CN105305440B - The hyperbolic cosine type maximal index absolute value Robust filter method of POWER SYSTEM STATE - Google Patents

Abstract

The invention discloses the hyperbolic cosine type maximal index absolute value Robust filter methods for the POWER SYSTEM STATE for belonging to dispatching automation of electric power systems field.Including step：Extract the active active and idle, branch of electric system node injection and reactive power and node voltage amplitude parameter；Hyperbolic cosine type maximal index absolute value robust state estimation basic model is established with this；Auxiliary variable is introduced to the hyperbolic cosine type maximal index absolute value robust state estimation basic model, has obtained hyperbolic cosine type maximal index absolute value robust state estimation equivalence model；And using former dual interior point, the hyperbolic cosine type maximal index absolute value robust state estimation equivalence model is solved.Sample calculation analysis shows that the present invention has very strong Robustness least squares and very high computational efficiency, has good future in engineering applications.

Description

Hyperbolic cosine maximum exponent absolute value robust estimation method for power system state

Technical Field

The invention belongs to the field of power system dispatching automation, and particularly relates to a hyperbolic cosine type maximum exponential absolute value robust estimation method for a power system state.

Background

Power system state estimation is the basis and core of an energy management system. Almost every large dispatch center now has installed a state estimator, and state estimation has become the cornerstone of safe operation of the power grid. Since 1970 foreign scholars first proposed state estimation, the research and application of state estimation has been carried out for over 40 years, and various state estimation methods have emerged in the meantime.

At present, the most widely used state estimation at home and abroad is Weighted Least Squares (WLS). The WLS model is simple and easy to solve, but the WLS model has poor tolerance. To enhance resistance to degradation, there are generally two approaches. The first method is to add bad data identification link after WLS estimation, such as maximum regularization residual error detection (LNR) or estimation identification method; the other is to use robust state estimation. Currently, Robust state estimation methods (Robust state estimation) proposed by scholars at home and abroad include Weighted least absolute value estimation (WLAV), non-quadratic criterion methods (QL, QC, etc.), state estimation with a Maximum yield (MNMR), and exponential objective function state estimation (MES), etc. The estimation performance of these robust state estimation methods still remains to be improved.

Disclosure of Invention

The invention aims to provide a hyperbolic cosine type maximum exponent absolute value robust estimation method for the state of an electric power system, which is characterized by being based on hyperbolic cosine type maximum exponent absolute value robust state estimation with good robust performance and high calculation efficiency; the method comprises the following steps:

a, extracting active power and reactive power injected into a node of a power system, branch active power and reactive power, and a node voltage amplitude parameter; thus establishing a hyperbolic cosine maximum exponential absolute value robust state estimation basic model;

b, introducing auxiliary variables into the hyperbolic cosine type maximum exponent absolute value robust state estimation basic model, and transforming to obtain a hyperbolic cosine type maximum exponent absolute value robust state estimation equivalent model;

and C, solving the hyperbolic cosine maximum exponent absolute value robust state estimation equivalent model by using a primary-dual interior point algorithm.

The hyperbolic cosine maximum exponential absolute value robust state estimation basic model of the step A is as follows:s.t.g(x)＝0，r＝z-h(x)，

wherein: z is equal to R^mFor measuring vectors, active and reactive power are injected into nodes, branch active and reactive power are injected into nodes, and node voltage amplitude values are measuredMeasuring; x is formed by RⁿThe state vector comprises the voltage amplitude of the node and the phase angles of other nodes except the balanced node; h is Rⁿ→R^mIs a non-linear mapping from the state vector to the measurement vector; r is_iIs the ith element of the residual vector r; g (x) Rⁿ→R^cConstraint for zero injection power equality; w is a_iThe weight, σ, measured for the ith quantity₀And σ₁Is a window width parameter.

The step B comprises the following steps: introducing non-negative relaxation variables u, v epsilon R^mThe hyperbolic cosine maximum exponential absolute value robust state estimation equivalent model obtained through transformation is as follows:s.t.g(x)＝0，z-h(x)-u+v＝0，u,v≥0。

and step C, solving the hyperbolic cosine type maximum exponent absolute value robust state estimation equivalent model by using a prime-dual interior point algorithm, specifically, enabling x to be⁽⁰⁾∈RⁿRepresents a flat start state variable (except for the reference node phase angle) consisting of all node voltage magnitudes and phase angles;

the step C comprises the following steps:

step C1: introducing Lagrangian functions

In the formula: λ ∈ R^cAnd pi, α e R^mIs a lagrange multiplier vector;

let x be a flat start state variable; selection of lambda⁽⁰⁾＝π⁽⁰⁾0 and u⁽⁰⁾,v⁽⁰⁾,α⁽⁰⁾,β⁽⁰⁾>0, where λ ∈ R^cAnd pi, α e R^mIs a lagrange multiplier vector, m is the number of measurements and c is the number of zero injection power constraints; let the central parameter rho epsilon (0,1) and the convergence criterion epsilon be 10^-3In a layer stackThe generation counter k is 0;

step C2, calculating the dual Gap (Gap) α^Tv+β^Tu, judging whether convergence occurs or not, if Gap<E, turning to the step C7, otherwise, entering the step C3;

step C3: solving a correction equation to finish the correction of the original variable and the dual variable to obtain [ dx ]^Tdλ^Tdπ^T]^TDv, du, d α and d β, specifically including:

step C31: calculating a disturbance parameter mu which is rho. Gap/2 m;

step C32: forming a Jacobian matrix corresponding to the measurement equation and the zero injection power constraintAndforming a Hessian matrix corresponding to the measurement equation and the zero injection power constraintAndwherein h (x) is the mapping from the state vector to the measurement vector, i.e. the measurement estimation value, and g (x) is 0, i.e. the zero injection power constraint;

step C33: calculating L_x＝G^Tλ-H^Tπ，L_λ＝g(x)，L_π＝z-h(x)-u+v， And

step C34 calculating γ ═ z-h (x) -u + v + AA-BB,

wherein AA, BB ∈ R^m，

Step C35: solving equationsTo obtain [ dx ]^Tdλ^Tdπ^T]^T；

Step C36: solving for dv_i＝k_1idπ_i+AA_iAnd du_i＝k_2idπ_i+BB_iWherein k is_1i＝a_iv_i-b_iu_i，k_2i＝c_iv_i-d_iu_i(ii) a And step C37: solving forAnd

step C4: calculating the correction step length theta of the original problem and the dual problem_PAnd theta_DWherein:

step C5: the variables that correct the original problem and the dual problem respectively are:

step C6: let the iteration counter k be k +1, go to step C2;

step C7: and outputting the optimal solution, and ending.

The hyperbolic cosine maximum exponent absolute value robust state estimation method has the advantages that the hyperbolic cosine maximum exponent absolute value robust state estimation can effectively restrain a plurality of bad data including the bad data of consistency in the estimation process, shows good robust performance, has high calculation efficiency, and is very suitable for practical engineering application. And solving the hyperbolic cosine maximum exponential absolute value robust state estimation equivalent model. The analysis of the examples shows that the method has strong tolerance, high calculation efficiency and good engineering application prospect.

Detailed Description

The invention provides a hyperbolic cosine maximum exponent absolute value robust estimation method of a power system state, and the invention is described in detail by combining with an embodiment.

The hyperbolic cosine maximum exponential absolute value robust estimation method of the state of the power system comprises the following steps:

step A: extracting active power and reactive power injected into nodes of the power system, branch active power and reactive power, and node voltage amplitude parameters; thus, a hyperbolical cosine maximum exponential absolute value robust state estimation (COSH-MEAV) basic model is established.

The basic model of COSH-MEAV is shown below

s.t.g(x)＝0 (2)

r＝z-h(x) (3)

In the formula: z is equal to R^mFor measuring vectors, the method usually comprises node injection active and reactive power, branch active and reactive power, node voltage amplitude measurement and the like; x is formed by RⁿA state vector comprising the node voltage magnitude and phase angle (excluding the balanced node phase angle); h is Rⁿ→R^mIs a non-linear mapping from the state vector to the measurement vector; r is_iIs the ith element of the residual vector r; g (x) Rⁿ→R^cConstraint for zero injection power equality; w is a_iThe weight, σ, measured for the ith quantity₀And σ₁Is a window width parameter.

And B: and introducing auxiliary variables into the hyperbolic cosine type maximum exponent absolute value robust state estimation basic model, and transforming to obtain the hyperbolic cosine type maximum exponent absolute value robust state estimation equivalent model.

Specifically, the objective function of the COSH-MEAV basic model, although continuous everywhere, is not derivable at 0, and thus it is difficult to directly solve. The models (1) - (3) can be converted into a everywhere derivable equivalent model.

Introducing a variable ξ ∈ R^mTo make it satisfy

|r_i|≤ξ_ii＝1,…,m (4)

Obtainable from the formulae (1) and (4),maximum equivalence isAnd max.

Introducing non-negative relaxation variables l, k epsilon to R^mThe inequality (4) is converted into two equalities and constrained to

r_i-l_i＝-ξ_ii＝1,…,m (5)

r_i+k_i＝ξ_ii＝1,…,m (6)

Introducing non-negative relaxation variables u, v epsilon R^mTo make it satisfy

u_i＝l_i/2 i＝1,…,m (7)

v_i＝k_i/2 i＝1,…,m (8)

From the formulae (5) to (8), it can be obtained

r_i＝u_i-v_ii＝1,…,m (9)

ξ_i＝u_i+v_ii＝1,…,m (10)

Bringing formula (9) into formula (3) can obtain the equivalent measurement constraint of

z-h(x)-u+v＝0 (11)

The equivalent model of the COSH-MEAV basic model given by the formulas (1) to (3) is

s.t.g(x)＝0 (13)

z-h(x)-u+v＝0 (14)

u,v≥0 (15)

The models (12) - (15) are COSH-MEAV equivalent models which are continuously derivable everywhere and can be solved by a gradient-based method.

And C: and solving the hyperbolic cosine maximum exponential absolute value robust state estimation equivalent model by using a primary-dual interior point algorithm.

(1) Solving method of COSH-MEAV equivalent model

It is noted that the COSH-MEAV equivalent models (12) - (15) are an optimization problem containing equality constraints and inequality constraints, and are suitable for solving by using a prime-dual interior point algorithm. For a better understanding of the invention for those skilled in the art, a detailed derivation is first given as follows:

introducing Lagrangian functions

In the formula: λ ∈ R^cAnd pi, α e R^mIs a lagrange multiplier vector.

To obtain the optimum value, the KKT condition can be used

In the formula:

in order to effectively solve the problems, the modern interior point method introduces a perturbation parameter mu >0 to relax the equations (22) and (23), thereby obtaining

The above equation can be solved by Newton method

Gdx＝-L_λ(27)

-Hdx-du+dv＝-L_π(28)

Wherein,

from the formulae (29) and (30), it is possible to obtain

By bringing the formulae (33), (34) into (31), (32)

Order toFrom the formulae (35) and (36)

dv_i＝k_1idπ_i+AA_i(37)

du_i＝k_2idπ_i+BB_i(38)

In the formula: k is a radical of_1i＝a_iv_i-b_iu_i,k_2i＝c_iv_i-d_iu_i，

By bringing the formulae (37), (38) into (28)

Hdx+Qdπ＝γ (39)

In the formula: q is R^m×mA diagonal matrix of diagonal elements Q_ii＝-k_1i+k_2i；γ＝z-h(x)-u+v+AA-BB，AA,BB∈R^m，AA_i,BB_iThe same as in formulae (37) and (38).

According to the equations (39), (26) and (27), the correction equation can be obtained as

The iteration can be continued by solving equation (40) to obtain dx, d λ and d π, equations (37) and (38) to obtain dv and du, and bringing the results into equations (33) and (34) to obtain d α and d β.

(2) Solving step of COSH-MEAV equivalent model

After introducing the derivation process of solving the COSH-MEAV equivalent model, the inventors summarize the solving steps as follows:

step C1, initializing to let x be flat start state variable; selection of lambda⁽⁰⁾＝π⁽⁰⁾0 and u⁽⁰⁾,v⁽⁰⁾,α⁽⁰⁾,β⁽⁰⁾>0; let the central parameter rho epsilon (0,1) and determine the convergence criterion value, and set the iteration counter to zero.

Specifically, let x⁽⁰⁾∈RⁿRepresents a flat start state variable (except for the reference node phase angle) consisting of all node voltage magnitudes and phase angles; selection of lambda⁽⁰⁾＝π⁽⁰⁾0 and u⁽⁰⁾,v⁽⁰⁾,α⁽⁰⁾,β⁽⁰⁾>0, where λ ∈ R^cAnd pi, α e R^mFor Lagrange multiplier vectors, m is the number of measurements and c is the number of zero injection power constraintsCounting; let the central parameter rho epsilon (0,1) and the convergence criterion epsilon be 10^-3And setting an iteration counter k to be 0.

Step C2, calculating the dual Gap (Gap) α^Tv+β^TAnd u, judging whether convergence occurs or not. In particular, if Gap<ε, then consider convergence and go directly to step C7; otherwise, the procedure proceeds to step C3.

Step C3: solving a correction equation to finish the correction of the original variable and the dual variable to obtain [ dx ]^Tdλ^Tdπ^T]^TDv, du, d α and d β.

Specifically, first, the perturbation parameter μ ═ ρ · Gap/2m is calculated, and then [ dx ] is obtained by solving equation (40)^Tdλ^Tdπ^T]^TSolving the formulas (37) and (38) to obtain dv, du, and solving the formulas (33) and (34) to obtain d α and d β.

Step C4: calculating the correction step length theta of the original problem and the dual problem_PAnd theta_DWherein:

step C5: the variables that correct the original problem and the dual problem respectively are:

step C6: let the iteration counter k be k +1, go to step C2; and

step C7: and outputting the optimal solution, and ending.

For a better understanding of the present invention and to show the advantages thereof over the prior art, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration specific embodiments.

Setting and utilizing IEEE standard system to check COSH-MEAV performance based on primal-dual interior point algorithmCan be used. The test uses full measurements, and the measured values are obtained by superimposing white noise (mean 0, standard deviation τ) on the results of the load flow calculation. For voltage measurement, take τ_V0.005 p.u.; for power measurements, take τ_PQ1 MW/MVar. The test environment is a PC, the CPU is Intel (R) core (TM) i3M370, the main frequency is 2.40GHz, and the memory is 2.00 GB.

1. Comparison of resistance to poor Performance

The inventors compared COSH-MEAV of the present invention with other state estimators to test the robustness of COSH-MEAV.

Setting 4 bad consistency data (P) on IEEE-14 system_1-2、Q_1-2、P₁、Q₁). The set poor measurement value and the measured accurate value are shown in table 1.

TABLE 1 COSH-MEAV IDENTIFICATION OF WEIED CONSISTENCY DATA IN IEEE 14 SYSTEMS

For comparison, first, the estimation is performed by using a widely used WLS, and the identification of bad data is performed by using LNR (abbreviated as WLS + LNR). The first recognition result is: the normalized residual of the 10 quantitative measures is greater than the threshold (3.0), the 10 quantitative measures being considered suspect data; where the maximum normalized residual measure is P_2-1The WLS is operated again after the measurement is deleted; at this time, P is found₂Normalized residual of (a) is maximal. The above process cycles 4 times, with 4 good measurements being discarded by the LNR as misinterpreted as suspect data, but true bad data still exists. It can be seen that WLS + LNR cannot identify poorly consistent data.

The evaluation results of applying the COSH-MEAV method are shown in Table 1. It was found that the estimated value of COSH-MEAV matched well with the true value even if there was poor consistency data in the measurement. Multiple tests of other IEEE systems also show that COSH-MEAV can automatically restrain bad data in the estimation process and has good tolerance.

2. Comparison of computational efficiencies

For efficiency comparison, the inventors tested four state estimators, WLS, WLAV, MNMR and COSH-meas, respectively, under normal metrology conditions, the latter three belonging to robust state estimators. In the test, the WLS is solved by a Newton method, and the other three state estimations are solved by an interior point method; and the MNMR adopts a two-stage method, namely, the WLS estimation is carried out in the first stage, and the estimation value of the WLS is calculated as the initial value of the MNMR estimation in the second stage.

The number of iterations and average computation time for convergence of the state estimates are shown in table 2 for a total of 50 simulation experiments. As can be seen from table 2, WLS is most computationally efficient among the four state estimators; in the last three robust state estimators, COSH-MEAV has the highest computational efficiency; and as the system scale increases, the number of iterations and the calculation time of COSH-MEAV increase slowly, so that COSH-MEAV is suitable for estimation of a practical large-scale system.

In conclusion, the COSH-MEAV provided by the invention can effectively inhibit a plurality of bad data including the bad data of consistency in the estimation process, shows good tolerance, has high calculation efficiency and is very suitable for practical engineering application.

TABLE 2 number of iterations and computation time for the four state estimators

Claims (1)

1. The hyperbolic cosine type maximum exponent absolute value robust estimation method of the state of the electric power system is based on hyperbolic cosine type maximum exponent absolute value robust state estimation with good robust performance and high calculation efficiency; the method comprises the following steps:

a, extracting active power and reactive power injected into a node of a power system, branch active power and reactive power, and a node voltage amplitude parameter; the method for establishing the hyperbolic cosine maximum exponential absolute value robust state estimation basic model comprises the following steps:

wherein: z is equal to R^mMeasuring vectors, including node injection active and reactive power, branch active and reactive power and node voltage amplitude measurement; x is formed by RⁿThe state vector comprises the voltage amplitude of the node and the phase angles of other nodes except the balanced node; h is Rⁿ→R^mIs a non-linear mapping from the state vector to the measurement vector; r is_iIs the ith element of the residual vector r; g (x) Rⁿ→R^cConstraint for zero injection power equality; w is a_iThe weight, σ, measured for the ith quantity₀And σ₁Is a window width parameter;

b, introducing auxiliary variables into the hyperbolic cosine type maximum exponent absolute value robust state estimation basic model, and transforming to obtain a hyperbolic cosine type maximum exponent absolute value robust state estimation equivalent model; introducing non-negative relaxation variables u, v epsilon R^mThe hyperbolic cosine maximum exponential absolute value robust state estimation equivalent model obtained through transformation is as follows:s.t. g (x) 0, z-h (x) -u + v 0, u, v ≧ 0; it is characterized in that the preparation method is characterized in that,

c, solving the hyperbolic cosine maximum exponent absolute value robust state estimation equivalent model by using a primary-dual interior point algorithm; specifically, let x⁽⁰⁾∈RⁿRepresenting a flat start state variable consisting of all node voltage magnitudes and phase angles, with the exception of the reference node phase angle; the step C comprises the following steps:

step C1: introducing Lagrangian functions

In the formula: λ ∈ R^cAnd pi, α e R^mIs a lagrange multiplier vector;

let x be a flat start state variable; selection of lambda⁽⁰⁾＝π⁽⁰⁾0 and u⁽⁰⁾,v⁽⁰⁾,α⁽⁰⁾,β⁽⁰⁾>0, where λ ∈ R^cAnd pi, α e R^mIs a lagrange multiplier vector, m is the number of measurements and c is the number of zero injection power constraints; let the central parameter rho epsilon (0,1) and the convergence criterion epsilon be 10^-3Setting an iteration counter k to be 0;

step C2, calculating the dual Gap (Gap) α^Tv+β^Tu, judging whether convergence occurs or not, if Gap<E, turning to the step C7, otherwise, entering the step C3;

step C3: solving a correction equation to finish the correction of the original variable and the dual variable to obtain [ dx ]^Tdλ^Tdπ^T]^TDv, du, d α and d β, specifically including:

step C31: calculating a disturbance parameter mu which is rho. Gap/2 m;

step C32: forming a Jacobian matrix corresponding to the measurement equation and the zero injection power constraintAndforming a Hessian matrix corresponding to the measurement equation and the zero injection power constraintAndwherein h (x) is the mapping from the state vector to the measurement vector, i.e. the measurement estimation value, and g (x) is 0, i.e. the zero injection power constraint;

step C33: calculating L_x＝G^Tλ-H^Tπ，L_λ＝g(x)，L_π＝z-h(x)-u+v， And

step C34 calculating gamma-z-h (x) -u + v + AA-BB, where AA, BB e R^m，

Step C35: solving equationsTo obtain [ dx ]^Tdλ^Tdπ^T]^T；

Step C36: solving for dv_i＝k_1idπ_i+AA_iAnd du_i＝k_2idπ_i+BB_iWherein k is_1i＝a_iv_i-b_iu_i，k_2i＝c_iv_i-d_iu_i；

Step C37: solving forAnd

step C4: calculating the correction step length theta of the original problem and the dual problem_PAnd theta_DWherein:

step C5: the variables that correct the original problem and the dual problem respectively are:

step C6: let the iteration counter k be k +1, go to step C2;

step C7: and outputting the optimal solution, and ending.