JPH10322907A - Power system simulator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve simulation accuracy of a power system simulator by fitting a digital calculating part which conducts calculation for simulating the condition of a power system, based on the condition of an analog simulator. SOLUTION: A node equation calculating part 14 calculates columnar vector data I'(t) and admittance matrix data Y'(t) from the data of an equivalent admittance YD(t) of the output of a calculating part 9 for method of two-stage least squares. Calculation of a node equation I'(t)=Y'(t)V(t) is conducted, columnar vector data V(t) is calculated, and columnar vector data V(t) are retreated to a digital side data retreat part 15. After the effective value vector data V1 (t) of the bus of a linking point are converted into instantaneous value data by an instantaneous value converting part 16, and is converted into an analog signal by a D/A converter 17 to produce the voltage of the bus of an actual linking point with an amplifier 19. As a result, it is possible reflect the calculated results of a digital simulator into the analog simulator.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a power system simulator for simulating the behavior of a power system to experiment or analyze the behavior of the power system.

[0002]

2. Description of the Related Art A power system simulator is an experimental device for analyzing characteristics and behavior of a power system by reproducing a phenomenon occurring in the power system. There are roughly three methods for actually configuring this power system simulator. The first is a method called an analog simulator, in which an electric circuit that is actually a part of a power system is constructed, the electric circuit is energized, and a phenomenon that occurs in the electric circuit is observed. This is a method for estimating phenomena that occur in the system. Note that the analog simulator may be configured from analog devices that are components of an actual power system.

[0003] The second is a method called a digital simulator, in which components constituting the power system are modeled by various methods using mathematical expressions and equations, and an electronic computer performs a numerical operation based on the modeling. Analyze the phenomena that occur in the power system. That is, this is a method of simulating a power system by a numerical operation by a computer.

[0004] A third method is a method called a hybrid simulator, in which a power system to be simulated is divided into two parts, one part is simulated by an analog simulator, and the other part is simulated by a digital simulator. It is. That is, the simulation method simulates one electric power system as a whole by combining an analog simulator and a digital simulator. In the case of this hybrid simulator, the configured analog simulator and digital simulator need to be appropriately linked to each other so as to simulate one power system as a whole with consistency.

FIG. 11 shows, for example, Electron Theory B 1993
VOL113 PP855 is a block diagram showing a linking method of a conventional hybrid simulator shown in "Development of Digital Real-Time System Total Analysis Simulator". In the figure, 101 to 104 represent components of an analog simulator, 101 is a generator, 102 and 10
4 is a bus, and 103 is a transmission line. 105 is transmission line 1
Numeral 106 denotes a current measuring device for measuring a current flowing through the voltage generating circuit 03, and numeral 106 denotes a voltage measuring device for measuring a voltage of the bus 104. 107
Numerals 117 represent digital simulators which are processed by the operation of the processor in the digital computer and include a linking function. This digital simulator
The progress of time is discretely incremented by a step time, and a predetermined operation is repeatedly performed at each time step, thereby performing an operation that simulates the progress of a phenomenon of the power system that progresses with time. Hereinafter, this step time is represented by T.

Reference numerals 107 and 108 denote A for converting the measured data into digital data at regular sampling time intervals.
The A / D converter 107 converts the measured voltage signal into digital data, and the A / D converter 108 converts the measured current into digital data. An effective value converter 109 converts the instantaneous value data of the voltage after the A / D conversion into effective value data.
Reference numeral denotes an effective value converter for converting instantaneous value data of the current after A / D conversion into effective value data.

The effective value data of the voltage converted by the effective value converter 109 is represented by a symbol V _A (t).

[0008] Here, t represents the sampling time. The concept of the effective value sampled at time t will be described. When converting the instantaneous value data into the effective value data, based on the instantaneous value data at two sampling points sampled with a time difference converted into a fixed angle (eg, 30 ° or 90 °). It is necessary to calculate the absolute value of the vector and the phase angle. In the case of the effective value sampled at the time t, the time t represents the sampling time of the latest instantaneous value data among a plurality of instantaneous data used for conversion to the effective value.

Similarly, the effective value data of the current at time t converted by the effective value
Represented by _A (t). Note that both V _A (t) and I _A (t) are data expressing the alternating current as a vector.

The sampling time interval in the A / D converters 107 and 108 is generally set to be finer than the step time width T in the digital simulator. However, the measured voltage and current effective value data is used for calculating the effective value in the digital simulator, and the digital simulator
Since the calculation is performed every time, the effective value conversion units 109, 1
The effective value data output by 10 is output at each time interval T.

Reference numeral 111 denotes two voltage effective value data _{VA with} respect to the latest step time T in the digital simulator.
(T), a data saving unit for saving V _A (t−T), 11
2 two current effective value data _{I A (t), I A} (t-
T) is a data saving unit for saving.

Reference numeral 113 denotes an operation unit for calculating vector data Y _D (t) and I _D (t) based on the data saved in the data saving units 111 and 112 by an operation according to the following formula. 114 denotes a node equation solution. Operation unit, 115 is a digital data saving unit, 116 is an instantaneous value conversion unit, 117
Denotes a D / A converter, 118 denotes a model operation unit, and 119 denotes an amplifier. Note that the four arithmetic operations in the calculation formula represent operations as complex numbers (vectors). _{Y D (t) = (I} A (t) -I A (t-T)) / (V A (t) -V A (t-T)) ... (1) I D (t) = I A ( t) −Y _D (t) V _A (t) (2)

FIG. 12 is a schematic diagram showing an example of a power system to be simulated by the hybrid simulator. In the figure, 121 is a generator, 122 is a bus, 123 is a transmission line, and 124 is a bus. Reference numeral 125 denotes a partial system including 124. The hybrid simulator shown in FIG. 11 includes a generator 101, a bus 122, a transmission line 123, and a bus 124 in FIG.
Simulated by an analog simulator consisting of the buses 102 and 104 and the transmission line 103, the partial system 125 in FIG.
Is simulated by a digital simulator.

That is, the power system to be simulated includes a portion simulated by an analog simulator and a portion simulated by a digital simulator, and both share a common bus 124.

The bus 124 is simulated by the bus 104 in the analog simulator shown in FIG. This figure 1
The bus 104 in 1 is simulated by both the digital simulator and the analog simulator in the hybrid simulator. In the hybrid simulator in FIG. 11, determining the voltage of the bus 104 is equivalent to simulating the entire power system in FIG. 12 with the analog simulator and the digital simulator as a whole with consistency. Hereinafter, the buses 104 to 124 are referred to as “coupling point buses”. Subsystem 12 in FIG.
A model for simulating 5 with a digital simulator is called a “digital system”.

This digital system is a model represented by the following node equation. I = YV (3) where

(Equation 5) Is a column vector representing the injection current flowing into each node of the subsystem 125,

(Equation 6) Is a column vector representing the voltage of each node of the subsystem 125,

(Equation 7) Is an admittance matrix in the sub-system 125.

Note that N is the total number of nodes in the partial system 125. Also, I ₁ , I ₂ ,...
V _1, V ₂ at I _N and equation (5), ..., V _N are each a vector quantity, it is a complex quantity representing a Y _11, Y ₁₂ ... admittance in equation (6). Equations (4), (5), (6)
Are time-varying, and are represented as follows with a variable t representing the time thereafter.

(Equation 8)

(Equation 9)

(Equation 10) In the digital system, the link point bus 1 in FIG.
The node number of 24 is 1.

[0018] I '(t) is a column vector obtained by changing the equation (7) I ₁ (t) of the node number 1 in the _{I 1 (t) + I D} (t). _ID (t) is the equation (2).

[Equation 11] Y ′ (t) is the same as Y (t), except that the driving point admittance Y ₁₁ (t) of node number 1 is represented by Y ₁₁ (t) + Y
_The admittance matrix is changed to _D (t). Y
_D (t) is equation (1).

(Equation 12)

V ₁ (t) represents the voltage of the link point bus. This is called a link point voltage. Y _D (t) and I _D (t) shown in the equations (1) and (2) are quantities representing the admittance of the analog simulator viewed from the digital system and the injection current from the analog simulator, respectively. '(T) and Y' (t) indicate that these are taken into account in the node equations of the digital system.

Hereinafter, the components in FIG. 11 will be described again. In a digital system in a digital simulator, a model of a device connected to each node such as a generator load is represented by an injection current, an equivalent admittance, or the like. Reference numeral 118 in FIG. 11 denotes a model calculation unit that calculates a temporal change such as the generator load. As a result of the model calculation, an injection current vector (Equation (7)) in the digital system at the relevant simulation time and an admittance matrix (Equation (9)) in the digital system are determined. Reference numeral 114 denotes a node equation solving unit that solves a node equation in the digital system and determines a voltage vector of each node. This solves the following simultaneous equations I ′ (t) = Y ′ (t) V (t) (12) which are node equations in the digital system to obtain a column vector V (t), and obtains each node of the digital system. Is determined. Reference numeral 115 denotes a data saving unit in the digital system, which saves the operation result of the digital simulator which is output to the outside as a simulation result.

The node equation I '(t) = Y' (t) V
As a result of solving (t), the link point voltage V ₁ (t) is determined. Reference numeral 116 denotes an instantaneous value converter for converting the effective value vector data of the link point voltage into an instantaneous value. Reference numeral 117 denotes a D / A converter that converts instantaneous value data of the link point voltage into an analog signal. 119 denotes an amplifier that generates an actual voltage at the link point, and generates a voltage of the bus 114 of the analog simulator. The bus 114 is a link point bus viewed from the analog simulator side.

Next, the operation of the digital simulator in the hybrid simulator shown in FIG. 11 will be described with reference to FIG. That is, the process of calculating the system state at time t will be described. First,
The signals measured by the voltage measurement unit 106 and the current measurement unit 105 are converted by the A / D converters 107 and 108 into A / D signals.
Conversion is performed (step ST131).

The A / D converted digital data is converted into effective value vector data by the effective value converters 109 and 110 (step ST132). As a result, the voltage of the analog input data at time t, the effective value data V _A of the current (t) I _A (t) is respectively output, these data are saved in the data saving unit 111 (step ST133).

Next, vector data Y _D (t) I _D (t) is calculated according to equations (1) and (2) (step S).
T134). Next, a model operation is performed on the digital simulator side to calculate the injection current column vector data I (t) of the digital system and the data Y (t) of the admittance matrix of the digital system at time t (step ST).
135).

In accordance with the equations (10) and (11), the injection current column vector data I '(t) of the digital system and the analog simulator at the link point bus are taken into account in the analog simulator, considering the current flowing into the link point bus. The data Y ′ (t) of the admittance matrix in consideration of the drive point admittance on the side is calculated. Thereafter, an operation for solving the node equation I ′ (t) = Y ′ (t) V (t) is performed to calculate a column vector V (t) representing the voltage distribution of the digital system (step ST136).

Next, the calculation result is saved (step ST137). The purpose of saving this data is to output the simulation result to the outside. Then, data V ₁ (t) representing the effective value vector of the bus at the link point
Is calculated (step ST138).
Next, the instantaneous value data is converted into an analog signal by the D / A converter 117 (step ST139), and an actual link point bus voltage is generated by the amplifier 119 according to the analog signal. As a prior art related to the above conventional example, there is JP-A-6-38372.

[0027]

The hybrid simulator, which is a conventional electric power system simulator, is constructed as described above. Therefore, an electric simulator which actually generates an electric phenomenon and an electric simulator which is numerically operated in accordance with a digital system model. Combining a digital simulator that simulates the phenomenon, on the digital simulator side,
By feeding back the voltage value and current value of the analog simulator measured at the link point and determining the link point voltage that is consistent with the actual voltage distribution of all power systems to be simulated, the electric power of the entire power system is determined. It simulates dynamic behavior.

In the hybrid simulator, it is important how the digital simulator calculates accurate numerical data that matches well with the electrical phenomena generated in the actual power system. Therefore, in order to perform the solving node equations taking into account the electrical phenomena of the analog simulator side of the connection point, approximating the characteristic of the voltage V _A and the current I _A of the analog simulator side of the connection point by the following linear expression (13) The characteristic (1)
Regarded as injection current from the transmission line 123 side of the link point bus 124 in the subsystem 125 to I _D in 3), Y _D
Is regarded as driving point admittance, and a node equation of the digital system is solved. _{Y D = @ I A / ∂V} A ... (13) I A = I D + Y D V A ... (14) Note that equation (1), (2) the formula (13), vector data Y from (14) _This is an expression for calculating _D and _ID .

Hereinafter, the vector data Y _D in the equation (14) is referred to as “equivalent admittance”. That referred voltage vector V _A measured in conjunction point of the analog simulator, the coefficient of the voltage vector V _A when the relationship between the current vector I _A expressed by Equation (14) and the "equivalent admittance".
The vector data _ID in the equation (14) is referred to as “equivalent injection current”.

In the conventional hybrid simulator, the equivalent admittance Y _D is calculated in accordance with the equation (1). Therefore, the equivalent admittance Y _D cannot be calculated with high accuracy. There was a problem that cannot be simulated.

The reason why the equivalent admittance Y _D cannot be accurately calculated by the conventional hybrid simulator will be described below. 1. In the digital simulator, since the discretization error is reduced by subdividing the step time width T, the step time width T is set as small as possible. However, when the interval time width T is reduced, in equation (1), V (t) ≒ V (t−T) (15), and V (t) −V (t−T) is a difference operation of digital data. , Significant loss of digits occurs, and the denominator of equation (1) has a very small number of significant digits as digital numerical data. The same applies to the molecule I (t) -I (tT). Further, V (t) -V (t-T) of the denominator is very small. Therefore, since the expression (1) has a very small amount with a small number of significant digits in the denominator, there is a problem that the error is significantly enlarged and the accuracy is extremely deteriorated.

2. In FIG. 1, the voltage and the current at the link point are measured by the ammeter side unit 105 and the voltmeter side unit 106. These measurement data generally include noise and harmonics. Therefore, the analog input data V _A (t) and I _A (t) after the effective value conversion include errors affected by these noises and harmonics, and as a result, the equations (1) and (2) There is a problem that the calculated equivalent admittance Y _D and equivalent injection current _ID are inaccurate.

3. Equation (1) is an equation for obtaining the equivalent admittance Y _D on the assumption that the frequency of the power system is equal to the reference frequency. However, if the system frequency is different from the reference frequency, the effective value vector data V (t), I
Since (t) is rotated in the vector diagram, can not be calculated accurately equivalent admittance Y _D in the formula (1), the accuracy of the equivalent admittance Y _D is a problem that poor. If the accuracy of the equivalent admittance Y _D is poor, when solving the node equation of the digital system, it is equivalent to erroneously measuring the transmission line impedance of the analog simulator and performing coordination, and the simulation accuracy of the hybrid simulator is reduced. There was a problem of getting worse.

The present invention has been made in order to solve the above-mentioned problems, and has improved the measurement and calculation accuracy of "equivalent admittance" and "equivalent injection current" representing the state of an analog simulator in a linked system of a hybrid simulator. It is an object of the present invention to accurately calculate these values and thereby improve the simulation accuracy of a power system simulator.

[0035]

According to a first aspect of the present invention, there is provided a power system simulator according to the present invention, wherein a state of the analog simulator is determined by a least square method based on data sampled at a plurality of sampling timings of voltage and current in the analog simulator. A least-squares method operation unit for performing an estimation operation, and a digital operation unit for performing an operation for simulating the state of the power system based on the estimated operation state data of the analog simulator.

The least-squares method calculation unit of the power system simulator according to the second aspect of the present invention is characterized in that the time at which the state of the analog simulator is calculated is t, and the times t, t-T, t
-2T, ..., t- (n- 1) measured at T a n voltage data V _A and (t-kT), n pieces of current data I _A (t
−kT), the expression

(Equation 13) Is calculated, and the digital calculator performs an operation to simulate the state of the power system at time t based on the data of the equivalent injection current and the equivalent admittance.

The least-squares method calculation unit of the power system simulator according to the third aspect of the present invention is characterized in that the time at which the state of the analog simulator is calculated is t, and the times t, t-T, t
-2T, ..., t- (n- 1) n -number of voltage data measured by T V _A (t-kT) and n current data I _A (t-
kT), the expression

[Equation 14] And the equivalent admittance that minimizes
_D = I calculates the equivalent injection current by _{A (t) -Y D V A} (t), the digital calculation section, based on the data of the equivalent injection current in the equivalent admittance and time t at time t of the power system at time t Is performed to simulate the state of.

In the power system simulator according to the fourth aspect of the invention, the least-squares method calculation unit sets the time at which the state of the analog simulator is calculated to be t, and the times t, t-T, t
-2T, ..., t- (n- 1) n -number of voltage data measured by T V _A (t-kT) and n current data I _A (t-
kT), based on equation (20)

(Equation 15) Thereby calculating the equivalent admittance to minimize, equivalent infusion operation section, I _D = calculated equivalent injection current by _{I A (t) -Y D V} A (t), the digital calculation unit equivalent admittance and time An operation for simulating the state of the power system at time t is performed based on the equivalent injection current data at t.

According to a fifth aspect of the present invention, there is provided a power system simulator, comprising: a frequency deviation calculating section for calculating a frequency deviation from a reference frequency of the power system; A digital calculator for simulating a state of a power system by calculating a state quantity of the analog simulator based on the corrected current and voltage data;

According to a sixth aspect of the present invention, a power system simulator performs the following arithmetic processing (a) to (e). (A) Calculate the frequency deviation from the reference frequency of the power system. (B) A low-pass filter is applied to the calculation result of (1), and the calculation result is set to Δf. (C) Time t, t−T, t−2T,..., T− (n−1)
N voltage vector data V _A (t) measured at T,
_VA (t−T), _VA (t−2T),..., _VA (t−
(N-1) T) and, n pieces of current vector data I _{A
(T), I A (t} -T), I A (t-2T), ..., I A
The following operation is performed on (t− (n−1) T) from k = 0 to n−1. V ′ _A (t−kT) = V _A (t−kT) exp (−j2
πΔf (n−k) T) I ′ _A (t−kT) = I _A (t−kT) exp (−j2
πΔf (nk) T) (d) Calculate the equivalent admittance that minimizes the following equation.

(Equation 16) (E) Considering the calculation result of (d) as an equivalent admittance amount of the analog simulator at time t,
The state of the power system at time t is calculated.

According to a seventh aspect of the present invention, there is provided a power system simulator, comprising: a measuring unit for measuring a voltage and a current in an analog simulator; voltage and current data outputted from the measuring unit; and a fixed equivalent supplied from the outside. An equivalent injection calculator for calculating an equivalent injection current based on the admittance is provided, and the digital calculator performs an operation for simulating a state of a power system based on the fixed equivalent admittance and the data of the equivalent injection current. is there.

An electric power system simulator according to the invention of claim 8 includes a least square method operation unit for estimating the state of the analog simulator by the least square method based on the fundamental wave component calculated by the discrete Fourier transform operation unit, The digital calculator performs an operation to simulate the state of the power system based on the estimated state data of the analog simulator.

[0043]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiment 1 FIG. 1 is a block diagram showing a hybrid simulator according to a first embodiment of the present invention. In the figure, reference numerals 1 to 4 denote components of an analog simulator, 1 is a generator, 2 and 4 are buses, and 3 is a transmission line. It is.

Reference numeral 5 denotes a current measuring device for measuring a current flowing through the power transmission line 3, and reference numeral 6 denotes a voltage measuring device for measuring the voltage of the bus 4, both of which constitute a measuring unit. 7,
Reference numeral 8 denotes an A / D converter for converting measurement data into digital data at regular sampling time intervals.
The / D converter 7 converts the measured voltage signal into digital data, and the A / D converter 8 converts the measured current signal into digital data.

Reference numeral 9 denotes an effective value converter for converting the instantaneous value data of the voltage after the A / D conversion into effective value data. 110 denotes the effective value data of the instantaneous value data of the current after the A / D conversion. This is an effective value converter for conversion.

Reference numeral 11 denotes a voltage data saving unit, which is link point voltage vector data V _A (t) and V _A (t−T) for the latest n pieces of sampling time after being sampled and converted to an effective value. , _VA (t−2T),..., _VA (t− (n−1) T) (16) are saved. Note that n is a fixed value, which is set in the digital simulator before starting the simulation.

T is the latest operation time on the digital simulator side, tT is the operation time one step before, and t-2T is the operation time two steps before. Since the data _VA (t) is newly calculated at the time of the latest calculation time t, the data _VA (t) is saved and the data _VA (t-nT) is discarded, so that the latest data _VA (t-nT) is always obtained. Data for the n-step time is saved.

[0048] 12 is a current data saving section, sampled by the latest after being converted into an effective value of n increments time of the linking points current vector data _{I A (t), I A} (t-T) , I _A (t−2T),..., I _A (t− (n−1) T) (17) are saved.

A least square method 13 calculates the equivalent injection current I _D and the equivalent admittance Y _D in the equation (14) by the least square method according to the data saved in the voltage data saving unit 11 and the current data saving unit 12. , 14 is a node equation calculation operation unit as a digital calculation unit, 15 is a data saving unit on the digital side, 16 is an instantaneous value conversion unit, 17
Is an A / D converter, 18 is a model operation unit, and 19 is an amplifier.

[0050] Hereinafter, in the least-squares method calculation unit 13, the equivalent injection current I _D (hereinafter, abbreviated as I _D) and equivalent admittance Y _D (hereinafter, Y _D and abbreviated) illustrating a method for calculating the. Equation (14) is k = 0, 1, ..., to n-1, higher than the _{I A (t-kT) =} I D + Y D V A (t-kT) ... (18) each of k I _D
And obtaining the value of Y _D. For this purpose, the sum of the squares of the absolute values of the difference vector between the right side and the left side of Expression (18) is considered, and I _D and Y _D are determined so as to minimize this. This method is a method called a least squares method, and the theory can be referred to in a known document describing the identification theory.

In the following, I _D Y is set so that D in the following equation is minimized.
A method for obtaining _D will be described.

[Equation 17] Next, I _D , Y _D , I _A (t−kT), V _A (t−kT)
Is represented by a vector using the real part and the imaginary part as follows. _{I D = K + jL (K} : real part of I _D, L: I imaginary part of _{D) Y D = G + jB} (G: the real part of Y _D, B: Y imaginary part of _{D) I A (t-kT} ) = _{I r (k) + jI i} (k) I r (k): the real part I _i of _{I a (t-kT) (} k): imaginary part V _a of the _{I a (t-kT) (} t-kT) = V _r (k) + jV _i (k) V _r (k): real part of _VA (t−kT) V _i (k): imaginary part of _VA (t−kT)

[0052] Then the following equation (20) representing the real part and an imaginary _{part, I D + Y D V A} (t-kT) -I A (t-kT) = K + jL + GV r (k) -BV i (k ) + J (GV _i (k) + BV _r (k)) − I _r (k) −jI _i (k) (20)

From this, D is calculated as follows.

(Equation 18) In order to obtain K, L, G, and B by the least square method, K, L, G, and B satisfying the following four equations are obtained. ∂ ＠ D / ∂K = 0 ∂∂D / ∂L = 0 (22) ∂∂D / ∂G = 0 ∂∂D / ∂B = 0

In the following, for example,

[Equation 19] Abbreviated as etc.

(Equation 20)

When the simultaneous linear equations of the equation (22) are expressed in a matrix by the above equations, the following equations are obtained.

(Equation 21)

A and U are shown below.

(Equation 22)

(Equation 23)

In the least-squares method operation unit 13 in FIG.
From the data saved in the data saving units 11 and 12, the formula (2)
5) The components of A and U in the equation (26) are calculated, and then K, L, G, and B are calculated by solving the equation (24) by Gaussian elimination. Thus, I _D and Y _D that minimize Expression (19) are calculated by the least squares method.

Hereinafter, the processing operation at each time step in the first embodiment will be described with reference to the flowchart of FIG. 2 while referring to FIG. That is, the process of calculating the system state at time t will be described. First, these analog input signals are sampled by the A / D converters 7 and 8 according to the voltage signal and the current signal measured by the voltage measuring unit 6 and the current measuring unit 5, and are converted into digital data. These are instantaneous value data (step ST1).

Next, effective value vector data is calculated by the effective value converters 9 and 10 according to the instantaneous value data. As a result, the effective value vector data V _A (t) of the link point voltage at time t is obtained as the output of the effective value converter 9. Further, the effective value vector data I _A (t) of the link point current at time t is obtained as the output of the effective value conversion unit 10 (step ST2).

Next, the effective value vector data V _A (t)
Is saved in the data saving unit 11, and the data saving unit 11 saves the data _VA (t−n) saved before the increment of n + 1.
Discard T). As a result, the data saving unit 11 stores the effective value vector data V _A (t), V _A (t−T), V _A (t−) of the link point voltage for n steps from the time t.
2T),..., _VA (t− (n−1) T) are stored.

Similarly, the effective value vector data I
_A (t) is saved to the data saving unit 12, and the data saving unit 12 saves the data I _A (t) saved before the increment of n + 1.
-NT). As a result the data saving unit of the linkage point current of n increments worth of going back from the time t to 12 rms vector data _{I A (t), I A} (t-T), I A (t-
2T), ..., a state where _{I A (t- (n-1} ) T) is stored (step ST3).

Next, proceeds to processing for calculating the equivalent admittance Y _D equivalent injection current I _D by the least squares method calculation unit 13 (step ST4). In the processing of the least-squares method operation unit 13, first, according to the data stored in the data saving unit 11 and the data stored in the data saving unit 12, each component of the matrix A shown in Expression (25) is , Equation (26)
Each component of the column vector U shown in FIG. Thereafter, an operation for solving the simultaneous linear equation shown in the equation (24) by the Gaussian elimination method is performed, and K, L,
An operation for obtaining G and B is performed. In equation (24), I _D
= K + jL, Y _D = G + jB, so that the equivalent admittance Y _D (t) and the equivalent injection current I _D (t) at time t were calculated.

Next, a model operation on the digital simulator side is performed by the model operation unit 18 (step ST).
5) The digital current injection current column vector data I (t) at time t and the digital admittance matrix data Y (t) are calculated. In addition, I (t),
Y (t) is shown in equations (7) and (9).

Next, in the node equation solving operation unit 14, the equivalent admittance Y _D (t) and the equivalent injection current I _D (t) which are the outputs of the least squares method operation unit 9 and the data which is the output of the model operation unit 18 From I (t) and data Y (t), column vector data I ′ (t) and admittance matrix data Y ′ (t) according to equations (10) and (11), respectively.
Is calculated. Thereafter, an operation for solving the node equation I ′ (t) = Y ′ (t) V (t) is performed by the Gaussian elimination method (step ST6), and the column vector data V representing the voltage distribution of the digital system at time t is obtained. (T) is calculated, and the column vector data V (t) is saved in the digital data saving unit 15 (step ST7).

Next, the effective value vector data V ₁ (t) (one component of V (t)) of the bus at the link point is converted into instantaneous value data by the instantaneous value converter 16 (step ST
8) A / D conversion is performed by the A / D converter 19 (step ST9) to generate a converted analog signal. In accordance with this analog signal, the voltage of the actual link point bus is generated by the amplifier 19. Thereby, the calculation result of the digital simulator is reflected on the analog simulator.

Thereafter, it is determined whether or not the simulation has been completed (step ST10). If YES, the operation is terminated. If NO, T is added to shift to the calculation of the next time step (step ST11). ).

As described above, according to the first embodiment, as the input data of the node equation of the digital system in the hybrid simulator, the expression I _A = I _D + representing the voltage and current characteristics of the analog simulator at the link point.
The equivalent injection current I _D and the equivalent admittance Y _D in Y _{D VA} are sampled by n latest link point voltage data V _A (t−kT) (k = 0, 1,
.., N-1) and the n latest link point current data I _A (t
−kT) (k = 0, 1,..., N−1), and is obtained by performing an estimation operation by the least-squares method in accordance with these many data, so that the equivalent injection current _ID and the equivalent admittance Y
_D estimation accuracy is improved. In addition, by using the least squares method, it is possible to eliminate noise mixing, shortage of the number of significant digits of the A / D converter, and error factors of digit cancellation in numerical calculation.

Therefore, since the node equation is solved after ensuring the accuracy of I _D and Y _D , there is an effect that the calculation accuracy of the simulation is improved and the simulation accuracy of the hybrid simulator is improved.

Embodiment 2 In the first embodiment, I _D and Y
Both values of _D are obtained by the least square method, and these are used as inputs to the node equation. However, the equivalent injection current I _D of the operation result by the least square method is discarded, and the equivalent admittance Y of the operation result by the least square method is replaced with Y. The latest sampling data V _A (t), I _A as voltage / current data at the link point with _D
A method of calculating the equivalent injection current _ID by the following equation using (t) may be used. _{I D = I A (t)} -Y D V A (t) ... (27)

The second embodiment employs an algorithm for calculating an equivalent injection current _ID according to this method and inputting the calculated value to a node admittance equation of a digital system. FIG. 3 is a block diagram showing the configuration of the hybrid simulator according to the second embodiment. The same parts as those in the first embodiment shown in FIG. In FIG. 3, reference numeral 31 denotes a calculation unit of the equivalent injection current _ID .

Next, the outline of the operation of the second embodiment will be described with reference to the flowchart of FIG. First, the voltage signal and the current signal measured at the link point are converted into digital data by the A / D converters 7 and 8 (step ST1).
Next, these are converted into effective value vector data by the effective value converters 9 and 10 (step ST2). The output of the effective value converter 9 is the effective value vector data V _A (t) of the voltage at the link point at time t, and the output of the effective value converter 10 is the effective value vector data I _A (t) of the current at the link point. It is.

Next, the effective value vector data V _A (t) is saved in the data saving section 11, and the effective value vector data I _{A is} stored.
(T) is saved in the data saving unit 12 (step ST
3). Next, the equivalent admittance Y _D (t) at time t is calculated by the least square method calculation unit 13 (step S).
T4). The least-squares method operation unit 13 includes link point voltage data _VA (t), _VA (t-T), and _{VA for} n steps that are retroactive from time t stored in the data saving unit 11.
(T−2T),..., V _A (t (n−1) T), and n that is retroactive from time t stored in the data saving unit 12
Increments partial linkage point current data _{I A (t), I A} (t-
_{T), I A (t-} 2T), ..., I A (t (n-1) T)
Are respectively input.

The processing for calculating the equivalent admittance Y _D in the least-squares method calculation unit 13 is the same as the processing for the least-squares method calculation in the first embodiment, and a duplicate description will be omitted. However, in the first embodiment, the equivalent injection current I _D together with the equivalent admittance Y _D by the least square method.
, But this equivalent injection current is discarded without being used in subsequent calculations. Next, V _A (t) which is the output of the effective value converter 9 and I _A which is the output of the effective value converter 10
(T), Y _D (t), which is the output of the least squares calculation unit, is input to the _ID calculation unit 31. Then, the _ID calculation unit 3
1, the equivalent injection current I _D (t) at time t is calculated by equation (27) (step ST12).

Next, in the model calculation section 18, the injection current column vector I (t) at the time t on the digital system side is obtained.
And the admittance matrix Y (t) (step ST
5), the calculation result I _D (t) of the _ID calculation unit 31 and the calculation result Y _{D of the} least squares method calculation unit 13 are sent to the node equation solving unit 14.
(T), the calculation result I (t), Y of the model calculation unit 18
(T) is input. Then, the node equation solver 1
4, the column vector data V (t) representing the voltage distribution of the digital system is calculated (step ST6). The calculation result V (t) is saved in the digital data saving unit 15 (step ST7), and the voltage data V ₁ (t) at the link point is converted into the instantaneous value conversion unit 16 (step ST7).
8) After the D / A converter 17 (step ST9), a voltage is generated by the amplifier 19 and returned to the analog simulator.

Thereafter, it is determined whether the simulation is completed (step ST10). If YES, the operation is terminated. If NO, T is added to shift to the calculation of the next time step (step ST11). ).
As described above, according to the second embodiment, as the input data of the node equation of the digital system in the hybrid simulator, the equivalent admittance Y _D in Equation (14) representing the voltage and current characteristics of the analog simulator at the link point is It is obtained from the voltage and current data at the latest n sampling timings by the least square method, and the equivalent injection current _ID is obtained from the latest voltage data V _A (t),
It was obtained from the latest current data I _A (t) by Expression (27).

Hereinafter, the reason why this method is effective in improving the simulation accuracy of the hybrid simulation will be described. Equivalent admittance Y _D in equation (14)
Is generally invariant unless the impedance of the transmission line of the analog simulator is changed, so the estimation accuracy of the equivalent admittance Y _{D is} obtained by using the least squares method based on as much sample data as possible for the link point voltage and current. Need to be improved.

On the other hand, the equivalent injection current _ID changes as the voltage of the voltage source on the analog simulator side changes. These can be described by mathematical expressions as follows. In FIG. 1, if the voltage vector of the generator 1 is E and the admittance as the reciprocal of the impedance of the transmission line 3 is Y, the following equation is established. _{(V A -E) Y = I} A ... (28) Therefore, the following equation holds. I _A = −EY + YV _A (29) Comparing Expression (14) and Expression (29), Y _D = Y, I _D
= −EY.

Since the voltage E of the generator 1 changes with time due to power fluctuations and the like, the equivalent injection current _ID also changes with time. The equivalent admittance Y _D is equal to the transmission line admittance Y. In the second embodiment, the equivalent injection current I _D
And for computing on the basis of the latest association point voltage data V _A (t) and the latest cooperation point current data I _A (t), it is possible to calculate the value responsive to the time variation of the voltage source of the analog simulator . That is, the operation of the digital simulator can quickly follow the state change on the analog simulator side. As a result, with respect to the system simulation operation and the linking function in the digital simulator, there is an effect that the followability of the analog simulator with respect to time change is improved, and the simulation accuracy of the hybrid simulator is improved.

Embodiment 3 In the second embodiment, the equivalent admittance Y _D is calculated by the least squares method, assuming that the equation (14) representing the voltage-current characteristic at the link point is used. , T, t−T, t−2T,..., T
The time variation of the equivalent injection current _ID in the time zone of − (n−1) T is approximated by a linear expression to _ID (t) = _Io− (t−T) H, and the analog simulator at the link point side of the voltage, as an expression representing the characteristic of the current _{I a (T) = I o} - (t-T) H + Y D V a (T) t- (n-1) T ≦ T <t ... (30) becomes the model And a method of identifying the equivalent admittance Y _D by the least square method.

The identification method will be described below in comparison with the second embodiment. Sample data to identify the equivalent admittance Y _D analog simulator side for solving the node equations for the digital system at time t in the second embodiment is the following data. _{V A (t), V A} (t-T), V A (t-2T), ..., V A (t (n-1) T) ( linkage point voltage _{data) I A (t), I} A ( t−T), I _A (t−2T),..., I _A (t (n−1) T) (coupling point current data)

On the other hand, in the third embodiment, since the equivalent injection current follows the model of equation (30), the square of the absolute value of the difference between the right and left sides in the following n equations is used. sum determines the smallest as equivalent admittance Y _D.

(Equation 24)

That is, Y _D is determined so that the following equation D is minimized.

(Equation 25) Here, vector representation of I _o , H, Y _D (complex number representation)
Is as follows. I _o = K + jL (K: real part, L: imaginary part) H = C + jF (C: real part, F: imaginary part) Y _D = G + jB (G: real part, B: imaginary part)

The minimum value of D shown in the equation (31) is as follows.
This is when Expression (32) below holds. This equation (3
In 2), the left side is a linear expression for K, L, C, F, G, and B, respectively. The K, L, C, F, G, all coefficients are sample data V _A (t-kT) of B, I _A (t-k
T) (k = 0, 1,..., (N-1)).

[0084]

(Equation 26) The above equation (32) is a simultaneous linear equation relating to the six variables K, L, C, F, G, and B, and calculates G and B by performing a solution operation by Gaussian elimination.

As described above, according to the third embodiment, in order to calculate the input data of the node equation of the digital system in the hybrid simulator, the equations representing the voltage and current characteristics of the analog simulator at the link point are equivalent. Since the equivalent admittance is identified by the least squares method after adopting a precise model taking into account the time change of the injection current, the equivalent admittance can be calculated more accurately, and the simulation accuracy of the hybrid simulator is improved. effective. In the third embodiment, the time change of the equivalent injection current is one time with respect to time.
Although a model represented by the following equation is used, a model represented by a quadratic equation may be used, and the estimation accuracy of the equivalent admittance by the least squares method can be further improved.

In the third embodiment described above, a model that considers the time variation of the equivalent injection current is employed in the equation representing the voltage and current characteristics of the analog simulator at the link point, and the equivalent admittance is determined by the least squares method. However, considering that the equivalent injection current changes over time, even if the frequency of the power system to be simulated does not match the reference frequency and has a deviation, it is possible to accurately estimate the equivalent admittance as shown in FIG. The relationship between the amounts of electricity of the analog simulator in FIG.

The reference frequency of the power system is f ₀ , the frequency of the simulated power system is f (f ≠ f ₀ ), or Δ
Let f = f ₀ −f. A voltage vector of the power generator 1 E, when the admittance of the transmission line J1-3 and Y, the linkage point of the hybrid simulator analog simulator shown in FIG. 1 is connected, the equivalent injection current I _D has the formula (29)
Thus, _ID = -EY (33). Assuming that the instantaneous value of the voltage vector E of the generator 1 in the single-phase model is e = e ₀ sin (2πft + δ) (34), e = e ₀ sin (2π (f ₀ −Δf) t + δ) = e ₀ sin (2πf ₀ t−2πΔft + δ) (35) where the reference frequency is f ₀ and the phase angle when the effective value vector E is expressed as a vector is −2πΔft + δ.

This is because the frequency f of the power system is equal to the reference frequency f
_0, that is, when Δf ≠ 0, the voltage vector E
Means that the phase angle changes with time.
Therefore, from equation (33), the equivalent injection current _ID also changes with time. Equation (1) is equivalent to the equivalent injection current _ID from the following two equations.
And the equivalent admittance Y _D is obtained. _{I A (t) = I D} + Y D V A (t) I A (t-T) = I D + Y D V A (t-T) ... (36) In other words, in the conventional hybrid simulator, from t-T Since the equivalent admittance Y _D is calculated based on the equation on the assumption that the equivalent injection current I _D does not change with time in the time change of t, when the frequency of the power system is different from the reference frequency or power fluctuations occur. When the equivalent injection current I _D changes with time, as in the case where it occurs, there is a problem that the equivalent admittance Y _D cannot be calculated accurately.

On the other hand, in the third embodiment, the value of the equivalent admittance Y _D is estimated by the least squares method in accordance with a model that considers the time variation of the equivalent injection current I _{D in} the equations representing the voltage and current characteristics of the analog simulator. Therefore, the equivalent admittance Y _D can be accurately estimated, and this has the effect of improving the simulation accuracy of the hybrid simulator.

Embodiment 4 FIG. 5 is a block diagram showing the configuration of the hybrid simulator according to the fourth embodiment. The same parts as those in the first and second embodiments shown in FIGS. . In FIG. 5, reference numeral 51 denotes a frequency deviation calculator for calculating the frequency deviation of the power system to be simulated according to the result of the system simulation calculation of the digital simulator. Here, the frequency deviation will be described. The reference frequency of the power system and f _0.
The frequency in the actual power system changes under the influence of the power supply and demand balance, and may be operated at a frequency slightly deviated from the reference frequency f ₀ . When the frequency of the actual power system is f, Δf = f−f ₀ is called a frequency deviation.

The model of the digital system in the digital simulator is calculated in accordance with a model in which the relational expression between voltage and current is represented in a stationary coordinate system (so-called Coulomb coordinate system) at a reference frequency f ₀ in a vector.
When the frequency of the power system is f, the instantaneous sine wave of the voltage is expressed as V
When expressed as sin (2πft) (t represents time), f =
because it is f ₀ + Delta] f from the Vsin (2πft) = Vsin (2π (f 0 + Δf) t) = Vsin (2πf 0 t + 2πΔft) ... (37), in the coordinate system stationary reference frequency f _0, the instantaneous value sine wave Is converted to an effective value vector,
The phase angle becomes 2πΔft. That is, the phase angle of the effective value vector changes with time. Next, it is assumed that the interval time width of the digital simulator is T and the system is in a steady state.
At that time, the voltage vector data V (t) at time t and the voltage vector data V (t−T) calculated one step before
When the frequency deviation is Δf, V (t) has a phase angle of 2πΔf with respect to V (t−T).
It is advanced by T.

Therefore, the phase angle of V (t) is represented by δ (t), V (t)
When the phase angle of (t−T) is expressed as δ (t−T), δ (t) −δ (t−T) = 2πΔfT (38) From Equation (38), the frequency deviation Δf becomes Δf = (δ (t) −δ) (T−T)) / 2πT (39) The frequency deviation calculating unit 51 calculates the frequency deviation Δf from the voltage vector data V (t) and V (t−T) saved in the digital data saving unit 15 according to the equation (39).

Reference numeral 52 denotes a low-pass filter, which outputs a steady-state frequency deviation by cutting off a sudden change component of the frequency deviation Δf calculated by the frequency deviation calculator 51. Here, the necessity of calculating the steady-state frequency deviation using a low-pass filter will be described. For example, when the state changes suddenly in the power system, such as when an accident occurs at time t, the voltage vector data V (t) changes greatly with respect to V (t-T), and the phase angle changes suddenly with it. .
At this time, the expression (39) does not represent the frequency deviation Δf, and an excessively large value is calculated instantaneously, and cannot be used for the subsequent calculation. Therefore, the low-pass filter 52 is provided to output the value of the frequency deviation in the steady state.

Reference numerals 53 and 54 are correction operation units. Here, what kind of calculation these correction calculations are will be described. When the state of the time t is calculated by the digital simulator, the data saving unit 11 stores the link point voltage vector data _VA (t), _VA , which is n steps back from the time t.
(T−T), V _A (t−2T),..., V _A (t− (n−
1) T) is evacuated. The correction operation unit 53 inputs these data and performs the next operation from k = 0 to k = n-1. _VA ′ (t−kT) = _VA (t−kT) exp (−j2πΔf (nk) T) (40) where Δf is the output of the low-pass filter 52. Similarly saved in the correction calculation unit 54 in the data saving unit 12 data _{I A (t), I A} (t-T), I A (t-2T), ..., I A (t- (n-1 ) T) (41) The following calculation is performed from k = 0 to n-1. I _A ′ (t−kT) = I _A (t−kT) exp (−j2πΔf (n−k) T) (42) Here, the meaning of the calculation by Expression (40) or Expression (42) will be described. .

When the frequency deviation is Δf, the time is set to (n) with respect to time t− (n−1) T that is n steps back from time t.
−k) When T is advanced, the phase angle becomes 2 by the frequency deviation Δf.
πΔf (nk) T is advanced. Equation (40), Equation (4)
The content of 2) is to correct the rotation of the vector caused by the frequency deviation Δf by rotating the vector in the opposite direction at this advanced angle for k = 0, 1,..., (N−1). It is. As a result, data for n steps obtained by removing the rotation of the vector caused by the frequency deviation Δf is obtained, and thereafter, various quantities are calculated according to the same formula as when the power system frequency is equal to the reference frequency f _0. Can be.

Next, as an operation of the fourth embodiment, at time t
The operation of calculating the system state by the digital simulator will be described with reference to FIG. After the A / D conversion of the voltage signal and the current signal measured at the link point with the analog simulator, the voltage signal is converted by the effective value converter 9 into
Each of the current signals is converted into effective value vector data by the effective value conversion unit 10. Through these processes, the link point voltage vector V _A (t) and the link point current vector I _A (t) at time t are obtained. Here, the conversion operation to these effective value vectors is performed such that the vector is displayed at coordinates that are stationary at the reference frequency f ₀ (hereinafter, referred to as Coulomb coordinates).

Next, V _A (t) is stored in the data saving section 11 and
_A (t) is saved in the data saving unit 12. As a result, the data saving unit 11 stores n pieces of link point voltage vector data _VA (t) and _VA (t−
T), _VA (t-2T), ..., _VA (t- (n-1)
T) is stored. The n number of associated points current vector data back n increments from the time t in the data saving unit _{12 I A (t), I} A (t-T), I A (t-2
T), ..., a state where _{I A (t- (n-1} ) T) is stored.

Next, the calculation shown in equation (40) is performed by the correction calculation unit 53, and the calculation results V _A '(t), V _A '
(T−T),..., V _A ′ (t− (n−1) T) are input to the least square method calculation unit. Further, the calculation shown in Expression (42) is performed by the correction calculation unit 54, and I _A '
_{(T), I A '(} t-T), ..., I A' (t- (n-
1) T) is input to the least-squares method calculation unit 13. Note that the steady-state frequency deviation Δf input to the correction calculation units 53 and 54 is
The result calculated by the low-pass filter 52 in the time step one step before (that is, the process of calculating the state at the time tT) is input. The least-squares method operation unit 13 uses an analog simulator by the least-squares method according to the n link point voltage vector data corrected by the correction calculation unit 53 and the n link point current vector data corrected by the correction calculation unit 54. Admittance Y at time t
An operation for estimating _D (t) is performed.

Next, in the _ID calculating section 31, the equation (27) is obtained.
Calculates the equivalent injection current I _D (t) of the analog simulator at time t. These Y _D (t), I _D
(T) is input to the node equation solving unit 14. Next, calculations are performed in the model calculation unit 18 and the node equation solving unit 14 to determine the voltage distribution of the digital system at time t. Also, the result of this operation is saved in the digital data saving unit 15. The model calculation unit 18 and the node equation solution calculation unit 14 calculate a digital system model according to a model represented by a vector expression in a Coulomb coordinate system. Next, the calculated link point voltage vector data is output as a signal to the amplifier 19 via the instantaneous value converter 16 and the D / A converter 17 to generate a link point voltage.
On the other hand, the frequency deviation calculation unit 51 calculates the frequency deviation Δf according to the calculation result of the digital system voltage vector which is the calculation result at the time t and the voltage vector one step before. Further, the steady-state frequency deviation is calculated by the low-pass filter 52. Thus, the calculation of the state at the time t is completed, and the time interval T is added to the time variable t.

As described above, according to the fourth embodiment, the operation for estimating the equivalent admittance of the analog simulator is performed after correcting the rotation of the current and voltage vectors caused by the frequency deviation. Is deviated from the reference frequency, the equivalent admittance of the analog simulator is accurately estimated, and the simulation accuracy of the hybrid simulator is improved. In addition, since the calculation of the frequency deviation is made to pass through the low-pass filter, the rotation of the vector is corrected according to the frequency deviation stabilized to the numerical value, and there is an effect that a stable calculation result can be obtained even when the system is suddenly changed.

Here, according to the fourth embodiment, the reason why the equivalent admittance can be accurately estimated even when there is a frequency deviation will be described below. For the sake of simplicity, it is assumed that, in the operation of estimating the equivalent admittance Y _D by the least square method, sampling data of the effective value is input in two steps. That is, it is assumed that n = 2. At this time, the data input to the operation of the least squares method is the following data. _{V A (t), V A} (t-T): linkage point voltage vector data _{I A (t), I A} (t-T): estimating calculation of the equivalent admittance Y _D by linking point current vector data method of least squares This is to find Y _D that minimizes the sum of squares of the absolute value of the difference between the left side and the right side of the following two equations. _{I A (t) = I D} + Y D V A (t) I A (t-T) = I D + Y D V A (t-T)

When n = 2, the number of unknowns ( _ID and Y _D ) and the number of equations match, so that the two equations have a solution in which the left side and the right side match, which is determined by the least squares method. It matches the operation result. Therefore, the equivalent admittance Y _D is calculated by the following equation. Y _D = when _{(I A (t) -I A} (t-T)) / (V A (t) -V A (t- T)) ... (43) the frequency deviation Δf is 0, the equivalent admittance Y The theoretical value of _D follows equation (43).

Next, V _A (t) and I _A (t) are displayed in polar coordinates as follows. _{V A (t) = V A} , t exp (jθ (t)) V A, t: absolute value θ (t): phase _{I A (t) = I A} , t exp (jδ (t)) I A, _t : absolute value δ (t): phase At this time, equation (43) becomes the following equation. Y _D = I _{A, t} exp (jδ (t)) − I _{A, tT} exp (jδ (t−T)) / V _{A, t} exp (jθ (t)) − V _{A, tT} exp (jθ (t -T)) ... (44)

Now, if the reference phase angle α is changed,

[Equation 27] Equation (43) does not depend on how to take the reference phase.

That is, regarding the calculation of the equivalent admittance, which is an amount independent of frequency, the phase angle is calculated as V _A
(T), V _A (t−T), I _A (t), I _A (t−T)
Only the relative phase of the four data needs to be considered. Next, it is assumed that the frequency deviation Δf is not 0 (f ≠ 0). At that time, when the time T has elapsed, Δf =
The phase of all vectors is advanced by 2πΔfT compared to the case of 0. Therefore, the phase differences δ (t) and δ (t−T) are Δf
When ≠ 0, it increases by 2πΔfT compared to when Δf = 0. Similarly, the phase differences θ (t) and θ (t−T) increase by 2πΔfT when Δf ≠ 0 compared to when Δf = 0.

Assuming that 2πΔfT = β, the frequency deviation Δ
Equation (4) on the assumption that the frequency deviation Δf = 0 when f ≠ 0
When calculated in 3), Y _D = I _{A, t} exp (δ (t) + β) −I _{A, tT} exp (δ (t−T)) / V _{A, t} exp (θ (t) + β) −V _{A, tT} exp (θ (t−T)) (46) Since β ≠ 0, the calculation is performed using a calculation formula different from the theoretical value shown in Expression (43). Therefore, when the frequency deviation is not 0, when the equivalent admittance is estimated by a model on the assumption that the frequency deviation is 0,
It cannot calculate accurately. In contrast, -2Paiderutaf the phase angle of the embodiment 4, _{V A (t), I A} (t)
After performing the operation of correcting by T = −β, the equivalent admittance is calculated, so that the calculation is performed by a calculation expression equivalent to the expression (43). Therefore, the equivalent admittance can be accurately estimated without being affected by the frequency deviation Δf.

Embodiment 5 FIG. FIG. 6 is a block diagram showing the configuration of the hybrid simulator according to the fifth embodiment. The same parts as those in the first embodiment shown in FIG. In FIG. 6, 61 is Y _D
A storage unit, sets stored externally before starting the simulation data representing the value of the equivalent admittance Y _D. Reference numeral 62 denotes a calculation unit for calculating the equivalent injection current _ID .
The equivalent injection current _ID is calculated by the following equation from the equation (14). _{I D = I A -Y D V} A ... (47) where I _A is the effective value vector data representing the linkage point current output from the effective value converting unit 10, V _A is output by the effective value converting unit 9 5 is effective value vector data representing the link point voltage.

Next, the outline of the operation of the fifth embodiment will be described with reference to the flowchart of FIG. First, the operation of calculating the state of the digital system at time t as the operation of the digital simulator will be described. A / D conversion is performed on the voltage value and the current value of the link point of the analog simulator measured by the voltage measuring unit 6 and the current measuring unit 5 (step ST1). Thereafter, these data are converted into effective value vector data (step ST2). Thus, the voltage vector V _{A at} the link point of the analog simulator measured at time t
(T), data of the current vector I _A (t) are obtained.
Next, in the _ID calculation section 62, the data V _A
(T), and I _A (t), Y _D following equation from the data Y _D equivalent admittance set in the storage unit _{61 I D = I A (t} ) -Y D V A (t) ... (48) To calculate the equivalent injection current _ID (step ST
13). This equivalent injection current _ID represents the equivalent injection current of the analog simulator at time t.

Next, after performing a model operation of the digital simulator (step ST5), a node equation of the digital system is solved (step ST6). The node equation solving calculation unit 14, the equivalent injection current I _D which is calculated by I _D calculation section 62 as an equivalent injection current data of the analog simulator at time t, the data of the set equivalent admittance Y _D storage section 61 Each is entered.
Since the other operation processing is the same as the operation of the first embodiment, the same step numbers are assigned and the duplicate explanation is omitted.

As described above, according to the fifth embodiment, data representing the equivalent admittance of the analog simulator for solving the node equation of the digital system is externally set as a fixed value before starting the simulation. did. Also, in the node equation solution processing of the digital system during the simulation, the equivalent admittance of the analog simulator is set to this fixed value, and the node equation solution operation is performed. As a result, the following effects can be obtained. 1. Since the process of estimating and calculating the equivalent admittance based on the measurement data of the analog simulator during the simulation can be omitted, the calculation speed on the digital simulator side is improved. Alternatively, the load on the processor that performs the calculation can be reduced. 2. Since the equivalent admittance is set to a fixed value, it is possible to eliminate error factors such as noise and harmonics in measurement performed in estimation calculation based on measurement data and digit cancellation in calculation, thereby improving the calculation accuracy of the hybrid simulator. . 3. Since the calculation is performed according to a model in which the equivalent admittance of the analog simulator is a fixed value without changing with time, the calculation stability is excellent. Here, the meaning of the fact that the calculation stability is excellent will be described in detail below.

For this reason, the behavior of the result of numerical calculation in the case of performing a hybrid simulation on the power system shown in FIG. 8 will be described as an example. In FIG. 8, 1 is a generator, 2 is a bus (at the end of the generator), 3 is a transmission line, and 4 is a connection point bus, and an electric circuit is realized by an analog simulator. 63 is a bus, 64 is a current source, 5 is a transmission line, and a model in a digital system is realized. The link point bus 4 is also included as a model on the digital system side. Accordingly, the digital system is a model of a power system including the link point bus 4, the bus 63, the current source 64, and the transmission line 65.

The symbols related to the description of FIG. 8 are as follows. V ₁ : Voltage vector of link point JI-4 in digital system V ₂ : Voltage vector of bus 4-4 Y ₁₂ : Admittance of transmission line 4-6 I ₂ : Current vector of current source 4-5 V _A : Analog simulator Link point J measured at
Voltage vector I _A of I-4: Transmission line J measured by analog simulator
Current vector of I-3 Y _D : Equivalent admittance viewed from the link point of the analog simulator _ID : Equivalent injection current viewed from the link point of the analog simulator

Since the values other than Y _D and Y ₁₂ change with time, they are denoted by V ₁ (t), V ₂ (t), etc. and (t). t represents time. Let T be the step time in the digital simulator. Since the digital system shown in FIG. 8 is configured as described above, the node equation in the digital system is as follows.

[Equation 28]

Therefore, the voltage is obtained by the following equation.

(Equation 29)

The process of obtaining a consistent voltage distribution by integrating an analog simulator and a digital system will be described below. 1. At time t, V _A (t) and I _A (t) are measured, and I _{D
(T) = I A (t} ) -Y D V by _A (t) I _D
(T) is obtained. 2. Substituting _ID (T) into equation (50), V ₁ (t), V
₂ (t) is obtained. In the fifth embodiment, equation (50) is used.
'S Y _D is a fixed value. In the prior art, Y _D is calculated for each time step. For the voltage V ₁ (t), the amplifier 19 outputs the voltage V ₁ (t) to the link point bus 4 of the analog simulator. 3. V _A (t
+ T) = V ₁ (t). Therefore,

[Equation 30] Becomes

Each time the time step by the interval time T is advanced, V ₁ and V are gradually increased according to the recurrence formula by the formula (51).
₂ converges to a consistent voltage distribution by integrating the electrical state of the analog simulator and the model of the digital system. In the link algorithm between the analog simulator and digital system in the hybrid simulator,
It is necessary to converge this convergence as quickly and stably as possible. In the conventional hybrid simulator, the equivalent admittance Y _D is calculated every time (time step). Therefore, the Y _D causes a measurement error, an insufficient number of bits of the A / D converter, a digit loss at the time of calculation, and the like. such as vibrations under the influence, the value of Y _D was numerically unstable.

As a result, since the coefficient of the recurrence equation (51) oscillates and does not hold a numerically stable constant value, the convergence of the recurrence equation deteriorates, and even if the time step is advanced, V
_1, or no V ₂ converges, V _1, V ₂ and the like can be observed phenomena such as causing a vibration or chattering. Alternatively, in FIG. 8, passing a major trends in the transmission line, when a simulation was performed to flow a tide values around the allowable limit not step out, the equivalent admittance Y _D can not be calculated stably when vibration, smaller than the allowable limit There was a problem that the simulation accuracy as a hybrid simulator was poor, such as a step-out immediately after the tide flow.

On the other hand, in the fifth embodiment, since the equivalent admittance Y _D is set to a constant value that does not change and the calculation is performed, the coefficient of the recurrence formula (51) is fixed without changing even if the time step is advanced. . As a result, the convergence of the recurrence formula (51) is significantly increased. In addition, as a result, unnecessary vibration phenomena and chattering phenomena of the voltage calculation results V ₁ and V ₂ are eliminated, calculation stability is improved, and simulation accuracy of the hybrid simulator is improved. Also, the equivalent admittance Y
Since the simulation is performed with _D being a constant value, there is an effect that even if a large tide flows in the transmission line, a stable simulation can be performed without step-out.

Next, in the fifth embodiment, the reason why the calculation stability is improved when the equivalent admittance of the analog simulator is set as a fixed value will be described in Japanese Patent Application Laid-Open No. Hei 6 (1994) -181605.
This will be described with reference to the prior art of Japanese Patent Application Laid-Open No. 38372/1990. This prior art shows a linking method between an analog device and a digital simulator, and the processing of the self-tuning regulator in this prior art is
This corresponds to the process of controlling the voltage at the link point such that a voltage distribution having consistency between the analog simulator and the digital system according to the fifth embodiment is obtained.

According to this prior art, in the self-tuning regulator, the condition that the value of the hybrid equivalent admittance does not change in order to change the output voltage of the calculation unit (ie, to determine the voltage at the link point by digital calculation). Below, the output voltage is changed assuming that the current of the analog device has changed at a point that matches the operating characteristics of the digital section. The term “hybrid equivalent admittance” in this prior art is a subordinate concept of the outline of equivalent admittance of the analog simulator in the fifth embodiment. Therefore, self-tuning
Since the tuning algorithm by the regulator is designed under the condition that the hybrid equivalent admittance does not change, it works well only when the hybrid equivalent admittance does not change.

However, in the prior art, the analog data is measured at each time step in the digital calculation to calculate the hybrid equivalent admittance, and the calculation method has a large digit loss in the calculation.
This value shows an unstable behavior due to noise error, digit drop, etc., and does not fall down to a constant value. As a result, there is a problem that the self-tuning regulator does not operate properly.

On the other hand, in the fifth embodiment, it is assumed that the hybrid equivalent admittance is a fixed constant value.
Since the self-tuning regulator is operated, the tuning operation of the self-tuning regulator operates well, and it is possible to quickly converge to a voltage distribution having consistency between the analog simulator and the digital system. Further, in the practical case, as described in the calculation formula above, the value of the hybrid equivalent admittance is equal to the admittance of the transmission line and is constant without change in theory. The method of calculating the hybrid equivalent admittance as a constant value is rational and is excellent in improving the performance of the self-tuning regulator.

Embodiment 6 FIG. First, an outline of the sixth embodiment will be described. Λ = 1 with respect to the reference frequency f _{0 of the} power system
/ F ₀ , λ is the period of the fundamental wave related to voltage and current,
T is an interval time width of the digital simulator. After measuring the voltage and current at the link point of the analog simulator, the hybrid simulator is operated under the condition that the sampling time width of the sampling for A / D conversion is also equal to the same time width T. Let λ be an integral multiple of T,
λ = NT (N: integer). Let the instantaneous value of the voltage sampled at time t be υ (t).

In the conventional hybrid simulator, when converting the instantaneous value data into the effective value vector data, for example, the data υ (t−λ / 4) sampled before λ / 4 together with υ (t) is converted as follows. Was used to calculate the effective value.

(Equation 31)

Here, N is divisible by 4 and λ
/ 4 corresponds to a phase of π / 2. In this case, if the measured analog data contains harmonics, the effective value of the fundamental wave component cannot be calculated accurately. In contrast,
In the sixth embodiment, sampling data １ (t), υ (t−T), υ (t−2T),..., Υ (t− (N−1) T) (53) The effective value vector data is calculated by performing the discrete Fourier transform. The method of calculating the effective value vector V by the discrete Fourier transform is given by the following equation.

(Equation 32)

Here, exp (-j2πk / N) is a complex number,

[Equation 33] Is data representing υ (t−kT) is real number data, and V of the operation result is complex number data. The complex number data V is the effective voltage vector data of the measured voltage obtained by the discrete Fourier transform. Similarly, for the current, the instantaneous value data i (t), i (t−T), i (t−2T),..., I (t− (N−1) T) of the current sampled over one cycle. (55) is used to calculate the effective value vector of the current by performing the calculation of the discrete Fourier transform by the following equation.

(Equation 34) Note that the theory of the discrete Fourier transform has been described in a large number of known documents describing signal analysis methods, and thus detailed description thereof is omitted.

FIG. 9 is a block diagram showing the configuration of the hybrid simulator according to the sixth embodiment. The same parts as those in the first embodiment shown in FIG. In the figure, reference numeral 91 denotes A / over one cycle.
D-converted sampling data of the instantaneous value of the link point voltage υ (t), υ (t−T),..., Υ (t− (N−1) T)
Is a data saving unit for saving data. 92 is A over one cycle
, I (t), i (t−T),..., I (t− (N−1)
T) is a data saving unit for saving. 93 is the equation (54)
By performing the operation of the discrete Fourier transform shown in (2), the effective value vector data _VA of the link point voltage at time t is obtained.
This is a discrete Fourier transform operation unit that calculates (t) by the following equation.

(Equation 35)

Numeral 94 denotes a discrete Fourier transform operation unit for calculating the effective value vector data I _A (t) of the link point current at the time t measured at the link point by performing the discrete Fourier transform operation shown in the equation (56). It is.

[Equation 36]

Next, the outline of the operation of the sixth embodiment will be described with reference to the flowchart of FIG. The overall processing flow is to perform processing for calculating the state at time t, which is updated by adding the step time width T, and when this processing is completed, T is added to a variable representing time, Move to the next time step. This repetition is repeated until the simulation is completed.

Next, the calculation for each time step will be described. That is, the process of calculating the system state at time t will be described. First, A / D conversion of signals measured by the voltage measuring unit 6 and the current measuring unit 5 is performed (step ST1).
Thus, instantaneous value data υ (t) of the link point voltage and instantaneous value data i (t) of the link point current at time t are obtained.

Next, with respect to these instantaneous value data, the instantaneous voltage data is saved to the data saving unit 91 and the instantaneous current data is saved to the data saving unit 92 (step ST1).
4). When the instantaneous value data υ (t) at time t is input to the data saving unit 91 in the processing of the time step at time t, the sampling data υ (t−NT) of N + 1 times before is input.
Is always discarded, N pieces of sampling data υ (t), υ (t−T), υ (t−2T),.
− (N−1) T) is held. Since the data is sampled N times at an interval of time T during one cycle λ = 1 / f ₀ , these N pieces of data are sampled data over one cycle. In the data saving unit 92, by performing the same operation, when the instantaneous value data sampled at the time t is input, the N pieces of sampling data i (t) and i (t-T) over one cycle are input. , I (t−2T),..., I
(T (N-1) T) is saved.

Next, by the discrete Fourier transform operation unit 93,
According to the data saved in the data saving unit 91, the formula (5)
By performing the calculation of 7), the effective value vector data V _A (t) of the link point voltage at time t is calculated (step ST15). This data is saved in the data saving unit 11. In addition, the discrete Fourier transform operation unit 94 performs the operation of Expression (58) according to the data saved in the data saving unit 92, thereby calculating the effective value vector data I _A (t) of the link point current at time t. I do. More effective value at time t by the processing vector data _{V A (t), I A} (t) is computed. The data I _A (f) is saved in the data saving unit 12.

The sixth embodiment is a modification of the first embodiment with respect to a method of calculating effective value vector data from instantaneous value data obtained by measuring and sampling analog data. Since the operation is the same as that of the embodiment, the same step numbers are assigned and duplicate explanations are omitted.

As described above, according to the sixth embodiment, the effective value vector data is calculated by calculating the fundamental component by the discrete Fourier transform from the instantaneous value sampling data of the current and the voltage measured at the link point. Waves and
Effective value vector data can be accurately calculated by eliminating the influence of noise. As a result, there is an effect of improving the simulation accuracy of the hybrid simulator.

In the above-described Embodiment 6, an example has been described in which the discrete Fourier transform is performed using all the sampling data over one cycle. However, the latest Fourier transform over half cycle, 1/3 cycle, and 1/4 cycle has been described. Sampling data may be used. The shorter the time zone of the sampling data input as the input of the discrete Fourier transform, the higher the speed of following the state change on the analog simulator side.

[0136]

As described above, according to the first aspect of the present invention, the state of the analog simulator is accurately estimated based on the data sampled at a plurality of sampling timings of the voltage and the current measured by the analog simulator. This has the effect of improving the calculation accuracy of the power system simulator.

According to the second aspect of the present invention, an estimation operation is performed by the least square method in accordance with the latest voltage data and current data that are sampled in the past, thereby obtaining an equivalent injection current and an equivalent admittance. Therefore, the estimation accuracy of the equivalent injection current and the equivalent admittance is improved. In addition, by using the least squares method, it is possible to eliminate noise contamination, an insufficient number of significant digits of the A / D converter, and an error factor of a digit drop in a numerical operation. Therefore, it is possible to solve the node equation while securing the accuracy of the equivalent injection current and the equivalent admittance, thereby improving the calculation accuracy of the simulation and improving the simulation accuracy of the hybrid simulator.

According to the third aspect of the present invention, the equivalent admittance and the equivalent injection current are calculated based on the latest voltage data and the latest current data. The calculated value can be calculated. That is, the operation of the digital simulator can quickly follow the state change on the analog simulator side. As a result, with respect to the system simulation operation and the linking function in the digital simulator, the follow-up property to the time change of the analog simulator is improved, and the simulation accuracy of the hybrid simulator is improved.

According to the fourth aspect of the invention, since the equivalent admittance is identified by the least square method in consideration of the time change of the equivalent injection current, the equivalent admittance can be calculated with high accuracy. This has the effect of improving the simulation accuracy of the hybrid simulator.

According to the fifth aspect of the present invention, the frequency deviation from the reference frequency of the electric power system is calculated, and the vector rotation caused by the frequency deviation of the current and voltage vector data measured by the analog simulator is calculated. Since the state quantity of the analog simulator is calculated based on the current and voltage data subjected to the correction calculation, the state quantity of the analog simulator can be accurately calculated even when the frequency of the power system does not match the reference frequency. The calculation can be performed, and the calculation accuracy of the power system simulator is improved.

According to the sixth aspect of the present invention, since a model taking into account the time variation of the equivalent injection current is adopted and the equivalent admittance is identified by the least square method, the equivalent admittance is calculated with high accuracy. It is possible,
This has the effect of improving the simulation accuracy of the hybrid simulator.

According to the seventh aspect of the present invention, the equivalent admittance of the analog simulator is externally set as a fixed value prior to the start of the simulation, so that the process of estimating and calculating the equivalent admittance can be omitted. Therefore, the calculation speed of the digital simulator can be improved, and the load on the processor that performs the calculation can be reduced. In addition, it is possible to eliminate noise and high frequency in measurement, which are observed in estimation calculation based on measurement data, or error factors such as cancellation of digits in calculation, thereby improving the calculation accuracy of the hybrid simulator.

According to the eighth aspect of the present invention, the effective value vector data is calculated by calculating the fundamental wave component by discrete Fourier transform from the current / voltage instantaneous value sampling data measured at the link point. Thus, the effective value vector data can be accurately calculated by eliminating the influence of high frequency and noise. As a result, the simulation accuracy of the hybrid simulator is improved.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a hybrid simulator according to a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating a processing operation according to the first embodiment;

FIG. 3 is a block diagram showing a hybrid simulator according to a second embodiment of the present invention.

FIG. 4 is a flowchart illustrating a processing operation according to the second embodiment;

FIG. 5 is a block diagram showing a hybrid simulator according to a fourth embodiment of the present invention.

FIG. 6 is a block diagram showing a hybrid simulator according to a fifth embodiment of the present invention.

FIG. 7 is a flowchart illustrating a processing operation according to the fifth embodiment.

FIG. 8 is a power system diagram.

FIG. 9 is a block diagram showing a hybrid simulator according to a sixth embodiment of the present invention.

FIG. 10 is a flowchart illustrating a processing operation according to the sixth embodiment.

FIG. 11 is a block diagram showing a linkage method of a conventional hybrid simulator.

FIG. 12 is a schematic diagram showing a power system.

FIG. 13 is a block diagram showing a conventional hybrid simulator.

[Explanation of symbols]

1 generator (analog simulator), 2 and 4 buses (analog simulator), 3 transmission line (analog simulator), 5 current measuring device (measuring unit), 6 voltage measuring device (measuring unit), 13 least square method calculation unit, 14 Node equation solution calculation unit (digital calculation unit), 51 frequency deviation calculation unit, 53, 54 correction calculation unit, 62 equivalent injection calculation unit, 93, 94 discrete Fourier transform calculation unit.

Claims (8)

[Claims] 1. A measuring unit for measuring a voltage and a current in an analog simulator, and a state of the analog simulator is determined by a least square method based on data obtained by sampling the voltage and the current output from the measuring unit at a plurality of sampling timings. A power system simulator comprising: a least-squares method calculation unit for performing an estimation calculation; and a digital calculation unit for performing a calculation for simulating a state of a power system based on the estimated state data of the analog simulator. 2. A method according to claim 1, wherein the least-squares-method calculating unit sets the time at which the state of the analog simulator is calculated to be t, and
T, t−2T,..., T− (n−1) T, n pieces of voltage data _VA (t), _VA (t−T), _VA (t−
_{2T), ..., V A (} t- (n-1) T) and, n-number of current data _{I A (t), I A} (t-T), I A (t-2
T),..., I _A (t− (n−1) T), Calculating an equivalent injection current and an equivalent admittance that minimize the following equation, and performing a simulation to simulate the state of the power system at time t based on the data of the equivalent injection current and the equivalent admittance. 2. The power system simulator according to 1. 3. The least-squares method calculation unit sets the time at which the state of the analog simulator is calculated to be t, and the times t, t−
T, t−2T,..., T− (n−1) T, n pieces of voltage data _VA (t), _VA (t−T), _VA (t−
_{2T), ..., V A (} t- (n-1) T) and, n-number of current data _{I A (t), I A} (t-T), I A (t-2
T),..., I _A (t− (n−1) T), And the equivalent admittance that minimizes
Calculates an equivalent injection current by _{D = I A (t) -Y} D V A (t), the digital calculation unit equivalent admittance at time t, based on the data of the equivalent injection current at time t, the power system The power system simulator according to claim 1, wherein an operation for simulating a state at time t is performed. 4. The least-squares method operation unit sets the time at which the state of the analog simulator is calculated to be t, and the times t, t−
T, t−2T,..., T− (n−1) T, n pieces of voltage data _VA (t), _VA (t−T), _VA (t−
_{2T), ..., V A (} t- (n-1) T) and, n-number of current data _{I A (t), I A} (t-T), I A (t-2
T),..., I _A (t− (n−1) T), Thereby calculating the equivalent admittance to minimize the equivalent injection operation unit _{I D = I A (t)} -Y D V by _A (t) calculates the equivalent injection current, digital computing unit time t
The power system simulator according to claim 1, wherein an operation for simulating a state of the power system at a time t is performed based on the data of the equivalent injection current in (1). 5. A frequency deviation calculating unit for calculating a frequency deviation from a reference frequency of a power system, a measuring unit for measuring current and voltage in an analog simulator, and a vector data of current and voltage output from the measuring unit. A correction calculation unit that corrects and calculates a vector rotation caused by the frequency deviation;
A power system simulator comprising a digital calculator for calculating a state quantity of an analog simulator based on the corrected current and voltage data to simulate the state of the power system. 6. The power system simulator according to claim 5, wherein the following operations (1) to (5) are performed. 1. Calculate the frequency deviation from the reference frequency of the power system. 2. The above 1. Is subjected to a low-pass filter, and the calculation result is defined as Δt. 3. Time t, tT, t-2T, ..., t- (n-1) T
N voltage vector data V _A (t), V
_A (t−T), V _A (t−2T), V _A (t− (n−
1) T) and n pieces of current vector data I _A (t), I
_A (t−T), I _A (t−2T),..., I _A (t− (n
-1) The following operation is performed on T) from k = 0 to n-1. V ′ _A (t−kT) = V _A (t−kT) exp (−j2
πΔf (n−k) T) I ′ _A (t−kT) = I _A (t−kT) exp (−j2
πΔf (nk) T) 4. Calculate the equivalent admittance that minimizes the following equation. (Equation 4) 5. 4 above. Is regarded as the equivalent admittance amount of the analog simulator at time t, and the state of the power system at time t is calculated. 7. A measuring unit for measuring voltage and current in an analog simulator, and an equivalent for calculating an equivalent injection current based on voltage data and current data output from the measuring unit and a fixed equivalent admittance given from outside. A power system simulator, comprising: an injection calculation unit; and a digital calculation unit that performs an operation for simulating a state of a current system based on the data of the fixed equivalent admittance and the equivalent injection current. 8. A measuring unit for measuring voltage and current in an analog simulator, and accumulating data of instantaneous value data of voltage data and current data output from the measuring unit for a fixed sampling period, and performing discrete Fourier transform. A discrete Fourier transform operation unit for calculating a fundamental wave component according to the above; a least square method operation unit for estimating and calculating the state of the analog simulator by a least square method based on the fundamental wave component; A power system simulator comprising: a digital calculation unit that performs an operation for simulating a state of a power system based on state data.