CN111614086A - Filtering estimation and prediction estimation method for multi-state variables of power system - Google Patents
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Abstract
The invention belongs to the technical field of filtering estimation and prediction estimation of state variables and discloses a filtering estimation and prediction estimation method for multi-state variables of a power system, which comprises the following steps: step 1: establishing a time point estimation method based on a Kalman filter; step 2: establishing a Kalman filter-based vector block state estimation method; and step 3: establishing block state real-time smooth estimation, filtering estimation and prediction estimation based on Kalman filtering; the model established by the method is more reasonable, accords with the actual situation, has higher actual use value, and effectively improves the working stability of the distributed power grid; the goal of minimizing the estimated error is achieved.
Description
Technical Field
The invention relates to the technical field of filtering estimation and prediction estimation of state variables, in particular to a filtering estimation and prediction estimation method for multi-state variables of a power system.
Background
Energy is an indispensable factor on which humans depend for survival and development. However, with global population growth and rapid economic development, humans are experiencing an unprecedented energy and environmental crisis. Because the traditional energy can not meet the urgent needs of human society and economic development, the solar photovoltaic power generation is taken as a clean and renewable new energy source with huge energy in the same living, and is gradually favored by people after wind power generation. The reason for this is that it is inexhaustible, safe and pollution-free, and is not limited by the resource distribution region. The sunlight irradiates the ground generally, solar energy is available everywhere, solar photovoltaic power generation is particularly suitable for remote areas without electricity, and the construction of a long-distance power grid and the electric energy loss on a power transmission line can be reduced.
The existing microgrid system in China mainly takes solar energy and wind energy as main materials, strong uncertainty exists, and the electricity consumption of a user also has certain uncertainty, and the uncertainty can be described by using a non-stationary random process. Particularly, in a microgrid system composed of distributed photovoltaic power generation and multiple loads, the changes of the power generation state, the energy storage state and the multiple loads are non-stationary processes. Therefore, for real-time estimation, especially prediction estimation, of these variables, a non-stationary model of multiple input multiple output should be constructed. However, most of the prediction methods commonly used in the prior art are methods based on statistical regression, and not only lack a state model, but also lack real-time recursion. Especially, when the non-stationarity is strong, the estimation and prediction effects are poor.
The problem is addressed herein by means of Kalman filtering with powerful capability to handle non-stationary processes. Kalman filtering is an optimal recursive filtering method proposed by american scholars Kalman (r.e.kalman) and buche (r.s.bucy) in 1960. The method considers the statistical characteristics of the measured value and the observed value, and is not only suitable for a stable random process, but also more importantly suitable for a non-stable random process. Kalman filtering is a method for optimally estimating the state of a system by using a linear system state equation and inputting and outputting observation data through the system. Kalman filtering does not require that both signal and noise are assumptions of a stationary process. The linear Kalman filtering is a Chinese linear optimal filter and has the excellent characteristics of real-time recursive estimation under the condition that modeling errors are white noise and performance indexes based on mean square errors. Therefore, since the Kalman filtering theory appeared, it has been applied to many departments such as communication systems, power systems, aerospace, environmental pollution control, industrial control, radar signal processing, etc., and has achieved many successful results. Point-to-point smoothing estimation, filtering estimation and prediction estimation can be realized by using Kalman filtering. Because the power utilization and power generation processes of the power system have strong non-stationary characteristics and obvious periodicity, the state variables in the period have strong coupling and relevance. In this project, the period is described as a state block, which may be a day, a week, a month or even a year, for which block state estimation is performed, which is a semi-real time estimation process. In order to achieve real-time estimation, a measurement equation is skillfully rewritten so as to realize real-time smoothing, filtering and prediction estimation of each state in a block.
Kalman filtering is an optimal recursive filtering method proposed by american scholars Kalman (r.e.kalman) and buche (r.s.bucy) in 1960. The method considers the statistical characteristics of the measured value and the observed value, and is not only suitable for a stable random process, but also more importantly suitable for a non-stable random process. Kalman filtering is a method for optimally estimating the state of a system by using a linear system state equation and inputting and outputting observation data through the system. Kalman filtering does not require that both signal and noise are assumptions of a stationary process. The linear Kalman filtering is a Chinese linear optimal filter and has the excellent characteristics of real-time recursive estimation under the condition that modeling errors are white noise and performance indexes based on mean square errors. Therefore, since the Kalman filtering theory appeared, it has been applied to many departments such as communication systems, power systems, aerospace, environmental pollution control, industrial control, radar signal processing, etc., and has achieved many successful results. Because the power utilization and power generation processes of the power system have strong non-stationary characteristics and obvious periodicity, the state variables in the period have strong coupling and relevance. In view of the excellent characteristics of Kalman filtering in the flight and stationary process, how to provide a Kalman filtering-based filtering estimation and prediction estimation method for multi-state variables of a power system is a technical problem to be solved by technical personnel in the field.
Disclosure of Invention
The invention provides a filtering estimation and prediction estimation method for multi-state variables of a power system, aiming at the problem that the estimation and prediction effects in the non-stationary process are poor in a micro-grid system composed of distributed photovoltaic power generation and multiple loads in the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme:
a filtering estimation and prediction estimation method for multi-state variables of a power system is designed, and comprises the following steps:
step 1: time point estimation method based on Kalman filter
1.1, establishing a time series dynamic model of the real-time change of the multi-state vector along with a time point as a state equation of a Kalman filter, and taking the real-time change of the multi-state variable along with the time point in the power system as an input quantity:
x(k+1)＝A(k+1,k)x(k)+w(k) (1)
wherein, in the formula (1), x (k) is an observation vector, a (k +1, k) is a state transition matrix, and w (k) is modeling noise; the corresponding observation equation is shown in equation (2):
y(k+1)＝C(k+1)x(k+1)+ν(k+1) (2)
wherein, C (k) in the formula (2) is an observation matrix, and v (k) is observation noise;
1.2 establishing Kalman Filter based on time point estimation method
1.2.1 first, it is assumed that an optimal estimate for the kth state x (k) has been obtained
And the corresponding estimation error covariance matrix P (k | k):
1.2.2 then, based on
And P (k | k), and further obtaining a predicted value
And prediction estimation error covariance P (k +1| k):
P(k+1|k)＝A(k+1,k)P(k|k)AT(k+1,k)+Qw(k) (6)
1.2.3 next, the optimal gain matrix K (K +1) is calculated:
K(k+1)＝A(k+1,k)P(k+1,k)HT(k+1)[H(k+1)P(k+1,k)HT(k+1)]-1(7)
1.2.4 obtaining the optimal estimated value of the state x (k +1)
And estimated error covariance P (k +1| k + 1):
P(k+1|k+1)＝[I-K(k+1)H(k+1)P(k+1,k)](10)
1.2.5, continuing to loop the process of 1.2.2-1.2.4 until the filtering is finished;
step 2: method for establishing vector block state estimation based on Kalman filter
2.1 firstly, regarding the whole variable in a time period as a vector block, establishing a dynamic system model of the multi-state vector block changing in time period as a state equation of a Kalman filter, and regarding the real-time change quantity of the multi-state vector block along with a time point in the power system as an input quantity:
X(m+1)＝A(m+1,M)X(m,M)+W(m)w(m,M) (11)
wherein, in the formula (11), X (M, M) is an observation vector, a (M +1, M) is a state matrix, and w (M) w (M, M) is modeling noise; the corresponding observation equation is shown in equation (12):
Y(m+1)＝HX(m+1)+V(m+1) (12)
wherein, in the formula (12), H is an observation matrix, and V (m +1) is observation noise;
the Kalman filter model as shown in equations (3) - (10) can obtain the estimated value of each state vector block
And an estimation error covariance matrix P (m + m):
2.2 establishing Kalman Filter model based on vector Block State estimation method
2.2.1 first, assume that the optimal estimate of the m-th vector chunk state has been obtained
And corresponding estimation error covariance matrix
2.2.2 based on
And
further obtaining the predicted value
And prediction estimation error covariance
2.2.3 calculate optimal gain array:
2.2.4 obtaining the optimal estimation value of the state block X (m +1)
And estimate error covariance
P(m+1|m+1)＝[I-K(m+1)H(m+1)P(m+1,m)](22)
2.2.5, continuing to loop the process of 2.2.2-2.2.4 until the filtering is finished;
and step 3: establishing Kalman filtering based block state real-time smooth estimation, filtering estimation and prediction estimation
3.1 first, formula (12) in step 2 is rewritten as follows:
y(m+1,k)＝H(m+1,k)X(m+1)+ν(m+1,k),m＝1,2,…；k＝1,2,…,M (23)
3.2, a real-time smooth estimation model is established, and real-time updating estimation is carried out on states x (m +1,1), x (m +1,2), L and x (m +1, k-1) before the current time k, wherein the model is as follows:
3.3, establishing a real-time filtering estimation model, and updating and estimating the state x (m +1, k) at the current k moment in real time, wherein the model is as follows:
3.4 establishing a real-time prediction estimation model for the state after the current k moment
x (M +1, k +1), x (M +1, k +2), L, x (M +1, M) are used for real-time prediction estimation, and the model is as follows:
3.5, taking a formula (11) as a state equation, and taking a formula (23) as a state model of a measurement equation to carry out a Kalman filter model;
3.6 building a Kalman Filter model in the Multi-State vector Block
3.6.1 first, assume that the optimal estimate for the mth time instant in the mth state block X (M) is known
Sum estimation error covariance matrix
3.6.2 based on
And
further obtaining a prediction value and a prediction estimation error covariance of the (m +1) th block state:
3.6.3 further results in an intra-block recursive filter:
3.6.4 loops through the 3.6.2-3.6.3 process until the filtering is complete.
Further, the modeling noise w (k) and the measurement noise v (k) satisfy the following statistical characteristics:
wherein Q (k) and R (k) are both error variance matrices, and the error variance matrices Q (k) and R (k) are symmetric non-negative definite matrices and symmetric positive definite matrices, respectively, S (k) ∈ Rn×m。
Further, the above formula (11) and formula (12)
R(m+1)＝diag{R(m+1,1),R(m+1,2),…,R(m+1,M)}，
Further, the measurement noise v (m, k) in the formula (23) has a statistical characteristic E { ν (m, k) } of 0; e { v (m, k) vT(m,j)}＝R(m,k)kjm＝1,2,…，k,j＝1,2,…,M。
Further, in the formula (39)
Further, before the first step, a sensor model of each state variable needs to be established:
yi(t)＝hi(x(t))+νi(t)，i＝1,2,…,N (40)
where N represents the number of sensors, X (t) represents a model of a state variable, hi(. cndot.) is a continuous function;
then, after the equation (40) is discretized by the equal period T, a discrete observation equation is obtained, wherein the discrete observation equation is
yi(kT)＝hi(x(kT),kT)+νi(kT)，i＝1,2,…,N (41)
Wherein h isiDenotes the measurement function of the corresponding sensor i, determined by the properties of the sensor, vi(kT) denotes measurement error; next, the following sequence model of the state variable x (kT) with time is established
x((k+1)T)＝f(x(kT),kT)+w(kT) (42)
Where f (x), (k), k ═ a (k +1, k) x (k) is a state transfer function, and w (kt) represents a modeling error.
Further, the multi-state variables include state variables of the distributed power generation units and state variables of each load of the power utilization.
Further, the time period in step 2 includes one hour, one day, one week, one month, or one year.
The invention provides a filtering estimation and prediction estimation method for multi-state variables of a power system, which has the beneficial effects that:
(1) the method comprises the steps of constructing a sequence model of each state variable changing along with time, considering the non-stationarity characteristic of the constructed model, converting the sequence model into a Kalman filtering framework for processing, and respectively establishing a real-time point estimation method of the state, a semi-real-time estimation method of the block state, a real-time block smoothing estimation method, a block filtering estimation method, a block prediction estimation method and other estimation methods by establishing a point filtering model, a block state model and a prediction model of relevant state variables; the method has strong applicability to non-stationary random processes, and effectively solves the problem of poor prediction results in the prior art;
(2) the method comprises the steps of constructing a recursion model of state variables changing along with time on the basis of a Kalman filtering framework, considering the specific characteristics of a non-stable process of the microgrid, constructing a distributed multi-load unit, considering the input and output dynamic models of natural factors such as temperature, humidity, wind speed and illumination radiation, analyzing the dynamic characteristics of the multi-load under different properties and the statistical characteristics of data generated by the multi-load change of an external unit, and constructing a prediction control model according to the statistical characteristics; compared with the prior art, the prediction estimation method considers more input and output influence factors, and the established model is more reasonable, conforms to the actual situation, has higher actual use value, and effectively improves the working stability of the distributed power grid;
(3) according to the method, the characteristics of minimized estimated error and strong robustness of estimated estimation are realized during the prediction processing process according to the characteristics of the non-stationary process of the microgrid.
Drawings
The invention will be further described in detail with reference to examples of embodiments shown in the drawings to which, however, the invention is not restricted.
FIG. 1 is a graph showing the comparison of predicted temperature and actual temperature in an embodiment of the present invention;
FIG. 2 is an error curve of the comparison of the predicted temperature and the actual temperature in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
The invention relates to a filtering estimation and prediction estimation method for multi-state variables of a power system, which comprises the following steps:
in this embodiment, temperature variation prediction is used as an input quantity of the method, and selected data is derived from historical data (source website: https:// close. dest.com.cn /) published by a meteorological station of qinghua university in 2017 in month 6, wherein a state transition matrix a (k +1, k) is shown in table 1, an initial state X (0) is 20.3, an initial estimation error covariance p (0) is 1, a modeling error w (k) is subject to normal distribution with a mean value of 0 and a standard deviation of 0.08, and an observation noise v (k) is subject to normal distribution with a mean value of 0 and a standard deviation of 0.2.
TABLE 1 State transition matrix A (k +1, k)
| A(2,1) | 0.9557 | A(10,9) | 1.076 | A(18,17) | 0.9869 |
| A(3,2) | 1.0103 | A(11,10) | 1.1576 | A(19,18) | 0.9767 |
| A(4,3) | 0.9643 | A(12,11) | 1.169 | A(20,19) | 0.9694 |
| A(5,4) | 0.9471 | A(13,12) | 1.1004 | A(21,20) | 0.9614 |
| A(6,5) | 0.9609 | A(14,13) | 1.0401 | A(22,21) | 0.9708 |
| A(7,6) | 0.9767 | A(15,14) | 1.0281 | A(23,22) | 0.985 |
| A(8,7) | 0.9821 | A(16,15) | 1.0273 | A(24,23) | 0.9656 |
| A(9,8) | 1.0364 | A(17,16) | 1.0133 | A(25,24) | 0.996 |
Firstly, establishing a sensor model of each state variable:
yi(t)＝hi(x(t))+νi(t)，i＝1,2,…,N (40)
wherein N represents the number of temperature sensors, X (t) represents a model of a temperature state variable, hi(. cndot.) is a continuous function;
then, after the equation (40) is discretized by the equal period T, a discrete observation equation is obtained, wherein the discrete observation equation is
yi(kT)＝hi(x(kT),kT)+νi(kT)，i＝1,2,…,N (41)
Wherein h isiDenotes the measurement function of the corresponding temperature sensor i, which is determined by the properties of the temperature sensor vi(kT) denotes measurement error; next, the following sequence model of the state variable x (kT) with time is established
x((k+1)T)＝f(x(kT),kT)+w(kT) (42)
Where f (x), (k), k ═ a (k +1, k) x (k) is a state transfer function, and w (kt) represents a modeling error.
Step 1: time point estimation method based on Kalman filter
1.1, establishing a time series dynamic model of the real-time change of the multi-state temperature vector along with the time point as a state equation of a Kalman filter, and taking the real-time change of the multi-state temperature variable along with the time point in the power system as an input quantity:
x(k+1)＝A(k+1,k)x(k)+w(k) (1)
wherein, in the formula (1), x (k) is an observation vector, a (k +1, k) is a state transition matrix, and w (k) is modeling noise; the corresponding observation equation is shown in equation (2):
y(k+1)＝C(k+1)x(k+1)+ν(k+1) (2)
wherein, C (k) in the formula (2) is an observation matrix, and v (k) is observation noise; the modeling noise w (k) and the measurement noise v (k) meet the following statistical characteristics:
wherein Q (k) and R (k) are both error variance matrices, and the error variance matrices Q (k) and R (k) are symmetric non-negative definite matrices and symmetric positive definite matrices, respectively, S (k) ∈ Rn ×m。
1.2 establishing Kalman Filter based on time point estimation method
1.2.1 first, it is assumed that an optimal estimate for the kth state x (k) has been obtained
And the corresponding estimation error covariance matrix P (k | k):
1.2.2 then, based on
And P (k | k), and further obtaining a predicted value
And prediction estimation error covariance P (k +1| k):
P(k+1|k)＝A(k+1,k)P(k|k)AT(k+1,k)+Qw(k) (6)
1.2.3 next, the optimal gain matrix K (K +1) is calculated:
K(k+1)＝A(k+1,k)P(k+1,k)HT(k+1)[H(k+1)P(k+1,k)HT(k+1)]-1(7)
1.2.4 obtaining the optimal estimated value of the state x (k +1)
And estimated error covariance P (k +1| k + 1):
P(k+1|k+1)＝[I-K(k+1)H(k+1)P(k+1,k)](10)
1.2.5, continuing to loop the process of 1.2.2-1.2.4 until the filtering is finished;
step 2: method for establishing temperature vector block state estimation based on Kalman filter
2.1, firstly, regarding the temperature variable in a time period as a vector block as a whole, establishing a dynamic system model of a multi-state vector block for time period change as a state equation of a Kalman filter, wherein the multi-state variable comprises a state variable of a distributed power generation unit and a state variable of each load of electricity consumption, and in the embodiment, the multi-state variable refers to a multi-state temperature variable comprising a temperature state quantity of a distributed power generation power supply and a temperature state variable of each load of electricity consumption; the time period in step 2 includes one day, one week, one month or one year, and the time period selected in this embodiment is one hour.
Taking the real-time change quantity of the multi-state vector blocks in the power system along with the time points as input quantity:
X(m+1)＝A(m+1,M)X(m,M)+W(m)w(m,M) (11)
wherein, in the formula (11), X (M, M) is an observation vector, a (M +1, M) is a state matrix, and w (M) w (M, M) is modeling noise; the corresponding observation equation is shown in equation (12):
Y(m+1)＝HX(m+1)+V(m+1) (12)
wherein, in the formula (12), H is an observation matrix, and V (m +1) is observation noise; in the formula (11) and the formula (12):
R(m+1)＝diag{R(m+1,1),R(m+1,2),…,R(m+1,M)}，
the Kalman filter model as shown in equations (3) - (10) can obtain the estimated value of each state vector block
And the estimation error covariance matrix P (m | m):
2.2 establishing Kalman Filter model based on vector Block State estimation method
2.2.1 first, assume that the optimal estimate of the m-th vector chunk state has been obtained
And corresponding estimation error covariance matrix
2.2.2 based on
And
further obtaining the predicted value
And prediction estimation error covariance
2.2.3 calculate optimal gain array:
2.2.4 obtaining the optimal estimation value of the state block X (m +1)
And estimate error covariance
P(m+1|m+1)＝[I-K(m+1)H(m+1)P(m+1,m)](22)
2.2.5, continuing to loop the process of 2.2.2-2.2.4 until the filtering is finished;
and step 3: establishing Kalman filtering based block state real-time smooth estimation, filtering estimation and prediction estimation
3.1 first, formula (12) in step 2 is rewritten as follows:
y(m+1,k)＝H(m+1,k)X(m+1)+ν(m+1,k),m＝1,2,…；k＝1,2,…,M (23)
the measurement noise v (m, k) in the formula (23) has a statistical characteristic E { ν (m, k) } of 0; e { v (m, k) vT(m,j)}＝R(m,k)kjm＝1,2,…，k,j＝1,2,…,M。
3.2, a real-time smooth estimation model is established, and real-time updating estimation is carried out on states x (m +1,1), x (m +1,2), L and x (m +1, k-1) before the current time k, wherein the model is as follows:
3.3, establishing a real-time filtering estimation model, and updating and estimating the state x (m +1, k) at the current k moment in real time, wherein the model is as follows:
3.4 establishing a real-time prediction estimation model for the state after the current k moment
x (M +1, k +1), x (M +1, k +2), L, x (M +1, M) are used for real-time prediction estimation, and the model is as follows:
3.5, taking a formula (11) as a state equation, and taking a formula (23) as a state model of a measurement equation to carry out a Kalman filter model;
3.6 building a Kalman Filter model in the Multi-State vector Block
3.6.1 first, assume that the optimal estimate for the mth time instant in the mth state block X (M) is known
Sum estimation error covariance matrix
3.6.2 based on
And
further obtaining a prediction value and a prediction estimation error covariance of the (m +1) th block state:
3.6.3 further results in an intra-block recursive filter:
in the formula (39):
3.6.4 loops through the 3.6.2-3.6.3 process until the filtering is complete.
The prediction results obtained in the above embodiment are shown in fig. 1 and attached table 2; 1,8,16,24 indicate the estimation and prediction of the state from the first, eighth, sixteenth and twenty-fourth points, respectively.
TABLE 2 estimation and prediction values from points
According to the prediction and the real results of the attached figures 1 and the table 2, the relative error between the real value and the predicted value of each point is calculated, and an error curve of the attached figure 2 and a prediction error numerical value of the table 3 are formed.
TABLE 3 prediction error
As can be seen from the error curves shown in fig. 2 and the prediction error values in table 3, the relative error between the prediction result and the true value is small (the relative error is between 0.003349 and 1.185067), the goodness of fit of the data is high, and the degree of fit is high; therefore, the actual estimation and prediction effects are ideal.
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 person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (8)
1. A filtering estimation and prediction estimation method for multi-state variables of a power system is characterized by comprising the following steps:
step 1: time point estimation method based on Kalman filter
1.1, establishing a time series dynamic model of the real-time change of the multi-state vector along with a time point as a state equation of a Kalman filter, and taking the real-time change of the multi-state variable along with the time point in the power system as an input quantity:
x(k+1)＝A(k+1,k)x(k)+w(k) (1)
wherein, in the formula (1), x (k) is an observation vector, a (k +1, k) is a state transition matrix, and w (k) is modeling noise; the corresponding observation equation is shown in equation (2):
y(k+1)＝C(k+1)x(k+1)+ν(k+1) (2)
wherein, C (k) in the formula (2) is an observation matrix, and v (k) is observation noise;
1.2 establishing Kalman Filter based on time point estimation method
1.2.1 first, it is assumed that an optimal estimate for the kth state x (k) has been obtained
And the corresponding estimation error covariance matrix P (k | k):
1.2.2 then, based on
And P (k | k), and further obtaining a predicted value
And prediction estimation error covariance P (k +1| k):
P(k+1|k)＝A(k+1,k)P(k|k)AT(k+1,k)+Qw(k) (6)
1.2.3 next, the optimal gain matrix K (K +1) is calculated:
K(k+1)＝A(k+1,k)P(k+1,k)HT(k+1)[H(k+1)P(k+1,k)HT(k+1)]-1(7)
1.2.4 obtaining the optimal estimated value of the state x (k +1)
And estimated error covariance P (k +1| k + 1):
P(k+1|k+1)＝[I-K(k+1)H(k+1)P(k+1,k)](10)
1.2.5, continuing to loop the process of 1.2.2-1.2.4 until the filtering is finished;
step 2: method for establishing vector block state estimation based on Kalman filter
2.1 firstly, regarding the whole variable in a time period as a vector block, establishing a dynamic system model of the multi-state vector block changing in time period as a state equation of a Kalman filter, and regarding the real-time change quantity of the multi-state vector block along with a time point in the power system as an input quantity:
X(m+1)＝A(m+1,M)X(m,M)+W(m)w(m,M) (11)
wherein, in the formula (11), X (M, M) is an observation vector, a (M +1, M) is a state matrix, and w (M) w (M, M) is modeling noise; the corresponding observation equation is shown in equation (12):
Y(m+1)＝HX(m+1)+V(m+1) (12)
wherein, in the formula (12), H is an observation matrix, and V (m +1) is observation noise; the Kalman filter model as shown in equations (3) - (10) can obtain the estimated value of each state vector block
And the estimation error covariance matrix P (m | m):
2.2 establishing Kalman Filter model based on vector Block State estimation method
2.2.1 first, assume that the optimal estimate of the m-th vector chunk state has been obtained
And corresponding estimation error covariance matrix
2.2.2 based on
And
further obtaining the predicted value
And prediction estimation error covariance
2.2.3 calculate optimal gain array:
2.2.4 obtaining the optimal estimation value of the state block X (m +1)
And estimate error covariance
P(m+1|m+1)＝[I-K(m+1)H(m+1)P(m+1,m)](22)
2.2.5, continuing to loop the process of 2.2.2-2.2.4 until the filtering is finished;
and step 3: establishing Kalman filtering based block state real-time smooth estimation, filtering estimation and prediction estimation
3.1 first, formula (12) in step 2 is rewritten as follows:
y(m+1,k)＝H(m+1,k)X(m+1)+ν(m+1,k),m＝1,2,…；k＝1,2,…,M (23)
3.2, a real-time smooth estimation model is established, and real-time updating estimation is carried out on states x (m +1,1), x (m +1,2), L and x (m +1, k-1) before the current time k, wherein the model is as follows:
3.3, establishing a real-time filtering estimation model, and updating and estimating the state x (m +1, k) at the current k moment in real time, wherein the model is as follows:
3.4 establish a real-time prediction estimation model, and carry out real-time prediction estimation on states x (M +1, k +1), x (M +1, k +2), L, x (M +1, M) after the current k moment, wherein the model is as follows:
3.5, taking a formula (11) as a state equation, and taking a formula (23) as a state model of a measurement equation to carry out a Kalman filter model;
3.6 building a Kalman Filter model in the Multi-State vector Block
3.6.1 first, assume that the optimal estimate for the mth time instant in the mth state block X (M) is known
Sum estimation error covariance matrix
3.6.2 based on
And
further obtaining a prediction value and a prediction estimation error covariance of the (m +1) th block state:
3.6.3 further results in an intra-block recursive filter:
3.6.4 loops through the 3.6.2-3.6.3 process until the filtering is complete.
2. The method for filtering estimation and prediction estimation of state variables of an electric power system according to claim 1, characterized in that the modeling noise w (k) and the measurement noise v (k) satisfy the following statistical characteristics:
wherein Q (k) and R (k) are both error variance matrices, and the error variance matrices Q (k) and R (k) are symmetric non-negative definite matrices and symmetric positive definite matrices, respectively, S (k) ∈ Rn×m。
3. The method for filter estimation and prediction estimation of state variables of power system according to claim 1, wherein the equations (11) and (12) are shown in the following formulas
R(m+1)＝diag{R(m+1,1),R(m+1,2),…,R(m+1,M)}，
4. The method of claim 1The method for filtering estimation and prediction estimation of state variables of the power system is characterized in that measurement noise v (m, k) in the formula (23) has the following statistical characteristic E { ν (m, k) } 0; e { v (m, k) vT(m,j)}＝R(m,k)kjm＝1,2,…，k,j＝1,2,…,M。
5. The method for filter estimation and prediction estimation of state variables of power system according to claim 1, characterized in that in the formula (39)
6. The method for filtering estimation and prediction estimation of state variables of an electric power system according to claim 1, wherein before the step 1, a sensor model of each state variable is established:
yi(t)＝hi(x(t))+νi(t)，i＝1,2,…,N (40)
where N represents the number of sensors, X (t) represents a model of a state variable, hi(. cndot.) is a continuous function;
then, after the equation (40) is discretized by the equal period T, a discrete observation equation is obtained, wherein the discrete observation equation is
yi(kT)＝hi(x(kT),kT)+νi(kT)，i＝1,2,…,N (41)
Wherein h isiDenotes the measurement function of the corresponding sensor i, determined by the properties of the sensor, vi(kT) denotes measurement error; next, the time-dependent order of the state variables x (kT) is established as followsColumn model
x((k+1)T)＝f(x(kT),kT)+w(kT) (42)
Where f (x), (k), k ═ a (k +1, k) x (k) is a state transfer function, and w (kt) represents a modeling error.
7. The method for filter estimation and prediction estimation of state variables of an electric power system according to claim 1, characterized in that the multi-state variables comprise state variables of distributed power generation units and state variables of loads using electricity.
8. The method for filtering estimation and prediction estimation facing to state variables of power system according to claim 1, wherein the time period in step 2 includes one hour, one day, one week, one month or one year.
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