JP4517106B2 - Critical failure removal time calculation method, program - Google Patents

Description

  The present invention relates to a critical fault removal time calculation method and program.

  As a new technique for analyzing the transient stability of the nonlinear phenomenon to be controlled, the present applicant calculates the critical fault removal time more accurately and quickly than the conventional simulation method or energy function method as disclosed in Patent Document 1. A critical fault elimination time calculation method is proposed. The outline of the technique disclosed in Patent Document 1 will be described below.

  First, the critical fault removal time will be described with reference to FIG. FIG. 1 is a schematic diagram showing the state of a one-machine infinite bus system (an example of a control target) without braking with the locus of the phase angle δ and the angular velocity ω of the generator. The critical trajectory 3 between the trajectory 2 when the fault becomes stable and the trajectory 4 when the fault becomes unstable is a dominant unstable equilibrium point PE (CUEP: controlling unstable equilibrium) as a singular point in the number theory. point). When the state of the power system changes with time along the failure locus 1 from the stable equilibrium point PA indicating the stable state, the failure is removed along the critical locus 3 when the failure is removed at the point PC on the failure locus 1. It is assumed that the above dominant unstable equilibrium point PE is reached over an infinite time in number theory. Therefore, if the fault is removed in a time shorter than the time from the stable equilibrium point PA to the point PC, the state of the power system can be restored to the stable state. The time from the stable equilibrium point PA to the point PC is referred to as a critical clearing time (CCT).

  Next, the critical fault removal time calculation method disclosed in Patent Document 1 will be described with reference to FIG.

First, the failure is a point on the trajectory 1 and the time of failure removal control target state (PC points shown in FIG. 1) is defined as a multidimensional state variables x ^0. Note that multi-dimensional state variable x ^0, since a point on the failed path 1 can be expressed as a function of clearing time τ shown in the following equation (1).

Moreover, multi-dimensional state variable x ¹ in the order of the state of the control object after clearing the multidimensional state variables x ⁰ to the start point of the critical path 3, the discrete time ^{t k (1 ≦ k ≦ m} + 1), x 2 ,... X ^m , x ^{m + 1} are defined. The multidimensional state variable x ^k (0 ≦ k ≦ m + 1) is a multidimensional variable (vector) composed of a plurality of components. For example, the paragraph number 35 in Patent Document 1, as components of the multidimensional state variables x, the phase angle δ in 1 machine infinite bus system model, the angular velocity omega, transient reactance behind voltage E, mechanical input P _M or the like is exemplified Has been.

Here, it is assumed that 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. Assuming that there is a multidimensional state variable x ^k (0 ≦ k ≦ m + 1), the state of the controlled object is from the state at the time of critical fault removal (x ⁰ ) to the dominant unstable equilibrium state (x ^{m + 1} ). Of the critical trajectory 3. The multidimensional state variable x ^k can be regarded as a solution of the following multidimensional nonlinear equation (power system equation) of (Expression 2) that expresses the nonlinear state of the controlled object.

By applying the formula trapezoidal against (Equation 2), while the multi-dimensional state variable x ^k and x ^{k + 1} adjacent to each other in a multi-dimensional state variable x ^k satisfies the following equation (3). Note that ε represents the Euclidean distance between the multidimensional state variables x ^k and x ^{k + 1} adjacent to each other.

By the way, it is known that the multidimensional state variable x ^{m + 1} which is the end point of the critical locus 3 is generally a dominant unstable equilibrium point CUEP. Therefore, as a constraint on (Equation 3), when the end point x ^{m + 1} of the critical locus 3 is designated as x ^u representing a predetermined value of the dominant unstable equilibrium point CUEP, the following (Equation 4-1) When the end point xm ^{+ 1} of the critical locus 3 is designated as an equilibrium condition representing the state of the dominant unstable equilibrium point CUEP, the following (Equation 4-2) is obtained.

Therefore, by solving the multiple simultaneous equations according to (Equation 4-1) or (Equation 4-2) which is the constraint condition of the end point x ^{m + 1} of the critical trajectory 3 (Equation 1), (Equation 2), (Equation 3) Then, the starting point x ⁰ of the critical locus 3 and, in turn, the critical fault removal time τ can be obtained.

特開２００７−５３８３６号公報 If a simulation method that directly solves the multiple simultaneous equations of (Equation 3) described above is employed, numerical errors resulting from approximation of the trapezoidal formula may accumulate and be maximized at the end point x ^{m + 1} of the critical locus 3. . For this reason, the left side in (Equation 3) is regarded as an error vector, and unknown variables τ, ε, x ¹ , x when minimizing the sum of the error vectors (norm) as in the following (Equation 5) ² ,... X ^m , x ^{m + 1} are obtained together.

JP 2007-53836 A

  By the way, the present applicant calculated the critical fault elimination time according to the above-mentioned method when the control target is a multi-machine power system in which a plurality of generators are connected. It was possible to recognize the need for improvement.

  The present invention has been made in view of such a problem, and the object of the present invention is to provide a failure removal time calculation method for accurately and quickly calculating a critical failure removal time of a power system in which a plurality of generators are connected, and To provide a program.

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：ｋは整数）と、前記多次元状態変数ｘ^０乃至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の間のユークリッド距離εと、を定義し、前記電力系統方程式、前記多次元状態変数ｘ^ｋ（０≦ｋ≦ｍ＋１）、前記ユークリッド距離εを用いて

として定義される誤差ベクトルμ^ｋを用いて

として定義される目的関数に対し、前記多次元状態変数ｘ^ｍ＋１の制約条件として、前記故障をした後に回復可能となる前記電力系統の状態と、前記故障をした後に回復不可能となる前記電力系統の状態と、の臨界となる前記電力系統の臨界状態の際に同期外れに至る発電機に係る前記多次元状態変数ｘ^ｍ＋１の要素に所定値を指定した上で、前記目的関数を最小化し、前記目的関数を最小化する前記多次元状態変数ｘ^０に基づいて、前記臨界となる故障除去時間τを求めること、を特徴とする。 The main aspect of the present invention for solving the above problems is that the critical time between the time when the power system connected to a plurality of generators becomes recoverable after failure and the time when the power system becomes unrecoverable after the power system fails A critical failure removal time calculation method for obtaining a failure removal time, which is a function of the failure removal time τ, a multidimensional state variable x ⁰ representing the state of the power system when the failure is removed, and the power Discretized between a multidimensional state variable x ^{m + 1} (m is an integer) indicating a dominant unstable equilibrium state as a system state, and the multidimensional state variables x ⁰ and x ^{m + 1} ,

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

With an error vector μ ^k defined as

As a constraint condition for the multidimensional state variable x ^{m + 1} , the state of the power system that can be recovered after the failure and the power system that cannot be recovered after the failure And specifying a predetermined value for the element of the multidimensional state variable x ^{m + 1} related to the generator that is out of synchronization in the critical state of the power system that becomes the critical state of the power system, and minimizing the objective function, The critical failure removal time τ is obtained based on the multidimensional state variable x ⁰ that minimizes the objective function.

Further, in the above-described method, the multidimensional state variable x ^{m + 1} constraint specifies a predetermined value to the multi-dimensional state variable x ^{m + 1} elements of the generator leading to desynchronization during the critical state A first constraint, and a second constraint that specifies a predetermined value for an element of the multidimensional state variable x ^{m + 1} related to the generator that does not fall out of synchronization in the critical state, and the first constraint The condition may be that the weight of the constraint condition is made larger than that of the second constraint condition.

  Moreover, it is said method, Comprising: The generator which loses | synchronizes in the said critical state is good also as being any one among several generators linked | connected with the said electric power grid | system.

Further, in the above method, the elements of the multidimensional state variable x ^{m + 1} related to the generator that is out of synchronization in the critical state are the phase angle of the generator that is out of synchronization in the critical state and An angular frequency may be used.

  Further, in the above method, the first constraint condition includes a third constraint condition that specifies predetermined values for a phase angle and an angular frequency of a generator that are out of synchronization in the critical state, and A fourth constraint that designates a predetermined value for an element other than the phase angle and angular frequency of the generator that is out of synchronization, and the third constraint is more weighted than the fourth constraint It is also possible to increase the attachment.

として定義される重みづけ制約条件を前記目的関数に加算した、

として定義される目的関数を最小化する前記多次元状態変数ｘ^０を求めること、 としてもよい。 Further, in the above-described method, the multidimensional state variable x ^u a is a predetermined value of the multi-dimensional state variable x ^{m + 1} to be specified as constraints of the multi-dimensional state variable x ^{m + 1,} of the multi-dimensional state variable x ^{m + 1} Defining a matrix W having the same number of rows and columns as the number of elements and indicating the weight of the constraint, and using the multidimensional state variables x ^u , x ^{m + 1} , and the matrix W,

The weighting constraint defined as is added to the objective function,

The multidimensional state variable x ⁰ that minimizes the objective function defined as

として定義される不等式による制約条件を付加すること、としてもよい。 Further, in the above method, a predetermined function g is used as a constraint condition of the multidimensional state variable x ^{m + 1.}

It is also possible to add a constraint by an inequality defined as

In the above method, the objective function and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) may be stored in association with each other in the process of minimizing the objective function. .

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：ｋは整数）と、前記多次元状態変数ｘ^０乃至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の間のユークリッド距離εと、を定義し、前記電力系統方程式、前記多次元状態変数ｘ^ｋ（0≦ｋ≦ｍ+1）、前記ユークリッド距離εを用いて

として定義される誤差ベクトルμ^ｋを用いて

として定義される目的関数に対し、前記多次元状態変数ｘ^ｍ＋１の制約条件として、前記故障をした後に回復可能となる前記電力系統の状態と、前記故障をした後に回復不可能となる前記電力系統の状態と、の臨界となる前記電力系統の臨界状態の際に同期外れに至る発電機に係る前記多次元状態変数ｘ^ｍ＋１の要素に所定値を指定した上で、前記目的関数を最小化する機能と、前記目的関数を最小化する前記多次元状態変数ｘ^０に基づいて、前記臨界となる故障除去時間τを求める機能と、を実現させるためのプログラムである。 Further, the main other present invention for solving the above-mentioned problems is that the time when the power system connected to a plurality of generators can be recovered after failure and the time when the power system cannot be recovered after failure. And a program for causing the information processing apparatus to realize a critical fault removal time of the information processing apparatus, wherein the information processing apparatus is a function of the fault removal time τ, and is a function of the power system when the fault is removed. a multidimensional state variables x ⁰ representing the state, the multi-dimensional state variable x ^{m + 1} showing the controlling unstable equilibrium as the state of the power system ^(m is an integer), and the multi-dimensional state variable x ⁰ and x ^{m + 1} Discretized between

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

With an error vector μ ^k defined as

As a constraint condition for the multidimensional state variable x ^{m + 1} , the state of the power system that can be recovered after the failure and the power system that cannot be recovered after the failure And specifying a predetermined value for the element of the multidimensional state variable x ^{m + 1} related to the generator that is out of synchronization in the critical state of the power system, which is the critical state of the power system, and minimizing the objective function A program for realizing a function and a function for obtaining the critical failure removal time τ based on the multidimensional state variable x ⁰ that minimizes the objective function.

  It is possible to calculate the critical fault removal time of an electric power system in which a plurality of generators are interconnected accurately and quickly.

=== Outline Explanation of Critical Failure Removal Time Calculation Method ===
With reference to FIG. 2, the critical fault removal time calculation method of the present embodiment will be described. In the figure, the state of the multi-machine power system of the present embodiment is a multidimensional state variable x ^k (0 ≦ k) discretized by discrete time t ^k (0 ≦ k ≦ m + 1; m is an integer). ≦ m + 1). Note that x ^k is composed of the elements shown in the following (Equation 6), and is hereinafter referred to as a state variable vector.

Note that in Equation _{(6), x gi} ^k is representing the state variable vector generator unit i (i = 1 to N) at discrete time ^{t k} as shown in the following (Equation 7).

Here, regarding the element shown in (Expression 7), δ _i ^{k represents} the phase angle (scalar amount) of the generator unit i at the time tk, and ω _i ^k represents the time of the generator unit i. It expresses the angular frequency (scalar quantity) in t ^k. The coordinates of δ _i ^{k and} ω _i ^k may be in the inertial center coordinate system or in other coordinate systems. X _Ri ^k represents another state variable vector including a control system variable related to the generator unit i, and x _sys ^k represents a vector including all other state variables.

  When a simplified model (for example, Xd ′ model) is used as the generator unit model, δ and ω are always included in the state variables. Also, in general, the equation of motion of the generator rotor is called the oscillating equation, δ is the phase angle of the generator rotor, and ω is the differential value of δ with respect to time t. Even in the case of a detailed model other than δ, δ and ω are always included in the state variables.

Further, depending on the control system model such as AVR (Automatic Voltage Regulator), governor, PSS (Power System Stabilizer), etc., the corresponding state variable (set of generator and control system) is determined. For example, when a generator unit model of an infinite bus system including AVR and governor is used for the generator unit i, x _gi ^k and x _R ^{i k} are respectively expressed by the following (formula 8-1) and (formula 8). -2). E _i ^k represents a transient reactance back voltage, and P _mi ^k represents a machine input.
x _gi ^k = [δ _i ^k , ω _i ^k , E _i ^k , P _mi ^k ] (equation 8-1)
x _Ri ^k = [E _i ^k , P _mi ^k ] (Equation 8-2)
Further, as an example of x _sys ^k , there are state variables of controllers such as SVC (Static Var Compensator) and SVG (Static Var Generator) installed in a generator unit, a substation unit or the like.

The nonlinear state of the multi-machine power system of the present embodiment is expressed by the following nonlinear equation (power system equation) of (Equation 9) using the state variable vector ^xk and the multidimensional function f shown in (Equation 6). Expressed. That is, the state variable vector x ^k represents a discrete solution of the multidimensional function f at a discrete time t ^k (0 ≦ k ≦ m + 1).

That is, the critical fault removal time calculation method of the present embodiment calculates the critical trajectory 3 of the multi-machine power system as a solution of the nonlinear equation of (Equation 9), and calculates the critical fault removal time based on this solution. is there. When obtaining the solution of (Equation 9), the critical multi-machine power system state that can be recovered after a failure and the multi-machine power system state that cannot be recovered after a failure are critical. Phase angle δ _{j of} a generator that is out of synchronization (step-out) in the critical state of the mechanical power system (hereinafter referred to as critical generator, and the generator number assigned to this critical generator is j) It takes into account that only the arrangement angular frequency ω _j is in an unstable equilibrium state.

Specifically, the constraint condition of the multidimensional state variable x ^{m + 1} that is the end point of the critical locus 3 is a constraint condition (first constraint condition) that specifies a predetermined value for the element of the multidimensional state variable x ^{m + 1} related to the critical generator. The weight of the constraint condition is made larger than the constraint condition (second constraint condition) for designating a predetermined value for the element of the multidimensional state variable x ^{m + 1} related to the generator that does not fall out of synchronization in the critical state. Furthermore, as a constraint condition related to the critical generator, a constraint condition (third constraint condition) for designating a predetermined value for the phase angle δ _j and the angular frequency ω _j of the critical generator, and the phase angle δ _j and the angle of the critical generator are specified. The constraint condition is weighted more than the constraint condition (fourth constraint condition) for designating a predetermined value for elements other than the frequency ω _j .

Therefore, instead of the constraint condition (Equation 4-1) or (Equation 4-2) of the end point x ^{m + 1} (k = m + 1) of the critical trajectory 3 in the previously proposed method (see JP 2007-53836 A). Thus, as in the following (Expression 10) and (Expression 11), only the phase angle δ _j ^{m + 1} and the angular frequency ω _j ^{m + 1} of the critical generator among the elements constituting x ^{m + 1} are set to the predetermined values δ _j ^u , ω it was decided to introduce a new constraint to be bound by _j ^u.

With respect to the predetermined value [delta] _j ^u, for example, it is possible to specify an appropriate value by using BCU method, BCU-Shadowing method which is a kind of energy function method. Specifically, by sequentially calculating the slope of this curved surface to find the path of the phase angle δ corresponding to the point PC and the point PE shown in FIG. 1 on the energy curved surface obtained from the power system model, The final point x ^u (including δ _j ^u ) based on the initial point x ⁰ (specify a predetermined value) of the critical locus can be obtained. As for the predetermined value omega _j ^u, can specify a particular value of the inertia center omega _c critical generators as follows (Equation 12).

Therefore, in the method proposed previously, the constraint condition is imposed on all the components of the end point x ^{m + 1} of the critical locus 3 as in (Equation 4-1) or (Equation 4-2). In the embodiment, as in (Equation 10) and (Equation 11), only some of δ _j ^{m + 1} and ω _j ^{m + 1} among the components of the end point x ^{m + 1} of the critical locus 3 or the weight is increased. We decided to impose constraints.

In this way, only the critical generator among the many generators existing in the multi-machine power system is focused, and only the phase angle δ _{j and the} angular frequency ω _{j of the} critical generator are increased or the weight is increased. By imposing constraints, it is no longer constrained by redundant constraints, the solution search space can be expanded effectively, and the critical fault elimination time τ can be calculated more accurately and more quickly. is what happened.

=== Detailed Description of Critical Fault Removal Time Calculation Method ===
Hereinafter, the critical fault removal time calculation method according to the present embodiment will be described in detail. By applying a trapezoidal approximation to the nonlinear equation of (Equation 9), the following equation (13) is established.

Here, k is the state of the multi-machine power system with the passage of the discrete time t ^k is an integer indicating the transition number when intermittently migration. Furthermore, x ^k represents a discrete vector corresponding to a continuous multi-dimensional state variable x. F (x ^k ) represents a discrete function vector corresponding to the continuous multidimensional function f (x). That is, f (x ^k ) is assumed to be equal to the time derivative dx ^k / dt of x ^k as shown in the following (Expression 14).

The nonlinear equation shown in (Equation 14) is defined for each model such as Anderson &Fouad's 3-machine 9 bus system (AF9), IEEE 6-machine 30 bus system (IEEE 30), and the like.

As illustrated in FIG. 1, a variable vector x ^k (= x ⁰ ) when k = 0 is set as a variable vector corresponding to the critical fault removal time CCT, and a variable vector x ^k when k = m + 1 is set. Assuming that (= x ^{m + 1} ) is a variable vector at the dominant unstable equilibrium point CUEP, x ^k in the equation of (Equation 14) indicates that the state of the multi-machine power system is the critical fault elimination time state (= x ⁰ ). The critical trajectory 3 up to the dominant unstable equilibrium state (= x ^{m + 1} ) is formed.

However, since the time difference (t ^{k + 1} −t ^k ) on the right side of the equation of (Equation 13) becomes infinitely large as it approaches the dominant unstable equilibrium point CUEP, in the present embodiment, the following (Equation 15) The Euclidean distance ε between two adjacent variable vectors illustrated in FIG. 1 is defined based on the equation shown in FIG.

Then, by using the Euclidean distance ε shown in (Equation 15) instead of the time difference (t ^{k + 1} −t ^k ) on the right side of the equation of (Equation 13), the equation of (Equation 13) becomes (Equation 16 ). The Euclidean distance ε is always constant without becoming infinite even when approaching the dominant unstable equilibrium point CUEP.

0 on the right side of the equation of (Equation 16) represents a zero vector, and the equation of (Equation 16) means (m + 1) multidimensional simultaneous equations. In other words, finding the solution of the multi-component simultaneous equation of (Equation 16) does not directly deal with infinite time, but directly converts the points x ^k of the equidistant (Euclidean distance ε) constituting the critical locus 3 of the multi-machine power system. Equivalent to seeking.

However, it is ideal that the right side of (m + 1) multiple simultaneous equations shown in (Equation 16) is all zero, but in reality, numerical errors due to the approximation of the trapezoidal formula described above occur. come. Therefore, as a method for obtaining a solution of the multiple simultaneous equations of (Expression 16), first, the left side in (Expression 16) is defined as an error vector μ ^k, and as shown in (Expression 17), the error vector μ ^k The sum of the magnitudes (norms) is defined as the objective function O.

Then, the problem of finding the solution of the multiple simultaneous equations of (Equation 16) is the variable vector x ^k that minimizes the objective function O of (Equation 17), the Euclidean distance ε, and the failure removal time τ (that is, the critical failure removal time τ). As an optimization problem for obtaining the above, the following (formula 18) was formulated. Since ^{x 0} is a function of as tau of which will be described later (equation 21), the parameters to be optimized by the following (Equation 18) is unknown variables ^tau, x 1 ~x ^m, and epsilon.

In (Equation 18), x ^k belongs to a set of N-dimensional real numbers, and Euclidean distance ε and failure removal time τ belong to a set of real numbers. Further, the error vector μ ^k (0 ≦ k ≦ m) shown in the same expression represents the left side of (Expression 16) as shown in the following (Expression 19). Incidentally, the error vector μ ^{k ′} shown in (Expression 18) represents a vector ^obtained by transposing the error vector μ ^k .

Further, when executing the solution search of (Expression 18), the constraint condition defined by the following (Expression 20) and (Expression 21) is imposed. (Expression 20) indicates that x ⁰ follows a function X _F (τ; x _pre ) of the failure removal time τ representing the failure locus 1 with the initial value x _pre as a starting point. (Expression 21) is an alternative expression of (Expression 4-1), and indicates that the end point x ^{m + 1} of the critical locus 3 is designated as a predetermined value x ^u representing the dominant unstable equilibrium point CUEP. Incidentally, mu ^{m + 1} represents the error vector between the endpoints x ^{m + 1} and controlling unstable equilibrium point x ^u of the critical path 3.

Moreover, when imposing a constraint (Equation 21), a multi-dimensional state variable x ^{m + 1} of the same number of elements have a number of well number column lines, the weighting of the constraints for each element of the multidimensional state variable x ^{m + 1} Define the specified square diagonal example W. Therefore, a weighting constraint condition that takes into account the weighting between elements of the multidimensional state variable x ^{m + 1} with respect to the constraint condition of (Formula 21) is defined as the following (Formula 22).

The objective function E obtained by adding the weighting constraint condition of (Expression 22) to the objective function O shown in (Expression 17) is defined by the following (Expression 23).

The optimization problem based on the above (Expression 18) or the like results in an optimization problem for obtaining unknown variables τ, x ^{1 to} x ^m , and ε that minimize the objective function E of (Expression 23). Become. That is, (Equation 18) is transformed into the following (Equation 24).

By the way, the multidimensional state variable x ^{m + 1} has elements shown in the following (Expression 25) corresponding to (Expression 6) and (Expression 7). That is, as a matrix component of the diagonal row example W, a diagonal element corresponding to δ _i ^{m + 1 and} ω _i ^{m + 1} (hereinafter referred to as a critical element) has “1” as a set value, and other diagonal elements ( In the following, the non-critical element) is set to a value sufficiently smaller than 1.

That is, by multiplying each element obtained by squaring the error vector μ ^{m + 1 represented} by (Expression 21) by the element (weighting) of the diagonal matrix W, the end point x ^{m + 1} of the critical locus 3 is expressed by (Expression 10). And δ _j ^{m + 1} , ω _j ^{m + 1 according} to (Equation 11) is subject to a highly weighted constraint condition, and elements of the end point x ^{m + 1} of the critical locus 3 other than δ _j ^{m + 1} , ω _j ^{m + 1} A constraint condition with a small weight is imposed.

  Here, an example of the diagonal matrix W corresponding to (Equation 25) is shown in the following (Equation 26). In addition, the diagonal matrix W shown in (Equation 26) has shown the case where all the generators of the target electric power system are made into critical generators for convenience of explanation. However, in reality, all the generators that make up the power system do not become critical generators, so if you designate one generator that is most likely to be unstable near the point of failure and make it the critical generator, It is enough. In other words, it is sufficient to set “1” only to the critical element corresponding to one designated critical generator. In addition, as a designation | designated method of a critical generator, it can designate based on the kinetic energy etc. which are obtained from the angular velocity after a failure, for example.

By the way, since the non-critical elements at the end point x ^{m + 1} of the critical locus 3 other than the critical elements δ _j ^{m + 1} and ω _j ^{m + 1} are substantially meaningless, it is not necessary to obtain a solution. The diagonal matrix W indicates that all non-critical elements are set to “0”. However, it is known that numerical calculation becomes unstable when zero is input in a calculation program that considers weights. As a non-critical element, an appropriate provisional setting value (which is sufficiently smaller than 1) can be regarded as practically zero. Value) is entered to execute the calculation.

  The flow of the critical fault removal time calculation method of the present embodiment will be described below using the flowchart shown in FIG.

First, a model representing a multi-machine power system for calculating the critical fault removal time is specified. Thus, the multidimensional function f and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) are specified (S300).

Next, a critical generator is specified among a plurality of generators linked to the multi-machine power system, and the phase angle related to the critical generator among the elements constituting the end point x ^{m + 1} of the critical locus 3 is determined. The constraints of (Equation 10) and (Equation 11) are set for δ _j ^{m + 1} and the angular frequency ω _j ^{m + 1} . Thereby, the constraint condition shown in (Expression 21) is set. Also, setting the constraint conditions shown in (Equation 20) with respect to the starting point x ⁰ of the critical path 3. Further, as shown in (Equation 24), each element (weighting) of the diagonal matrix W is set as the weighting of the constraint condition of each element of the end point x ^{m + 1} of the critical locus 3. Thus, all constraint conditions and their weights are set (S301).

Next, a solution search for minimizing the objective function E shown in (Equation 23) is executed (S302). As a result, while dispersing the error along the critical path 3 up to the controlling unstable equilibrium from the state at the time of critical clearing, obtain such starting point x ⁰ critical locus 2 (S302). Then, with respect to x ⁰ This obtained to calculate the critical clearing time τ by applying the equation (Equation 20) (S303).

In the course of executing a solution search that minimizes the objective function E shown in (Equation 23), the transition between the objective function E and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) is stored in a predetermined memory. In addition, the objective function E and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) stored in the memory after the solution search are displayed in time series, thereby confirming the search route and falling into the local optimal solution. It is possible to visually check whether or not there is any.

  As described above, according to the present embodiment, the multiple simultaneous equations of (Equation 16) are not solved sequentially from the state at the time of removing the critical fault to the dominant unstable equilibrium state, but collectively by the solution search of (Equation 24). By solving in this manner, a more accurate calculation result for the critical locus 3 is given, and as a result, the accuracy of the critical fault removal time τ can be improved.

Further, when searching for the solution of (Equation 24), as a constraint condition of (Equation 21), a constraint condition is imposed only on the critical generator element among the elements constituting x ^{m + 1} , and the solution (fault removal) It is constrained to a generator that does not affect the critical trajectory 3 by not imposing any constraints on the generator elements that have little impact on the accuracy of time) or by making the constraint weights smaller than the critical generator. Therefore, the solution space to be searched can be expanded, and the critical fault removal time τ can be obtained more accurately and quickly.

Furthermore, the phase angle δ _j ^{m + 1} and the angular frequency ω _j ^{m + 1} are limited as the elements of the critical generator, and the phase angle δ _j ^{m + 1} and the angular frequency ω _j ^{m + 1} are different from the phase angle δ _j ^{m + 1} and have little influence on the accuracy of the solution. No constraint condition is imposed on the variable, or a solution space to be searched without being bound by a state variable that does not affect the critical trajectory 3 by relaxing the constraint condition than the phase angle δ _j ^{m + 1} and the angular frequency ω _j ^{m + 1.} The critical fault removal time τ can be obtained more accurately and more quickly.

In the case of the solution search method according to (Equation 24), a constraint condition based on an inequality according to (Equation 27) can be further added. Note that g (x) may employ a function that means a generator limiter or the like added to this model.

However, the constraint condition by the inequality of (Equation 27) can be targeted only for the phase angle δ _j ^{m + 1} and the angular frequency ω _j ^{m + 1} related to the critical generator, as described above. Also, the new equality constraint condition can be handled in the same manner as the constraint condition based on the inequality in (Equation 27). As a result, even if the constraint condition increases, it is possible to effectively suppress the search solution space from being narrowed, and the critical fault removal time τ can be obtained more accurately and more quickly.

=== Program ===
The critical fault elimination time calculation method of the above-described embodiment is executed by an information processing apparatus including the CPU 110, the memory 120, the keyboard, the input device 130 such as a mouse, and the display device 140 such as a liquid crystal display and a cathode ray tube shown in FIG. The The information processing apparatus is, for example, a computer or workstation that functions as a PSS operated by an operator who is engaged in the operation of the power system. The PSS is a known device disclosed in, for example, Japanese Patent Laid-Open No. 10-28326.

The memory 120 stores a program 125 for calculating the above-described critical fault elimination time, and the CPU 110 calls and executes the program 125 from the memory 120. In addition, the memory 120 also stores information related to the function f, intermediate data such as state variable vectors x ^{0 to} x ^u and error vectors.

  The above-described embodiment is intended to facilitate understanding of the present invention, and is not intended to limit the present invention. The present invention is changed and improved without departing from the gist thereof, and the present invention includes equivalents thereof.

It is a schematic diagram which displays the discretized multidimensional state variable. It is the schematic diagram which represented the nonlinear phenomenon of the 1 machine infinity bus system without braking with the locus in a phase plane. It is a flowchart explaining the critical fault removal time calculation method. It is the figure which showed the structure of information processing apparatus.

Explanation of symbols

1 Failure locus
2 Trajectory indicating the state of the power system that can return to the stable state after the failure is removed 3 Critical trajectory 4 Trajectory 100 indicating the state of the power system that cannot return to the stable state after the failure is removed Information Processing device 110 CPU
120 Memory 125 Program 130 Input Device 140 Display Device

Claims (9)

Critical failure removal time calculation to find the critical failure removal time of the time that can be recovered after the failure of the power system connecting multiple generators, and the time that cannot be recovered after the failure of the power system A method,
A multidimensional state variable x ⁰ that is a function of the fault removal time τ and represents the state of the power system when the fault is removed;
A multidimensional state variable x ^{m + 1} (m is an integer) indicating a dominant unstable equilibrium state as the state of the power system;
Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} ,

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

With an error vector μ ^k defined as

For an objective function defined as
As a constraint condition of the multidimensional state variable x ^{m + 1} , the power system state that can be recovered after the failure and the state of the power system that cannot be recovered after the failure are critical. Specifying a predetermined value for the element of the multidimensional state variable x ^{m + 1} related to the generator that is out of synchronization in the critical state of the power system, and then minimizing the objective function,
A critical fault elimination time calculation method, characterized in that the critical fault elimination time τ is obtained based on the multidimensional state variable x ⁰ that minimizes the objective function. The critical fault removal time calculation method according to claim 1,
The constraint condition of the multidimensional state variable x ^{m + 1} is
A first constraint that specifies a predetermined value for an element of the multidimensional state variable x ^{m + 1 associated with} the generator that is out of synchronization in the critical state;
A second constraint that specifies a predetermined value for an element of the multidimensional state variable x ^{m + 1} relating to the generator that does not fall out of synchronization in the critical state;
Have
Making the weighting of the constraint condition greater than the second constraint condition for the first constraint condition;
A critical fault elimination time calculation method characterized by the following. The critical fault removal time calculation method according to claim 2,
The generator that is out of synchronization in the critical state is any one of a plurality of generators linked to the power system,
A critical fault elimination time calculation method characterized by the following. The critical fault removal time calculation method according to claim 2 or 3,
The elements of the multidimensional state variable x ^{m + 1} for the generator that is out of synchronization during the critical state are:
The phase angle and angular frequency of the generator that will be out of synchronization during the critical state,
A critical fault elimination time calculation method characterized by the following. The critical fault removal time calculation method according to claim 4,
The first constraint condition is:
A third constraint that specifies predetermined values for the phase angle and angular frequency of the generator that will be out of synchronization in the critical state;
A fourth constraint condition that specifies predetermined values for elements other than the phase angle and angular frequency of the generator that are out of synchronization in the critical state;
Have
Making the weight of the constraint condition larger than the fourth constraint condition for the third constraint condition;
A critical fault elimination time calculation method characterized by the following. A critical fault removal time calculation method according to any one of claims 2 to 5,
A multidimensional state variable x ^u is the predetermined value of the multi-dimensional state variable x ^{m + 1} to be specified as constraints of the multi-dimensional state variable x ^{m + 1,}
A matrix W having the same number of rows and columns as the number of elements of the multidimensional state variable x ^{m + 1} and indicating the weight of the constraint condition;
And using the multidimensional state variables x ^u and x ^{m + 1} and the matrix W,

The weighting constraint defined as is added to the objective function,

Determining the multidimensional state variable x ⁰ that minimizes the objective function defined as
A critical fault elimination time calculation method characterized by the following. The critical fault removal time calculation method according to any one of claims 1 to 6,
As a constraint condition of the multidimensional state variable x ^{m + 1} , using a predetermined function g

Adding constraints with inequalities defined as
A critical fault elimination time calculation method characterized by the following. A critical fault removal time calculation method according to any one of claims 1 to 7,
Storing the objective function and the multidimensional state variable x ^k (0 ≦ k ≦ m + 1) in association with each other in the process of minimizing the objective function;
A critical fault elimination time calculation method characterized by the following. An information processing apparatus for obtaining a critical failure removal time of a time that can be recovered after a failure of a power system connected to a plurality of generators, and a time that cannot be recovered after a failure of the power system A program to be realized,
In the information processing apparatus,
A multidimensional state variable x ⁰ that is a function of the fault removal time τ and represents the state of the power system when the fault is removed;
A multidimensional state variable x ^{m + 1} (m is an integer) indicating a dominant unstable equilibrium state as the state of the power system;
Discretized between the multidimensional state variables x ⁰ and x ^{m + 1} ,

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

With an error vector μ ^k defined as

For an objective function defined as
As a constraint condition of the multidimensional state variable x ^{m + 1} , the power system state that can be recovered after the failure and the state of the power system that cannot be recovered after the failure are critical. A function of minimizing the objective function after designating a predetermined value for the element of the multidimensional state variable x ^{m + 1} related to the generator that is out of synchronization in the critical state of the power system;
A function for determining the critical failure removal time τ based on the multidimensional state variable x ⁰ that minimizes the objective function;
A program to realize

Images