CN108462205A - A kind of Damping Characteristic of Interconnected Power System control method adapting to wind-powered electricity generation stochastic volatility - Google Patents
A kind of Damping Characteristic of Interconnected Power System control method adapting to wind-powered electricity generation stochastic volatility Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention belongs to electric power project engineering field more particularly to a kind of Damping Characteristic of Interconnected Power System control methods adapting to wind-powered electricity generation stochastic volatility, including：The power system stabilizer, PSS group coordinated for multiple typical wind power output operating condition designs；Multiple time-varying Kalman filter are designed for different operating conditions；The Wide-area Measurement Information from PMU is separately input in the corresponding time-varying Kalman filter of each different operating condition and is tracked to system condition in acquisition electric system, and the power system stabilizer, PSS that switching matches.It can quickly and accurately judge that system currently runs subspace using the self adaptive control measure based on Kalman filter, and the corresponding controller of adaptive switching, it being capable of effectively tracking system stochastic and dynamic behavior, it, also being capable of effectively suppression system low-frequency oscillation in the case where wind-powered electricity generation fluctuates widely at random.
Description
Technical field
The invention belongs to electric power project engineering field more particularly to a kind of interconnecting electric powers adapting to wind-powered electricity generation stochastic volatility
System damping control method.
Background technology
With the energy shortages getting worse in worldwide, the generation technology that taps a new source of energy is extremely urgent.In recent years
Come, wind-power electricity generation has become one of clean energy resource with fastest developing speed in China, and installed capacity is growing day by day, it is contemplated that 2020
Year, installed capacity of wind-driven power will at least up to 1.5 hundred million kW.The stochastic volatility of the primary energy such as wind energy determines wind-powered electricity generation output work
The stochastic volatility of rate, with the continuous expansion of wind-electricity integration scale, the randomness of system, fluctuation sex expression obtain more violent.
The design of conventional electric power system controller is all i.e. system component parameter, service condition and disturber under typical operating condition
Formula carries out in the case of having given.But since wind-powered electricity generation has intermittent and strong stochastic volatility so that based on typical operation work
The traditional controller of condition design shows adaptability obviously insufficient defect, it is difficult in wind power output wide fluctuations
Carry out effective damping.So the self-adaptive damping control strategy that research can adapt to wind-powered electricity generation random fluctuation characteristic has become certainty
Trend.
Since the random fluctuation of wind speed makes the output of wind power change frequently, it is difficult to accurately captured, therefore,
How system stochastic and dynamic is tracked and seems particularly difficult to the identification of system.How adaptation wind-powered electricity generation is designed
The damping controller of stochastic volatility is a urgent problem.
Invention content
In view of the above-mentioned problems, the present invention proposes a kind of Damping Characteristic of Interconnected Power System control adapting to wind-powered electricity generation stochastic volatility
Method processed, including：
The power system stabilizer, PSS group coordinated for multiple typical wind power output operating condition designs；For different operation works
Condition designs multiple time-varying Kalman filter；The Wide-area Measurement Information from PMU is separately input to each difference in acquisition electric system
The corresponding time-varying Kalman filter of operating condition in and system condition is tracked, and the power train that switching matches
System stabilizer.
The time-varying Kalman filter obtains the estimated value of busbar difference on the frequency, with the amount of obtaining after substantial amount measured value
Residual error is surveyed, and multiple spot adduction is carried out to measurement and is averaged, further obtains chi-squared variable mean value；Become according to each card side
The relative probability that amount mean value is distributed in confidence interval effectively tracks current system operating mode.
Busbar difference on the frequency of the Wide-area Measurement Information between each generator.
The Discrete Dynamic equation of the time-varying Kalman filter is as follows：
Wherein, x (n) and x (n-1) is state vector, and z (n) is observable measurement, is obtained by Discrete Dynamic equation
To Φ, Γ and H-matrix, Φ (n, n-1) are the discrete forms of state matrix A, and Γ (n, n-1) is input matrix, H (n, n-
1), H (n) is observing matrix, and w (n-1), w (n) are process noises, are indicated with Gaussian sequence, and ε (n) is to measure noise,
It is indicated with Gaussian sequence, it is assumed that process noise and measurement noise are independent from each other, and each sampled point is satisfied by following
Formula：
E { w (n) }=0 (2)
E{w(j)wT(n) }=Q (n) δjn (3)
E { ε (n) }=0 (4)
E{ε(n)εT(j) }=R (n) δjn (5)
E{w(n)εT(j) }=0 (6)
Wherein E [] indicates that desired value, Q (n) are the covariance matrix of w (n), and R (n) battle arrays are the covariance square of ε (n) differences
Battle array, n and j indicate different moments sampled point, δjnIt is Dirac functions,
The design method of the time-varying Kalman filter includes：
Given state vector sum covariance matrix initial value, new value is acquired by iteration；In each sampled point, in conjunction with survey
Magnitude is updated state vector, Kalman filter gain and covariance matrix；To state vector estimated value and association side
Poor Matrix Estimation value carries out temporal update；Define the chi-squared variable characterization observation residual error of quadratic form；By predicted value and measurement
Value is compared, and gap between the two is further increased by kalman gain, and Wide-area Measurement Information is input to Kalman filtering
Prediction next time is carried out in device, the chi-squared variable of quadratic form is extended, and multiple spot summation is averaged to obtain multiple spot card
Square mean variable value.
The chi-squared variable and multiple spot chi-squared variable mean value obey the chi square distribution that degree of freedom is m, and m is observation point
Number.
The beneficial effects of the present invention are：It can be accurately fast using the self adaptive control measure based on Kalman filter
The judgement system of speed currently runs subspace, and the corresponding controller of adaptive switching, being capable of effective tracking system stochastic and dynamic
Behavior also being capable of effectively suppression system low-frequency oscillation in the case where wind-powered electricity generation fluctuates widely at random.
Description of the drawings
Fig. 1 is the control strategy structure chart of the present invention；
Fig. 2 is 16 machine, the 68 node configuration of power network in embodiment；
Fig. 3 is system frequency and damping ratio changed power curve figure with the wind；
Fig. 4 is the system dynamic response figure under different controllers under different wind-powered electricity generation permeabilities；
Fig. 5 is chi-squared variable distribution of mean value probability density figure
Fig. 6 is system dynamic response figure when wind power integration power changes
Specific implementation mode
Below in conjunction with the accompanying drawings, it elaborates to embodiment.
Since the random fluctuation of wind speed makes the output of wind power change frequently, it is difficult to accurately captured, therefore,
Need using in system can measurement the behavior of system stochastic and dynamic is effectively captured.In this regard, the present invention proposes one kind
The Damping Characteristic of Interconnected Power System control method for adapting to wind-powered electricity generation stochastic volatility, as shown in Fig. 1, including：
The power system stabilizer, PSS group coordinated for multiple typical wind power output operating condition designs；For different operation works
Condition designs multiple time-varying Kalman filter；The Wide-area Measurement Information from PMU is separately input to each difference in acquisition electric system
The corresponding time-varying Kalman filter of operating condition in and system condition is tracked, and the power train that switching matches
System stabilizer.
The time-varying Kalman filter obtains the estimated value of busbar difference on the frequency, with the amount of obtaining after substantial amount measured value
Residual error is surveyed, and multiple spot adduction is carried out to measurement and is averaged, further obtains chi-squared variable mean value；Become according to each card side
The relative probability that amount mean value is distributed in confidence interval effectively tracks current system operating mode.
Busbar difference on the frequency of the Wide-area Measurement Information between each generator.
The Discrete Dynamic equation of the time-varying Kalman filter is as follows：
Wherein, x (n) and x (n-1) is state vector, and z (n) is observable measurement, is obtained by Discrete Dynamic equation
To Φ, Γ and H-matrix, Φ (n, n-1) are the discrete forms of state matrix A, and Γ (n, n-1) is input matrix, H (n, n-
1), H (n) is observing matrix, and w (n-1), w (n) are process noises, are indicated with Gaussian sequence, and ε (n) is to measure noise,
It is indicated with Gaussian sequence, it is assumed that process noise and measurement noise are independent from each other, and each sampled point is satisfied by following
Formula：
E { w (n) }=0 (2)
E{w(j)wT(n) }=Q (n) δjn (3)
E { ε (n) }=0 (4)
E{ε(n)εT(j) }=R (n) δjn (5)
E{w(n)εT(j) }=0 (6)
Wherein E [] indicates that desired value, Q (n) are the covariance matrix of w (n), and R (n) battle arrays are the covariance matrix of ε (n),
N and j indicates different moments sampled point, δjnIt is Dirac functions,
The design method of the time-varying Kalman filter includes：
Given state vector sum covariance matrix initial value, new value is acquired by iteration；In each sampled point, in conjunction with survey
Magnitude is updated state vector, Kalman filter gain and covariance matrix；To state vector estimated value and association side
Poor Matrix Estimation value carries out temporal update；Define the chi-squared variable characterization observation residual error of quadratic form；By predicted value and measurement
Value is compared, and gap between the two is further increased by kalman gain, and Wide-area Measurement Information is input to Kalman filtering
Prediction next time is carried out in device.The chi-squared variable of quadratic form is extended, and multiple spot summation is averaged to obtain multiple spot card
Square mean variable value.
The chi-squared variable and multiple spot chi-squared variable mean value obey the chi square distribution that degree of freedom is m, and m is observation point
Number.
System design of the time-varying Kalman filter mainly for time-varying system or containing time-varying disturbance, can utilize
Online measuring amount recognizes system.Accordingly, time-varying Kalman filter is separately designed to each operation subspace, and combined
The Wide-area Measurement Information of PMU obtained the operation subspace where system.
The design procedure of time-varying Kalman filter is specific as follows：
(1) given state vector x and covariance matrix P initial values x (1 │ 0) and P (1 │ 0), new value is acquired by iteration；
X (0) is t=0 moment initial values,For the predicted value of initial time.
(2) in each sampled point, in conjunction with measured value, using formula (8) to state vector x (n |), Kalman filter increases
Beneficial K (n) and covariance matrix P (n |) are updated.
(3) temporal update is carried out to state vector estimated value and covariance matrix value using formula (9).
WhereinTo be the state estimation being worth to according to last moment measurement,Be according to it is current when
Carve the state estimation for measuring and being worth to.P (n | n) is the covariance matrix of prediction, and P (n | n-1) it is updated covariance square
Battle array.
P (n | n)=E (x (n)-x (n | n) } x (n)-x (n | n) }T)
P (n | n-1)=E (x (n)-x (n | n-1) } x (n)-x (n | n-1) }T) (10)
Measurement residuals are indicated with tilde：
Z (k) is measured value,For predicted value,For the measurement residuals being worth to using measured value and prediction.
Measure covariance matrix SkIt is expressed as：
For measurement residuals.
Define the chi-squared variable characterization observation residual error of quadratic form：
C (k) is chi-squared variable.
Wherein C (k) is chi-squared variable, and the mean value due to measuring noise ε (n) is zero, R (n) white Gaussian noise covariances
Matrix indicates that therefore, C (k) obeys the chi square distribution that degree of freedom is m,
C (k)~χ2(m) (14)
Wherein m is the number of observation point, and k indicates k-th of sampled point.
Kalman filter gain is fed back in model and is predicted again, the area of comparison prediction model and observation
Not, such method can further increase the mismatch degree between model.When observation comes from matching operating point, card side
The mean value of variable gradually tends to the number equal to sampled point:
E (C (k))=m (15)
When measured value and Kalman filter mismatch, chi-squared variable mean value E (C (k)) will be greater than m.In electric system
In, single-point judging result confidence level is little, in order to obtain more accurate identification result, is extended to formula (13)：
z(k+l)、C(k+l)、Sk+lIt is measurement residuals, measured value after respectively extending, pre-
Measured value, measures covariance matrix at chi-squared variable.
Multiple spot adduction is carried out to chi-squared variable and is averaged to obtain multiple spot chi-squared variable mean value L (k+l)：
Wherein, L (k+l) obeys the chi square distribution that degree of freedom is m：
L (k+l)~χ2(m) (19)
The behavior of system stochastic and dynamic is effectively tracked using confidence interval and Ka Fang verifications, it is most suitable to select
Damping controller.L (k+l) obeys the chi square distribution that degree of freedom is m, then the desired value of L (k+l) is just it is known that and being m
μ=E (L (k+l))=m (20)
μ is the desired value of L (k+l).
Confidence level is set as the bilateral confidence interval of α：
The quantiles of upper α/2 for being α for confidence level,The quantiles of lower α/2 for being α for confidence level.
The chi-squared variable mean value interval CI for being distributed in confidence interval is then：
L(k+l)、Respectively chi-squared variable mean value interval lower limiting value and upper limit value；
Obey the probability density Pr for the chi-squared variable mean value Li that degree of freedom is mLiFor：
Wherein Γ () is Gamma functions.
Relative probability density β is obtained using Bayesian formulaiFor：
S is the total number of the Kalman filter of design, LjFor the corresponding multiple spot chi-squared variable of j-th of Kalman filtering
Mean value.From formula (25) as can be seen that chi-squared variable mean value LiSmaller, the matching degree of i-th of operating condition is higher, accordingly may be used
To judge current system operating condition, to the corresponding controller of switching.
The present invention using 68 node of IEEE16 machines as shown in Figure 2 interacted system verify this method validity and can
Row.Generator uses 6 rank detailed models, excitation to use IEEE-DC1 type excitations.Wind power plant (the Wind of double-fed wind turbine composition
Farm, WF) it is connected on busbar 69, model uses WT3 models, and it is 0MW that wind power plant, which is initially accessed capacity, and original permeability is
0%.Using in the system known to modal analysis method, there are 4 inter-area low-frequency oscillation patterns, and frequency of oscillation and damping are such as
Shown in table 1.
1 inter-area low-frequency oscillation dominant pattern of table
| Pattern | 1 | 2 | 3 | 4 |
| Frequency | 0.3109 | 0.4579 | 0.5696 | 0.7791 |
| Damping ratio (%) | 7.58 | -0.24 | 3.87 | 3.43 |
Here is to be made that analysis to containing large-scale wind power multi area interconnected system damping characteristic：The wind power plant maximum is defeated
It is 4048MW to go out power, and maximum wind permeability is 22.5%.It is obtained under different wind power output powers using modal analysis method
4 frequencies of oscillation and damping ratio, as shown in Figure 3.As can be seen that with the increase of wind power output power, pattern 1 and pattern 3
Damping ratio increases, and the damping ratio of pattern 2 first increases, rear to reduce.The damping ratio of pattern 4 with wind power output power increase
It is gradually reduced, becomes from positive damping for negative damping.Since the stochastic volatility of wind energy causes the output of wind power plant also to have very greatly
Stochastic volatility, in this case, the damping characteristic of system also has changed a lot therewith, in certain serious feelings
Under condition, system unstability can be caused.
For different wind power outputs, 10 typical conditions are obtained, carry out PSS parameter coordination respectively.Closed-loop system is obtained to shake
It swings frequency and damping ratio is as shown in table 2, it can be seen that PSSs is coordinated corresponding based on each group designed under typical condition
It, being capable of effectively suppression system low-frequency oscillation under operating mode.
The damping of 2 closed loop oscillation mode of table and frequency
The time-domain-simulation of 30s is carried out as shown in figure 4, when t=1s using different PSS groups for 4 kinds of scenes, and circuit 1-2 is female
Generation instantaneity three-phase shortcircuit, duration of short-circuit 80ms, simulation scenarios are as follows at line 1：
1) scene 1, wind power output power 450MW, the corresponding 2nd group of coordination PSSs of input operating mode 2 obtain interconnection
1-2 active power response curves are as shown in solid black lines；Input operating mode 6 maps corresponding 6th group of coordination PSSs, is got in touch with
Line active power response curve is as shown in black dotted lines.
2) scene 2, wind power output power 2250MW, the corresponding 6th group of coordination PSSs of the operating mode that puts into operation 6 are obtained
Interconnection 41-42 active power response curves are as shown in solid black lines；The corresponding 2nd group of coordination PSSs of the operating mode that puts into operation 2,
Interconnection active power response curve is obtained as shown in black dotted lines.
3) scene 3, wind power output power 1800MW run the corresponding 3rd group of coordination PSSs of sub- operating mode 3, obtained connection
Winding thread 42-52 active power response curves are as shown in solid black lines；The corresponding 7th group of coordination PSSs of the operating mode that puts into operation 7, obtains
To interconnection active power response curve as shown in black dotted lines.
4) scene 4, wind power output power 2700MW, the corresponding 7th group of coordination PSSs of operating condition 7, obtained contact
Line 50-51 active power response curves are as shown in solid black lines；The corresponding 3rd group of coordination PSSs of the operating mode that puts into operation 3, obtains
Interconnection active power response curve is as shown in black dotted lines.
From fig. 4, it can be seen that when wind power output power is matched with designed PSS groups, system oscillation can be had
Effect inhibits；And unmatched controller is difficult to calm down oscillation.The stochastic volatility of wind energy causes the output of wind power plant also to have very
Big fluctuating range has changed a lot so as to cause the frequency of oscillation and damping ratio of system.In this case, according to
It is difficult to adapt to be likely to occur random fluctuation according to the controller of single specific typical operation point design.Therefore, it is necessary to utilize
Self adaptive control tracks system random behavior into Mobile state, to the corresponding controller of switching.
Assuming that system operation wind power output power be 3600MW under, due to the stochastic volatility of wind energy, wind-powered electricity generation output work
Rate drops to 3600MW in t=5s, and it is perturbed in t=5s to be equivalent to system, at this point, Kalman filter starts
Sampled value is calculated, obtains that corresponding chi-squared variable mean value is as shown in table 3, and confidence level is set as 98%, it can from table 3
To find out, when the 1st sampled point, the corresponding chi-squared variable mean value of all operating conditions is all distributed in confidence interval, can not be distinguished
Other current system conditions；When reaching the 7th sampled point, operating condition 4 is removed, other operating modes increase gradually with observation point
Confidence level is gradually lost, corresponding chi-squared variable mean value is outside confidence interval.At this point, can determine whether that system currently runs work
Condition is operating mode 4, i.e., wind power output power is 1350MW.The distribution probability and relative probability of chi-squared variable mean value as shown in figure 5,
As can be seen that over time, sampled point gradually increases, the probability of the corresponding chi-squared variable mean value of unmatched operating mode
0 is gradually become, the chi-squared variable mean value of the subspace to match remains certain probability, relative probability 1.Therefore, from
Relative probability may determine that current system operates under the operating mode of wind power output power 1350MW, such as Fig. 5 black heavy line institute
Show.
The chi-squared variable mean value of 3 each Kalman filter of table
Time-domain-simulation is carried out to the system under the scene as shown in fig. 6, wherein black dotted lines are not put into any PSSs's
System dynamic response curve；Black dotted line curve be wind power after 3600MW drops to 1350MW, still using operation work
The corresponding 9th group of PSSs of condition 9 (wind power 3600MW)；Solid black lines curve is Kalman filter to current system shape
State carries out after effectively capturing and after judging, adaptive switching operating mode 4 (wind power 1350MW) mapping the corresponding 4th
The system dynamic response curve obtained after group PSSs.It can be seen from the figure that using based on the self-adaptive controlled of Kalman filter
Measure processed can quickly and accurately judge that system currently runs subspace, and the corresponding controller of adaptive switching, can be effective
Tracking system stochastic and dynamic behavior, in the case where wind-powered electricity generation fluctuates widely at random, also can effectively suppression system low frequency shake
It swings.
This embodiment is merely preferred embodiments of the present invention, but scope of protection of the present invention is not limited thereto,
Any one skilled in the art in the technical scope disclosed by the present invention, the change or replacement that can be readily occurred in,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims
Subject to.
Claims (6)
1. a kind of Damping Characteristic of Interconnected Power System control method adapting to wind-powered electricity generation stochastic volatility, which is characterized in that including：
The power system stabilizer, PSS group coordinated for multiple typical wind power output operating condition designs；It is designed for different operating conditions
Multiple time-varying Kalman filter；The Wide-area Measurement Information from PMU is separately input to each different operation in acquisition electric system
In the corresponding time-varying Kalman filter of operating mode and system condition is tracked, and the power system stability that switching matches
Device.
2. according to method shown in claim 1, which is characterized in that the time-varying Kalman filter obtains estimating for busbar difference on the frequency
Measurement residuals are obtained after evaluation, with substantial amount measured value, and multiple spot adduction is carried out to measurement and is averaged, and are further obtained
Chi-squared variable mean value；The relative probability being distributed in confidence interval according to each chi-squared variable mean value carries out current system operating mode
Effectively tracking.
3. according to method shown in claim 1, which is characterized in that busbar frequency of the Wide-area Measurement Information between each generator
Difference.
4. according to method shown in claim 1, which is characterized in that the Discrete Dynamic equation of the time-varying Kalman filter is such as
Under：
Wherein, x (n) and x (n-1) is state vector, and z (n) is observable measurement, and Φ is obtained by Discrete Dynamic equation,
Γ and H-matrix, Φ (n, n-1) are the discrete forms of state matrix A, and Γ (n, n-1) is input matrix, H (n, n-1), H (n)
It is observing matrix, w (n-1), w (n) are process noises, are indicated with Gaussian sequence, and ε (n) is to measure noise, uses white Gaussian
Noise sequence indicates, it is assumed that process noise and measurement noise are independent from each other, and each sampled point is satisfied by following formula：
E { w (n) }=0 (2)
E{w(j)wT(n) }=Q (n) δjn (3)
E { ε (n) }=0 (4)
E{ε(n)εT(j) }=R (n) δjn (5)
E{w(n)εT(j) }=0 (6)
Wherein E [] indicate desired value, Q (n) be w (n) covariance matrix, R (n) battle arrays be ε (n) differences covariance matrix, n with
J indicates different moments sampled point, δjnIt is Dirac functions,
5. according to method shown in claim 1, which is characterized in that the design method of the time-varying Kalman filter includes：
Given state vector sum covariance matrix initial value, new value is acquired by iteration；In each sampled point, in conjunction with measured value pair
State vector, Kalman filter gain and covariance matrix are updated；To state vector estimated value and covariance matrix
Estimated value carries out temporal update；Define the chi-squared variable characterization observation residual error of quadratic form；Predicted value and measured value are carried out
Comparison, gap between the two further increased by kalman gain, by Wide-area Measurement Information be input in Kalman filter into
The prediction of row next time, is extended the chi-squared variable of quadratic form, and multiple spot summation is averaged to obtain multiple spot chi-squared variable
Mean value.
6. according to method shown in claim 5, which is characterized in that the chi-squared variable and multiple spot chi-squared variable mean value are obeyed certainly
By spending the chi square distribution for m, m is the number of observation point.
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| CN110531957A (en) * | 2019-09-11 | 2019-12-03 | 北京智芯微电子科技有限公司 | The online test method of randomizer |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109657380A (en) * | 2018-12-26 | 2019-04-19 | 华北电力大学 | A kind of double-fed fan motor field Dynamic Equivalence based on Extended Kalman filter |
| CN110531957A (en) * | 2019-09-11 | 2019-12-03 | 北京智芯微电子科技有限公司 | The online test method of randomizer |
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