of random nature existing in many load places of power system, we add several jamming signals in different places to the real power system and take two jamming signals as example among them. U, y denote input and output signals of the power system, e denotes a stationary random interference signal with a mean value of zero and variance of lambda, r denotes an excitation signal independent of the signal e, G(q ,0) denotes a forward channel power system identification model, H(q,O) denotes a filter model of the forward channel interference signal e, K(q,O) represents the feedback path of WADC model, and theta represents the power system model parameters to be identified, t=1 ,2..
[06] In that prior art, the Runge-Kutta iterative identification method is the most similar WADC construction method to that of the present invention, which is an important kind of implicit or explicit iteration method for simulating the solution of ordinary differential equations. In addition, that method can be well applied in the field of power system identification and control, but the identification precision of the Runge-Kutta iterative identification method is not high enough, Moreover, the power system identification model identified by the Runge-Kutta iterative identification method has a long time to reach stability under the WADC action, and the stability performance of power system is still not very good.
[07] Recursive Least Squares Method: The recursive least square method means system parameters to be identified. After acquiring new measurement data each time, the results of the previous estimation are corrected by using the new measurement data based on the result of previous estimations, so as to derive new parameter estimation values recursively. Thus, with the introduction of new measurement data, parameter estimation is carried out continuously until the estimated value reaches a satisfactory level of accuracy. The basic idea of recursive least squares is:
[08] New estimate +( .1 Old estimate + Amendment
[09] v-gap distance: It can be simply understood as the distance between two frequency responses, representing a measure of the distance of two transfer functions, and abbreviated as v-gap, and represented by the symbol 6v. The v-gap distance of the transfer function matrix G1 and the transmission function matrix G2 is expressed as:
max r(G, (e), G,(e)),
,3,,(Gr, G2) If satisfied ()()
1,Or
(i+CGG)(ew) 0,Vo, And wno(1+G G2 )+r(G)- (G)=0
[010] where, G*(ejo)=G(e-j o) and i(G) denotes numbers of open right half-plane poles of G, I(G) represents the number of closed right half-plane poles of G, wno(G) denotes circle numbers of the transfer function G's Nyquist curve that surround the dot anticlockwise, and when G has poles on the imaginary axis, the Nyquist curve will avoid these poles. K(G1, G2) denotes the Chord distance of the projection point obtained by the projection of G1 and G2 onto the unit Riemannian sphere.
[011] Stability margin: The stability margin of the stable closed-loop system [G, K] is denoted by b, and if the closed-loops [G and K] are unstable, then b = 0.
[012] The calculation formula of stability margin is
1 b(G,,KJ) = 1K (2 JT (G,, Ki) )
[013] Where T (Gi, Ki) is the transfer function matrix of closed-loop system, Gi is the power system identification model obtained by the ith identification, and Ki is the
WADC model constructed by the ith identification. According to FIG. 1, the expression of T (Gi, Ki) is shown in equation (3):
G, 1 T(G,,K,)= IGK (3). 1 K _1+G, 1+G,
[014] An object of the present invention is to provide a method of constructing an iterative identification WADC for improving the stability of power system. Based on a recursive least square and v-gap distance iterative identification method, the optimal identification model and the wide-area damping optimal controller model can be obtained, so as to improve the control stability of the power system.
[015] The present invention provides a method of constructing an iterative identification WADC for improving the stability of power system, which is characterized in the following steps:
(1) A low-order power system initial model G and its corresponding initial WADC model K are selected from the literature.
(2) A white noise signal is used as an initial excitation signal, and a recursive least square method is used to identify an initial model G of a low-order power system. After the identification, the power system identification model set Bi including the initial model G of the low-order power system is obtained.
(3) According to the basic theory of v-gap, the v-gap distance 6v (Gi, Bi) between the power system model Gi and the power system identification model set Bi is obtained by using the v-gap formula (1), and the maximum distance 6wc(Gi ,Bi) based on the power system model Gi is obtained in turn according to the v-gap distance 6wc(Gi,Bi) by using the formula (4) as below
9wc ( G,,B= max.5, (Gi,,G,) (4)
Namely, when i = 1, the maximum distance between GI and the power system identification model set Bi is obtained, and when i = 2, the maximum distance between G2 and the set of power system identification models Bi is obtained, and the maximum distances between i= 3, 4, 5. 100 power system models Gi and Bi are obtained in turn.
(4) The WADC corresponding to the power system identification model set Bi is defined as Ki, and according to the basic theory of stability margin, the stability margin b (Gi, Ki) based on the power system model Gi and the WADC Ki are obtained according to the formula (3).
(5) Improve the WADC stability performance according to the stability performance condition of closed-loop power system.
The stability margin b(Gi ,Ki) is compared with the maximum distance 6wc(Gi ,Bi) obtained in Step (3), and a set satisfying the stability margin b(Gi ,Ki) is screened out which is greater than the maximum distance 6wc(Gi ,Bi) between the power system model Gi and the power system identification model set Bi. If such condition is not met, then let
Ki*=KP, T*=T(G,,K*)' Then a WADC K,=G, 1(PAS+S) -1I, is
obtained, in which Si= (1+GiKi)- 1 =(+G 1 S -, P is a single input single-output transfer function. Kop is the optimal WADC designed for the optimal power system model corresponding to the maximum distance 6wc(Gi ,Bi) in the power system identification model set Bi;
(6) According to values of 6v (Gi, Bi) and b(Gi ,Ki) obtained in Step (3), select a few setsx of power system identification models which satisfy the formula 6v (G, Bi) -6 v (Gi, bi) I < and6 min (G and Bi) < F, and r is a constant that is infinitesimal. If the condition is satisfied, proceed to Step (7). If that condition is not satisfied, and then return to Step (2) to perform a re-identification process;
(7) Select the corresponding power system identification model with the smallest 6v(Gi, Bi) from the few power system recognition sets obtained in Step (6). As an optimal power system identification model Gop (a model has a minimum distance from the real power system model and satisfies the power system stability) is obtained by the identification, and according to Step (5), a corresponding WADC model Kop is obtained, and the construction is finished.
(8) In that method, a method of constructing an iterative identification WADC for improving the stability of a power system is provided, and the method combines the recursive least square method with the v-gap distance basic theory. The power system optimal model and the WADC optimal model can be obtained to improve power system stability, and a new idea is proposed for solving this problem. Both the theory and the embodiments of the present invention show that the method can obtain a power system model satisfying the stability performance of the power system, and finally achieve the purpose of improving the stability of power system in order to make it more suitable for identification and control of the power system.
[016] FIG. 1 is a schematic structural diagram of a power system identification model employed by the method of the present invention.
[017] Fig. 2 is a flow diagram of this present invention method.
[018] FIG. 3 is a v-gap distance diagram between the initial model G and the power system identification model set Bi of the present invention.
[019] FIG. 4 is a power system output response diagram based on an iterative identification method according to an embodiment of the present invention.
[020] The invention provides a method of constructing an iterative identification WADC for improving the stability of a power system, which will be described in further detail below with reference to the accompanying drawings and specific embodiments.
[021] An iterative identification WADC construction method for improving the stability of a power system is provided in the present invention. The overall flow is as shown in FIG. 2, and the method comprises the following steps:
(1) A low-order power system initial model G and its corresponding initial wide-area damping controller model K are selected from the literature.
(2) In that method, a white noise signal is used as an initial excitation signal, and a recursive least square method is used to identify an initial model G of a low-order power system, After the identification, the power system identification model set Bi including the initial model G of the low-order power system is obtained.
(3) According to the basic theory of v-gap, The v-gap formula (1) is used to find the distance 6v(Gi, Bi) of v-gap between a power system model Gi (Gi here is any element in the set of power system identification models Bi (i = 1, 2, 3. 100)) and power system identification model set Bi, which is described as below
max r(G,(e"), G2(e`)),
,,(GI,G )= If satisfied(*(1 1, or
(1+G*G-)(eJ");0,Vr», And wno(1+G 1 G2 )+q(G 2 )- #(G1 )=0
According to the v-gap distance 6v (Gi, Bi) and formula (4), the maximum distance 6wc(Gi ,Bi) based on the power system model Gi is obtained in turn. That is, when i = 1, the maximum distance between G Iand the power system identification model set Bi is obtained. When i =2, the maximum distance between G2 and the power system identification model set Bi is obtained. Take each power system model with i =3, 4, 5 ... 100 in turn, the maximum distance between Gi and power system identification model set Bi is embodied in the following formula
5,c(G,,Bj)=max3,(GI,G,) (4)
(4) The WADC corresponding to each power identification system in the power system identification model set Bi is denoted as Ki, the stability margin b (Gi, Ki) based on power system model Gi and WADC Ki are obtained according to the stability margin theory.
The formula for calculating the stability margin is
b (G,,K = (2) JT(Gj,Kj 1 )
The expression of T (Gi, Ki) is shown in Equation (3):
G, 1 1+GK. 1+GK. T (Gi,,Kj)= 1+Gj I+ j (3) 1 K 1+GK,1+GK,
(5) Improve the stability performance of WADC according to the closed-loop stability performance condition of power system. Compare stability margin b (Gi, Ki) obtained from Step 4 with the obtained power system model Gi and further compare with the maximum distance 6wc(Gi ,Bi) among the power system identification model set Bi, select the power system identification model that satisfies the stability margin b (Gi, Ki) greater than the maximum distance 6wc(Gi ,Bi) and proceed to Step (6); If there is no power system recognition model meeting the screening condition, then let
K> = K., T* =T (G,,)
, And obtain the wide-area damping controller Kj ,={G-(PAS+ S,) in
which S=($ +GK )', SP=(s+GK()', =S -S a single input single-output transfer function, Kop is the optimal WADC designed for the optimal power system model corresponding to the maximum distance 6wc(Gi ,Bi) in the power system identification model set Bi;
(6) According to 6v (Gi, Bi) obtained in Step (3), we select the values that satisfy the closed-loop system performance improvement conditions (G and Bi) -6v-v / < Eand 6vmin (G). Bi) < E (, is a constant of infinitesimal, in this embodiment, F is taken as 0.005, and the smaller this value is, the higher the accuracy of identification is. A few sets of power system identification models can be selected according to the achieved accuracy.
Closed-loop system performance improvement condition 1: 1 6v (G, Bi) 6V (Gi, Bi) I < F, determine whether the absolute value of the difference between the power system identification model and the v-gap distance of the initial power system model is less than or equal to the set error s, and the smaller this absolute value is, the higher the identification accuracy is;
The closed-loop system performance improvement condition 2:6vmin (G
,Bi)<s, 6vmin (G,Bi) is the v-gap minimum distance between power system model Gi and power system identification model set Bi. It is determined whether the v-gap minimum distance is less than or equal to the setting error E, and the smaller the distance is, the closer the optimal power system identification model Gop obtained by the final identification is to the initial power system model G.
If there is a power system identification model that satisfies the above mentioned two closed-loop system performance improvement conditions, the process proceeds to Step (7). If there is no power system identification model satisfying the condition, return to Step (2) for the next identification.
(7) In the obtained power system identification set x, the power system identification model with the minimum value of v-gap distance 6v (Gi, Bi) is selected which actually is the optimal power system identification model Gop (the model has the smallest distance from the real power system model G and satisfies the power system stability) obtained by the identification. And also according to Step (5), the optimal WADC model Kop corresponding to the model is obtained, and the construction is finished.
[022] According to the above conclusions, it is a good choice to construct a WADC based on recursive least square method and v - gap distance. In comparison with that prior art, the invention improves the control stability of the power system, and it is more suitable for the application of power system identification and control.
[023] In this paragraph below, the method of this invention is described in further detail with reference to set a specific example:
(1) One third-order power system initial model G and its corresponding initial WADC model K are selected, and the transfer function model is as follows:
G= z +3z+2 K -0.2797Z +0.1336z-0.0606 z9+5z+5.25z+5 z 3 +0.5430z2-0.5078z-0.0098
(2) The white noise signal is used as the initial excitation signal, and the recursive least square method is used to identify the initial model G of the low-order power system. After the identification, the power system identification model set Bi including the initial model G of the third-order power system is obtained.
(3) According to the related theory of v-gap, the following v-gap formula is used.
max K(G 1 (e"r), G2 (e"`)),
,(GI G2) If satisfied (*) (1)
Li or 3 (l+GG)(e ")# OV , And wvno(1 + GG )+4-r(GO)- (G,)= 0
The v-gap distance 6v (Gi, Bi) between the power system model Gi (which is an element in the set Bi of power system identification models) and the set Bi is calculated:
maxx(G,(e" A eW"))b
(1+GB )(en) O,Vo>Andwno(1+iG*B)+r](B,)- fj(G,)-0(*)
And according to the v-gap distance 6v (Gi, Bi), the maximum distance 6wc(Gi ,Bi) based on the power system model Gi is obtained.
5c (GB, )=max 3,(G, G,) G~eB
The v-gap distance between the initial model G of the third-order power system and the power system identification model set Bi can be obtained, as described in Fig 4. The distance between the power system model obtained from the first identification and the last identification, and the initial model G of the third-order power system becomes smaller and smaller, Finally, the v-gap distance between the optimal power system identification model Gop and the third-order power system initial model G is 0. 01059.
(4) According to the basic theory of stability margin, the stability margin b (Gi, Ki) based on the power system model Gi and the WADC Ki is obtained.
1 b (G,, K, T(G,,K
) In which, T(Gi ,Ki) is described in the formula as below
G_ 11~ 1+ G K 1+GK] 1 K
Therefore, during the process of applying the iterative identification method, the stability margin b (Gi, Ki) corresponding to each identification data, the v-gap distance value between the identification model, and the real model are as shown in Table 1.
Table 1 Frequency stability margin and v-gap distance value corresponding to each identification parameter data during the application of iterative identification method.
Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 stable 0.0424 0.0263 0.0413 0.0322 0.1278 0.1273 margin v-gap 0.2782 0.2828 0.2922 0.3589 0.0555 0.1055 distance
Group 7 Group 8 Group 9 Group 10 Group 11 Group 12 stable 0.1328 0.1118 0.1130 0.1130 0.1124 0.1124 margin v-gap 0.0517 0.0118 0.0124 0.0125 0.0106 0.0106 distance
(5) Improve the stability performance of wide-area damping control according to the closed-loop stability performance condition of power system.
The stability margin b (Gi, Ki) is compared with the maximum distance
6wc(Gi,Bi) obtained in Step (3) to screen out the margin b (Gi, Ki) whose stability is satisfied, which is greater than the set of the maximum distance. 6wc(Gi ,Bi) is between the power system model Gi and the set Bi of power system identification models and proceeds to Step (6). If not satisfied, let
K = K, T =T (G, K*Th K =G,- 1 PAS+S)'-1} is
obtained, in which Si=(1+GiKi)-S=(+K , ASS -, P isa single input and single output transfer function, Kop is the optimal WADC designed for the optimal power system model corresponding to the maximum distance 6wc(Gi ,Bi) in the power system identification model set Bi.
[024] In Step (6), the corresponding power system identification model with the smallest 6v (Gi, Bi) is selected from the few power system identification sets which is the optimal power system identification model Gop (the model has the smallest distance from the real power system model and satisfies the power system stability) obtained by the identification. and according to Step (5), a corresponding WADC model Kop is obtained.
[025] According to above steps, the identification parameters of the optimal third order power system identification model and the corresponding optimal WADC model can be finally obtained as
ai:5 .0142 bi:1 .0835 a2:5 .3237 b2:2 .9540 a3:5 .0670 b3:2 .1717
S 1.835z'+2.9540z +2-1717 z +5.0142z 2-+5.3237z+5.0670
= -0.3137z 2 + 0.1403z -0.0344 z +0.6161z 2 0.5109z-0.0730
[026] In the final result, 6vmin(G ,Bi) = 0 .0106<0 .05 and b (Gop, Kop)= 0.01124, The output response curve of the power system model identification process by the iterative identification method is shown in FIG. 4. The closest to the initial model G of the third-order power system is 0.427 dB in amplitude and the response time is about 11s.
[027] The above is merely a preferred example of the present invention, which is not limited to the above embodiments. Any partial modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the invention.
[028] Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms, in keeping with the broad principles and the spirit of the invention described herein.
[029] The present invention and the described embodiments specifically include the best method known to the applicant of performing the invention. The present invention and the described preferred embodiments specifically include at least one feature that is industrially applicable.
Claims (2)
1. A method of constructing an iterative identification WADC for improving the stability of a power system is characterized and the method comprises the following steps (1) A low-order power system initial model G and its corresponding initial WADC model K are selected from the literature. (2) The white noise signal is used as the initial excitation signal, and the recursive least square method is used for the initial model of the low order power system. G performs identification, and obtains a power system identification model set Bi including a low-order power system initial model G after the identification; (3) According to the basic theory of v-gap, the v-gap distance 6v (Gi, Bi) between the power system model Gi and the power system identification model set Bi is obtained by using the v-gap formula (1), and the maximum distance 6wc(Gi ,Bi) based on the power system model Gi is obtained in turn according to the v-gap distance 6wc(Gi ,Bi) by using the formula (4) as below 9({G,,B,)==max9,(G,,G,) (4) GpcBi
In the formula, Gi is now an element in the power system identification model set Bi. When i=1, the maximum distance between G1 and the power system identification model set Bi is obtained. When i=2, the maximum distance between G2 and the power system identification model set Bi is obtained. The maximum distance between i=3, 4, 5 ... 100, power system model Gi and power system identification model set Bi is obtained in turn. (4) The WADC corresponding to the power system identification model set Bi is recorded as Ki, and the stability margin b (Gi, Ki) based on the power system model Gi and the WADC Ki is obtained according to the basic theory of stability margin and formula (3); (5) Improving the stability of WADC based on the stability performance conditions of closed-loop power system,
The stability margin b(Gi ,Ki) is compared with the maximum distance 6wc(Gi ,Bi) obtained in Step (3), and a set satisfying the stability margin b(Gi ,Ki) is screened out which is greater than the maximum distance 6wc(Gi ,Bi) between the power system model Gi and the power system identification model set Bi. If such condition is not met, then let So a WADC can obtain in which Si=(1+GiKi)-l P is a single-input single output transfer function, Kop is the optimal WADC designed for the optimal power system model corresponding to the maximum distance 6wc(Gi ,Bi) in the power system identification model set Bi; According to the values of 6v (Gi, Bi) and b(Gi ,Ki) obtained in Step (3), select a few sets V of power system identification models which satisfy the formula 6v (G, Bi) -6 v (Gi, bi) I <Fand6 min (G and Bi) <8, , is a constant that is infinitesimal; If the condition is satisfied, proceed to the Step(7), and if that condition is not satisfied, return to Step (2) to perform a re identification process; (7) In Step (6), the corresponding power system identification model with the smallest 6v (Gi, Bi) is selected from the few power system recognition sets. As the optimal power system identification model Gop obtained by the identification, the model has the minimum distance from the real power system model and satisfies the power system stability. And according to Step (5), a corresponding WADC model is obtained.
2. The method is for iteratively identifying a WADC according to claim 1, wherein the step of obtaining a stability margin is b (Gi) based on the power system model Gi and the WADC is Ki, Ki) The formula is: 1 b(G,, K,)= (2) jT (G,, K, )( The expression of T (Gi, Ki) is shown in equation (3): G 11 I1+GK, 1+GK T(G,,K,= ' J ) (3). 1 K
[1-+GK, 1+GKj
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113595102A (en) * | 2021-06-24 | 2021-11-02 | 国网浙江省电力有限公司嘉兴供电公司 | Control method for damping low-frequency oscillation of power system based on energy storage power supply |
| CN113904347A (en) * | 2021-09-30 | 2022-01-07 | 广东电网有限责任公司 | Parameter optimization method and device for additional damping controller of controllable phase shifter |
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2020
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113595102A (en) * | 2021-06-24 | 2021-11-02 | 国网浙江省电力有限公司嘉兴供电公司 | Control method for damping low-frequency oscillation of power system based on energy storage power supply |
| CN113904347A (en) * | 2021-09-30 | 2022-01-07 | 广东电网有限责任公司 | Parameter optimization method and device for additional damping controller of controllable phase shifter |
| CN113904347B (en) * | 2021-09-30 | 2024-04-23 | 广东电网有限责任公司 | Parameter optimization method and device for controllable phase shifter additional damping controller |
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