CN107306033B - Power system additional damping control method considering wide-area signal multi-time lag - Google Patents

Power system additional damping control method considering wide-area signal multi-time lag Download PDF

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CN107306033B
CN107306033B CN201610243418.4A CN201610243418A CN107306033B CN 107306033 B CN107306033 B CN 107306033B CN 201610243418 A CN201610243418 A CN 201610243418A CN 107306033 B CN107306033 B CN 107306033B
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CN107306033A (en
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马燕峰
张佳怡
赵书强
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North China Electric Power University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24Arrangements for preventing or reducing oscillations of power in networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention belongs to the field of power system stability control, and particularly relates to a design method of a damping controller considering time lag of a plurality of wide area transmission signals. Aiming at the low-frequency oscillation problem of an interconnected wide-area power system and the condition that a wide-area transmission signal has a plurality of transmission delays, a design method of a wide-area multi-time-lag additional damping controller is provided, and comprises the steps of establishing a multi-time-lag linearization model, selecting an input signal and an installation place for an interval low-frequency oscillation mode, and designing the additional damping controller suitable for the multi-time-lag power system. The stability criterion of a multi-time-lag system constructed by the Lyapunov-Krasovski theory is converted into the feasibility problem of a linear matrix inequality, the control parameters can be directly solved, and the inconvenience of iterative parameter solving by using an intelligent algorithm in the traditional method is avoided. The controller in the invention can effectively inhibit the low-frequency oscillation of the power system within the range of the given time lag upper limit, has strong adaptability and robustness, and has simple structure and easy engineering realization.

Description

Power system additional damping control method considering wide-area signal multi-time lag
Technical Field
The invention belongs to the field of power system stability control, and particularly relates to a design method of a wide area additional damping controller considering time delay influence of a plurality of wide area transmission signals.
Background
With the vigorous development of modern construction of socialist in China, the power industry is expanding at unprecedented scale and speed, and China is gradually forming a strategic pattern of 'business to the east, mutual supply of south and north'. At present, the power development of China already enters cross-regional power grid interconnection, and after national power grids are interconnected, China forms a multi-regional interconnected wide area power system. However, the low-frequency oscillation phenomenon in the cross-region interconnected power grid is increasingly serious, the safety of the power grid and the cross-region electric energy scheduling are affected, and the safe and stable operation of a power system is threatened.
The traditional low-frequency oscillation suppression method mainly adopts measures for providing extra damping, and mainly adopts excitation control such as a power system stabilizer and the like. However, controllers that use local signals as feedback inputs have very limited damping of the inter-zone oscillation mode due to the controllable observability. With the further expansion of the scale of the interconnected power grid, the damage of the interval oscillation mode to the power system deepens along with the complexity of the power grid, and the stability of the power system cannot be ensured only by designing the controller by using the local signal.
Under the background of 'internet +', with the deep fusion of the power industry and information and the continuous development of internet power, technologies such as networking, digitalization, intellectualization and the like are developed, the wide-area information in the wide-area feedback signal in the wide-area measurement system is utilized to realize the control of the power grid, the dynamic performance of the interconnected power grid system can be effectively improved, and the development trend of the future power grid is formed. The wide area measurement system creates possibility for distributed synchronous measurement, stability analysis and wide area optimization coordination control of a regional interconnected power system, but the wide area information has obvious time delay in links of transmission, exchange, processing and the like, the time delay can be as high as hundreds of milliseconds, if the time delay problem is not well processed, the performance of the damping controller can be further deteriorated, and the wide area safety of the power system is damaged. Therefore, the time-lag link of wide-area control is deeply considered, and the method has great significance for optimizing the performance of the controller and improving the wide-area safe and stable operation of the power system.
In order to solve the problems, scholars at home and abroad carry out a series of researches and obtain great results. The inventor designs a wide-area PID damping controller (patent number 201510492610.2) suitable for a power system with random time lag, designs a power system output feedback control method (patent number 201310189887.9) based on WAMS signal experiments in robust control theory, and designs a multi-FACTS time lag-resistant coordination control method (patent number 201310189887.9) based on a free weight matrix method by Huangliujiangdong, Sun Huadong, Yijun and the like. The gazee, the anhai cloud and the dawn propose a stabilization criterion of a multi-time-lag power system (patent number: 200810151217.7), but the method focuses on solving a time-lag stabilization domain, and the method does not relate to how to design a controller for stabilizing the multi-time-lag power system and the control effect of the controller. Generally, at present, research on the control stability of a multi-time-lag power system is less, from the aspect of a control method, time-lag robust control is still the main means of damping control of the multi-time-lag power system, but the solution method is generally complex, and a simple solution for exploring the multi-time-lag robust stability control of the power system has certain practical application value.
Disclosure of Invention
Aiming at the defects that the low-frequency oscillation suppression of a multi-time-lag power system based on a wide area measurement system is insufficient and the step of solving parameters by a robust control method which is one of main control methods is complex, the invention designs a multi-time-lag wide area power system damping controller capable of directly solving the control parameters, and elaborates the control structure of the controller and the parameter solving method in detail.
The wide-area additional damping controller not only considers the influence of delay of a plurality of transmission signals, but also overcomes the defect that the traditional robust control method has complex steps of repeated iterative optimization by means of an intelligent algorithm, can directly solve control parameters, and provides a new way for inhibiting low-frequency oscillation of a multi-time-lag power system.
In order to achieve the purpose, the technical scheme provided by the invention is as follows:
the improvement of the method is that a multi-time-lag system stability criterion derived by a Lyapunov-Krasovski functional theory is utilized to convert a control stabilization problem into a feasibility problem of a linear matrix inequality, so that control parameters are directly solved, and inconvenience of iterative parameter solving by an intelligent algorithm in a traditional method is avoided. Mainly comprises the following specific steps:
step (1): linearizing the system near a balance point to obtain a state space model of the power system;
step (2): the installation position of the controller and the selection of input signals are carried out by utilizing the controllable observability;
and (3): solving parameter Bi', wherein B1′=[B 10 … 0],…,Bi′=[0 … 0 B i0 …0],…,,Bq′=[0 0 … Bq];
And (4): it is determined whether a time lag upper bound is known. If the time lag is known, directly entering the step (6), otherwise entering the step (5) to solve the time lag stability upper limit;
and (5): when the time lag upper limit is unknown, iteratively solving the time lag upper limit by a method of assuming the time lag upper limit and judging whether the linear matrix inequality is feasible by utilizing a multi-time lag stability criterion of the power system;
and (6): using a given time lag upper limit or a solved time lag upper limit, adopting feasp of LMI Toolbox in Matlab to solve two linear matrix inequalities, using solved matrixes N and W, and using Kc=NW-1Calculating a control matrix Kc
And (7): using control matrix KcCalculating and solving gain K of wide area additional damping controlleri
In step (5) described herein, the time lag stability upper limit may be specifically calculated according to the following sub-steps:
step (5-1): selecting a group of time lags small enough as initial values to ensure that 2 linear matrix inequalities have feasible solutions, and entering (5-2);
step (5-2): and judging whether the LMI has a feasible solution or not by using a feasp method in the Matlab LMI Toolbox. If feasible solution exists, switching to (5-3), otherwise, switching to (5-4);
step (5-3): when a feasible solution exists, the solution is recorded and the time lag is changed to tau1=τi+10ms, repeat step (5-2);
step (5-4): and (4) recording the time lag size meeting 2 linear inequalities when no feasible solution exists, taking the time lag size as the time lag upper limit, and entering the step (6).
In step (5) described herein, the adopted multi-lag power system stability criterion is the criterion used in step (6).
In step (6) described herein, the multi-lag linear system is represented in the form of
Figure BSA0000128948900000021
Where x (t) is an n-dimensional state variable, u (t) is a q-dimensional control input,
Figure BSA0000128948900000022
denotes the initial state of x (t), τ1,τ2,…,τnIs a time lag constant, a normal number
Figure BSA0000128948900000023
Is an upper time lag limit and satisfies
Figure BSA0000128948900000024
In step (6) described herein, the multi-lag power system stability criterion is used as, for a given scalar quantity
Figure BSA0000128948900000031
If there is a positive scalar quantity
Figure BSA0000128948900000032
And
Figure BSA0000128948900000033
and a matrix
Figure BSA0000128948900000034
N and W satisfy det (W) ≠ 0, such that the following linear matrix inequality holds, then this multi-lag system is asymptotically stable, and the controller parameter that stabilizes the system is denoted Kc=NW-1
Wherein the linear matrix inequality is
Figure BSA0000128948900000035
W>0
Wherein
Figure BSA0000128948900000036
Figure BSA0000128948900000037
12=[B1N B2N … BqN]
Figure BSA0000128948900000038
Θ12=[AW B1N … BqN]T[I I … I]
Figure BSA0000128948900000039
Figure BSA00001289489000000310
Figure BSA00001289489000000311
Θ14=diag{WT,NT,…,NT}
Figure BSA00001289489000000312
In the step (7) of the present invention, the control matrix KcCalculating and solving gain K of wide area additional damping controlleriBy a specific method ofc=[K1′ … Ki′ … Kq′]TFind the corresponding Ki', then Ki=Ki′Ci -1Finding Ki
Compared with the prior art, the invention has the beneficial effects that:
(1) the power system damping control design method considering the influence of the transmission delay of a plurality of wide-area signals is provided, and the controller has a good control effect under a single transmission delay or a plurality of transmission delays;
(2) the robust control method overcomes the defect that the traditional robust control method has complex steps of repeated iterative optimization by means of an intelligent algorithm, can directly solve the control parameters, and simplifies the solving steps. The designed controller has a simple structure and is easy for engineering realization;
(3) the controller in the invention can effectively inhibit the low-frequency oscillation of the power system within the range of the given time lag upper limit, has strong adaptability and robustness, provides a new way for inhibiting the low-frequency oscillation of the multi-time lag power system, and has good engineering application value.
Drawings
FIG. 1 is a multi-lag power system model
FIG. 2 is a flow chart of the damping control solving steps of the multi-lag power system
FIG. 3 is a 2-zone 4 machine system
FIG. 4 is a simulation curve of the proposed control method under different communication transmission delays
FIG. 5 is a simulation curve under large interference conditions
FIG. 6 is a simulation plot of different control scheme comparisons at a given time lag
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings, but the embodiments of the present invention are not limited thereto.
The invention designs an additional damping controller considering multiple time lags aiming at the phenomenon that a plurality of communication delays exist in signals when a power system carries out feedback control by utilizing remote signals. At this time, a block diagram of the multi-lag power system is shown in fig. 1. The state equation of the multi-time-lag power system adopting the linearized state space model is
Figure BSA0000128948900000041
Wherein y (t) is a measurable output signal, yi(t) is a skew output signal, u (t) is a control signal, and a positive number τiFor the signal transmission delay on the ith WAMS transmission link, i is 1, 2, … q, and q is the number of transmission links. In the context of figure 1 of the drawings,
Figure BSA0000128948900000042
is a time-lag link.
For the multi-lag linear power system as above, the additional feedback controller is designed as follows
Figure BSA0000128948900000043
Wherein, i is 1, …, q, q is the number of control links.
The parameter selection steps of the power system damping controller considering multiple time lags are shown in fig. 2, and specifically include the following steps:
step (1): linearizing the system near a balance point to obtain a state space model of the power system;
step (2): the installation position of the controller and the selection of input signals are carried out by utilizing the controllable observability;
and (3): solving parameter Bi', wherein B1′=[B 10 … 0],…,Bi′=[0 … 0 B i0 … 0],…,Bq′=[0 0 … Bq];
And (4): it is determined whether a time lag upper bound is known. If the time lag is known, directly entering the step (6), otherwise entering the step (5) to solve the time lag stability upper limit;
and (5): when the time lag upper limit is unknown, iteratively solving the time lag upper limit by a method of assuming the time lag upper limit and judging whether the linear matrix inequality is feasible by utilizing a multi-time lag stability criterion of the power system;
and (6): using a given time lag upper limit or a solved time lag upper limit, adopting feasp of LMI Toolbox in Matlab to solve two linear matrix inequalities, using solved matrixes N and W, and using Kc=NW-1Calculating a control matrix Kc
And (7): using control matrix KcCalculating and solving gain K of wide area additional damping controlleri
The specific contents of each step have been described in detail in the specification, and are not specifically described here.
The key point of the invention is that the gain K of the damping controller in the step (7)iThe derivation of (1) is explained in detail below with respect to the solution method.
To find the controller parameter KiThe shape of the power systemThe state space expression is converted into a form suitable for use in the criterion of the present invention. To this end, the control feedback signal for each control link in FIG. 1 is written as ui(t-τi)=Kiyi(t-τi)=KiCix(t-τi)=Ki′x(t-τi) And is brought into the expression of the original power system to obtain the expression
Figure BSA0000128948900000051
The above formula is reformed by
Figure BSA0000128948900000052
In the formula, Kc=[K1′ … Ki′ … Kq′]T,B1′=[B 10 … 0],…,Bi′=[0 … 0 B i0 …0],…,Bq′=[0 0 … Bq]。
By the derivation, the multi-lag power system can be converted into a system used by the stabilization criterion. Therefore, the control parameters can be conveniently solved by the method of the step (7).
The method designed by the invention is verified by the simulation example.
To verify the control performance of the power system additional damping controller proposed herein, which accounts for multiple time lags, a simulation analysis was performed using a 4-machine 2-zone power system.
The 4-machine 2-zone power system shown in fig. 3 has two generators in each zone, and the influence of a speed regulating system is not considered. Linearization is carried out near an operation point, wherein a synchronous generator adopts a 3-order model, an excitation system adopts a 1-order model, and x (t) [ [ delta ]1,Δω1,ΔE′q1,ΔEqe1,…,Δδ4,Δω4,ΔE′q4,ΔEqe4]T. The modal analysis of the open loop system is carried out to obtain table 1, and the system can be known to have two regionsModes (mode 2 and mode 3) and one section mode (mode 1). The mode 1 is weak damping, and the generators G1 and G3 can be known as leading sets through analyzing participation factors.
TABLE 1 Low frequency oscillation mode analysis
Mode(s) Characteristic value Damping ratio Participating machine set Type (B)
1 -0.1000±3.9639i 0.0252 1,2.3,4 Interval mode
2 -1.0101±7.0561i 0.1417 3,4 Regional mode
3 -0.7630±7.2479i 0.1047 1,2 Regional mode
In order to improve the interval mode damping ratio, a wide-area additional damping controller is added. The wide-area additional damper selects the angular speed of the generator as a wide-area feedback control signal to inhibit low-frequency oscillation in an interval mode, and the output of the controller acts on an excitation system of the generator.
Simulation experiment I: simulation verification of control scheme provided by the invention under different time lags
The wide-area additional damping controller considering multiple time lags proposed by the invention is marked as a control scheme 1. The addressing and the selection of the input signals are carried out by a controllable observability method, and finally, the angular speed difference delta omega of the generators G1 and G3 is adopted13Angular velocity difference Δ ω between G2 and G424As input signals for feedback control, u acts on the excitation systems of G1 and G2, respectively1=ΔEqe1,u2=ΔEqe2. Considering the delay of two paths of transmission signals, it is marked as tau13、τ24. The gain of the controller to be solved is Kc1_1、Kc1_2Is provided with
Figure BSA0000128948900000061
Controller gain KcIn the form of
Figure BSA0000128948900000062
Wherein K1=[0 K c1_10 0],K2=[0 K c1_20 0],Kc∈R2×16,K1,K2∈R1×4
The delay time of the actual power system generally does not exceed 0.1 s. Thus, the power system communication transmission delay is given as tau firstiThe parameter controlled at this time was calculated as 0.1 s. Calculated when tau is13=τ24When the time is 0.1s, solving through a feasp function of Matlab LMIToolbox, judging that a feasible solution exists in the system at the moment, and controlling the gain K in the scheme 1 at the momentc1_1=-2.0894,Kc1_2=-6.8671. Therefore, when the time is more than 0 and less than 0.1s, the system can be gradually stabilized.
And carrying out a simulation experiment on the obtained feedback controller. The glitch setting is that the excitation voltage of G2 generates 5% step disturbance at 1.1s and returns to normal at 1.2s, and the simulation result of the power system is shown in FIG. 4. It can be seen that the system is stable without any control, but needs more than 15s to reach a stable state, and the system has low-frequency oscillation in an interval mode, and the damping is very weak.
The control scheme provided by the invention is subjected to simulation verification at different time lags, and the simulation result of the system is shown in fig. 5. It can be known that as the signal transmission delay τ increases, the control effect of the obtained controller gradually deteriorates. The system is in no delay, when tau13=0.05s,τ240.1s and τ13=τ24Can be kept stable under the condition of 0.1s, and the control effect is weakened in turn when tau is13=τ24The system is in a critical stable state when the time is 0.15s, and when the time is tau13=τ24The system cannot be kept stable at 0.2 s. Simulations show that the method proposed herein can accommodate time delays within an upper time lag limit, with rationality and effectiveness.
And (2) simulation experiment II: simulation verification of control scheme provided by the invention under large interference
In order to verify the control effect of the multi-time-lag additional damping controller under the condition of large disturbance, the fault is set to be a three-phase short-circuit fault when the bus 7 is in 0.1s, and the automatic reclosing is successful after 0.1 s. The simulation curve of the power system is shown in fig. 5. Therefore, under the condition that the system generates large disturbances such as three-phase short circuit, the power system without the controller continues low-frequency oscillation and cannot recover stability, after the multi-time-lag additional damping control provided by the invention is added, the interval low-frequency oscillation is restrained, the system quickly recovers a stable running state, and the multi-time-lag wide-area additional damping controller provided by the invention still has a good control effect under the condition of large disturbance.
And (3) simulation experiment III: the control scheme provided by the invention is compared with other control schemes in control effect under a given time lag
To prove the effectiveness of the control scheme provided by the invention, 2 control schemes are adopted for comparative simulation verification.
The control scheme of the wide-area additional damping control without considering multi-time lag is recorded as a control scheme 2, the address of the control scheme is consistent with the structure of the controller and the control scheme 1, the parameters are calculated by a particle swarm algorithm, and the target function is designed to be the maximum interval mode damping ratio. The gain of the controller to be solved is Kc2_1、Kc2_2Is provided with
Figure BSA0000128948900000071
The wide-area additional damping control scheme considering single time lag is recorded as a control scheme 3, and the angular speed difference delta omega between G1 and G3 is adopted13Acting as an input to the feedback controller on the excitation system of G1. The gain of the controller to be solved is Kc3_1Is provided with
u1(t-τ1)=Kc3_1Δω13(t-τ1)
The parameter setting method is a damping control scheme which is provided by the text and considers multiple time lags, and the time lag is single at the moment. Controller gain KcIn the form of
Kc=K′1=[0 0 K10]
K1=[0 K c3_10 0]
Kc∈R2×16,K1∈R1×4
Calculated, for the control scheme 2 without considering time lag, the control parameter Kc2_1=-59.6532,Kc2_2-7.4969. For consideration of τ13 Control scheme 3 with single lag time of 0.1s, and control parameter Kc3_1=-6.7927。
The following is a comparative simulation experiment of the obtained feedback controller. The glitch setting is the same as in the first simulation experiment, and the simulation curve of the power system is shown in fig. 6. It can be seen that the system is stable without any control, but needs more than 15s to reach a stable state, and the system has low-frequency oscillation in an interval mode, and the damping is very weak. When a wide-area control scheme is adopted to restrain interval low-frequency oscillation of the power system, the control scheme 1 and the control scheme 3 can generate a damping effect on the system, so that a power angle and a rotor angular speed are stable within 10s, and the adaptability and the effectiveness of the method provided by the invention are verified. And after the damping control scheme 1 considering multiple time lags is adopted, the oscillation is settled in a shorter time, the damping effect is stronger, and the damping control scheme has a better effect than the damping control scheme 3 only considering single time lag. And the control scheme 2 which is designed without considering time lag cannot adapt to the condition that the signal has transmission time lag, and the system cannot be stable.
Finally, it should be noted that: the above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. A method of designing a wide area additional damping controller that accounts for skew effects of a plurality of wide area transmission signals, said method comprising the steps of:
step (1): linearizing the system near a balance point to obtain a state space model of the power system;
step (2): the installation position of the controller and the selection of input signals are carried out by utilizing the controllable observability;
and (3): solving parameter Bi', wherein B1′=[B10 … 0],…,Bi′=[0 … 0 Bi0 … 0],…,Bq′=[0 0 … Bq];
And (4): judging whether a time lag upper limit is known or not; if the time lag is known, directly entering the step (6), otherwise entering the step (5) to solve the time lag stability upper limit;
and (5): when the time lag upper limit is unknown, iteratively solving the time lag upper limit by a method of assuming the time lag upper limit and judging whether the linear matrix inequality is feasible by utilizing a multi-time lag stability criterion of the power system;
and (6): using a given time lag upper limit or a solved time lag upper limit, adopting feasp of LMI Toolbox in Matlab to solve two linear matrix inequalities, using solved matrixes N and W, and using Kc=NW-1Calculating a control matrix Kc
And (7): using control matrix KcCalculating and solving gain K of wide area additional damping controlleri
In the step (1), the state equation of the multi-time-lag power system adopting the linearized state space model is
Figure FSB0000186342190000011
Wherein y (t) is a measurable output signal, ui(t) is a control signal, a positive number τiFor the signal transmission delay on the ith WAMS transmission link, i is 1, 2, … q, and q is the number of transmission links;
in said step (6), the multi-lag power system stability criterion is adopted as, for a given scalar quantity
Figure FSB0000186342190000018
If there is a positive scalar quantity
Figure FSB0000186342190000012
And
Figure FSB0000186342190000013
and a matrix
Figure FSB0000186342190000014
N and W satisfy det (W) ≠ 0, such that the following linear matrix inequality holds, then this multi-lag system is asymptotically stable, and the controller parameter that stabilizes the system is denoted Kc=NW-1
Wherein the linear matrix inequality is
Figure FSB0000186342190000015
W>0
Wherein
Figure FSB0000186342190000016
Figure FSB0000186342190000017
12=[B1N B2N … BqN]
Figure FSB0000186342190000021
Θ12=[AW B1N … BqN]T[I I … I]
Figure FSB0000186342190000022
Figure FSB0000186342190000023
Figure FSB0000186342190000024
Θ14=diag{WT,NT,…,NT}
Figure FSB0000186342190000025
2. The method according to claim 1, wherein in step (5), the upper time lag stability limit is calculated in particular in several sub-steps:
step (5-1): selecting a group of time lags small enough as initial values to ensure that 2 linear matrix inequalities have feasible solutions, and entering (5-2);
step (5-2): judging whether the LMI has a feasible solution or not by using a feasp method in the Matlab LMI Toolbox; if feasible solution exists, switching to (5-3), otherwise, switching to (5-4);
step (5-3): when a feasible solution exists, the solution is recorded and the time lag is changed to taui=τi+10ms, repeat step (5-2);
step (5-4): and (4) recording the time lag size meeting 2 linear inequalities when no feasible solution exists, taking the time lag size as the time lag upper limit, and entering the step (6).
3. The method of claim 1, wherein in step (7), a control matrix KcCalculating and solving gain K of wide area additional damping controlleriBy a specific method ofc=[K1′ … Ki′ … Kq′]TFind the corresponding Ki', then Ki=Ki′Ci -1Finding Ki
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