JP3031891B2 - Reactive power dynamics analysis method of power system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing dynamic power characteristics of a system load in a power system.

2. Description of the Related Art With the recent remoteness and centralization of power sources, it has been recognized that the necessity of more precise system analysis for system expansion and operation planning, such as system stability evaluation, has been recognized. Load characteristics in power system analysis,
In particular, modeling of voltage dependence is a very important issue. In order to further improve the accuracy of the load characteristic model, it is necessary to consider not only static characteristics but also dynamic characteristics, and various studies have been made on modeling methods of dynamic characteristics, parameter changes, synthesis methods, and the like. Considering the dynamic characteristics of the load characteristic model means that an analysis model of a first-order lag system is set for dynamic changes in the active power P and the reactive power Q as shown in FIG. 1, and the dynamic characteristics are analyzed from the model. It is.

Conventionally, as the dynamic characteristic analysis model, the following equations (8) and (9) have been proposed as corresponding to active power and reactive power, respectively.

[0003]

(Equation 8)

(Equation 9) Where V ₀ : voltage before the voltage step change V _i : voltage after the voltage step change V _k : voltage at the k-th sample during the voltage step change V _k−1 : k−1-th voltage during the voltage step change At the time of sample
Voltage V ': Rated voltage Delta] t: distance P _i measurement data, Q _i: value obtained from the dynamic characteristic analysis model (valid electrostatic
Force, reactive power) Np, Nq: load characteristics constant (active power, reactive power) Ap, Aq: the dynamic characteristic analysis model gain (active power, no
Active power) Tp, Tq: time constant of dynamic characteristic analysis model (active power, no
Active power) P _0, Q _0: voltage change before the effective, reactive power values K _0: apparent power above formula (8), (9), the load characteristic constant Np, Nq, is a static characteristic parameter, found It is a value that is estimated by humans or automatically based on data. Also,
The parameters Ap, Aq, Tp, Tq are determined by some trials. Further, the parameter K _{0 in the} equation (9) representing the reactive power dynamic characteristic analysis model is a value of the apparent power. The apparent power K ₀ is inserted into the reactive power dynamic characteristic analysis model for the following reason.

FIG. 2 shows a system model on the secondary side of the bank, but the charging capacity connected in parallel to the load cannot be directly measured on the primary side of the bank. Therefore,
The apparent power is obtained from the active power P and the reactive power Q, and the apparent power is inserted into a model formula as shown in Expression (9) so that the dynamic characteristic analysis can be performed while compensating for the variation in the capacity.

[0005]

In FIG. 2, the charge capacity of the system load must be naturally compensated for in analyzing the dynamic characteristics of the load. In the model, there was a problem that accurate analysis could not be performed because charging capacity was compensated by obtaining apparent power. It should be noted that it is not necessary to insert an apparent power value in Expression (8), which represents the active power dynamic characteristic analysis model, since the charge capacity is irrelevant. Therefore, a precise analysis is possible for the dynamic characteristic analysis model of the active power.

It is an object of the present invention to reduce the charging capacity of a system load to C
An object of the present invention is to provide a method capable of performing more accurate analysis of the reactive power dynamic characteristic by estimating the term as a term and considering the estimated value of the term C.

[0007]

According to a first aspect of the present invention, there is provided a method for analyzing a reactive power dynamic characteristic of a power system, comprising: setting a reactive power dynamic characteristic analysis model corrected by an estimated value of a C term; The characteristic is analyzed.

[0008] Now, when analyzing the reactive power Q in the load L in FIG. 2, the charge capacity of the system load connected in parallel to the load L under the condition that the measurement data can be obtained only from the primary side of the bank. It is necessary to subtract the reactive power based on C. Therefore, the equation (10) is set by giving a step-like voltage change.

[0009]

(Equation 10) The left term of the equation (10) represents the reactive power Q at the load after the step-like voltage change, the coefficient part of the right term represents the reactive power Q at the load before the voltage change, and the A part of the variable part represents the static characteristic. This term and the part B represent terms relating to dynamic characteristics, respectively.
That is, the reactive power Q at the load after the voltage change is the Q at the load before the voltage change, and A
By multiplying the term, the dynamic characteristic portion can be obtained by multiplying the B term. Since the charging capacity C of the system load can be considered as a constant impedance characteristic, the reactive power can be expressed as being proportional to the square of the voltage with respect to a voltage change. As for the capacitance C, as in the same equation (10), for the left term representing Q at the load after the voltage change, as for C ( V _i / V ′) ² , for the Q at the load before the voltage change, ( Right section), rated voltage corrected C
(V ₀ / V ′) ² . In the above equation (10), regarding the charging capacity C of the system load,
Estimate by any method. The estimated value of the charging capacity C is C
It is called the term estimate. Similarly, the load characteristic constant Nq of the reactive power is estimated by an arbitrary method.

C term estimated value and reactive power load characteristic Nq
Is obtained, Expression (11) in which Aq and Tq are unknowns can be obtained from Expression (10).

[0011]

[Equation 11] Equation (11) is an equation representing the reactive power dynamic characteristic analysis model corrected by the C-term estimated value. The equation (11) differs from Equation (9), there is no apparent power fields K _0. For this reason,
The parameters Aq and Tq in the equation (11) can be estimated with high accuracy, and the analysis of the dynamic characteristics of the reactive power can be refined.

The estimated value of the C term and the load characteristic constant Nq of the reactive power are described in, for example, the following steps (I) to (I).
(K). Regarding this method, the present applicant has disclosed in Japanese Patent Application No. 8-180484 (Japanese Patent Application Laid-open No.
327). The following is an overview.

(I) From equation (12), (P, Q, V) is corrected at the rated voltage (V ') to estimate C'. However,
Initially, C 'and Nq are set to arbitrary values.

[0014]

(Equation 12) (J) From the following equation (13), Nq is estimated from C ′ estimated in step (I) and the voltage step change data.

[0015]

(Equation 13)

Equations (12) and (13) are obtained by removing the dynamic characteristic portion (part B) from equation (10).

[0017] However, Q, V: measured data (reactive power, voltage) Q ', C': rated voltage when the correction data (reactive power, charge capacity value of the system load (C section)) Q _0, V _0: Voltage Data before step change (reactive power, voltage) Q ₁ , V ₁ : data after voltage step change (reactive power, voltage) Nq: load characteristic constant of reactive power In equation (12), C ′ and Nq are related to each other In step (I), appropriate values are substituted for C ′ and Nq (for example, C ′ = 0, Nq = 0) in step (I), and the PQ correlation data (P ′, Q ′) after the correction of the rated voltage is applied. , V ′) are obtained from the measurement data P, Q, V. The curve shown in FIG. 3 is obtained from the PQ correlation data (P ', Q', V '), and the C-term estimated value (C') is obtained by the least square method or the like. continue,
Nq is estimated from the obtained C-term estimated value and the voltage step change data. This Nq estimation is performed using equation (13). The estimated Nq is closer to the true value than the initially set arbitrary value. Subsequently, using the Nq and C ', the PQ correlation data (P', Q ', V') after the rated voltage correction is obtained by equation (12), and the C term estimated value is obtained again. Also, Nq is estimated from equation (13). By repeating this operation, the C-term estimated value and Nq are closer to the true value and converge. When Nq converges to an appropriate range, Nq and C-term estimated values are determined. In the above iterative operation, the unknown C-term estimated value and Nq are initially set to appropriate values. However, even if these values are far from the true values, it is simulated that these values do not diverge. Has been confirmed by

By the above method, the C-term estimated value and Nq can be obtained with high accuracy.

Next, how to determine the gain Aq and the time constant Tq of the dynamic characteristic portion in the above equation (11) will be described. A
Since q and Tq are unknowns in equation (11) and there are no other equations using these as variables, Aq is calculated using equation (14) representing the error evaluation function while assuming the value of the time constant Tq.
And the value of Tq are converged and determined.

[0020]

[Equation 14] The above equation (14) while indicating error evaluation function of the reactive power, W _i of the equation is a weighting function, where, based on the weight functions W _i by the following equation (15) Set. The weighting function _Wi is obtained empirically, but may be one.

[0021]

(Equation 15) Hereinafter, Aq, T are determined by the procedures of steps (L) to (P).
Find q. (L) Tq is within a certain range, for example, -100 to 600 m
(M) to (O) are performed in sec. (M) Calculate Aq. Aq is determined by the following equations (16) and (17).

(Equation 16)

[Equation 17] Here, equation (14) can be a function of only Aq when Tq is fixed, and in that case, Aq is expressed by equation (14)
Is obtained by partially differentiating. Equations (16), (1
7) is the result of partial differentiation of equation (14).

[0022] (N) Next, determine the theoretical value Q _i by substituting the Aq and Tq (i = 1~N). Q _i is obtained by the above equation (11). (O) Obtain the error evaluation function εq between the theoretical value and the actually measured value. εq is obtained by the above equation (14). (P) Tq and Aq when the error evaluation function εq obtained by the above equation (14) is minimized are obtained as true values.

According to the above procedure, the estimated value of the C term, the reactive power load characteristic constant Nq, the gain Aq,
All time constants Tq have been determined. Therefore, thereafter, the dynamic characteristics of the reactive power Q _i can be analyzed by Expression (11) representing the dynamic characteristic analysis model of the reactive power.

In the above equation (11), the reactive power Q _i is not used because the apparent power K ₀ as shown in the equation (9) is not used.
Can improve the accuracy of the dynamic characteristic analysis.

[0025]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A configuration of a load characteristic recording apparatus according to an embodiment of the present invention will be described below with reference to FIGS.

FIG. 4 is a block diagram showing the configuration of the entire apparatus. In FIG. 4, reference numeral 100 denotes a terminal device provided on the site, and 101 denotes a monitoring device provided in a control room. The insulation / conversion circuit 1 insulates the three-phase voltage / current signal and converts it into a voltage signal at a predetermined transformation ratio. Filter 2 is not affected by aliasing errors due to sampling,
The components above a predetermined frequency are removed. The sample hold circuit 3 samples and holds the input signal at a predetermined timing. The multiplexer 4 selects one of the plurality of sample and hold circuits 3 and supplies it to the AD converter 5. The AD converter 5 converts this into digital data. The microcomputer 6 selects the multiplexer 4 and reads the data converted by the AD converter 5. The communication interface 7 is a terminal device 100
The microcomputer 6 transmits various kinds of measurement data to the monitoring device 101 via the communication interface 7. On the other hand, in the monitoring device 101, the communication interface 8 performs data transmission control with the terminal device 100, and the microcomputer 9 receives various measurement data from the terminal device 100 via the communication interface 8. The display 11 and the plotter 13 are used to output measured values and the like, and the microcomputer 9 outputs data via the display interface 10 and the plotter interface 12.

FIG. 5 is a flowchart showing the processing procedure of sampling and characteristic value calculation. First, when a predetermined sampling timing comes, three-phase voltage / current signals are sampled (for example, every five minutes), and A
Read the D conversion value. Then, the active power P and the reactive power Q are calculated. Next, when it is time to output the Nq and C-term estimated values, the following procedure is repeated.

(Q) From the actual PQ correlation data, P'-Q 'correlation data after rated voltage correction is obtained (Equation (1)
2)). However, initially, C 'and Nq are set to arbitrary values. The obtained P'-Q 'correlation data is drawn, and the C term (C') is estimated by the least square method or the like. (R) Nq is estimated from equation (13) using C ′ estimated in step (Q) and the voltage step change data (V ₀ → V ₁ ). The voltage step change data is
Change data V ₀ and V ₁ when a step change (disturbance) occurs in the measured (actual) voltage are used. (S) The step (Q) and subsequent steps are repeated a predetermined number of times using C ′ estimated in the step (Q) and Nq estimated in the step (R) until Nq converges to a predetermined level (here, 0. 95 <(Nq _i / Nq _{i + 1} ) <1.0
5), the above steps (Q) and (R) are repeated, and when the convergence to a certain level is reached, the estimated values of the Nq and C terms at that time are output.

Subsequently, the gain Aq and the time constant Tq are obtained by the following procedure. (T) Tq is from (U) to -100 to 600 msec.
(W) is performed. (U) Calculate Aq. Aq is determined by the above equations (16) and (17). (V) Next, a theoretical value Q _i is obtained (i = 1 to N). Q _i is obtained by the above equation (11). (W) An error function εq between the theoretical value and the actually measured value is obtained. εq is obtained by the above equation (14). (X) Tq and Aq when the error function εq obtained by the above equation (14) is minimized are obtained as true values.

By the above procedure, the estimated value of the C term, the reactive power load characteristic constant Nq, the gain Aq,
All time constants Tq have been determined. After that, the dynamic characteristic analysis of the reactive power is performed by the equation (11) into which these values are substituted.
The minimum value in step (X) is specifically determined by the following procedure.

First, based on the measured data, the time constant Tq at which the error of the error evaluation function of the equation (14) is minimized is -100 to -6.
It is searched and found in a width of 00 ms, but first 35 ms
Search (20 divisions) at ec intervals to find the minimum value. Assuming that the value is 75 ms, the next processing is 75 ms
92.5 msec on the plus side with ec as the center (= 35/2 +
75), minus side 57.5 msec (= -35 / 2 +
75) to calculate the minimum value. Do the same thing,
The process is repeated until the step width on the plus side and the minus side to be finally searched becomes smaller than 0.005 msec.

When Tq is obtained, Aq is subsequently obtained.
Since Aq is obtained by partially differentiating the error evaluation function, the results of the partial differentiation are expressed by Expressions (16) and (17).
Aq is obtained for each assumed Tq, and the minimum value is selected from among them.

FIG. 6 shows parameters obtained under certain conditions (cases 1 to 3). When the reactive power dynamic characteristic analysis model is not corrected with the C term estimated value (see the column of C term = 0 in the figure), the static characteristic parameter Nq and the dynamic characteristic parameter gain Aq are negative, but the C term estimation is not performed. It can be seen that the value is corrected by correcting the value (the accuracy is good). FIG.
Shows an example of actual measurement data in case 3.

In the above embodiment, the dynamic characteristic analysis model of the reactive power has been described. However, the above equation (8) is used for the dynamic characteristic analysis model of the active power, and the equation (8) is used for the gain Ap of the same equation. 18) and (19).

[0035]

(Equation 18)

[Equation 19] Equations (18) and (19) are obtained by partially differentiating Equation (20) of the error evaluation function.

[0036]

(Equation 20) Therefore, the parameter gain Ap and the time constant Tp can be obtained by the same method as that for Aq and Tq. As described above, it is not necessary to consider the C term in the dynamic characteristic analysis model formula of the active power.

As described above, by assuming that the dynamic characteristic analysis model of the reactive power is corrected by the estimated value of the C term, A
The accuracy of q and Tq is improved, and the analysis becomes more accurate.

[0038]

According to the present invention, the apparent power term is not included in the reactive power dynamics analysis model equation, and the charging capacity value of the system load is compensated by the estimated value of the C term. Can be realized.

[Brief description of the drawings]

FIG. 1 is a diagram showing a dynamic change with respect to a step voltage change of active power and reactive power.

FIG. 2 is a diagram showing a system model on the secondary side of a bank.

FIG. 3 is a diagram illustrating a method of correcting a rated voltage of PQ correlation data to obtain C ′.

FIG. 4 is a block diagram showing a configuration of a load characteristic recording device.

FIG. 5 is a flowchart showing a procedure for obtaining a dynamic characteristic parameter.

FIG. 6 is a diagram showing an example of a dynamic characteristic parameter analysis result.

FIG. 7 is a view showing an example of actual measurement data.

Continuation of the front page (72) Inventor Kunio Matsuzawa 1-3-1 Uchisaiwaicho, Chiyoda-ku, Tokyo Tokyo Electric Power Company (72) Inventor Yuichi Nakao 1-3-1 Uchisaiwaicho, Chiyoda-ku, Tokyo Tokyo Electric Power Company (56) References JP-A-10-28327 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) H02J 3/00-5/00 G01R 21/00 G01R 29/00 Practical files (PATOLIS) Patent file (PATOLIS)

Claims (3)

(57) [Claims] 1. An estimated value of a charging capacity C of a system load (hereinafter, referred to as an estimated value).
After obtaining the C-term estimated value) and the load characteristic constant of the reactive power (hereinafter, referred to as Nq) by an arbitrary method, the reactive power dynamic characteristic analysis model of the following equation (1) corrected by the C-term estimated value is obtained. A reactive power dynamic characteristic analysis method for a power system, characterized by analyzing a reactive power dynamic characteristic by: (Equation 1) Where V ₀ : voltage before the voltage step change V _i : voltage after the voltage step change V _k : voltage at the k-th sample during the voltage step change V _k−1 : k−1-th voltage during the voltage step change At the time of sample
Voltage V ': Rated voltage Delta] t: distance measurement data Q _i: value calculated from the dynamic characteristic analysis model Aq: gain of dynamic characteristic analysis model Tq: the time constant of the dynamic specific analytical model Q _0: voltage change before the reactive power value 2. Time series data of reactive power of a power system;
From the voltage step change data, the following steps (A) to
The method for analyzing reactive power dynamic characteristics of a power system according to claim 1, wherein the C term estimated value and Nq are obtained by (C). (A) From the following equation (2), the PQ correlation data (P, Q,
V) is corrected to correlation data at the rated voltage (V '), and C'
Is estimated. However, initially, C 'and Nq are set to arbitrary values. (B) From the following equation (3), Nq is estimated from C ′ estimated in step (A) and the voltage step change data. C estimated by the (C) step (A) 'calculated to Nq is repeated predetermined times following steps (A) using the Nq estimated as in step (B), also, C in this case' the
Obtained as a C-term estimate. (Equation 2) (Equation 3) Here, Q, V: time series data of reactive power of the power system (reactive power, voltage measurement data ) V ': rated voltage Q', C ': corrected data at rated voltage (reactive power, charging capacity C of system load) )) Q ₀ , V ₀ : Data before voltage step change (reactive power, voltage) Q ₁ , V ₁ : Data after voltage step change (reactive power, voltage) 3. The reactive power dynamic characteristic parameter T of the equation (1)
3. The reactive power dynamic characteristic analysis method for a power system according to claim 1, wherein q and Aq are obtained by the following steps (D) to (H). (D) Tq is set to an arbitrary value Tq ₁ , Tq ₂ , Tq ₃ ,.
..Steps (E) to (G) at each value when Tq _n is set
Is calculated . (E) Aq is calculated from equations (4), (5) and (6). (F) From equation (1) of the dynamic characteristic analysis model, the value (theoretical value) Q
_Ask for _i . (G) An error function εq between the theoretical value Q _i and the actually measured value Qm _i , which is the measurement data, is obtained from equation (7). (H) Tq and Aq when the error function εq is minimized are set to true values. (Equation 4) (Equation 5) (Equation 6) (Equation 7) Where V ₀ : voltage before the voltage step change V _i : voltage after the voltage step change V _k : voltage V _k−1 at the k-th sample during the voltage step change: k−1-th during the voltage step change At the time of sample
Voltage V ': Rated voltage Delta] t: distance measurement data W _i: weighting function Qm _i: measured data Q _i: value obtained from the dynamic characteristic analysis model (theory) Aq: gain of dynamic characteristic analysis model Tq: Dynamic particular Time constant Q _{0 of} analysis model : reactive power value εq before voltage change : error evaluation function