JP6518941B2 - Critical failure removal time calculation device, critical failure removal time calculation method, and program - Google Patents

Description

  The present invention relates to a critical failure removal time calculation device, a critical failure removal time calculation method, and a program.

  If a fault such as a ground fault occurs in some of the transmission lines in the power system, the generator accelerates and becomes unstable. At this time, if the failure is removed by a relay or the like within a sufficiently short time, the power system becomes stable, but if it takes a long time to remove the failure, the power system becomes unstable. The boundary between such stability and instability is called critical, and the failure removal time that becomes critical is called the critical clearing time (CCT).

  An outline of critical fault removal time and its calculation method will be described with reference to FIGS. 1 and 2. FIG. 1 is a schematic diagram showing the state of a one-machine infinite bus system without braking represented by a locus of a phase angle δ and an angular velocity ω of a generator. FIG. 2 is a schematic view in which the discretized multidimensional state variable is represented by Euclidean distance ε.

  In FIG. 1, the state of the power system changes with time from the stable equilibrium point PA along the failure locus 1 due to the occurrence of a failure. At this time, when the fault is removed in a time (point PB) shorter than the time from the stable equilibrium point PA to the point PC, the state of the power system changes along the trajectory 2 and can be restored to a certain stable state. . On the other hand, when the failure is removed in a time (point PD) longer than the time from the stable equilibrium point PA to the point PC, the state of the power system diverges along the trajectory 3 and can not recover to the stable state. Then, when the fault is removed at point PC on fault locus 1, the state of the power system takes a time of infinity in theory along critical locus 3 and a dominant unstable equilibrium point PE (Controlling Unstable Equilibrium Point: It is supposed to reach CUEP). The time from such a stable equilibrium point PA to the point PC is the critical fault removal time.

Patent Literatures 1 and 2 disclose an example of such a method of calculating the critical failure removal time. As shown in FIG. 2, the fault is a point on the trajectory 1 and the time of failure removal of power system state (PC points shown in FIG. 1) is defined as a multidimensional state variables x ^0. Since the multidimensional state variable x ⁰ is a point on the fault locus 1, it can be expressed as a function of the fault removal time τ represented by the following equation.

また、故障除去後の電力系統の状態を、離散的な時刻ｔ^ｋ(１≦ｋ≦ｍ＋１)の順に多次元状態変数ｘ^１，ｘ^２，・・ｘ^ｍ，ｘ^ｍ＋１と定義する。多次元状態変数ｘ^ｋ（０≦ｋ≦ｍ＋１）は、それぞれ複数の成分から成る多次元変数（ベクトル）である。

Further, the state of the power system after the fault removal is defined as multidimensional state variables x ¹ , x ² ,... X ^m , x ^{m + 1 in} the order of discrete time t ^k (1 ≦ k ≦ m + 1). Multidimensional state variables x ^k (0 ≦ k ≦ m + 1) are multidimensional variables (vectors) each composed of a plurality of components.

Then, the multidimensional state variable x ⁰ (k = 0) is a vector corresponding to the critical fault removal time, and the multidimensional state variable x ^{m + 1} (k = m + 1) is a vector at the dominant unstable equilibrium point CUEP. And, the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) is a critical locus 3 from the state of the power system from the state at fault removal (x ⁰ ) to the state of dominant unstable equilibrium (x ^{m + 1} ) Configure Such a multidimensional state variable x ^k can be regarded as a solution of the following multidimensional non-linear equation (power system equation) representing the non-linear state of the power system.

この（式１．２）に対して台形公式を適用することで、相互に隣接する多次元状態変数ｘ^ｋ及びｘ^ｋ＋１は、次式で関係付けられる。ここに、εは、多次元状態変数ｘ^ｋ及びｘ^ｋ＋１の間のユークリッド距離を表している。

By applying the trapezoidal rule to this (Equation 1.2), the multidimensional state variables x ^k and x ^{k + 1} adjacent to each other are related by the following equation. Here, ε represents the Euclidean distance between multidimensional state variables x ^k and x ^{k + 1} .

ところで、臨界軌跡３の終点である多次元状態変数ｘ^ｍ＋１は、一般的に支配的不安定平衡点ＣＵＥＰであると考えられる。そこで、（式１．３）に関する制約条件は、臨界軌跡３の終点ｘ^ｍ+1を支配的不安定平衡点ＣＵＥＰの所定値を表したｘ^ｕとして指定する場合には、次の（式１．４）となり、あるいは、臨界軌跡３の終点ｘ^ｍ＋１を支配的不安定平衡点ＣＵＥＰの状態を表した平衡条件として指定する場合には、（式１．５）となる。

By the way, multidimensional state variable x ^{m + 1} which is an end point of critical trajectory 3 is generally considered to be a dominant unstable equilibrium point CUEP. Therefore, when specifying the end point x ^{m + 1} of the critical trajectory 3 as x ^u representing a predetermined value of the dominant unstable equilibrium point CUEP, the constraint condition related to (Equation 1.3) is the following (Equation 1 Or when the end point x ^{m + 1} of the critical locus 3 is designated as the equilibrium condition representing the state of the dominant unstable equilibrium point CUEP, equation (1.5).

従って、上述した（式１．１）−（式１．３）、及び、臨界軌跡３の終点ｘ^ｍ＋１の制約条件である（式１．４）又は（式１．５）による多元連立方程式を解くことによって、臨界軌跡３の始点ｘ^０、ひいては臨界となる故障除去時間τを求めることができる。

Therefore, the multiple simultaneous equations according to (Equation 1.1)-(Equation 1.3) described above and (Equation 1.4) or (Equation 1.5) which is a constraint condition of the end point x ^{m + 1} of the critical trajectory 3 By solving, the starting point x ⁰ of the critical trajectory 3 and hence the critical failure removal time τ can be determined.

However, when the multiple simultaneous equations of (Equation 1.3) are directly solved, there is a possibility that numerical errors resulting from the trapezoidal rule may be accumulated and maximized at the end point x ^{m + 1} of the critical trajectory 3. For this reason, the left side of (Equation 1.3) is treated as an error vector, and unknown variables τ, ε, x ¹ , x which minimize the sum of error vectors (norms) as in the following (Equation 1.6) ² ... X ^m , x ^{m + 1} are obtained at once.

JP 2007-53836 A Patent No. 4517106

  However, if the unstable equilibrium point is specified as the end point of the critical trajectory and the calculation is performed, a solution may not be obtained.

  Therefore, the present invention aims to reliably obtain a solution in the calculation of critical failure removal time.

として定義される電力系統方程式に従う複数の多次元状態変数ｘ^ｋ（１≦ｋ≦ｍ＋１：ｋ、ｍは整数）と、前記多次元状態変数ｘ^０ないしｘ^ｍ＋１の中で相互に隣接する多次元状態変数ｘ^ｋ及びｘ^ｋ＋１の間の移動時間Δｔと、を用いて

として定義される第１の誤差ベクトルμ_ＴＺ ^ｋと、前記電力系統のポテンシャルエネルギーが前記始点から前記終点に向かって前記軌跡に沿って変化する方向と、前記故障の除去後の安定平衡点から見た前記終点の方向と、の内積を成分として含む第２の誤差ベクトルμ_Ｅと、正の対角要素を有する正方の対角行列Ｗと、を用いて

として定義される目的関数を最小化する第１の情報装置と、前記目的関数が最小化されたときの前記多次元状態変数ｘ^０及び当該多次元状態変数ｘ^０に対応する前記故障除去時間τを求める第２の情報装置と、を備える。 The main present invention for solving the above-mentioned problems is the criticality of the time when recovery becomes possible after failure of the power system in which a plurality of generators are connected, and the time when recovery becomes impossible after failure of the power system. Critical fault removal time calculating device for determining a fault removal time, the multidimensional state variable x ⁰ which is a function of the fault removal time τ and represents the state of the power system when the fault is removed; between the multi-dimensional state state variables x ⁰ indicates the end point of the trajectory representing a temporal change in state of the power system as a start point variables x ^{m + 1 (m} is an integer), and the multi-dimensional state variable x ⁰ and x ^{m + 1} Discretized with

And a plurality of multidimensional state variables x ^k (1 ≦ k ≦ m + 1: k, m is an integer) according to the power system equation defined as and multidimensional states adjacent to each other among the multidimensional state variables x ⁰ to x ^{m + 1} Using a movement time Δt between state variables x ^k and x ^{k + 1}

A first error vector μ _TZ ^k defined as, a direction in which the potential energy of the power system changes along the trajectory from the start point to the end point, and a stable equilibrium point after removal of the fault Using a second error vector μ _E including the inner product of the direction of the end point as a component, and a square diagonal matrix W having positive diagonal elements

A first information device that minimizes the objective function defined as, wherein the clearing time the objective function corresponds to the multidimensional state variables x ⁰ and the multi-dimensional state variables x ⁰ when it is minimized τ A second information device for obtaining

  Other features of the present invention will become apparent from the accompanying drawings and the description of the present specification.

  According to the present invention, it is possible to reliably obtain a solution in the calculation of critical failure removal time.

It is a schematic diagram which represented the state of one machine infinite bus system without braking by the locus of phase angle delta of a generator, and angular velocity omega. It is a schematic diagram which displays the multidimensional state variable discretized by Euclidean distance (epsilon). It is a schematic diagram which displays the multidimensional state variable discretized by movement distance (DELTA) t. It is a flowchart which shows the calculation method of critical fault removal time. It is a figure which shows the structure of a critical fault removal apparatus.

  At least the following matters will be made clear by the present specification and the description of the accompanying drawings.

=== Calculation method of critical failure removal time ====
A method of calculating the critical failure removal time according to the present embodiment will be described with reference to FIGS. 2 and 3. In FIG. 2 and FIG. 3, the state of the power system is a multidimensional state variable x ^k (0 ≦ k ≦ m + 1; k, discretized at discrete time t ^k (0 ≦ k ≦ m + 1; m is an integer) m is an integer). The multidimensional state variable x ^k is a state variable vector including an element ^represented by the following equation.

ただし、ω_ｉ ^ｋ、θ_ｉ ^ｋは、離散的な時刻ｔ^ｋにおける発電機ユニットｉ（ｉ＝１〜ｎ）の角周波数、位相角をそれぞれ表わす。

Here, ω _i ^k and θ _i ^k respectively represent the angular frequency and phase angle of the generator unit i (i = 1 to n) at discrete time t ^k .

The state of the power system in this embodiment is expressed by the non-linear equation (power system equation) of the following equation using the state variable vector x ^k and the multidimensional function f described above.

あるいは、上述の電力系統方程式は、状態変数ｘ^ｋと従属変数ｙ^ｋとを用いて、等価なシステム表現である次式で表されてもよい。

Alternatively, the power system equation described above may be expressed by the following equation, which is an equivalent system expression, using the state variable x ^k and the dependent variable y ^k .

ここでは、電力系統の臨界軌跡３を、（式２．２）で表現された非線形方程式の解（つまり、状態変数ベクトルｘ^ｋ）として求め、この解に基づいて臨界となる故障除去時間τを算出することとする。もっとも、非線形方程式は（式２．３）で表現されてもかまわない。

Here, the critical locus 3 of the power system is determined as the solution of the nonlinear equation expressed by (Equation 2.2) (that is, the state variable vector x ^k ), and the fault removal time τ which becomes critical based on this solution is obtained. It will be calculated. However, the non-linear equation may be expressed by (Equation 2.3).

In this embodiment, error vectors μ _TZ , μ _I and μ _E are formulated based on the following (a) to (c) in order to obtain the critical locus 3 of the power system, and the square sum of these formulas is displayed Since the solution which minimizes the objective function to be calculated is calculated, it will be described in detail below.
(A) Two adjacent points on the critical locus satisfy the trapezoidal rule.
(B) The start point of the critical locus is on the fault locus (initial condition).
(C) The end point of the critical trajectory (also called an end point) satisfies the end condition.

<< Trapezoid formula >>
The approximation of the trapezoidal rule is applied to solve the non-linear equation of (Equation 2.2) numerically. Then, the following equation is established between the multidimensional state variables x ^k and x ^{k + 1} (1 ≦ k ≦ m) adjacent to each other.

また、移動時間Δｔを、多次元状態変数ｘ^ｋ，ｘ^ｋ＋１の間を移動する時間（ｔ^ｋ＋１−ｔ^ｋ）として定義する。この移動時間Δｔを用いて（式２．４）を表現すると、次のようになる。

Also, define the travel time Delta] t, as a multidimensional state variable ^{x k,} time to move between ^{x k + 1 (t k +} 1 -t k). Expressing (Expression 2.4) using this movement time Δt, the following is obtained.

この（式２．５）から、次式で定義される第１の誤差ベクトルμ_ＴＺ ^ｋを得る。

From this (Equation 2.5), a first error vector μ _TZ ^k defined by the following equation is obtained.

あるいは、隣接する多次元状態変数ｘ^ｋ，ｘ^ｋ＋１の間のユークリッド距離εを

Alternatively, the Euclidean distance ε between adjacent multidimensional state variables x ^k and x ^{k + 1} is

として定義すると、上述した（式２．５）は、次式で表される。

When defined as, the above (Equation 2.5) is represented by the following equation.

よって、第１の誤差ベクトルμ_ＴＺ ^ｋは、上述したユークリッド距離εを用いて、次式として定義されてもよい。

Therefore, the first error vector μ _TZ ^k may be defined as the following equation using the Euclidean distance ε described above.

なお、（式２．６）、（式２．９）をまとめて表現すると、次式で表される。

It is to be noted that (Expression 2.6) and (Expression 2.9) can be expressed collectively by the following expression.

なお、計算の実行にあたっては、移動距離Δｔ，ユークリッド距離εのいずれを用いても差し支えない。また、計算時間の短縮と計算の安定性を両立させるべく、最初の数回の反復計算ではユークリッド距離εを用い、それ以降の計算では移動距離Δｔを用いてもよい。

Note that either of the movement distance Δt and the Euclidean distance ε may be used in the execution of the calculation. In addition, in order to make the calculation time shorter and the calculation stability compatible, the Euclidean distance ε may be used in the first few iterations, and the movement distance Δt may be used in the subsequent calculations.

<< Initial conditions >>
As described above, the starting point x ⁰ of the critical trajectory 3 is on the fault trajectory 1. This condition can be expressed by the following equation because it means that the variable vector x ⁰ is based on the fault removal time τ at which it becomes critical.

＜＜終端条件＞＞
本実施形態では、臨界軌跡３の終点ｘ^ｍ＋１の満たすべき終端条件として、（ｉ）ポテンシャルエネルギーの条件、（ｉｉ）運動エネルギーの条件、及び（ｉｉｉ）２点間の距離の最小化、の３つを用いる。上記（ｉ）ポテンシャルエネルギーの条件は、解を確実に得るために有効な条件であり、残りの２つの条件は、適宜ポテンシャルエネルギーの条件と組み合わされて用いられることで確実性が更に向上する。以下、上記（ｉ）−（ｉｉｉ）の各条件を説明する。

<< Termination condition >>
In the present embodiment, the terminal conditions to be satisfied of the end point x ^{m + 1} of the critical trajectory 3 are (i) the condition of potential energy, (ii) the condition of kinetic energy, and (iii) minimizing the distance between two points. Use one. The condition of the (i) potential energy is an effective condition for obtaining a solution reliably, and the remaining two conditions are used in combination with the conditions of the potential energy as appropriate to further improve the certainty. Hereinafter, each condition of said (i)-(iii) is demonstrated.

(I) Potential energy conditions: μ _PEBS
As described above, the end point of critical trajectory 3 is generally considered to be an unstable equilibrium point, but when performing the calculation, specifying an unstable equilibrium point as a termination condition gives a solution. It may not be. As a result of the inventors' investigation, it was found that the calculation becomes stable when the terminal point is specified so that the unstable equilibrium point exists on the potential energy boundary surface called PEBS (Potential Energy Boundary Surface). This indicates that the end point of the critical trajectory may exist not only at the above-described unstable equilibrium point but also on the PEBS connected to the unstable equilibrium point. In general, μ _PEBS = 0 is a condition that holds on PEBS. Therefore, in the present embodiment, such conditions are taken into consideration at the end point of the critical trajectory 3. That is, at the end point of the critical trajectory 3, one of the end conditions is that _μPEBS is minimized.

Here, if the potential energy surface is compared to the topography, the stable region is a basin-like region, and the unstable region is outside the basin. And the critical state that is the boundary between the stable area and the unstable area can be compared to the ridgeline of the mountain that surrounds the basin. Then, the condition that μ _PEBS = 0 mentioned above is the direction in which the potential energy of the electric power system changes along the critical trajectory 3 from the start point to the end point, and the direction of the end point seen from the stable equilibrium point after removal of the fault. , Can be rephrased as orthogonal. That is, the end condition is that the inner product of these two directions is zero.

とすると、上述した２つの方向はそれぞれ

で表される（座標θ^ｍの上に付されたチルダは、座標が慣性中心座標系に変換されていることを表す（次の（式２．１２）の但し書き参照）。よって、μ_ＰＥＢＳは次式で表される。なお、次式において、変数の右肩に付された記号Ｔは転置を表す。 Therefore, the potential energy of the power system is V _P, and the coordinates of the termination point, the angular velocity at the termination point, and the coordinates of the stable equilibrium point after fault elimination are each

Then, the above two directions are

In represented by (tilde attached to on the coordinate theta ^m represents the coordinates are converted into inertial-centered coordinate system (see proviso of the following (equation 2.12)). Thus, mu _PEBS is It is represented by the following equation: In the following equation, the symbol T attached to the right shoulder of the variable represents transposition.

このようなμ_ＰＥＢＳが臨界軌跡の終点において最小になることが、ポテンシャルエネルギーの条件である。

It is a condition of potential energy that such _μPEBS is minimized at the end point of the critical trajectory.

(Ii) condition of kinetic energy: μ _KE
At the end of critical trajectory 3, the kinetic energy of all generators in the power system should be minimal. Therefore, the termination condition is that the following μ _KE becomes minimum at the end point.

もっとも、（式２．１３）における発電機の回転角速度ω^ｍは慣性中心座標系に変換されているので、μ_ＫＥは終端点において極小となる。この条件により終点を検出する。

However, since the rotational angular velocity ω ^m of the generator in (Equation 2.13) is converted to the inertial center coordinate system, μ _KE is minimized at the terminal point. The end point is detected by this condition.

(Iii) Minimizing the distance between two points: μ _dist
The inventors discovered that, in addition to the case where the critical trajectory 3 converges to the unstable equilibrium point, there are cases where the critical trajectory 3 asymptotically approaches the PEBS under the potential energy condition of (i) above. Then, in both cases, focusing on the fact that the distance between the two points x ^m and x ^{m + 1} leading to the end point is minimized, this was used as the termination condition. This termination condition is expressed by the following equation.

ここで、ｗ_ｄｉｓｔは任意の定数であり、例えば０．１である。なお、２点間の距離が速度に比例することからすれば、（式２．１４）は、（式２．１３）と論理的に矛盾せず、相乗的な効果を有する。

Here, w _dist is an arbitrary constant, for example, 0.1. Note that, since the distance between two points is proportional to the velocity, (Expression 2.14) is not logically contradictory to (Expression 2.13), and has a synergistic effect.

(Iv) Summary of termination conditions
A point where the square of the second error vector μ _E (Eq. 2.16) of (Eq. 2.15) containing (i)-(iii) described above as a component is added to the objective function of the least squares method, and the point is minimized The calculation can be stabilized by detecting the

ただし、この第２の誤差ベクトルμ_Ｅの全ての成分を最小化問題の中に入れる必要はない。本実施形態において、ポテンシャルエネルギー条件は非常に有効であるから、必ずμ_Ｅに入れることとする。残りの２つの条件をμ_Ｅに加えると、更に計算が安定化する。

However, not all components of this second error vector μ _E need to be included in the minimization problem. In the present embodiment, since the potential energy conditions it is very effective, and putting always mu _E. Adding the remaining two conditions to μ _E further stabilizes the calculation.

Here, when adding the second error vector μ _E to the objective function, a square diagonal matrix W having positive diagonal elements may be used as a weighting as in the following equation.

例えば、ａ_１＝ａ_２＝ａ_３＝１のとき、（式２．１７）は、（式２．１６）における｜μ_Ｅ｜^２に一致する。また、ａ_１＝ａ_３＝０、ａ_２＝１のとき、（式２．１７）は、｜μ_ＰＥＢＳ｜^２になる。このように、状況に応じて重み付けＷの成分を変化させることで、計算を更に安定化することができる。なお、第２の誤差ベクトルμ_Ｅは、上記以外の条件を成分として含んでもよい。

For example, when a ₁ = a ₂ = a ₃ = 1, (Expression 2.17) matches | μ _E | ² in (Expression 2.16). Also, when a ₁ = a ₃ = 0 and a ₂ = 1, (formula 2.17) becomes | μ _PEBS | ² . Thus, the calculation can be further stabilized by changing the component of the weighting W depending on the situation. The second error vector μ _E may include conditions other than the above as components.

<< Constraint condition function μ _step >>
There are rare cases in which the solution converges to the stable equilibrium point SEP and a valid solution can not be obtained. This is because the above-mentioned termination condition may be satisfied also in SEP. In the case where the solution converges to SEP, the step width of the travel time Δt or the Euclidean distance ε becomes zero, and a phenomenon is observed in which all points in the critical trajectory 3 converge to the SEP. This phenomenon is called zero convergence.

In order to avoid such zero convergence, maximization of the movement time Δt or Euclidean distance ε may be added to the objective function. Specifically, the following constraint function μ _step defined as a function of the movement time Δt or the reciprocal of the Euclidean distance ε is minimized according to the trapezoidal rule used.

ここで、Ｔ_Δｔ、Ｔ_ε、ｗ_ｓｔｅｐは定数である。例えば、Ｔ_Δｔ＝１／ｍ、Ｔ_ε２０／ｍ、ｗ_ｓｔｅｐ＝１が好ましいが、これらの値に限られない。

Here, T _Δt , T _ε and w _step are constants. For example, T _Δt = 1 / m, T _ε 20 / m, and w _step = 1 are preferable, but not limited to these values.

By adding the constraint condition function μ _step to the objective function, it is possible to avoid the zero convergence phenomenon and to reliably obtain a valid solution.

<< Minimizing Objective Function >>
From the above discussion, the objective function in this embodiment can be written as follows.

そして、（式２．１９）で表される目的関数を最小化させる変数ベクトルｘ^ｋ、移動時間Δｔ（又はユークリッド距離ε）、終端条件μ_Ｅの各成分、臨界となる故障除去時間τを求める。このような最適化問題を解くにあたり、上述した（式２．１１）により定義される初期条件μ_Ｉを含む制約条件を課している。なお、かかる最適化問題の計算手法として、例えばニュートン・ラフソン法が用いられる。

Then, find the variable vector x ^k that minimizes the objective function expressed by (Eq. 2.19), travel time Δt (or Euclidean distance ε), each component of the termination condition μ _E , and fault removal time τ that becomes critical . In solving such an optimization problem, constraints including the initial condition μ _I defined by (Equation 2.11) described above are imposed. For example, the Newton-Raphson method is used as a calculation method of such an optimization problem.

=== Flow of calculation of critical failure removal time ===
A flow of calculating the critical failure removal time in the present embodiment will be described with reference to FIG. FIG. 4 is a flow chart showing the flow of calculating the critical failure removal time τ.

First, in step S1, a model representing a power system for which a critical fault removal time τ is to be determined is specified. Thereby, the multidimensional function f and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) are specified. Then, in step S2, the initial condition μ _I of the critical trajectory 3 (Eq. 2.11), the termination condition μ _E of the critical trajectory 3 (Equation 2.12-Equation 2.14), and the weighting W for each component of the termination condition Set At the same time, as necessary, the condition μ _step on the step width (Equation 2.18.1 or Equation 2.18.2) is set. This determines the objective function shown in (Expression 2.19).

When the objective function is determined, in step S3, solution search for the optimization problem, that is, minimization of the objective function is performed. By the execution of calculations, calculates a clearing time τ corresponding to the start point x ⁰ and the starting point x ⁰ of the critical path 3.

In the process of executing solution search in step S3, the transition between the objective function and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) is stored in a predetermined memory, and stored in the memory after the solution search. By displaying the objective function and the multidimensional state variable x ^k in time series, it is possible to confirm the search path and to confirm whether or not the local optimum solution is involved.

=== Critical failure removal time calculation device, program ===
The calculation of the critical failure removal time τ in the present embodiment is executed by the critical failure removal time calculation device 100. The critical failure removal time calculation device 100 is, for example, a computer or a workstation operated by an operator who operates an electric power system, and as shown in FIG. 5, the CPU 101, a display device 102 such as a liquid crystal display, a keyboard, An input device 103 such as a mouse, a memory 104, and a storage device 105 are provided.

The CPU 101 reads a program and data from the storage device 105 into the memory 104 to execute a calculation. The function of the first information device to perform the set and minimization of the objective function in step S1-S3 described above, corresponds to the start point x ⁰ and the starting point x ⁰ of the critical path 3 when the objective function is minimized The CPU 101 executes the function of the second information device that executes the calculation of the failure removal time τ.

In the storage unit 105, a program for calculating the critical failure removal time described above, for example, the program of the Newton-Raphson method described above, or the unknown variables x ^{0 to} x ^{m + 1} , τ, using this Newton-Raphson method A program group (critical failure removal time calculation program) including a program for performing optimization of Δt, ε, etc. is stored. The storage device 105 also stores information related to the function f, state variable vectors x ^{0 to} x ^{m + 1} , intermediate data including an error vector, and the like.

として定義される電力系統方程式に従う複数の多次元状態変数ｘ^ｋ（１≦ｋ≦ｍ＋１：ｋ、ｍは整数）と、多次元状態変数ｘ^０ないしｘ^ｍ＋１の中で相互に隣接する多次元状態変数ｘ^ｋ及びｘ^ｋ＋１の間の移動時間Δｔと、を用いて

として定義される第１の誤差ベクトルμ_ＴＺ ^ｋと、電力系統のポテンシャルエネルギーＶ_Ｐが始点から終点に向かって軌跡３に沿って変化する方向と、故障の除去後の安定平衡点から見た終点の方向と、の内積を成分として含む第２の誤差ベクトルμ_Ｅと、正の対角要素を有する正方の対角行列Ｗと、を用いて

として定義される目的関数を最小化する第１の情報装置を備える。また、目的関数が最小化されたときの多次元状態変数ｘ^０及び当該多次元状態変数ｘ^０に対応する故障除去時間τを求める第２の情報装置を備える。なお、第１の誤差ベクトルμ_ＴＺ ^ｋは、多次元状態変数ｘ^ｋ及びｘ^ｋ＋１の間のユークリッド距離εを用いて

として定義されてもよい。 As described above, the critical failure removal time calculation device 100 is a function of the failure removal time τ, and is a multidimensional state variable x ⁰ representing the state of the power system when the failure is removed, and a multidimensional state variable x ⁰ Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} and the multidimensional state variables x ^{m + 1} (m is an integer) indicating the end point of the trajectory 3 representing the temporal change of the state of the power system starting from

A plurality of multidimensional state variables x ^k (1 ≦ k ≦ m + 1: k, m is an integer) according to the power system equation defined as and a multidimensional state adjacent to each other among the multidimensional state variables x ⁰ to x ^{m + 1} Using a movement time Δt between variables x ^k and x ^{k + 1}

The direction in which the first error vector mu _TZ ^k, the potential energy V _P of the power system is changed along the trajectory 3 towards the end from the starting point which is defined as the end point as viewed from the stable equilibrium point after removal of the fault Using a second error vector μ _E including the inner product of the directions of and as a component, and a square diagonal matrix W having positive diagonal elements

A first information device that minimizes an objective function defined as In addition, a second information device is provided which obtains a multidimensional state variable x ⁰ when the objective function is minimized and a fault removal time τ corresponding to the multidimensional state variable x ⁰ . Note that the first error vector μ _TZ ^k is calculated using the Euclidean distance ε between the multidimensional state variables x ^k and x ^{k + 1}

It may be defined as

  According to this embodiment, by specifying the unstable equilibrium point, it is possible to avoid the situation where the calculation is not stable and to find the solution surely.

The second error vector μ _E preferably further includes kinetic energy μ _KE of the generator in the power system as a component. This further stabilizes the calculation.

In addition, the second error vector μ _E further includes the distance μ _dist between two points reaching the end point in the trajectory as a component, thereby improving the stability of the calculation.

として定義される目的関数を最小化することが好ましい。かかる実施形態によれば、解が安定平衡点に収束することを回避することができるため、妥当な解を確実に得ることができる。 Also, the first information device uses a third error vector μ _STEP defined as a function of the reciprocal of the travel time Δt or the reciprocal of the Euclidean distance ε

It is preferable to minimize the objective function defined as According to such an embodiment, it is possible to avoid that the solution converges to the stable equilibrium point, so that a valid solution can be surely obtained.

  The above embodiments are for the purpose of facilitating the understanding of the present invention, and are not for the purpose of limiting the present invention. The present invention can be modified and improved without departing from the gist thereof, and the present invention also includes the equivalents thereof.

1 fault locus 2 locus showing the state of the power system which can return to the stable state after the fault is removed 3 critical locus 4 showing the state of the power system which can not return to the stable state after the fault is removed Trajectory 100 critical failure removal time calculation device 101 CPU
102 display device 103 input device 104 memory 105 storage device

Claims (8)

Critical failure removal time calculation for determining the failure removal time that becomes critical between the time when recovery becomes possible after failure of the power system where multiple generators are connected and the time when recovery becomes impossible after failure of the power system A device,
A multidimensional state variable x ⁰ which is a function of the fault removal time τ and which represents the state of the power system when the fault is removed;
A multidimensional state variable x ^{m + 1} (m is an integer) indicating an end point of a locus representing temporal change of the state of the power system starting from the multidimensional state variable x ⁰ ;
Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} ,

And a plurality of multidimensional state variables x ^k (1 ≦ k ≦ m + 1: k, m is an integer) according to the power system equation defined as
Using a movement time Δt between multidimensional state variables x ^k and x ^{k + 1} adjacent to each other among the multidimensional state variables x ⁰ to x ^{m + 1}

A first error vector μ _TZ ^k defined as
A component including an inner product of a direction in which potential energy of the power system changes along the locus from the start point to the end point, and a direction of the end point viewed from a stable equilibrium point after removal of the fault as a component An error vector μ _{E of} 2,
Using a square diagonal matrix W with positive diagonal elements

A first information device minimizing an objective function defined as
Wherein the multi-dimensional state variables x ⁰ and a second information device for determining the clearing time τ corresponding to the multi-dimensional state variable x ⁰ when the objective function is minimized,
A critical fault removal time calculation device comprising: Critical failure removal time calculation for determining the failure removal time that becomes critical between the time when recovery becomes possible after failure of the power system where multiple generators are connected and the time when recovery becomes impossible after failure of the power system A device,
A multidimensional state variable x ⁰ which is a function of the fault removal time τ and which represents the state of the power system when the fault is removed;
A multidimensional state variable x ^{m + 1} (m is an integer) indicating an end point of a locus representing temporal change of the state of the power system starting from the multidimensional state variable x ⁰ ;
Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} ,

And a plurality of multidimensional state variables x ^k (1 ≦ k ≦ m + 1: k, m is an integer) according to the power system equation defined as
Using the Euclidean distance ε between the multidimensional state variables x ^k and x ^{k + 1} adjacent to each other among the multidimensional state variables x ⁰ to x ^{m + 1}

A first error vector μ _TZ ^k defined as
A component including an inner product of a direction in which potential energy of the power system changes along the locus from the start point to the end point, and a direction of the end point viewed from a stable equilibrium point after removal of the fault as a component An error vector μ _{E of} 2,
Using a square diagonal matrix W with positive diagonal elements

A first information device minimizing an objective function defined as
Wherein the multi-dimensional state variables x ⁰ and a second information device for determining the clearing time τ corresponding to the multi-dimensional state variable x ⁰ when the objective function is minimized,
A critical fault removal time calculation device comprising: The critical failure removal time calculation device according to claim 1, wherein the second error vector μ _E further includes kinetic energy of a generator in the power system as a component. The critical failure removal time calculation device according to any one of claims 1 to 3, wherein the second error vector μ _E further includes, as a component, a distance between two points reaching an end point in the trajectory. The first information device uses a third error vector μ _STEP defined as a function of the reciprocal of the travel time Δt.

The critical fault removal time calculation device according to claim 1, wherein the objective function defined as is minimized. The first information device uses a third error vector μ _STEP defined as a function of the reciprocal of the Euclidean distance ε

The critical fault removal time calculation device according to claim 2, wherein the objective function defined as is minimized. Critical failure removal time calculation for determining the failure removal time that becomes critical between the time when recovery becomes possible after failure of the power system where multiple generators are connected and the time when recovery becomes impossible after failure of the power system Method,
A multidimensional state variable x ⁰ which is a function of the fault removal time τ and which represents the state of the power system when the fault is removed;
A multidimensional state variable x ^{m + 1} (m is an integer) indicating an end point of a locus representing temporal change of the state of the power system starting from the multidimensional state variable x ⁰ ;
Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} ,

And a plurality of multidimensional state variables x ^k (1 ≦ k ≦ m + 1: k, m is an integer) according to the power system equation defined as
Using a movement time Δt between multidimensional state variables x ^k and x ^{k + 1} adjacent to each other among the multidimensional state variables x ⁰ to x ^{m + 1}

A first error vector μ _TZ ^k defined as
A component including an inner product of a direction in which potential energy of the power system changes along the locus from the start point to the end point, and a direction of the end point viewed from a stable equilibrium point after removal of the fault as a component An error vector μ _{E of} 2,
Using a square diagonal matrix W with positive diagonal elements

Minimize the objective function defined as
The critical fault removal time calculation method, wherein the multidimensional state variable x ⁰ when the objective function is minimized and the fault removal time τ corresponding to the multidimensional state variable x ⁰ are determined. In order to determine the critical failure removal time, the critical time between the time when the power system in which multiple generators are connected is broken and the time when the power system becomes recoverable and the time when the power system fails can not be recovered ,
A multidimensional state variable x ⁰ which is a function of the fault removal time τ and which represents the state of the power system when the fault is removed;
A multidimensional state variable x ^{m + 1} (m is an integer) indicating an end point of a locus representing temporal change of the state of the power system starting from the multidimensional state variable x ⁰ ;
Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} ,

And a plurality of multidimensional state variables x ^k (1 ≦ k ≦ m + 1: k, m is an integer) according to the power system equation defined as
Using a movement time Δt between multidimensional state variables x ^k and x ^{k + 1} adjacent to each other among the multidimensional state variables x ⁰ to x ^{m + 1}

A first error vector μ _TZ ^k defined as
A component including an inner product of a direction in which potential energy of the power system changes along the locus from the start point to the end point, and a direction of the end point viewed from a stable equilibrium point after removal of the fault as a component An error vector μ _{E of} 2,
Using a square diagonal matrix W with positive diagonal elements

A first function to minimize the objective function defined as
A second function of determining the clearing time τ of the objective function corresponds to the multidimensional state variables x ⁰ and the multi-dimensional state variables x ⁰ when it is minimized,
A program that runs

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