JP2006262655A - Transfer function calculating method and program of generator torque for evaluating pss control parameters - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily evaluate PSS control parameters, and to simplify the correction work of the control parameters, as much as possible. <P>SOLUTION: A transfer function calculating method of generator torque for evaluating the PSSs control parameters comprises a step of contracting an electric power system to a one-unit infinity busbar for a local mode; a step of contracting the power system to a single-unit single load 3-branch for a wide-area mode; a step of determining the dynamic block diagram of a generator, based on a detecting method of a ΔP+Δω type, then computing constants K1 to K6 in the dynamic block diagram separately for the wide-area mode and the local mode; a step of determining the general transfer function of PSSs by each control parameter of the Δω-type PSS and the ΔP-type PSS, after equivalence conversion of shaking suppression effects of the Δω-type PSS and the ΔP-type PSS; a step of computing an AVR transfer function from the AVR control parameter; and a step of computing the generator torque transfer function separately for the wide-area mode and the local mode making use of the constants in the dynamic block diagram, the general transfer function of the PSSs, and the AVR transfer function. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  TECHNICAL FIELD The present invention relates to a method for calculating a generator torque transfer function used for evaluating a control constant of a power system stabilizer (Power System Stabilizer, hereinafter abbreviated as PSS) for stabilizing the power system, and a program therefor. Is.

  Due to the difficulty of locating power plants in the vicinity of large cities, the power system is becoming larger and more complex due to the increased capacity and remote distribution of power sources and wide-area interconnection of power interchange. Therefore, not only a short-period oscillation phenomenon (hereinafter referred to as local mode) of about 1 second due to the generator alone, but also a long-period oscillation phenomenon (hereinafter referred to as wide-area mode) of about 3 seconds with poor damping affecting the wide area of the system. ) May occur and adversely affect the stability of the system.

  For stabilization of such a large-scale power system, PSS added to the generator excitation device is effective. As an element of the generator excitation device, the PSS detects the fluctuation of the power system from changes in the generator active power, angular velocity, etc., and generates a stabilization signal for suppressing the fluctuation of the system according to the detected value. A stabilization signal is added to the terminal voltage setting value of the generator excitation system to adjust the field voltage to suppress power fluctuation.

  As shown in Fig. 1, the current PSS control constant design method uses a Bode diagram in which the power system is reduced to a one-machine infinite bus system, and is effective in suppressing local mode. Since the phase difference between the machine and the infinite bus becomes large, it is impossible to realize the fluctuation of the wide area mode, and therefore, it is difficult to suppress the wide area mode.

Therefore, a reduced model has been developed to stabilize the wide area mode. This is a system in which an intermediate load is introduced between the synchronous machine and the contraction point (single-machine intermediate load model), paying attention to the basic equation of the synchronous machine's oscillation cycle and the fluctuation phenomenon of the interconnection system. (Non-Patent Document 1)
Michigami, "Development of multiple PSS to suppress long-period oscillation of interconnected system and study on oscillation model", IEEJ Transactions B, IEEJ, Jan. 1995, Vol.115, No.1, 42P

In this contraction model, the active power P _L of the intermediate load is made equal to the active power P _g of the generator, and the reactive power Q _L is determined so that the voltages at the intermediate point and the infinite bus are equal. The position of the intermediate load is appropriately installed near the generator. It is possible to realize a medium load and long-period fluctuation when the infinite system changes the generatrix of reactance X _s reactive power Q _g the generator as a parameter in this state.

However, in an actual power system, P _L = P _g is not satisfied, and the position of the load is not appropriate. In addition, the reactance Xs obtained from long-period fluctuation does not reflect the dynamic instability phenomenon existing in the actual power system. Furthermore, in the one-machine intermediate load model, the influence of the reduced load near the generator on the dynamic stability is not considered, but the voltage characteristics of the load are not only the dynamic stability of the generator but also the control constant of the PSS. The setting is also considered to have an influence. This is because the load varies depending on the season and time zone. Therefore, the generator torque transfer function determined using such inaccurate conditions is inaccurate. Since it is problematic to evaluate the suitability of the PSS control constant using such an inaccurate generator torque transfer function, the control constant of the PSS is finally determined by the stability analysis by an actual multi-machine system. It was necessary to evaluate the suitability of the system, and the labor was excessive.

  In general, PSS includes ΔP-type PSS that detects fluctuations in the power system from changes in generator active power and Δω-type PSS that detects from changes in angular velocity. The effect is designed independently. Since the independently designed ΔP-type PSS and Δω-type PSS interfere with each other in some cases, it is necessary to correct the control constant of the PSS by stability analysis using a multi-machine system. It is desired to design and consider all of them.

Therefore, in order to solve the first problem, the present inventor, as a system contraction method expressing the electric power system by one machine and one load, saves the phase of the generator and the voltage characteristics of the load (one machine and one load). 3 branch) was used (Non-Patent Document 2). By reducing the multi-machine system to one machine and one load using this contraction method, the external reactance of the one-machine intermediate load model can be obtained, and the dynamic instability phenomenon existing in the actual power system can be reflected.
Yamagishi, Hosoki, Komami, Minakami, “A Study on Reduction of Electric Power System Including Induction Machine”, Proceedings of the IEEJ Power Energy Division Conference (Volume B), IEEJ, August 2002, 673P

  Non-Patent Document 2 described above describes the following contents. First, as shown in FIG. 14 (a), it is considered that a system before contraction in which two partial systems are paralleled is contracted into one system as shown in FIG. 14 (b). That is, two branches B connected in series between the contraction point A and the generator G are interposed, and another branch B is branched from the node N interposed between the two branches B to be terminated. It is the system which connects load L to.

縮約点から各発電機又は負荷に至るブランチのインピーダンスＺと有効電力Ｐの積の累計を複素位相θと呼ぶことにする。そして、θの実部は近似的に、有効電力による電圧上昇又は降下に相当する。θの虚部は、近似的に縮約点から見た発電機もしくは負荷の位相をラジアン単位で表した値となる。ここで系統のインピーダンスによる損失は量的に少ないので無視すると、各発電機の複素位相θ_iG、縮約後の発電機の複素位相θ_Gは、以下の関係式（b２）（b３）で表される。但し、Z_iS:縮約点から分岐箇所までの短絡インピーダンス、Z_iG:分岐箇所から発電機までの短絡インピーダンス、P_iG:発電機有効電力、P_iL:負荷消費電力、i＝１,２とする。

また、各負荷の複素位相θ_iL、縮約後の負荷の複素位相θ_Lも同様に以下の関係式（b４）（b５）で表される。但し、Z_iL:分岐箇所から負荷までの短絡インピーダンスとする。

Here, as represented by the following formula (b1),

The cumulative product of the impedance Z of the branch from the contraction point to each generator or load and the active power P is referred to as a complex phase θ. The real part of θ corresponds approximately to a voltage increase or decrease due to active power. The imaginary part of θ is a value that approximately represents the phase of the generator or the load as viewed from the contraction point in radians. Here, since the loss due to the impedance of the system is small in quantity, if ignored, the complex phase θ _iG of each generator and the complex phase θ _G of the reduced generator are expressed by the following relational expressions (b2) and (b3). Is done. However, Z _iS : Short-circuit impedance from the contraction point to the branch point, Z _iG : Short-circuit impedance from the branch point to the generator, P _iG : Generator active power, P _iL : Load power consumption, i = 1, 2 To do.

Similarly, the complex phase θ _{iL of} each load and the complex phase θ _L of the reduced load are also expressed by the following relational expressions (b4) and (b5). However, Z _iL : Short-circuit impedance from the branch point to the load.

以上の（b２）から（b７）の関係式を利用して、縮約前後の有効・無効電力損失を比較すると、縮約前後でかかる損失が保存され、以下の関係式（b８）が成立する。

Assuming that the weighted average by the transmission end active power of the generator θ _G is stored (matched or approximated) before and after contraction, and that the weighted average by the reception end active power of the load θ _L is stored, The following relational expressions (b6) and (b7) are obtained.

Using the relational expressions (b2) to (b7) above, comparing the active and reactive power losses before and after contraction, the loss is preserved before and after contraction, and the following relational expression (b8) holds .

Here, in order to obtain the impedances Z _S , Z _G , Z _L of the three branches after contraction, the relational expressions (b2) to (b7) of the complex phases θ _G , θ _L and the lower order from the contraction point The existing general formula (short-circuit capacity method) for determining the short-circuit capacity (Z _S + Z _G + Xd ′) by looking at the system is used. Here, Xd ′ is the direct-axis transient reactance of the generator after contraction, and is obtained by a general formula separately. Then, the relational expressions (b3) and (b6) and the relational expressions (b5) and (b7) are combined into one function expression, and the existing general expression for obtaining the short-circuit capacity described above is used for these two function expressions. For example, for three unknowns (Z _S , Z _G , Z _L ), there are three relational expressions using such unknowns as variables, so the unknowns can be obtained. And it is pointed out that even if the subordinate system is complex and large-scale, it is possible to finally reduce it to one machine, one load and three branches by repeating the above procedure.

  In the one-machine, one-load, three-branch method described above, since the impedance of the load branch is taken into consideration, it is considered that the voltage stability of the load is preserved and the stability of the power system can be calculated with high accuracy.

  The present invention was created in consideration of the above circumstances, and its purpose is to adopt a model (one machine, one load, three branches) reflecting a dynamic instability phenomenon existing in an actual power system, and a ΔP type PSS. And the suppression effect of the Δω-type PSS are considered together, thereby making it easy to evaluate the control constant of the PSS and simplifying the correction work of the control constant as much as possible.

  The method of grasping the PSS fluctuation suppression effect in the one-machine, one-load, three-branch model considering the load characteristics in the vicinity of the generator is as follows. The dynamic stability is a problem in a partial system that is loosely connected to the main system, and when it is reduced, it is expressed as shown in FIG. In transient stability, the impedance of the load branch becomes a problem, but in the dynamic stability analysis that handles minute changes, the action of the load branch can be included in the voltage characteristics of the load.

ここで、Ｐg：発電機有効電力、 Ｑt：発電機無効電力、 Ｑg：中間ノード点における発電機ブランチの無効電力、Ｐs：中間ノード点における無限大母線ブランチの有効電力、 Ｑs：中間ノード点における無限大母線ブランチの無効電力、 Ｐl(エル)：負荷消費有効電力、 Ｑl(エル)：負荷消費無効電力、 Ｑc：調相設備無効電力、Ｖt：発電機端子電圧 Ｖl(エル)：中間ノード点における電圧 δt：発電機端子における位相 δl(エル)：中間ノード点における位相である。なお、Ｑl(エル)は下記式（１−６）で表される。

At this time, the tidal current state is as shown in equations (1-1) to (1-5).

Where Pg: generator active power, Qt: generator reactive power, Qg: reactive power of generator branch at intermediate node point, Ps: active power of infinite bus branch at intermediate node point, Qs: at intermediate node point Reactive power of infinite bus branch, Pl (L): Load consumption active power, Ql (L): Load consumption reactive power, Qc: Phase adjustment equipment reactive power, Vt: Generator terminal voltage Vl (L): Intermediate node point Δt: Phase at the generator terminal δl (el): Phase at the intermediate node point. Ql is expressed by the following formula (1-6).

負荷の電圧特性（有効・無効電力）および調相設備の電圧特性をα、β、γとし、負荷消費有効電力、無効電力の微小変化分ΔＰg、ΔＱl(エル)、ΔＱcを微小変化分ΔＶl(エル)で表すと、下記式（７−１）〜（７−３）となる。負荷は季節や時間帯によって変動するので、負荷の電圧特性を考慮することは重要である。定電力性の負荷が多い場合を考慮するにはα、βに小の値を入れ、逆に少ない場合を考慮するにはα、βに大の値を入れる。なお、γの値は既知で、一定値である。

These minute changes are expressed by equations (2) to (6).

The voltage characteristics (active / reactive power) of the load and the voltage characteristics of the phase adjusting equipment are α, β, γ, and the minute changes ΔPg, ΔQl (el) and ΔQc of the load active power and reactive power ΔVl ( L), the following formulas (7-1) to (7-3) are obtained. Since the load varies depending on the season and time zone, it is important to consider the voltage characteristics of the load. To consider the case where there is a large constant power load, enter a small value in α and β, and conversely, enter a large value in α and β to consider the case where the load is small. The value of γ is known and is a constant value.

そして、（７−１）から（８−２）式より（９）式が得られる。

この関係式を用いて４個の微小変化分のうち２個を消去できる。同期機と無限大母線の間の関係を知りたいのであるから、消去すべきは負荷分岐点の諸量の方である。そこで左側から行列を掛け算して（つまり行のみの演算を行って）左辺の行列を単位行列に変換すると、（１０）式のような形になる。これを用いて以後に表れるΔδl(エル)、ΔＶl(エル)を消去するのである。

また、（１０）式を展開して（１０−１）式が得られる。

Here, the balance condition for the minute change of the active / reactive power at the load branch point is expressed by the following equations (8-1) and (8-2).

Then, equation (9) is obtained from equations (7-1) to (8-2).

Using this relational expression, two of the four minute changes can be erased. Since we want to know the relationship between the synchronous machine and the infinite bus, what should be eliminated is the amount of load branching points. Therefore, when the matrix on the left side is converted into a unit matrix by multiplying the matrix from the left side (that is, calculating only the row), the form is as shown in equation (10). By using this, Δδl (el) and ΔVl (el) appearing thereafter are erased.

Further, expression (10-1) is obtained by expanding expression (10).

Here, when the equation (10-1) is substituted into the equations (2) and (3) and Δδl (el) and ΔVl (el) are deleted, equations (11) and (12) are obtained.

ここで、Ｅq ：横軸リアクタンス背後電圧、δ：発電機内部位相、Ｘq：横軸同期リアクタンス、Ｘd’：直軸過渡リアクタンス、Ｉd：電気子電流の直軸成分、Ｉq ：電気子電流の横軸成分、Ｖd：端子電圧の直軸成分、Ｖq：端子電圧の横軸成分、ψfd：界磁巻線の磁束鎖交である。 The inside of the generator is as shown in equations (13) to (19).

Here, Eq: horizontal reactance back voltage, δ: generator internal phase, Xq: horizontal axis synchronous reactance, Xd ': direct axis transient reactance, Id: direct axis component of electron current, Iq: transverse of electron current Axial component, Vd: direct-axis component of terminal voltage, Vq: horizontal-axis component of terminal voltage, ψfd: flux linkage of field winding.

Here, by using Pg1, Pg2, Qt1, and Qt2 in the equations (11) and (12), the minute changes of Id and Iq are calculated as in the following equations (20-1) and (20-2).

ここまで準備してＰg
、Ｑt の微小変化分を下記（２３）（２４）式のように求める。

（２３）、（２４）式に（１１）、（１２）、（２０−１）、（２０−２）、（２１）、（２２）式を代入して整理すれば関係式（２５）を得る。

式（２５）の行列の各要素は（２５−１）から（２５−８）式の通りとなる。

（２５）式も左から行列を掛け算して左辺を単位行列にでき、（２６）式のようになる。

また、（２６）式を展開して（２６−１）式のようになる。

Further, the minute change of Vd and Vq is calculated as in the following equations (21) and (22).

Prepare so far, Pg
, Qt is obtained by the following equations (23) and (24).

By substituting the equations (11), (12), (20-1), (20-2), (21), (22) into the equations (23), (24) and rearranging, the relational equation (25) can be obtained. obtain.

Each element of the matrix of Expression (25) is as shown in Expressions (25-1) to (25-8).

Equation (25) can also be multiplied by a matrix from the left to make the left side a unit matrix, as shown in Equation (26).

Further, expression (26) is expanded to become expression (26-1).

ここにＫ１：発電機出力に対する発電機内部位相微分係数、Ｋ２：発電機出力に対する発電機端子電圧微分係数とすると、これらは下記式（２８）（２９）となる。

Subsequently, the result of the following expression (27) is obtained by substituting the expression (26) into the expression (11).

If K1 is a generator internal phase differential coefficient with respect to the generator output and K2 is a generator terminal voltage differential coefficient with respect to the generator output, these are expressed by the following equations (28) and (29).

それ故、下記式（３１）から（３２）式が得られる。但し、Ｋ３：界磁巻線の界磁鎖交に対する界磁巻線の界磁鎖交微分係数、Ｋ４：界磁巻線の界磁鎖交に対する発電機内部位相微分係数。

(26)式から直接次の関係を得る。但し、Ｋ５：発電機端子電圧に対する発電機内部位相微分係数、Ｋ６：発電機端子電圧に対する界磁巻線の界磁鎖交微分係数。

（２７）〜（３６）式の関係から図３に示す１機１負荷３ブランチの発電機動態ブロック図が得られる。 The most basic description of the field magnetic flux is as shown in the following equation (30).

Therefore, the following equations (31) to (32) are obtained. Where K3: field linkage differential coefficient of field winding with respect to field linkage of field winding, K4: generator internal phase differential coefficient with respect to field linkage of field winding.

The following relationship is obtained directly from the equation (26). However, K5: Generator internal phase differential coefficient with respect to generator terminal voltage, K6: Field linkage differential coefficient of field winding with respect to generator terminal voltage.

From the relationship of the equations (27) to (36), the generator dynamic block diagram of one machine, one load and three branches shown in FIG. 3 is obtained.

それ故下記（３７−１）式が導かれる。

ここで、ΔＰ型ＰＳＳによる伝達関数をＧp（ｓ）、Δω型ＰＳＳによる伝達関数をＧω(s) とすると、ΔＰ＋Δω型ＰＳＳの総合的な伝達関数は下記式（３８）となり、この伝達関数を用いることで、ΔＰ型およびΔω型ＰＳＳの相互影響を調べることができる。

When the field magnetic flux ψfd is arranged from the block diagram of FIG. 3, the following equation (37) is obtained.

Therefore, the following expression (37-1) is derived.

Here, if the transfer function by the ΔP type PSS is Gp (s) and the transfer function by the Δω type PSS is Gω (s), the total transfer function of the ΔP + Δω type PSS is expressed by the following equation (38). By using it, the mutual influence of ΔP type and Δω type PSS can be examined.

但しGi：電圧検出回路のゲイン、Ti：電圧検出回路の遅れ時定数、Ga：ＡＶＲ定常ゲイン、Ta：ＡＶＲの遅れ時定数、Teu：ＡＶＲの位相進み補償時定数、Ted：ＡＶＲの位相遅れ補償時定数、Hb：乱調防止回路のフィードバックゲイン、Tb：乱調防止回路の遅れ時定数。
また、ＰＳＳブロック図は図５のように表されることから、Ｇ(s)は下記式（３８−２）のように表される。

但しT_rp：ΔP型PSSのリセット回路時定数、 G_p：ΔP型PSSの定常ゲイン、T_u1：ΔP型PSSの位相進み補償時定数第１段、T_u2：ΔP型PSSの位相進み補償時定数第２段、T_d1：ΔP型PSSの位相遅れ補償時定数第１段、T_d2：ΔP型PSSの位相遅れ補償時定数第２段、
Δω型PSS定数としてはT_rω：Δω型PSSのリセット回路時定数、 G_ω：Δω型PSSの定常ゲイン、T_uu1：Δω型PSSの位相進み補償時定数第１段、T_uu2：Δω型PSSの位相進み補償時定数第２段、T_dd1：Δω型PSSの位相遅れ補償時定数第１段、T_dd2：Δω型PSSの位相遅れ補償時定数第２段。 Since the AVR block diagram is expressed as shown in FIG. 4, the AVR transfer function F (s) is expressed by the following equation (38-1).

Where Gi: voltage detection circuit gain, Ti: voltage detection circuit delay time constant, Ga: AVR steady gain, Ta: AVR delay time constant, Teu: AVR phase lead compensation time constant, Ted: AVR phase delay compensation Time constant, Hb: Feedback gain of anti-stabilization circuit, Tb: Delay time constant of anti-stabilization circuit.
Further, since the PSS block diagram is represented as shown in FIG. 5, G (s) is represented as the following equation (38-2).

However, T _rp : ΔP-type PSS reset circuit time constant, G _p : ΔP-type PSS steady gain, T _u1 : ΔP-type PSS phase lead compensation time constant 1st stage, T _u2 : ΔP-type PSS phase lead compensation Constant second stage, T _d1 : Phase delay compensation time constant first stage of ΔP type PSS, T _d2 : Phase delay compensation time constant second stage of ΔP type PSS,
[Delta] [omega type PSS as constant _T rω: Δω type PSS reset circuit time constant, G _omega: steady-state gain of [Delta] [omega type PSS, T _UU1: first stage phase lead compensation time constant of [Delta] [omega type _PSS, T uu2: Δω type PSS Phase lead compensation time constant second stage, T _dd1 : Δω-type PSS phase delay compensation time constant first stage, T _dd2 : Δω-type PSS phase delay compensation time constant second stage.

そして、ｓ＝ｊωと置き換えれば、系全体のΔＴmからΔδに至る伝達関数は下記式（４０)のようになる。

そして、電力動揺の角周波数ωsは（４０）式の分母の実部＝０を解いて下記式（４１）の通りである。

この角周波数における系全体の制動トルク係数は下記式（４２）の通りである。

Further, the synchronization torque coefficient Ks and the braking torque coefficient Kd excluding the generator-specific braking force are defined as in Expressions (39) and (39-1) using Expressions (37) and (38).

If replaced with s = jω, the transfer function from ΔTm to Δδ of the entire system is expressed by the following equation (40).

Then, the angular frequency ωs of the power fluctuation is expressed by the following formula (41) by solving the real part = 0 of the denominator of the formula (40).

The braking torque coefficient of the entire system at this angular frequency is expressed by the following equation (42).

但しＭ：同期機の慣性定数、Ｄ：同期機の制御係数
従って開ループ一巡伝達関数は、工学的には位相反転している状態を正とするので、発電機トルク伝達関数と発電機回転子伝達関数を利用して下記式（４４）のように書ける。

It is well known that the gain margin or phase margin of the open loop circuit transfer function can be used for stability determination. The synchronization / braking torque coefficient is an amount corresponding to the feedback gain of the route from Δδ to ΔPg. Needless to say, the forward gain is the generator rotor route from -ΔPg to Δδ, and since the Δω-type PSS has already been transferred to the ΔP-type, the generator-rotor transfer function is expressed by the following equation (43). Can be written as

However, M is the inertia constant of the synchronous machine, D is the control coefficient of the synchronous machine, and therefore the open-loop circuit transfer function is positive when the phase is inverted in terms of engineering, so that the generator torque transfer function and the generator rotor Using the transfer function, it can be written as the following equation (44).

従って、１機１負荷３ブランチ（広域モード）のＰＳＳ制御定数の適否の判別は、この閉ループ一巡伝達関数で分かり、不安定である場合は、ある周波数において開ループ一巡伝達関数はゲイン余裕、位相余裕が負になる。 The closed-loop circuit transfer function can be expressed by the following equation (45).

Therefore, the suitability of the PSS control constant of one machine, one load and three branches (wide area mode) can be determined by this closed loop circuit transfer function. If unstable, the open loop circuit transfer function has a gain margin and a phase at a certain frequency. The margin becomes negative.

  On the other hand, when determining the stability of the PSS control constant of the one-machine infinite bus (local mode), when calculating K1 to K6, Xs is set to approximately 0, and Pl (El) is set to 0. The generator torque transfer function can be obtained by calculating the above, and then suitability can be determined in the same manner.

  The present invention realizes a wide-area mode that is close to an actual system by utilizing a one-machine, one-load, three-branch system reduction method for realizing a wide-area mode. By this method, the accurate coefficient K1, K2, K3, K4, K5, and K6 in the block diagram of one machine, one load, and three branches can be obtained. It becomes possible.

  In the present invention, when calculating K1, K2, K3, K4, K5, and K6 in the block diagram of one machine, one load and three branches, the voltage characteristic of the load in the vicinity of the generator is taken into consideration, so the dynamic stability is deteriorated. The effect of PSS can be grasped even when the load of the constant power characteristics causing the load is large or small, and the semi-optimization of the PSS control constant having high robustness is possible.

  In the present invention, K1, K2, K3, K4, K5, and K6 calculated from the system in which the local mode is a problem and K1, K2, K3, K4, K5, and K6 that are calculated from the system in which the wide area mode is a problem By using the two types of generator torque transfer functions, the effects of PSS in both the local mode and the wide-area mode can be grasped, and the PSS control constant having high robustness can be quasi-optimized.

  The present invention converts the effect of the Δω type PSS into the ΔP type, that is, advances the amount of delay of the generator by 1 / (M · s + D), thereby obtaining the collective effect of the ΔP type + Δω type PSS. It is to grasp. From this, it becomes possible to grasp the influence of mutual interference between the ΔP type and the Δω type.

  In addition, since one machine infinite bus close to the real system and one machine, one load and three branches are adopted for the local mode and wide area mode, the stability analysis by the real system is not required, and the work to bring the PSS control constants close to optimum. It becomes easy to do.

  The stability evaluation method for the PSS control constant is executed by a computer sequentially executing a reduction program for one machine, one load, three branches, a generator torque transfer function calculation program, and a PSS control constant stability evaluation program. Use the method that the operator confirms.

When a reduction program for one machine, one load and three branches is executed by a computer, a data input step S1, a power flow calculation step S2, a complex phase calculation step S3, a weighted average calculation as shown in FIG. Step S4, short-circuit impedance calculation step S5, branch impedance calculation step S6 are sequentially performed, and the computer performs various means (data input means 7, power flow calculation means 8, complex phase calculation means 9, weighted average calculation as shown in FIG. It functions as means 10, short-circuit impedance calculating means 11, and branch impedance calculating means 12, and impedances Z _S , Z _L , and Z _{G of} three branches of one machine, one load, and three branches are obtained.

When this program is executed, first, the data input means 7 functions to execute the data input step S1. In the data input step S1, the table-like input / output form 13 stored in the storage device is read and the input / output form 13 is displayed on the output device as shown in Table 1. The input / output form 13 has both an input form and an output form, and is provided with a heading column indicating input / output items related to a branch (track) and an input / output column for each heading column.

The input form corresponds to each branch before contraction, FROM: upper node number, TO: lower node number, R: real part of impedance, X: imaginary part of impedance, name, P _G : generator of lower node Active power, P _L : Load power consumption of lower node, W _G : Headings composed of generator rated capacity of lower nodes are described in order in a horizontal row, and an input field is provided below the heading. Although a heading column named “branch” is not provided, a branch is specified by specifying an upper node number and a lower node number.

Output form is current, complex phase real part / imaginary part, G (FROM) / B (FROM): real part / imaginary part of short-circuit admittance corresponding to upper node, G (TO) / B (TO): lower node The heading of the real part and the imaginary part of the short-circuit admittance corresponding to is described in a horizontal row, and an output field is provided below the heading. Also, output headings that are not directly related to the branch before contraction (for example, total active power, complex phase real part total, complex phase imaginary part total, weighted average real part, weighted average imaginary part, Z =: contraction Short-circuit impedance at point, Z _S =: contracted uppermost branch impedance, Z _G =: contracted generator-side branch impedance, Z _L =: contracted load-side branch impedance, Loss: loss) Is provided, and a corresponding output field is provided below it.

Here, as a subordinate system of the power system before contraction, a state is assumed in which a plurality of branches are radially branched from the contraction point (the highest node) as shown in FIG. Humans number the subordinate nodes according to the following rules.
a): From the highest node to the end node, number each node that passes through one route in order (from young to old, 1, 10, 11, 20, 21, 30, 31, etc.) )wear.
b): However, if there are multiple lower branches connected to the upper node, any one branch is arbitrarily selected, and the following numbers are assigned to the lower nodes of the selected branch (for example, , There are two branches for the upper node No. 10, but the lower node of the lower branch is assigned No. 11). b.1): When there is only one lower branch connected to each upper node, the next number is assigned to the lower node of that branch (for example, the lower node is numbered 10 with respect to the upper node 1) )
c): Repeat the rules from a) to b.1) and number the end nodes (for example, number 11).
d): After numbering the end node, return to the upper node of the branch having the end node as the lower node (for example, return to the 10th node for the 11th end node).
e): It is checked whether another branch branches to the lower node on the returned upper node.
e.1): If another branch is found as a result of the check, it is checked whether each lower node of all branches is numbered.
e.2): If there is one or more sub-nodes that are not numbered as a result of the examination, select one of the sub-nodes or one of the sub-nodes and select the next number. (For example, 20 is assigned to a lower node that is not numbered with respect to the 10th node). Then, follow the laws of a) to f).
e.3): On the other hand, if all lower nodes are numbered, the process returns to the immediately preceding upper node. And follow the laws of e) to f).
e.4): As a result of the examination, if another branch does not branch to the lower node in the returned upper node, the operation returns to the upper node. And follow the laws of e) to f).
f): When all nodes are numbered, the numbering is finished.

  In accordance with the above rules, in the input column in the horizontal row of the input form table, as shown in Table 1, the upper node number and lower node number, impedance, lower node generator active power, lower node The user inputs the load power consumption and the generator rated capacity of the lower node from the input device as numerical data. The generator active power, load power consumption, and generator rated capacity are input only when the lower node of each branch is a terminal node, and are not input when the node is not a terminal node. Upon receiving the input completion notification, various input data are stored in the storage device, and the input data are displayed as they are on the input form. Subsequently, the power flow calculation means 8 functions to execute the power flow calculation step S2. The

  Note that in the input form table, when attention is paid to the numbers of the lower nodes, it can be seen that all the lower node numbers are different, and there is only one lower node corresponding to one number. From this, it can be said that the branch connected to the lower node can be selected by selecting the lower node, and as a result, the connection state between the branch and each node can be grasped.

これは、下位側のブランチの潮流を加算することで上位側のブランチの潮流が求まることを意味する。 The tidal current calculation step S2 is created based on the following idea. As shown in FIG. 9, assuming a state where the branches of the lower system are radially branched from node i to j and k, the power flow of the branch on the contraction point side is expressed by the following formula (b9). The

This means that the flow of the upper branch can be obtained by adding the flow of the lower branch.

  In the power flow calculation step S2 based on the above idea, first, the oldest number (30 in Table 1) is extracted from the FROM (higher node) numbers, and the generator active power and load of each branch corresponding to the extracted FROM are extracted. The power consumption is read from the storage device and summed, and the total result is displayed as a branch flow in the output form and stored in the storage device. Here, the generator active power is summed as a positive value and the load power consumption is summed as a negative value (for example, 0.01 in the 30-31 branch). Subsequently, the oldest old number is extracted from the FROM numbers (20 in Table 1), and the generator active power and load power consumption of each branch corresponding to the extracted FROM are read from the storage device and summed (FROM 20 In the case of No., the total value is 0), and further, the branch flow with the number corresponding to the TO number corresponding to the extracted FROM as the FROM number is read from the storage device (the flow of the No. 30 branch is 0.01), Add to the total value (0.01) and display the calculation result in the output form. Thereafter, all branch flows are calculated in the same manner, and the results are displayed. That is, all branch tides are calculated by sequentially calculating the branch tides from the oldest number to the younger number among the FROM numbers. When all the branch power flows are calculated, the complex phase calculation means 9 functions and the complex phase calculation step S3 is executed.

つまり、今求めようとする下位ノードの複素位相は、その下位ノードに接続する上位側のブランチの複素位相に、上位ノードの複素位相を加算することによって表される（例えば、下位ノード１０の複素位相の実部は、上位ノード１の複素位相が０であるので、上位側のブランチの複素位相の実部に等しくなり、Ｒ（0.1）×潮流（−0.05）＝−0.005となる。）。従って、下位ノードの番号うち若番号から老番号の方向に逐次計算することにより、各ブランチの下位ノードの複素位相が求まる。 The complex phase calculation step S3 is created based on the following idea. The complex phase of each node viewed from the contraction point is expressed as shown in the following formula (b10). Where θ: complex phase, i: upper node number, j: lower node number.

That is, the complex phase of the lower node to be obtained now is expressed by adding the complex phase of the upper node to the complex phase of the upper branch connected to the lower node (for example, the complex phase of the lower node 10). The real part of the phase is equal to the real part of the complex phase of the upper branch since the complex phase of the upper node 1 is 0, and R (0.1) × tidal current (−0.05) = − 0.005. Therefore, the complex phase of the lower node of each branch can be obtained by sequentially calculating the lower node number from the younger number to the old number.

  In the complex phase calculation step S3 based on the above-described idea, the above equation (b10) is read from the storage device, and the real part and imaginary part of the impedance of the corresponding branch according to the order from the lower number to the old number in the lower node. (R · X), the branch flow is read from the storage device and substituted into the above formula (b10) to solve the calculation formula, and the calculation result is divided into a real part and an imaginary part and displayed in each output column and stored. Save to device. When the complex phases of all the lower nodes are calculated, the weighted average calculating unit 10 functions to execute the weighted average calculating step S4.

一方、各負荷のノードにおける複素位相の加重平均は、下記式（ｂ１２）で表される。

The weighted average calculation step S4 calculates a weighted average of complex phases at each generator node and each load node, and is created based on the following concept. The weighted average of complex phases at each generator node is expressed by the following equation (b11).

On the other hand, the weighted average of complex phases at each load node is expressed by the following equation (b12).

  In the weighted average calculation step S4 based on the above idea, the above formulas (b11) and (b12), the branch flow, and the real and imaginary parts of the complex phase are read from the storage device and substituted into the above formulas (b11) and (b12). Then, the calculation formula is solved, and the value of the calculation result and the denominator / numerator value of each formula are displayed in the corresponding output column and stored in the storage device. Subsequently, the short-circuit impedance calculating unit 11 functions to execute the short-circuit impedance calculating step S5.

但し、Z_jkはブランチインピーダンス（Z_jk＝R_jk＋jX_jk）、Z_kはノードkから下位方向を見た場合の短絡インピーダンスを示す。ノードkが末端ノードで発電機の場合は，発電機による短絡インピーダンスを考慮し、 Z_k＝jX_k＝j（1/発電機定格容量）×0.3とする。末端ノードが負荷の場合にはその負荷の短絡インピーダンスは∞でありZ_k=∞となる。
従って、ノードの老番号から若番号に向かって順番に各ノードの短絡インピーダンスを計算することによって、縮約点から発電機を見た短絡インピーダンスが求まる。なお、今回は、以後の計算のし易さを考慮して、上記式の逆数（短絡アドミタンス）である下記式（ｂ１５）

に基づいて各ノード毎に短絡アドミタンスを計算する。但し，末端ノードの場合はZ_jk=0とし、発電機の場合はY_j=Y_k=1/Z_k=-j×発電機定格容量/0.3、負荷の場合はY_j=Y_k=1/Z_k=1/∞=0となる。 The short-circuit impedance calculation step S5 is created based on the following idea. Here, the short-circuit impedance Z at the contraction point, the direct-axis transient reactance X _d ′ of the generator after contraction, and the impedance (Z _S + Z) of the two branches connecting the contraction point and the generator after contraction _G ) is finally determined. Assuming that the branch of the lower system branches radially from node i to j and k as shown in FIG. 9, the short-circuit impedance of node j is expressed by the following equation (b13).

However, Z _jk represents a branch impedance (Z _jk = R _jk + jX _jk ), and Z _k represents a short-circuit impedance when the lower direction is viewed from the node k. When node k is a terminal node and is a generator, Z _k = jX _k = j (1 / generator rated capacity) x 0.3 considering the short-circuit impedance of the generator. When the terminal node is a load, the short-circuit impedance of the load is ∞ and Z _k = ∞.
Therefore, by calculating the short-circuit impedance of each node in order from the old number of the node to the young number, the short-circuit impedance of the generator viewed from the contraction point can be obtained. In this case, in consideration of ease of subsequent calculations, the following formula (b15) which is the reciprocal (short-circuit admittance) of the above formula

Based on the above, the short-circuit admittance is calculated for each node. However, Z _jk = 0 for the end node, Y _j = Y _k = 1 / Z _k = -j × generator rated capacity / 0.3 for the generator, Y _j = Y _k = 1 for the load / Z _k = 1 / ∞ = 0.

発電機定格容量Ｗ_Ｇｉの逆数は発電機定格容量を基準容量に合わせていることを表す。また、0.3は直軸過渡リアクタンスを意味し、本来は各発電機固有の値を用いるべきである。しかし、直軸過渡リアクタンスは発電機の種類や大きさによらず自己容量ベースでほぼ３０％であるので、上記式（ｂ１６）の定数（一定値）として、0.3を設定してある。このようにすれば、入力データーが少なくてすみ、入力ミスによる計算間違いを減らせる。なお、入力フォームに直軸過渡リアクタンスの入力欄を設けても良いが、入力ミスの確率が上がる。最終的には最上位ノードの短絡アドミタンスＹを短絡インピーダンスＺに変換し、下記式（ｂ１７）のように最上位ノードの短絡インピーダンスＺから直軸過渡リアクタンスX_d’を引いて、縮約点と縮約後の発電機を繋ぐ直列接続した２本のブランチのインピーダンスZ_S+Z_Ｇを求める。

Further, the short-circuit admittance at the uppermost node includes the reduced direct-axis transient reactance X _d ′ of the generator after reduction, and it is necessary to remove that amount. Here, the straight axis transient reactance after contraction is expressed by the following equation (b16).

The reciprocal of the generator rated capacity W _Gi represents that the generator rated capacity is matched to the reference capacity. Moreover, 0.3 means a direct-axis transient reactance, and the value peculiar to each generator should be used originally. However, since the direct-axis transient reactance is approximately 30% on a self-capacity basis regardless of the type and size of the generator, 0.3 is set as the constant (constant value) in the above formula (b16). In this way, input data can be reduced and calculation errors due to input errors can be reduced. Although the input form may be provided with an input field for direct-axis transient reactance, the probability of an input error increases. Finally, the short-circuit admittance Y of the highest node is converted into a short-circuit impedance Z, and the direct-axis transient reactance X _d ′ is subtracted from the short-circuit impedance Z of the highest node as shown in the following equation (b17). The impedance Z _S + Z _G of two branches connected in series connecting the reduced generator is obtained.

3.1）：次に、その下位ノードにおけるブランチの上位ノードの番号と対応するインピーダンスの実部・虚部（Ｒ、Ｘ）を記憶装置から読み込み、上記式（ｂ１５）を解いて、計算結果を上位ノードの短絡アドミタンスとして実部と虚部に分けて出力フォームの対応する出力欄に表示すると共に記憶装置に保存する。
2.2）：一方、1）の抽出結果が１以上の場合は、同じ番号を付けている上位ノードの、短絡アドミタンスと上記式（ｂ１５）を記憶装置から読み込み、式（ｂ１５）を解いて、計算結果を実部と虚部に分けて出力フォームの対応する出力欄に表示すると共に記憶装置に保存する。
3.2）：次に、3.1）と同様の処理を行なう。
４）：１）〜3.2）の処理を繰り返し、最終的には最も若番の下位ノードについて上記処理を行うことによって、最も若番の上位ノードの短絡アドミタンスが算出される。
５）最上位ノードの短絡アドミタンスには、縮約後の発電機の直軸過渡リアクタンスX_d’の分を含んでいるので、その分を除去するために、下記式（ｂ１６）と全ての発電機ノードの発電機定格容量を記憶装置から読み込み、各発電機ノードについて下記式（ｂ１６）を解き、それら計算結果の総和を計算し、その計算結果を縮約後の直軸過渡リアクタンスX_d’として、記憶装置に保存する。

引き続き、最上位ノードの短絡アドミタンスを逆数に変換して、最上位ノードの短絡インピーダンスを求め、その計算結果を縮約点における短絡インピーダンスとして出力フォームに表示すると共に記憶装置に保存する。また、縮約点における短絡インピーダンスＺ、直軸過渡リアクタンスX_d’、下記式（ｂ１７）を記憶装置から読み込んで、その式を解き、その計算結果を、縮約点と縮約後の発電機を繋ぐ直列接続した２本のブランチのインピーダンスとして記憶装置に保存する。

その後にはブランチインピーダンス算出手段１２が機能して、ブランチインピーダンス算出ステップＳ６が実行される。 In the short-circuit impedance calculation step S5 based on the above idea, the following processing is performed in order from the oldest number of nodes to the youngest number.
1): First, the number of the lower node in each branch is read from the storage device, and the upper node assigned the same number as that lower node is extracted.
2.1): Next, if the extraction result is 0, since it is a terminal node, the generator rated capacity (W _G ) and the following equation (b15) corresponding to the read lower node are read from the storage device and the equation is solved. The calculation result is divided into a real part and an imaginary part as a short-circuit admittance of the lower node, and is displayed in the corresponding output column of the output form and stored in the storage device. If the terminal node is other than the generator (load), the generator rated capacity (W _G ) corresponding to the read lower node is not entered. In this case, the short-circuit admittance calculation result is Set to 0.

3.1): Next, the real part / imaginary part (R, X) of the impedance corresponding to the number of the upper node of the branch in the lower node is read from the storage device, the above equation (b15) is solved, and the calculation result is The short-circuit admittance of the node is divided into a real part and an imaginary part and displayed in the corresponding output column of the output form and is stored in the storage device.
2.2): On the other hand, if the extraction result of 1) is 1 or more, the short-circuit admittance and the above equation (b15) of the higher-level node assigned the same number are read from the storage device, and the equation (b15) is solved to calculate The result is divided into a real part and an imaginary part and displayed in the corresponding output field of the output form and saved in the storage device.
3.2): Next, the same processing as in 3.1) is performed.
4) The processing of 1) to 3.2) is repeated, and finally the above processing is performed for the youngest lower node, whereby the short-circuit admittance of the youngest upper node is calculated.
5) Since the short-circuit admittance of the most significant node includes the reduced direct-axis transient reactance X _d ′ of the generator after reduction, in order to remove this amount, the following formula (b16) and all power generation The generator rated capacity of the generator node is read from the storage device, the following equation (b16) is solved for each generator node, the sum of the calculation results is calculated, and the calculated result is reduced to the reduced direct-axis transient reactance X _d ′ Is stored in the storage device.

Subsequently, the short-circuit admittance of the highest node is converted into an inverse number to obtain the short-circuit impedance of the highest node, and the calculation result is displayed on the output form as the short-circuit impedance at the contraction point and stored in the storage device. Further, the short-circuit impedance Z, the direct-axis transient reactance X _d ′ at the contraction point, the following formula (b17) are read from the storage device, the formula is solved, and the calculation result is expressed as the contraction point and the contracted generator. Are stored in a storage device as impedances of two branches connected in series.

Thereafter, the branch impedance calculating means 12 functions to execute the branch impedance calculating step S6.

すると、下記式（ｂ１６．１）のように計算が行われる。

続いて、下記式（ｂ１６．２）のように計算し、

計算結果の出力欄には-0.045と表示する。 If the processing of 2.1) described above is specifically described with reference to FIG. 8 and Table 1, for example, when the lower node is No. 31, it is a terminal node, so the generator rated capacity W _G31 (0.02) First, 0.02 means 20 MVA, so the following formula (b16) is used to match the reference capacity of 1000 MVA.

Then, calculation is performed as in the following formula (b16.1).

Then, it calculates like the following formula (b16.2),

-0.045 is displayed in the output field of the calculation result.

In the branch impedance calculation step S6, the algorithm described in the section of the prior art is used, and the calculation results obtained in the weighted average calculation step S4 and the short-circuit impedance calculation step S5 (generator complex phase: θ _G , load complex phase: θ _L , two branch impedances Z _S + Z _G ) connected in series connecting the contraction point and the reduced generator, and the following three formulas (b17), (b18), and (b19) are read from the storage device: Substituting variables into the three equations, solving the three simultaneous equations, calculating the branch impedances Z _S , Z _G , Z _L of the three branches branching to the contracted Y type, and the calculation results in the output form It is displayed in the corresponding output field and saved in the storage device.

When the above steps are completed, the three branch impedances Z _S , Z _G , and Z _L after contraction are obtained, and the contract program of one branch, one load and three branches is completed.

  Next, when the generator torque transfer function calculation program is executed, the computer functions as various means, and as shown in FIGS. 10 and 11, input field display step S14, K1 to K6 calculation step S15, ΔP + Δω type PSS transmission. A function calculation step S16, an AVR transfer function calculation step S17, and a generator torque transfer function calculation step S18 are sequentially performed.

When this program is executed, the input field display means 19 first functions to execute the input field display step S14. In the input column display step S14, the input / output form (see Tables 2 and 3) stored in the storage device is read and displayed on the output device. Tables 2 and 3 are divided for convenience for the sake of convenience.

The input / output form is divided into an input form and an output form, and an item and its data input field are associated with the upper input form. Examples of the generator constant include Xd, Xd ′, TdO ′, Xq, M, and D. Examples of the AVR control constant include Gi, Ti, Ga, Ta, Teu, Ted, Hb, and Tb. ΔP-type PSS control constants are T _rp , G _p , _{Tu 1} , _{Tu 2} , T _d1 , T _d2 ,
The Δω type PSS control constant _{T rω,} G ω, include _{T uu1, T uu2, T dd1} , T dd2. Examples of the active / reactive power of the load and the voltage characteristic constant of the phase adjusting equipment include α, β, and γ. Examples of the system voltage include Vb, Vl (el), and Vt. As constant for 1 machine 1 load 3 _{branch, X t, X S, P} g, P I and the like, one-machine 1 load 3 results in branch contraction program (impedance Z _G, Z _S) and in that Since the input values (generator output P _G , load P _L ) are stored in the storage device, these values are read and the values of Z _G , Z _S, P _G , P _L are changed to X _t , X _S , P _g, automatically input to each data entry field as the value of P _I, use these values as the values for the wide-area mode. In the case of the local mode for one machine infinite bus, the values of X _t and P _g are used as they are, but the value of X _S can be regarded as 0 in the calculation used for the denominator of division. For a value as small as 0.001 (for example, 0.001) and a value of Pl, 0 is applied as a default condition. On the other hand, the user inputs constants that are not related to one machine, one load, and three branches. A known value is entered for the generator constant and the AVR control constant. As the ΔP-type and Δω-type PSS control constants, first, appropriate values that are empirically grasped are entered. Further, the values relating to the voltage characteristics of the load are values for confirming whether or not the stability can be maintained even if these values are slightly changed. For example, values of α: 0 to 3 and β: 0 to 4 are set. Put in. As the value related to the voltage characteristic of the phase adjusting equipment, a known value that is empirically known, for example, 2 is entered. For the system voltage, a known value is entered in both the local mode and the wide area mode. In response to the notification of the completion of input, various input data are stored in the storage device, and the input data are displayed as they are on the input form. Subsequently, the K1 to K6 calculation means 20 functions, and the K1 to K6 calculation step S15. Is executed.

K1 to K6 calculation step S20 reads necessary values and formulas sequentially for each wide-area mode and local mode (formulas described in the column of means for solving the problem), performs calculations listed below, and stores the results. Save to device. The P _S is calculated by using the equation (8-1) described above. δl (el) is calculated using the above-described equation (1-2). The [delta] _t is calculated by using the equation (1-1) described above. Qt is calculated using the above-described equation (1-3). Qg is calculated using equation (1-4). Qs is calculated using equation (1-5). Ql is calculated using the formula (1-6). Qc is calculated using equation (8-2). Eq is calculated using equation (13). δ is calculated using Equation (14). Id is calculated using equation (16). Iq is calculated using equation (17). Vd is calculated using equation (18). Vq is calculated using equation (19).

  Next, A13, A14, A23, and A24 are calculated using Expression (10-1). Next, Pg1 and Pg2 are calculated using Equation (11). Qt1 and Qt2 are calculated using Equation (12). Id1, Id2, and Id3 are calculated using Expression (20-1), and Iq1, Iq2, and Iq3 are calculated using Expression (20-2). B11, B12, B13, B14, B21, B22, B23, and B24 are calculated using Expression (25). B15, B16, B25, and B26 are calculated using Equation (26).

  Finally, K1 to K6 are calculated for each of the wide-area mode and the local mode using Expressions (28), (29), (32), (33), (35), and (36). Then, the result is saved in the storage device and output to the output form as shown in Tables 2 and 3.

  When the K1 to K6 calculation step S15 is completed, the various transfer function calculation units 21 to 23 function, and the ΔP + Δω type PSS transfer function calculation step S16, the AVR transfer function calculation step S17, and the generator torque transfer function calculation step S18 are sequentially performed. Is called. Specifically, the PSS total transfer function is calculated using equation (38-1), the AVR transfer function is calculated using equation (38-2), and the generator torque transfer function is calculated using equation (39-1). The program is stored in the storage device, and the generator torque transfer function calculation program ends.

Subsequently, a stability evaluation program for the PSS control constant is executed. Here, as shown in FIG. 10 or FIG. 11, various calculation means 24 and 25 function, and an open loop transfer function calculation step S26 and a closed loop transfer function calculation step S27 are sequentially performed. The user determines whether the control constants of the ΔP type PSS and the Δω type PSS are appropriate. First, in the open-loop circuit transfer function calculation step S26, the open-loop circuit transfer function B (s) corresponding to the frequency f = 0.1 to 10 (Hz) is calculated using the equations (43) and (44). The result is output to the output column in Tables 2 and 3 (example: 36 rows and H columns in Table 2). Subsequently, the following processing is performed in order to clarify the stability of the phase margin. Since s = jω, B (s) is expressed by the following formula (46).
B (s) = B (jω) = X + jY (46)
Therefore, B (s) is output in the form of X + jY.
Then, the gain B (dB) obtained by converting B (s) into dB is calculated by the following equation (47), and the result is output to the output column.
B (dB) = 20 log√ (X ² + Y ² ) (47)
Subsequently, the value φB (4.5 deg) obtained by dividing the phase φB (s) of B (s) by 4.5 (deg) from the viewpoint of making the graph display compact, and the result is calculated by the following formula (48). Is output to the output field.
φB (deg) = (arctan (Y / X)) / 4.5 (48)
At this time, with reference to the values of the open loop circuit B (s) and φB (deg) for each frequency, B (s) is positive and the phase of φB (s) is delayed by 180 or more (−180). /4.5 = less than -40 (deg)), it is judged unstable because there is no phase margin, and 1 is entered in the output column (eg, row 36 column E in Table 2). Otherwise, it is determined to be stable and 0 is output.

Subsequently, a closed loop transfer function calculation step is executed, and a closed loop loop transfer function C (s) corresponding to the frequency f = 0.1 to 10 (Hz) is calculated using Expression (45), and the result is output to the output column. (Example: 36 rows, E columns in Table 2). Subsequently, in order to clarify the stability of the phase characteristics, the following processing that reflects the stability of the phase margin is performed. C (s) is represented by the following formula (49).
C (s) = C (jω) = X + jY (49)
Therefore, C (s) is displayed in the output field in the form of X + jY.
Then, a gain C (dB) obtained by converting C (s) into dB is calculated by the following equation (50), and the result is output to the output column.
C (dB) = 20 log√ (X ² + Y ² ) (50)
Subsequently, for those having a phase margin, that is, having an unstable value of 0, the value of C (dB) = 20 log√ (X ² + Y ² ) is reflected as it is and displayed as a graph. On the other hand, those having no phase margin, that is, those having an unstable value are displayed in a graph as a value that clearly distinguishes C (dB) from others, for example, 39.9. In this manner, as shown in the graph of Table 3, it can be clearly seen that the output is unstable when the output is discontinuous at a predetermined oscillation frequency. FIG. 12 is an enlarged view of the left graph in Table 3. On the other hand, when the phase margin is not reflected, it becomes a continuous form as shown in FIG. 13, and it is not known at a glance that it is unstable. Then, as shown in Table 3, the graph display in the local mode and the wide area mode is output so as to be able to be contrasted, so that the stability in both modes can be grasped at once. Moreover, as shown in the lower side of Table 3, in both modes, the maximum value of gain C (dB) is output to the output column, and when the output value is 10 or less, the double circle is set larger than 10 as stable. If it is 20 or less, a single circle is output as a little stable, and if it is larger than 20 and 35 or less, it is output as slightly unstable x, and if it is 35 or more, it is output as unstable and a double x is output. Based on these output results, the user determines whether the control constants of the ΔP type and the Δω type PSS are appropriate. If it is determined that the control constant is inappropriate, G _p , G _ω , then T _d1 , T _dd1 , then T _u1 , depending on the degree of inappropriateness. T _UU1, then T _d2, T _dd2, to adjust the control constants to the next in the order of _{T u2,} T uu2, so as to obtain an appropriate output result by running the program again.

It is a figure which shows the one machine infinite model. It is a figure which shows a 1 machine 1 load 3 branch model. It is a figure which shows the generator dynamic block diagram of 1 machine 1 load 3 branches. It is a block diagram of AVR. It is a block diagram of ΔP + Δω type PSS. It is the flowchart which executed the 1 machine 1 load 3 branch contraction program. It is a block diagram which shows the computer which performed the 1 machine 1 load 3 branch reduction program. It is drawing which shows the subordinate system before contraction. It is explanatory drawing of the calculation method of a tidal current. It is the flowchart which performed the generator torque transfer function calculation program and the stability evaluation program of the PSS control constant. It is a block diagram which shows the computer which performed the generator torque transfer function calculation program and the stability evaluation program of the PSS control constant. It is a graph which shows the wide mode closed loop gain which considered the phase margin of the frequency characteristic. It is a graph which shows the wide mode closed loop gain which does not consider the phase margin of a frequency characteristic. (A) and (b) are drawings showing subordinate systems before and after contraction.

Claims (2)

A method for calculating a generator torque transfer function in order to evaluate a control constant of a PSS for stabilizing a generator,
Contracting the power system to one infinite bus for local mode;
Contracting the power system to one machine, one load and three branches for wide area mode;
The dynamic block diagram of the generator is determined based on the ΔP + Δω type detection method, and the voltage characteristics of the load are used as variables, and the constants K1, K2, K3, K4, K5, and K6 in the dynamic block diagram are used for the wide mode and the local mode. The step of calculating separately for
Determining the total transfer function of ΔP + Δω-type PSS by each control constant of Δω-type PSS and ΔP-type PSS after equivalently converting the vibration suppression effect of Δω-type PSS and ΔP-type PSS;
Calculating an AVR transfer function from the AVR control constant;
The generator torque transfer function is separately calculated for the wide mode and the local mode using the constants in the dynamic block diagram, the overall transfer function of the ΔP + Δω type PSS, and the AVR transfer function. Generator torque transfer function calculation method for PSS control constant evaluation. Depending on the control constants of the Δω-type PSS and ΔP-type PSS, both when the power system is contracted with one machine and three loads for the wide-area mode and when the power system is contracted with one machine infinite bus for the local mode In order to evaluate the stability of the PSS, in order to calculate the generator torque transfer function that is a guide for the evaluation,
Generator constant, AVR control constant, ΔP-type PSS control constant, Δω-type PSS control constant, voltage characteristic constant of load and phase adjusting equipment, system voltage, load power factor, one machine infinite bus model and one machine, one load An input field display step for displaying a data input field for branch impedance, generator active power, and load power consumption according to the three-branch model;
Constants K1, K2, K3, K4, K5, and K6 in the dynamic block diagram of the generator determined based on the ΔP + Δω type detection method are used separately for the wide mode and local mode using the input data in the data entry field. Calculating the total transfer function of ΔP + Δω-type PSS from the control constants of Δω-type PSS and ΔP-type PSS after equivalently converting the vibration suppression effect of Δω-type PSS and ΔP-type PSS,
Calculating an AVR transfer function from the AVR control constant;
Calculating the generator torque transfer function separately for the wide mode and the local mode using the constants in the dynamic block diagram, the overall transfer function of the ΔP + Δω type PSS, and the AVR transfer function; Generator torque transfer function calculation program for control constant evaluation.

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