JP2012093137A - Method and apparatus for measuring ac electrical quantity - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and an apparatus that enable measurement of AC electrical quantity with high accuracy.SOLUTION: First, a gauge voltage is calculated by normalizing a voltage amplitude that has been obtained by performing a square integration operation on voltage instantaneous value data for continuous at least three points obtained by sampling AC voltage to be measured at a sampling frequency two times that of the AC voltage or higher. Second, a gauge differential voltage is calculated by normalizing a value that has been obtained by performing a square integration operation on differential voltage instantaneous value data for three points that represent distances between peaks of voltage instantaneous value data of neighboring two points in voltage instantaneous value data for continuous at least four points including the voltage instantaneous value data for the three points used to calculate the gauge voltage. Finally, an amplitude of the AC voltage is calculated using the gauge voltage and the gauge differential voltage.

Description

  The present invention relates to an AC electricity quantity measuring device and an AC electricity quantity measuring method.

  In recent years, as the power flow in the power system has become more complex, it has become necessary to supply power with high reliability and quality, and in particular, the amount of AC electricity that measures the amount of electricity in the power system (AC electricity amount). The need for improved performance of measuring devices is increasing.

  Conventionally, as this type of alternating current electric quantity measuring device, for example, there are those shown in Patent Documents 1 and 2 below. In Patent Document 1 (protection control measurement system) and Patent Document 2 (wide area protection control measurement system), the frequency of the actual system is obtained with the change component (differential component) of the phase angle as the change from the rated frequency (50 Hz or 60 Hz). The method is disclosed.

  In these documents, the following formulas are disclosed as formulas for obtaining the frequency of the actual system, but these formulas are also formulas presented by Non-Patent Document 1 below.

2πΔf = dφ / dt
f (Hz) = 60 + Δf

JP 2009-65766 A JP 2009-71637 A

“IEEE Standard for Synchrophasors for Power Systems” page 30, IEEE Std C37.118-2005.

  As described above, the methods disclosed in Patent Documents 1 and 2 and Non-Patent Document 1 are methods for obtaining a phase angle change component by differential calculation. However, the change of the instantaneous frequency value of the actual system is frequent and complicated, and the differential calculation is very unstable. For this reason, for example, there has been a problem that sufficient calculation accuracy cannot be obtained for frequency measurement.

  In addition, since the above method calculates the rated frequency (50 Hz or 60 Hz) as an initial value, a measurement error occurs when the measurement target is operating outside the system rated frequency at the start of the calculation. Thus, when the degree of deviation from the system rated frequency is large, there is a problem that the measurement error becomes very large.

  The present invention has been made in view of the above, and even when the measurement object is operating outside the system rated frequency, the AC electricity quantity measurement that enables highly accurate measurement of the AC electricity quantity is possible. It is an object of the present invention to provide an apparatus and an AC electric quantity measurement method.

  In order to solve the above-described problems and achieve the object, an AC electrical quantity measuring device according to the present invention is configured to sample at least three consecutive AC voltages to be measured at a sampling frequency that is twice or more the frequency of the AC voltage. A gauge voltage calculation unit that calculates a gauge voltage obtained by normalizing a voltage amplitude obtained by square integral calculation of the voltage instantaneous value data of the point, and three points sampled at the sampling frequency and used for calculating the gauge voltage. The value obtained by the square integral calculation of the differential voltage instantaneous value data of three points representing the distance between the tips of two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the voltage instantaneous value data. A gauge difference voltage calculation unit for calculating a normalized gauge difference voltage; and the alternating current using the gauge voltage and the gauge difference voltage. Characterized by comprising a voltage amplitude calculator that calculates an amplitude of pressure, the.

  The AC electricity quantity measuring apparatus according to the present invention has an effect that it is possible to measure the AC electricity quantity with high accuracy even when the measurement target is operating outside the system rated frequency.

FIG. 1 is a diagram illustrating a gauge voltage group and a gauge differential voltage group on a complex plane. FIG. 2 is a diagram illustrating the relationship between the gauge voltage and the gauge differential voltage. FIG. 3 is a diagram illustrating a group of gauge powers on the complex plane. FIG. 4 is a diagram illustrating a gauge differential power group on a complex plane. FIG. 5 is a diagram illustrating a functional configuration of the AC electricity quantity measuring device according to the present embodiment. FIG. 6 is a flowchart showing the flow of processing in the AC electrical quantity measurement device. FIG. 7 is a diagram illustrating a waveform of the voltage instantaneous value at the time of executing the first simulation, a gauge voltage calculated based on the voltage instantaneous value, a gauge differential voltage, and a measured voltage amplitude. FIG. 8 is a diagram showing a waveform of an instantaneous current value at the time of executing the first simulation, a gauge current, a gauge differential current, and a measured current amplitude calculated based on the instantaneous current value. FIG. 9 is a diagram illustrating a gauge active power, a gauge differential active power, and a measured active power according to the first simulation. FIG. 10 is a diagram illustrating gauge reactive power, gauge differential reactive power, and measured reactive power according to the first simulation. FIG. 11 is a diagram illustrating the measurement result of the power factor by the first simulation. FIG. 12 is a diagram illustrating a waveform of a voltage instantaneous value at the time of executing the second simulation, a gauge differential voltage calculated based on the voltage instantaneous value, and a measured voltage amplitude. FIG. 13 is a diagram illustrating a waveform of an instantaneous current value when the second simulation is executed, a gauge differential current calculated based on the instantaneous current value, and a measured current amplitude. FIG. 14 is a diagram illustrating the gauge differential active power and the measured active power according to the second simulation. FIG. 15 is a diagram illustrating gauge reactive power, gauge differential reactive power, and measured reactive power according to the second simulation. FIG. 16 is a diagram illustrating a power factor measurement result by the second simulation.

  An AC electricity quantity measuring device and an AC electricity quantity measuring method according to embodiments of the present invention will be described below with reference to the accompanying drawings. In addition, this invention is not limited by embodiment shown below.

(Embodiment)
In describing the AC electricity quantity measuring apparatus and the AC electricity quantity measuring method according to the present embodiment, first, the concept (algorithm) of the AC electricity quantity measuring method forming the gist of the present embodiment will be described, and then the present embodiment will be described. The configuration and operation of the AC electricity quantity measuring device according to the embodiment will be described. In the following description, among lowercase letters in the alphabet, those with parentheses (for example, “v (t)”) represent vectors, and those without parentheses (for example, “v ₂ ”) represent instantaneous values. Shall. In addition, alphabetic capital letters (for example, “V _g ”) represent effective values or amplitude values.

  FIG. 1 is a diagram illustrating a gauge voltage group and a gauge differential voltage group on a complex plane. In FIG. 1, on the complex plane, the current voltage rotation vector v (t) and the voltage rotation vector v (t−) at the time before the sampling 1 period T (time corresponding to the sampling frequency 1 step width) before the current time. T), a voltage rotation vector v (t-2T) at a time point 2 sampling (2T) before the current time point, and a voltage rotation vector v (t-3T) at a time point 3 sampling (3T) time point before the current time. Yes.

  Now, consider these four voltage rotation vectors. First, these four voltage rotation vectors are rotation vectors that rotate counterclockwise on the complex plane at the same rotation speed, and are expressed as follows using the sampling period T.

  In the above equation (1), V is a voltage amplitude. Further, ω is a rotational angular velocity and is expressed by the following equation.

  In the above equation (2), f is an actual frequency. Moreover, the sampling 1 period T in the equation (1) is expressed by the following equation.

In the above equation (3), f _S is a sampling frequency. Further, α shown in the equation (1) is a rotation phase angle that means an angle at which the voltage vector rotates on the complex plane in the time of one sampling period T.

  Next, the four voltage rotation vectors {v (t), v (t−T), v (t−2T), v (t−3T)} shown in FIG. 1 are converted into {v (t), v ( t-T), v (t-2T} as a first group, and {v (t-T), v (t-2T), v (t-3T)} as a second group 1, for example, in the first group, the voltage vectors (v (t), v (t−2T)) on both sides of the first group are intermediate voltage vectors ( v (t−T)), which is the same in the second group, and the voltage vectors (v (t−T), v (t−3T)) on both sides are intermediate voltage vectors. Symmetry with respect to (v (t−2T)).

  Each of the three voltage rotation vectors constituting the first and second groups forms one voltage rotation vector group that rotates counterclockwise on the complex plane at the same rotation speed and is normalized as described later. One voltage amplitude value is defined. Due to these properties, a group of these three voltage rotation vectors is defined as a gauge voltage group.

Next, a calculation formula of the gauge voltage V _g which is an amplitude value (normalized amplitude value) of the gauge voltage group will be described. First, the equation for calculating the gauge voltage V _g is defined as follows:

In the above equation (4), v ₂ is the real part of the second voltage rotation vector in the gauge voltage group, v ₁ is the real part of the first voltage rotation vector in the gauge voltage group, and v ₃ is the _third part in the gauge voltage group. The real part of the voltage rotation vector of

  In the above equation (5), the symbol “Re” indicates the real part of the complex vector component. Here, if the expression (5) is substituted into the right side of the expression (4), it is expanded as the following expression.

That is, the gauge voltage V _g is expressed by the following equation.

As represented by the above equation (7), the gauge voltage V _g is represented by the product of the voltage amplitude V and the sine function of the rotational phase angle α. Here, since the frequency f and the rotation phase angle α have a one-to-one correspondence, the gauge voltage V _g corresponding to the constant frequency f is a constant value, and the relationship between the gauge voltage V _g and the frequency f is the gauge voltage. It is converted into the relationship between V _g and the rotational phase angle α. For this reason, if the rotational phase angle α is known, the voltage amplitude V can be known.

Further, when further consideration is given to the above equation (7), the following characteristics become clear (however, the actual frequency fluctuation range is set to “0 to f _S / 2”).

(A) When the rotational phase angle α is 90 degrees, the gauge voltage V _g and the voltage amplitude V are equal. The actual frequency is 1/4 of the sampling frequency.
(B) When the rotational phase angle α is smaller than 90 degrees, if the sampling frequency f _S is increased (the sampling 1 cycle time T is decreased), the rotational phase angle α is also decreased and the gauge voltage V _g is decreased. On the other hand, when the sampling frequency f _S is lowered (when the sampling one cycle time T is increased), the rotational phase angle α is also increased, and the gauge voltage V _g is increased.
(C) On the other hand, when the rotational phase angle α is greater than 90 degrees, if the sampling frequency f _S is increased (the sampling 1 cycle time T is decreased), the rotational phase angle α is also decreased and the gauge voltage V _g is increased. Become. On the other hand, when the sampling frequency f _S is lowered (when the sampling 1 cycle time T is increased), the rotational phase angle α is also increased, and the gauge voltage V _g is decreased.
(D) Although the limit of the rotational phase angle α is 180 degrees, the actual frequency at this time is ½ of the sampling frequency. That is, this property is the property of the sampling theorem in the communication field.

Next, the gauge differential voltage will be described with reference to FIG. In Figure 1, v (t) and _{v (t-T) v 2} (t) is the voltage difference vector and, v (t-T) and v v ₂ is the voltage difference vector (t-2T) and The voltage difference vector v ₂ (t−2T) between (t−T), v (t−2T) and v (t−3T) is shown. These three voltage difference vectors are expressed by the following equation using the voltage amplitude V, the rotation angular velocity ω, and the rotation phase angle α, similarly to the three voltage rotation vectors described above.

Referring to FIG. 1, among the three voltage difference vectors, the voltage difference vectors (v ₂ (t), v ₂ (t−2T)) whose phases are advanced are intermediate voltage difference vectors (v ₂ ( It can be seen that there is symmetry with respect to t−T)). These three voltage difference vectors form one voltage difference vector group that rotates counterclockwise on the complex plane at the same rotation speed, and one normalized value (gauge difference voltage as described later). ) Is defined. Due to these properties, a group of these three voltage difference vectors is defined as a gauge difference voltage group.

Next, a calculation formula of the gauge differential voltage V _gd that is the amplitude value (normalized amplitude value) of the gauge differential voltage group will be described. First, the calculation formula of the gauge differential voltage V _gd is defined as follows.

In the above equation (9), v ₂₂ is the real part of the second voltage difference vector (v ₂ (t−T)) in the gauge difference voltage group, and v ₂₁ is the first voltage difference vector (v in the gauge difference voltage group). the real part of the ₂ (t)), v ₂₃ is the real part of the third voltage rotation vector in the gauge voltage group _{(v 2 (t-2T)} ), are calculated respectively using the following equation.

Here, by substituting the formula (10) into the formula in the square root symbol on the right side of the formula (9) and rearranging (expansion of the formula is omitted), the gauge differential voltage V _gd is expressed by the following formula.

As expressed by the above equation (11), the gauge differential voltage V _gd is a product of twice the voltage amplitude V, a sine function of the rotational phase angle α, and a sine function of ½ of the rotational phase angle α. It is represented by Similarly to the gauge voltage V _g , the frequency f and the rotation phase angle α have a one-to-one correspondence. Therefore, the gauge differential voltage V _gd corresponding to a constant frequency is a constant value, and the gauge differential voltage V _gd and the frequency The relationship with f is converted into the relationship between the gauge differential voltage V _gd and the rotational phase angle α.

  Further, the following relational expression is obtained from the above expressions (7) and (11).

  Therefore, the following relational expression is obtained from the expression (12).

  Moreover, the following relational expression is obtained from the expression (13).

さらに、回転位相角αの正弦関数値は、ゲージ電圧Ｖ_gおよびゲージ差分電圧Ｖ_gdを用いて、次式のように表される。

Furthermore, the sine function value of the rotational phase angle α is expressed as follows using the gauge voltage V _g and the gauge differential voltage V _gd .

  Therefore, the voltage amplitude V can be calculated by the following equation using the above equations (7) and (14).

  This expression (16) is an expression for calculating the voltage amplitude V by directly using time-series voltage data, and is a very important calculation expression. If the input voltage waveform is a pure sine wave, it is possible to measure the voltage amplitude without error by using the above equation (16). Also, if there is noise in the voltage waveform, increase the number of members that make up the gauge voltage group and gauge differential voltage group, or perform moving average processing on the calculation results of gauge voltage, gauge differential voltage, and voltage amplitude. By doing so, the calculation accuracy of the voltage amplitude V can be improved.

Next, a relational expression between the gauge voltage and the gauge differential voltage is derived. First, the rotational phase half-angle (half of the rotational phase angle: alpha / 2) Expressed the sine function by a factor k _g, the coefficient k _g can be expressed by the following equation.

  When this equation (17) is substituted into the above equation (16), the voltage amplitude V can be expressed by the following equation.

  Further, from the equation (16), the following equation and the following equation are established.

  If the above equations (19) and (20) are not satisfied, it may be determined that the input waveform is not a pure sine wave.

  Further, in the above equation (16), when the voltage amplitude is 1, the following equation regarding the gauge voltage and the gauge differential voltage is established.

  FIG. 2 is a diagram showing the relationship between the gauge voltage and the gauge differential voltage based on the above equation (21). When the voltage amplitude is 1, the gauge voltage varies in the range of 0V to 1V as shown by the broken line in FIG. 2, and at this time, the gauge differential voltage takes a value as shown by the thick solid line in FIG. It can be understood from FIG. 2 that the maximum value of the gauge differential voltage is slightly deviated from the point at which the gauge voltage takes the maximum value.

  In order to further consider the relationship between the gauge voltage and the gauge differential voltage, a relational expression between the cosine function value of the rotation phase angle, the gauge voltage, and the gauge differential voltage is shown. This relational expression can be derived from the above equation (17) and a half-angle formula of a trigonometric function.

  In the above equation (22), α = 0 ° and α = 180 ° are points that cannot be measured (singular points). When α = 90 °, the following relational expression is established.

  Furthermore, the following equation and the following equation are mathematically established in the n gauge voltage trains and the n gauge differential voltage trains in the period of one sampling period (T).

  Also, the following two relational expressions can be obtained from the above expressions (25) and (26).

  By the way, calculation formulas of gauge voltage and gauge differential voltage by a gauge voltage group by three voltage rotation vectors (3 sampling points) and a gauge differential voltage group by four voltage rotation vectors (4 sampling points) are shown so far. However, the calculation of the gauge voltage and the gauge differential voltage is not limited to these sampling points, and the number of sampling points can be increased. Therefore, the calculation formula when the number of sampling points is increased will be presented below.

  First, the calculation formula of the gauge voltage by (n−2) gauge voltage groups using n sampling points (n is 3 or more) voltage rotation vectors is as follows.

  Here, the time series data by each voltage instantaneous value can be expressed by the following equation.

  Similarly, the calculation formula of the gauge differential voltage by (n−2) gauge differential voltage groups using (n + 1) number of sampling points (n is 3 or more) voltage rotation vectors can be generalized as follows.

  Further, time series data based on each differential voltage instantaneous value can be expressed by the following equation.

  In the above description, the calculation procedure for measuring (calculating) the voltage amplitude V, which is one of typical AC electric quantities, has been described through the equations (1) to (16). Next, a calculation procedure for measuring (calculating) the current amplitude I which is another typical AC electric quantity will be described.

  In addition, although description is mixed, "voltage amplitude" is a numerical value which is not dependent on the frequency of an alternating voltage while being a true value of alternating voltage amplitude. On the other hand, the gauge voltage is a voltage amplitude calculated using a group of gauge voltages on the complex plane, and is a numerical value dependent on the frequency of the AC voltage. These relationships are the same for other AC electric quantities.

  Next, a method for calculating the current amplitude will be described. Note that the derivation procedure for the current amplitude calculation method is the same as that for the voltage amplitude, and only the relational expression of the main points is presented below.

First, equation gauge current I _g by the sampling number n (n is 3 or more) using a current rotation vector (n-2) number of gauge current group (not shown) is expressed by the following equation.

  Here, the time series data by each current instantaneous value can be expressed by the following equation.

  Similarly, the calculation formula of the gauge differential current by the gauge differential current group having the current rotation vector of n sampling points (n is 3 or more) can be generalized as follows.

  Here, the time series data by each differential current instantaneous value can be expressed by the following equation.

Further, by applying the analogy of the equation (17), the sine function value of the rotation phase half angle (α / 2) can be expressed by the following equation using the gauge current I _g and the gauge differential current I _gd .

  Similarly, the current amplitude I can be expressed as the following equation by analogy application of the equation (16) indicating the voltage amplitude V.

  If it is considered that the current and the voltage are oscillating at the same frequency, the following equation can be expressed by substituting equation (16) into sin α in equation (37).

  Next, a gauge power group, a gauge active power group, and a gauge reactive power group, which are concepts newly proposed in the present invention, will be described with reference to FIG. Here, FIG. 3 is a diagram illustrating a gauge power group on the complex plane. In FIG. 3, on the complex plane, the current voltage rotation vector v (t), the voltage rotation vector v (t−T) at one sampling period (T) before the current time, and the two sampling periods ( 2T) The voltage rotation vector v (t−2T) at the previous time point, the current rotation vector i (t−T) at the time point one sampling (T) before the current time, and the current at the time point two sampling periods (2T) before the current time A rotation vector i (t-2T) is shown.

  In FIG. 3, the three voltage rotation vectors can be expressed by the following equations.

  Similarly, the two current rotation vectors can be expressed by the following equations.

  Here, the three voltage rotation vectors shown in the above equation (39) and the two current rotation vectors shown in the above equation (40) are defined as a gauge power group.

  Next, the gauge active power will be described. First, the formula for calculating the gauge active power is given by the following formula.

  That is, the gauge active power is obtained by two voltage rotation vectors v (t) and v (t−T) that are members of the gauge power group and two current rotation vectors i (t−T) and i (t−2T). Is calculated using For this reason, these four rotation vectors v (t), v (t−T), i (t−T), and i (t−2T) used for the calculation of the gauge active power are defined as a gauge effective power group. . That is, the gauge active power group is configured with some members of the gauge power group.

  In addition, each voltage instantaneous value and each current instantaneous value in the above equation (41) are the real part of the voltage rotation vector, and are expressed by the following equation and the following equation.

  Further, if the equations (42) and (43) are substituted into the right side of the equation (41), the gauge effective power Pg is developed as the following equation.

That is, the gauge effective power _Pg is expressed by the following equation.

  Next, gauge reactive power will be described. The equation for calculating the gauge reactive power is given by the following equation.

  That is, the gauge reactive power includes two voltage rotation vectors v (t−T) and v (t−2T) that are members of the gauge power group, and two current rotation vectors i (t−T) and i (t− 2T). Therefore, these four rotation vectors v (t−T), v (t−2T), i (t−T), and i (t−2T), which are used for the calculation of the gauge reactive power, are referred to as a gauge reactive power group. Define. In other words, the gauge reactive power group is configured with some members of the gauge power group that are different from the gauge active power group and have different members from the gauge active power group.

  Each voltage instantaneous value in the above equation (46) is a real part of the voltage rotation vector, and is expressed by the following equation (each current instantaneous value in the above equation (46) is as shown in the equation (43). Is).

Further, if the equations (47) and (43) are substituted into the right side of the equation (46), the gauge reactive power _Qg is developed as the following equation.

That is, the gauge reactive power _Qg is expressed by the following equation.

  Furthermore, using the equations (7), (32), (45), and (49), the cosine function value of the voltage-current phase angle φ can be expressed by the following equation.

Further, the cosine function values of the voltage current phase angle φ, the sign of the gauge reactive power Q _g, i.e. whether the circuit characteristics of the measurement object is in-dunk drawers properties, depending on whether the conductance properties, as follows Can be expressed as

(When the characteristic to be measured is inductivity: Q _g <0)

(When the characteristic to be measured is conductance: Q _g > 0)

  Next, a formula for calculating the active power P, which is one of typical AC electric quantities, will be described. The effective power P is a product of the cosine function value of the voltage amplitude V, the current amplitude I, and the phase angle φ between the voltage and current. Using the equations (16), (37), (45), and (49), Can be expressed as:

The above equation (53) is a very important equation. The gauge active power P _g , gauge reactive power Q _g , cosine function value and sine function value of the rotational phase angle α included in the equation (53) can all be directly calculated from instantaneous value time series data. . Therefore, the active power P can be directly calculated using the instantaneous value time series data.

When the circuit characteristic to be measured is pure inductance (pure inductance circuit) or pure conductance (pure conductance circuit), the active power P is zero, and the gauge active power is calculated by the above equation (53). There is a relationship of the following equation between P _g and gauge reactive power Q _g .

Therefore, when the sampling frequency (f _s = 1 / T) is four times the actual frequency f, the rotational phase angle α is 90 degrees, and the gauge effective power Pg in the pure inductance circuit or the pure conductance circuit is zero.

  Next, a formula for calculating reactive power Q, which is one of typical AC electric quantities, will be described. The reactive power Q is a product of a sine function value of the voltage amplitude V, the current amplitude I, and the voltage-current phase angle φ, and in the case of a pure inductance circuit, the equations (16), (37), and (51) are And can be expressed as:

  Further, in the case of a pure conductance circuit, the reactive power Q can be expressed as the following equation using the equations (16), (37), and (52).

Further, the calculation formula of the gauge active power P _g by the voltage rotation vector of n sampling points (n is 3 or more) and (n−2) gauge active power groups using n current rotation vectors is as follows. It is expressed by a formula.

  Here, the time series data by each voltage instantaneous value and each current instantaneous value can be expressed by the following equations.

  The time series data of the voltage rotation vector and the current rotation vector can be expressed by the following equations.

Furthermore, the equation for calculating the gauge reactive power Q _g by using n voltage sampling vectors (n is 3 or more) and (n−2) gauge reactive power groups using n current rotation vectors is as follows. It is expressed by a formula.

  In order to increase the measurement accuracy (calculation accuracy), the following two measures can be considered. The first strategy is to increase the number of samplings (the number of symmetric groups) when calculating the gauge active power, gauge reactive power, cosine function value and sine function value of the rotational phase angle. By increasing the number of symmetric groups used in the calculation, the quantization error can be reduced and the influence of noise can be reduced.

  The second policy is to perform a moving average on the gauge active power, gauge reactive power, cosine function value and sine function value of the rotation phase angle. By this moving average process, the influence of noise can be greatly reduced.

  Next, a formula for calculating the power factor PF, which is one of typical AC electric quantities, will be described. The power factor PF is a cosine function value of the voltage-current phase angle φ, and can be expressed by the following equation as shown in the equation (50).

Next, a gauge difference power group, a gauge difference active power group, and a gauge difference reactive power group, which are concepts newly proposed in the present invention, will be described with reference to FIG. Here, FIG. 4 is a diagram showing a gauge differential power group on the complex plane. In FIG. 4, on the complex plane, the current differential voltage is based on the current voltage rotation vector v (t) and the current rotation vector i (t−T) one sampling period (T) before the current time. Rotation vector v ₂ (t), differential voltage rotation vector v ₂ (t−T) at one sampling period (T) before the current time, differential voltage rotation vector v ₂ at two sampling times (2T) before the current time (t-2T), the differential current rotation vector i ₂ (t-T) sampling one period (T) before the time than the present time, sampling two cycles (2T) before the time than the present time differential current rotation vector i ₂ (t -2T).

  In FIG. 4, the three differential voltage rotation vectors can be expressed by the following equations.

  Similarly, the two current rotation vectors can be expressed by the following equations.

  Here, the three voltage rotation vectors shown in the above equation (62) and the two current rotation vectors shown in the above equation (63) are defined as a gauge differential power group.

  Next, the gauge differential active power will be described. First, the equation for calculating the gauge differential active power is given by the following equation.

That is, the gauge differential active power is obtained by two differential voltage rotation vectors v ₂ (t) and v ₂ (t−T) that are members of the gauge differential power group and two differential current rotation vectors i ₂ (t−T). , I ₂ (t−2T). Therefore, these four rotation vectors v ₂ (t), v ₂ (t−T), i ₂ (t−T), and i ₂ (t−2T), which are used to calculate the gauge difference active power, It is defined as an active power group. That is, the gauge difference active power group is configured with some members of the gauge difference power group.

  In addition, each voltage instantaneous value and each current instantaneous value in the above equation (64) are the real part of the voltage rotation vector, and are expressed by the following equation and the following equation.

Further, if the expressions (65) and (66) are substituted into the right side of the expression (64), the gauge differential effective power P _gd is developed as the following expression.

That is, the gauge differential active power P _gd is expressed by the following equation.

  Next, the gauge differential reactive power will be described. The formula for calculating the gauge differential reactive power is given by the following formula.

That is, the gauge differential reactive power includes two differential voltage rotation vectors v ₂ (t−T) and v ₂ (t−2T), which are members of the gauge differential power group, and two differential current rotation vectors i ₂ (t− T), i ₂ (t−2T). Therefore, these four rotation vectors v ₂ (t−T), v ₂ (t−2T), i ₂ (t−T), and i ₂ (t−2T) used for the calculation of the gauge differential reactive power are It is defined as a gauge differential reactive power group. That is, the gauge difference reactive power group is configured with some members of the gauge difference power group.

  Each voltage instantaneous value in the above equation (69) is a real part of the voltage rotation vector, and is expressed by the following equation (each current instantaneous value in the above equation (69) is as shown in the equation (66). ).

Further, if the expressions (70) and (66) are substituted into the right side of the expression (69), the gauge differential reactive power Q _gd is developed as the following expression.

That is, the gauge differential reactive power Q _gd is expressed by the following equation.

  Further, if the expressions (68) and (72) are used, the cosine function value of the voltage-current phase angle φ can be expressed by the following expression.

  Further, if the above equation (73) is substituted into the above equation (11) and the above equation (36) is substituted into the above equation, the following equation is obtained.

The cosine function value of the voltage-current phase angle φ depends on the sign of the gauge differential reactive power Q _gd , that is, the gauge reactive power depending on whether the circuit characteristic to be measured is inductance or conductance. As in the case of Q _g , it can be expressed as the following formula.

(When the characteristic to be measured is _inductivity : Q _gd <0)

(When the characteristic to be measured is _conductance : Q _gd > 0)

  Note that the gauge differential power is calculated so that the DC component of the voltage and current is canceled when the difference component is obtained, and therefore, calculation with higher accuracy is possible than when the gauge power is used.

  Next, a formula for calculating the effective power P using the gauge differential power will be described. The effective power P is a product of the cosine function value of the voltage amplitude V, the current amplitude I, and the phase angle between the voltage and current φ. Using the equations (16), (37), (68), and (72) Can be expressed as:

The above expression (77) is a very important expression. The gauge differential active power P _gd , gauge differential reactive power Q _gd , cosine function value and sine function value of the rotation phase angle α included in the equation (77) are all calculated directly from the instantaneous value time series data. Can do. Therefore, the active power P can be directly calculated using the instantaneous value time series data.

  Next, a calculation formula for reactive power Q using gauge differential power is presented. First, the reactive power Q in the inductance circuit can be expressed by the following equation using equations (73) to (75).

  The reactive power Q in the conductance circuit can be expressed as the following equation.

Next, a calculation method using a plurality of cage differential power groups will be described. First, the calculation formula of the gauge differential active power P _gd by (n−2) gauge differential active power groups using (n + 1) sampling rotation points (n is 3 or more) voltage rotation vectors and current rotation vectors is as follows: It is expressed by a formula.

  Here, the time series data by each voltage instantaneous value and each current instantaneous value can be expressed by the following equations.

  The time series data of the voltage rotation vector and the current rotation vector can be expressed by the following equations.

The calculation formula of the gauge differential reactive power Q _gd by (n−2) gauge differential reactive power groups using (n + 1) sampling points (n + 1) (n is 3 or more) voltage rotational vectors and current rotational vectors is as follows: It is expressed by a formula.

  Next, a relational expression between the gauge active power and the gauge differential active power is derived. First, according to the equations (45) and (68), the relationship shown in the following equation is established between the gauge active power and the gauge differential active power.

  From the above equation (84), the rotational phase angle α is obtained as follows.

  Further, if the rotational phase angle α obtained by the above equation (85) is substituted into the following equation, the system frequency f which is one of typical AC electric quantities can be obtained.

In the above equation (86), f _s is the sampling frequency.

  Next, a relational expression between the gauge reactive power and the gauge differential reactive power is derived. First, according to the equations (49) and (72), the relationship shown in the following equation is established between the gauge reactive power and the gauge differential reactive power.

  From the equation (87), the rotational phase angle α is obtained as follows.

  Further, the system frequency f can be obtained by substituting the rotational phase angle α obtained by the equation (88) into the equation (86).

  In the above description, the method for calculating the system frequency f from the gauge active power and the gauge differential active power and the method for calculating the system frequency f from the gauge reactive power and the gauge differential reactive power have been described. In this case, if the input waveform is a sine wave or close to a sine wave, the correct system frequency is measured. Therefore, if the correct system frequency is measured by these methods, it can be determined whether or not the input waveform is a sine wave, and can be used as a relay element in the system protection control device.

  Next, an application using the above algorithm (calculation method) will be exemplified. Recently, the introduction of digital energy meters with communication functions called smart meters has begun mainly in the United States and Europe, and this movement is spreading in Japan. The above-described technique uses various voltage values such as a voltage using a voltage rotation vector and a current rotation vector that constitute a gauge voltage group, a gauge differential voltage group, a gauge current group, and a gauge differential current group on a complex plane. Amplitude, current amplitude, active power, reactive power, system frequency, and power factor are calculated with high accuracy and are suitable for this smart meter. In the case of an electric power system, the system frequency is operated at a commercial frequency (50 Hz, 60 Hz), so that a large deviation does not occur in the system frequency during normal operation.

  First, in this application example applied to a smart meter, the sampling frequency is set to four times the system frequency. For example, when the system frequency is 50 Hz, the sampling frequency is 200 Hz. When the system frequency is 60 Hz, the sampling frequency is 240 Hz. When the system frequency and the sampling frequency have these values, the rotational phase angle α is obtained as follows.

  From the above equation (7), the voltage amplitude V is obtained as follows.

From this equation (90), the voltage amplitude V and the gauge voltage V _g are equal. Moreover, the voltage amplitude V is calculated | required like following Formula by said (11) Formula.

From this equation (91), the voltage amplitude V becomes 1 / √2 of the gauge differential voltage V _gd . Since the gauge differential voltage V _gd is not affected by the direct current component as compared with the gauge voltage V _g , it can be said that the value obtained by the equation (91) is more accurate than the equation (90).

  Further, the current amplitude I is obtained by the following equation from the above equation (32).

From this equation (92), the current amplitude I and the gauge current _Ig are equal. Further, the current amplitude I is obtained by the following equation from the above equation (34).

From this equation (93), the current amplitude I becomes 1 / √2 of the gauge differential current I _gd . Since the gauge differential current I _gd is not affected by the direct current component as compared with the gauge current I _g , it can be said that the value obtained by the equation (93) is more accurate than the equation (92).

  Furthermore, the active power P is obtained by the following equation by the above equation (45).

From this equation (94), the active power P and the gauge effective power _Pg are equal. Further, the active power P is obtained by the following equation from the above equation (68).

From this equation (95), the active power P is ½ of the gauge differential effective power P _gd . Note that the gauge differential effective power P _gd is not affected by the direct current component as compared with the gauge power P _g, and therefore it can be said that the value obtained by the expression (95) is more accurate than the expression (94).

  Moreover, the reactive power Q is calculated | required like following Formula by said (49) Formula.

By this equation (96), the reactive power Q and the gauge reactive power Q _g are equal. Moreover, the reactive power Q is calculated | required like following Formula by said (72) Formula.

According to the equation (95), the reactive power Q is ½ of the gauge differential reactive power Q _gd . Note that the gauge differential reactive power Q _gd is not affected by the DC component as compared with the gauge reactive power Q _g, and therefore the value obtained by the equation (95) is more accurate than the equation (94). .

  Further, the power factor PF is obtained by the following equation using P and Q obtained by the above equation.

  Here, when the sampling frequency is four times the system frequency, the rotational phase angle α moves in units of 90 °. At this time, the sine function value and cosine function value of the rotational phase angle are either 0 or ± 1. For this reason, even when calculating a plurality of desired AC electric quantities, the calculation process is simplified, and even if a low-performance CPU is used, an increase in processing load can be suppressed. It is done.

  When the sampling frequency is four times the system frequency, the gauge voltage group, the gauge differential voltage group, the gauge current group, and the gauge differential current group can be set to reduce the effects of system noise and quantization error due to sampling. What is necessary is just to increase the number of the voltage rotation vector and current rotation vector which comprise, or to perform a moving average process with respect to each calculation result of a gauge voltage, a gauge current, a gauge differential voltage, and a gauge differential current.

  Next, the functional configuration and the operation of the AC electricity quantity measuring device according to the present embodiment will be described with reference to FIGS. Here, FIG. 5 is a diagram showing a functional configuration of the AC electricity quantity measuring device 100 according to the present embodiment, and FIG. 6 is a flowchart showing a processing flow in the AC electricity quantity measuring device 100.

  As shown in FIG. 5, the AC electricity quantity measuring apparatus 100 according to the present embodiment includes an AC voltage / current instantaneous value data input unit 1, a gauge voltage calculation unit 2, a gauge differential voltage calculation unit 3, a rotational phase angle / frequency. Calculation unit 4, voltage amplitude calculation unit 5, gauge current calculation unit 6, gauge difference current calculation unit 7, current amplitude calculation unit 8, gauge active power calculation unit 9, gauge difference active power calculation unit 10, gauge reactive power calculation unit 11 , Gauge difference reactive power calculation unit 12, active power calculation unit 13, reactive power calculation unit 14, interface 15, and storage unit 16. The interface 15 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 16 performs a process of storing measurement data, a calculation result, or the like.

  In the above configuration, the AC voltage / current instantaneous value data input unit 1 performs processing for taking in the instantaneous voltage value and the instantaneous current value from the instrument transformer (PT) and the current transformer (CT) provided in the power system. Perform (step S100). The captured data of the instantaneous voltage value and the instantaneous current value are stored in the storage unit 16.

  The gauge voltage calculation unit 2 calculates a gauge voltage using a plurality of predetermined voltage instantaneous value data forming the above-described gauge voltage group (step S101). The gauge voltage calculation process can be explained as follows when it is described in a comprehensive manner including the above-described algorithm concept. That is, the gauge voltage calculation unit 2 satisfies, for example, the square integral calculation of at least three consecutive voltage instantaneous value data sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured in order to satisfy the sampling theorem. The voltage amplitude obtained by the above is normalized with the amplitude value of the AC voltage, and is processed as a gauge voltage. In the present embodiment, as the square integration calculation, the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product other than the intermediate time among the three voltage instantaneous value data is added and averaged. The formula is illustrated (see formula (3)).

  Further, the gauge differential voltage calculation unit 3 calculates a gauge differential voltage using a plurality of predetermined voltage instantaneous value data forming the above-described gauge differential voltage group (step S102). The gauge differential voltage calculation unit 3 can also be described generally as follows. That is, the gauge differential voltage calculation unit 3 is sampled at the sampling frequency, and the adjacent 2 in the voltage instantaneous value data of at least four consecutive points including the three voltage instantaneous value data used when calculating the gauge voltage. For example, a value obtained by, for example, square integral calculation of the differential voltage instantaneous value data of the three points representing the distance between the tip voltage instantaneous value data is normalized with the amplitude value of the AC voltage and calculated as a gauge differential voltage. In the present embodiment, as the square integration calculation, the difference between the square value of the differential voltage instantaneous value at the intermediate time and the differential voltage instantaneous value product other than the intermediate time among the three differential voltage instantaneous value data is calculated. An expression for averaging is illustrated (see Expression (9)).

  The rotation phase angle / frequency calculation unit 4 uses the gauge voltage calculated by the gauge voltage calculation unit 2 and the gauge difference voltage calculated by the gauge difference voltage calculation unit 3 to rotate the rotation phase corresponding to one sampling period. The angle is calculated, and the frequency of the power system is calculated using the calculated rotation phase angle and sampling cycle (step S103).

  The voltage amplitude calculator 5 calculates the voltage amplitude using the gauge voltage calculated by the gauge voltage calculator 2 and the gauge differential voltage calculated by the gauge differential voltage calculator 3 (step S104). The voltage amplitude is calculated using the gauge voltage calculated by the gauge voltage calculation unit 2 and the rotation phase angle calculated by the rotation phase angle / frequency calculation unit 4 without using the gauge differential voltage. May be.

  The gauge current calculation unit 6 calculates a gauge current using a plurality of predetermined current instantaneous value data forming the above-described gauge current symmetry group (step S105). In order to satisfy the sampling theorem, the gauge current calculation unit 6 obtains the current instantaneous value data of at least three consecutive points sampled at a sampling frequency twice or more the frequency of the alternating current to be measured by, for example, square integration calculation. The current amplitude is normalized with the amplitude value of the alternating current, and a process of calculating as a gauge current is performed. In this embodiment, as the square integral calculation, the difference between the square value of the current pressure instantaneous value at the intermediate time and the current instantaneous value product other than the intermediate time among the three points of current instantaneous value data is added and averaged. (See equation (32)).

  Further, the gauge differential current calculation unit 7 calculates the gauge differential current using a plurality of predetermined current instantaneous value data forming the above-described gauge differential current group (step S106). The gauge differential current calculation unit 7 can also be described generally as follows. That is, the gauge differential current calculation unit 7 is sampled at the sampling frequency, and the adjacent 2 in the current instantaneous value data of at least 4 points including the current instantaneous value data of 3 points used in calculating the gauge current are adjacent to each other. For example, a value obtained by, for example, square integration calculation of the differential current instantaneous value data of the three points representing the distance between the tips of the current instantaneous value data of the points is normalized with the amplitude value of the alternating current and is calculated as a gauge differential current. In the present embodiment, the difference component between the square value of the differential current instantaneous value at the intermediate time and the differential current instantaneous value product other than the intermediate time among the three differential current instantaneous value data as the square integral calculation. Is an example of adding and averaging (see equation (34)).

  The current amplitude calculator 8 calculates the current amplitude using the gauge current calculated by the gauge current calculator 6 and the gauge differential current calculated by the gauge differential current calculator 7 (step S107). The current amplitude is calculated using the gauge current calculated by the gauge current calculation unit 6 and the rotation phase angle calculated by the rotation phase angle / frequency calculation unit 4 without using the gauge differential current. May be.

  The gauge active power calculation unit 9 calculates the gauge active power using the plurality of predetermined voltage instantaneous value data and the plurality of predetermined current instantaneous value data forming the above-described gauge power group (step S108). More specifically, the gauge active power calculation unit 9 is the latest measuring time 2 of three predetermined voltage instantaneous value data sampled at a sampling frequency twice or more the frequency of the AC voltage to be measured. Instantaneous voltage value data at two points and current instantaneous values at two points earlier in measurement time out of three instantaneous current value data sampled at this sampling frequency and sampled at the same time as the predetermined three instantaneous voltage values A process of normalizing a value obtained by a predetermined product difference calculation with data and calculating as a gauge active power is performed. In the present embodiment, as the square integral calculation, the difference component of the voltage / current product obtained by reversing the time sequence between the two instantaneous voltage values at the later measurement time and the two instantaneous current values at the earlier measurement time is added. The equation to be averaged is illustrated (see equation (41)).

  The gauge difference active power calculation unit 10 calculates the gauge difference active power using the plurality of predetermined voltage instantaneous value data and the plurality of predetermined current instantaneous value data forming the above-described gauge difference power group (step S109). More specifically, the gauge difference active power calculation unit 10 calculates the voltage of two adjacent points in the voltage continuous value data of four predetermined points sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured. Among the three differential voltage instantaneous value data representing the tip-to-tip distance between the instantaneous value data, the differential voltage instantaneous value data of two points whose measurement time is late and the voltage instantaneous value of the predetermined four points sampled at this sampling frequency The difference between two points of early measurement time among the three points of differential current instantaneous value data representing the distance between the two points of adjacent current instantaneous value data in the four points of current instantaneous value data sampled at the same time as A process of normalizing a value obtained by a predetermined product difference calculation with current instantaneous value data and calculating as a gauge difference active power is performed. In the present embodiment, as the square integral calculation, the difference component of the voltage-current product obtained by reversing the time sequence between the two differential voltage instantaneous values at the later measurement time and the two differential current instantaneous values at the earlier measurement time. The formula which adds and averages is illustrated (refer to Formula (64)).

  The gauge reactive power calculation unit 11 calculates the gauge reactive power using a plurality of predetermined voltage instantaneous value data and a plurality of predetermined current instantaneous value data forming the above-described gauge power group (step S110). In more detail, the gauge reactive power calculation unit 11 calculates the time of the measurement time 2 of the three predetermined voltage instantaneous value data sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured. Normalize the value obtained by the predetermined product difference calculation using the instantaneous voltage value data of the point and the instantaneous current value data of the two points sampled at this sampling frequency and sampled at the same time. To calculate the gauge reactive power. In the present embodiment, as an example of the square integral calculation, an equation for averaging the difference components of the voltage-current products at different times in the two voltage instantaneous values and the two current instantaneous values is illustrated. (Refer to equation (46)).

  The gauge difference reactive power calculation unit 12 calculates the gauge difference reactive power using a plurality of predetermined voltage instantaneous value data and a plurality of predetermined current instantaneous value data forming the above-described gauge difference power group (step S111). More specifically, the gauge difference reactive power calculation unit 12 calculates the voltage at two adjacent points in the voltage continuous value data of four consecutive points sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured. Of the three differential voltage instantaneous value data representing the tip-to-tip distance between the instantaneous value data, the differential voltage instantaneous value data of two points whose measurement time is early, and the differential voltage instantaneous value of the two points sampled at this sampling frequency By normalizing the value obtained by a predetermined product difference calculation based on the instantaneous voltage value of the three points that is the source of the current value and the instantaneous current value data of the two points obtained from the instantaneous current value data of the three points sampled at the same time Processing to calculate the gauge differential reactive power is performed. In the present embodiment, as an example of the square integral calculation, an equation for averaging the difference components of the voltage-current products at different times between the two differential voltage instantaneous values and the two differential current instantaneous values is illustrated. (See equation (46)). An example is shown in which the difference component of the voltage-current product obtained by reversing the time sequence between two differential voltage instantaneous values at two later measurement times and two differential current instantaneous values at earlier measurement times is averaged ((69 ) See formula).

  The active power calculation unit 13 is calculated by the gauge active power calculated by the gauge active power calculation unit 9, the gauge reactive power calculated by the gauge reactive power calculation unit 11, and the rotation phase angle / frequency calculation unit 4. The effective power is calculated using the rotation phase angle (step S112). Other than this, for example, the gauge difference active power calculated by the gauge difference active power calculation unit 10, the gauge difference reactive power calculated by the gauge difference reactive power calculation unit 12, and the rotation phase angle / frequency calculation unit The active power may be calculated using the rotational phase angle calculated in step 4.

  The reactive power calculation unit 14 includes a gauge voltage calculated by the gauge voltage calculation unit 2, a gauge current calculated by the gauge current calculation unit 6, a gauge effective power calculated by the gauge active power calculation unit 9, and a gauge invalidity. The reactive power is calculated using the gauge reactive power calculated by the power calculation unit 11 and the rotational phase angle calculated by the rotational phase angle / frequency calculation unit 4 (step S113). In addition to this, for example, the gauge difference voltage calculated by the gauge difference voltage calculation unit 3, the gauge difference current calculated by the gauge difference current calculation unit 7, and the gauge difference active power calculation unit 10 were calculated. The reactive power may be calculated using the gauge differential reactive power, the gauge differential reactive power calculated by the gauge differential reactive power calculator 12, and the rotational phase angle calculated by the rotational phase angle / frequency calculator 4. Absent.

  In the last step S114, the process for determining whether or not to end the above-described overall flow is performed. If it is not the end (step S114, No), the processes from step S100 to S113 are repeated.

  Next, a simulation result performed on the AC electricity quantity measuring device of the present embodiment will be described. Table 1 below shows parameters when the first simulation is executed. In this simulation, as shown in Table 1, the actual frequency is a non-integer.

  FIG. 7 is a diagram illustrating a waveform of the voltage instantaneous value at the time of executing the first simulation, a gauge voltage calculated based on the voltage instantaneous value, a gauge differential voltage, and a measured voltage amplitude. In FIG. 7, the waveform connecting the black diamond marks represents the instantaneous voltage value, the waveform connecting the black square marks represents the gauge voltage, the waveform connecting the black triangle marks represents the gauge differential voltage, and the waveform connecting the x marks represents the measured voltage. It represents the amplitude.

  When the instantaneous voltage value shown in the graph of FIG. 7 is used, the gauge voltage is calculated as in the following equation, and it can be seen that it matches the theoretical value (equation (7)).

  Similarly, the gauge differential voltage is calculated as in the following equation, and it can be seen that it matches the theoretical value (Equation (11)).

  As can be seen from FIG. 7 and the above equations (99) and (100), the gauge differential voltage is larger than the gauge voltage. This is because the sampling frequency is small. Yes.

  In addition, the voltage amplitude is calculated by the following equation using equation (16).

  FIG. 8 is a diagram showing a waveform of an instantaneous current value at the time of executing the first simulation, a gauge current, a gauge differential current, and a measured current amplitude calculated based on the instantaneous current value. In FIG. 8, the waveform connecting the black diamond marks represents the instantaneous current value, the waveform connecting the black square marks represents the gauge current, the waveform connecting the black triangle marks represents the gauge differential current, and the waveform connecting the x marks represents the measured current. It represents the amplitude.

  When the instantaneous current value shown in the graph of FIG. 8 is used, the gauge current is calculated as shown in the following formula, and it can be seen that it matches the theoretical value.

  Similarly, it can be seen that the gauge differential current is also calculated as the following equation and agrees with the theoretical value.

  As is apparent from FIG. 8, the gauge differential current has a value larger than that of the gauge current, and this is because the sampling frequency is small.

  In addition, the current amplitude is calculated by the following equation using Equation (37).

  FIG. 9 is a diagram illustrating a gauge active power, a gauge differential active power, and a measured active power according to the first simulation. In FIG. 9, the waveform connecting the black diamond marks represents the gauge active power, the waveform connecting the black triangle marks represents the gauge differential active power, and the waveform connecting the black square marks represents the measured active power.

  Here, first, theoretical values of active power and reactive power are obtained. The theoretical values of the active power and the reactive power can be calculated as the following equations and the following equations.

  Next, active power is calculated. First, the gauge active power and the gauge differential active power can be calculated as follows:

  Further, the sine function value of the rotational phase angle is calculated by the following equation using equation (15).

  Furthermore, the sine function value of the rotation phase half angle is calculated by the following equation using equation (13).

同様に、（２２）式により、回転位相角の余弦関数値は次式のように計算される。

Similarly, the cosine function value of the rotational phase angle is calculated by the following equation using Equation (22).

By substituting the above calculation result into the equation (53), the active power is calculated as the following equation. Note that the gauge reactive power Q _g, and using the results of described below (114) below.

  As is clear from the comparison between the calculation result obtained by the equation (112) and the equation (105), it can be seen that the measurement result agrees with the theoretical value.

Further, by substituting the above calculation result into the equation (77), the active power is calculated as the following equation. For the gauge differential reactive power Q _gd , the result of equation (115) described below is used.

  As is apparent from the comparison between the calculation result obtained by the equation (113) and the equation (105), the measurement result using the gauge differential power (gauge differential active power and gauge differential reactive power) also agrees with the theoretical value. I understand.

  FIG. 10 is a diagram illustrating gauge reactive power, gauge differential reactive power, and measured reactive power according to the first simulation. In FIG. 10, the waveform connecting the black diamond marks represents the gauge reactive power, the waveform connecting the black triangle marks represents the gauge differential reactive power, and the waveform connecting the black square marks represents the measured reactive power.

  Next, reactive power is calculated. First, the gauge reactive power and the gauge differential reactive power can be calculated as follows:

  By substituting the above calculation result into the equation (55) or the equation (56), the reactive power is calculated as the following equation.

  As is clear from the comparison between the calculation result obtained by the equation (116) and the equation (106), it can be seen that the measurement result is in agreement with the theoretical value.

  Further, by substituting the above calculation result into the formula (78) or the formula (79), the reactive power is calculated as the following formula.

  As is clear from the comparison between the calculation result of the equation (117) and the equation (106), the measurement result using the gauge differential power (gauge differential active power and gauge differential reactive power) is also consistent with the theoretical value. I understand.

  FIG. 11 is a diagram showing the measurement result of the power factor by the first simulation, and the measurement result (calculation result) is as follows.

  The calculation result of the theoretical value is omitted, but the measurement result of the power factor agrees with the theoretical value.

  Next, the second simulation will be described. Table 2 below shows parameters when the second simulation is executed. In this simulation, as shown in Table 2, the sampling frequency is set to four times the actual frequency (corresponding to the application example described above).

  FIG. 12 is a diagram illustrating a waveform of a voltage instantaneous value at the time of executing the second simulation, a gauge differential voltage calculated based on the voltage instantaneous value, and a measured voltage amplitude. In FIG. 12, the waveform connecting the black diamond marks represents the instantaneous voltage value, the waveform connecting the black triangle marks represents the gauge differential voltage, and the waveform connecting the x marks represents the measured voltage amplitude. When the sampling frequency is four times the actual frequency, the gauge voltage matches the voltage amplitude, so that the graph display is omitted.

  Using the voltage instantaneous value shown in the graph of FIG. 12, the gauge differential voltage and the voltage amplitude are calculated as in the following formula and the following formula, and it can be seen that they match the theoretical values.

  Thus, even if the sampling frequency is low, a highly accurate measurement result (calculation result) regarding the voltage amplitude can be obtained.

  FIG. 13 is a diagram illustrating a waveform of an instantaneous current value when the second simulation is executed, a gauge differential current calculated based on the instantaneous current value, and a measured current amplitude. In FIG. 13, the waveform connecting the black diamond marks represents the instantaneous current value, the waveform connecting the black triangle marks represents the gauge differential current, and the waveform connecting the x marks represents the measured current amplitude. Note that when the sampling frequency is four times the actual frequency, the gauge current matches the current amplitude, so the graph display is omitted.

  When the instantaneous current value shown in the graph of FIG. 13 is used, it can be seen that the gauge differential current and the current amplitude are calculated by the following equations and the following equations and agree with the theoretical values.

  Thus, even if the sampling frequency is low, a highly accurate measurement result (calculation result) regarding the current amplitude can be obtained.

  FIG. 14 is a diagram illustrating the gauge differential active power and the measured active power according to the second simulation. In FIG. 14, the waveform connecting the black triangle marks represents the gauge differential active power, and the waveform connecting the black square marks represents the measured active power. Note that when the sampling frequency is four times the actual frequency, the gauge active power and the active power coincide with each other, and the display on the graph is omitted.

  When the instantaneous voltage value shown in the graph of FIG. 12 and the instantaneous current value shown in the graph of FIG. 13 are used, the gauge differential active power and the measured active power are calculated as follows:

  Although the calculation result of the theoretical value is omitted, the measurement result of the active power agrees with the theoretical value. The active power may be obtained from the gauge differential active power as shown in the following equation, which matches the result of the above equation (124).

  Thus, even if the sampling frequency is low, a highly accurate measurement result (calculation result) regarding active power can be obtained.

  FIG. 15 is a diagram illustrating gauge reactive power, gauge differential reactive power, and measured reactive power according to the second simulation. In FIG. 15, the waveform connecting the black diamond marks represents the gauge reactive power, the waveform connecting the black triangle marks represents the gauge differential reactive power, and the waveform connecting the black square marks represents the measured reactive power. Note that when the sampling frequency is four times the actual frequency, the gauge reactive power and the measured reactive power have the same absolute value and different signs.

  When the instantaneous voltage value shown in the graph of FIG. 12 and the instantaneous current value shown in the graph of FIG. 13 are used, the gauge differential reactive power and the measured reactive power are calculated as follows:

  Although the calculation result of the theoretical value is omitted, the measurement result of the reactive power agrees with the theoretical value. The reactive power may be obtained from the gauge differential reactive power as in the following equation, which is consistent with the result of the above equation (127).

  Thus, even if the sampling frequency is low, a highly accurate measurement result (calculation result) regarding reactive power can be obtained.

  FIG. 16 is a diagram illustrating a power factor measurement result by the second simulation, and the measurement result (calculation result) is as follows.

  The calculation result of the theoretical value is omitted, but the measurement result of the power factor agrees with the theoretical value.

  As described above, according to the AC electrical quantity measurement device of the present embodiment, at least three consecutive voltage instants obtained by sampling the AC voltage to be measured at a sampling frequency that is twice or more the frequency of the AC voltage. The voltage amplitude obtained by the square integral calculation of the value data is normalized and calculated as a gauge voltage, sampled at the sampling frequency, and at least four consecutive voltage instantaneous value data used when calculating the gauge voltage Normalizing the value obtained by the square integral operation of the differential voltage instantaneous value data of three points representing the distance between the tips of the voltage instantaneous value data of two adjacent points in the voltage instantaneous value data of the point, and calculating it as a gauge differential voltage; Since the gauge voltage and gauge differential voltage are used to calculate the amplitude of the AC voltage, whether the measurement target is the system rated frequency or not. Even when operating off, it is possible to measure with high precision AC electric quantity.

  As described above, the present invention is useful as an AC electricity quantity measuring device and an AC electricity quantity measuring method that enable high-accuracy AC electricity quantity measurement.

1 AC voltage / current instantaneous value data input unit 2 Gauge voltage calculation unit 3 Gauge differential voltage calculation unit 4 Rotation phase angle / frequency calculation unit 5 Voltage amplitude calculation unit 6 Gauge current calculation unit 7 Gauge differential current calculation unit 8 Current amplitude calculation unit 9 Gauge active power calculation unit 10 Gauge differential active power calculation unit 11 Gauge reactive power calculation unit 12 Gauge differential reactive power calculation unit 13 Active power calculation unit 14 Reactive power calculation unit 15 Interface 16 Storage unit 100 AC electricity quantity measuring device

Claims (14)

A gauge voltage obtained by normalizing the voltage amplitude obtained by the square integral operation of at least three consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is twice or more the frequency of the AC voltage is calculated. A gauge voltage calculation unit;
Between tips of adjacent two voltage instantaneous value data in at least four consecutive voltage instantaneous value data including three voltage instantaneous value data sampled at the sampling frequency and used for calculating the gauge voltage A gauge difference voltage calculation unit for calculating a gauge difference voltage obtained by normalizing a value obtained by a square integral operation of three points of differential voltage instantaneous value data representing a distance;
A voltage amplitude calculator that calculates the amplitude of the AC voltage using the gauge voltage and the gauge differential voltage;
An AC electric quantity measuring device comprising: Calculates the gauge current obtained by normalizing the current amplitude obtained by the square integral operation of at least three consecutive current instantaneous value data obtained by sampling the alternating current to be measured at a sampling frequency twice or more the frequency of the alternating current. A gauge current calculation unit;
Between tips of adjacent two current instantaneous value data in at least four consecutive current instantaneous value data including three current instantaneous value data sampled at the sampling frequency and used when calculating the gauge current A gauge difference current calculation unit for calculating a gauge difference current obtained by normalizing a value obtained by square integral calculation of three points of difference current instantaneous value data representing a distance;
A current amplitude calculator that calculates the amplitude of the alternating current using the gauge current and the gauge differential current;
An AC electric quantity measuring device comprising: Of the three consecutive voltage instantaneous value data sampled at a sampling frequency that is at least twice the frequency of the AC voltage to be measured, the voltage instantaneous value data of two points that are later in measurement time and the sampling frequency are sampled. The value obtained by a predetermined product difference calculation using the current instantaneous value data of two points earlier in the measurement time out of the current instantaneous value data of the three points sampled at the same time as the voltage instantaneous value of the predetermined three points. A gauge active power calculation unit for calculating normalized gauge active power;
The voltage instantaneous value data at two points whose measurement time is early among the three consecutive voltage instantaneous value data sampled at the sampling frequency, and the same time as the voltage instantaneous value at the two points sampled at the sampling frequency A gauge reactive power calculation unit that calculates a gauge reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with current instantaneous value data of two points sampled in
A rotational phase angle calculator that calculates a rotational phase angle in one cycle time of sampling using the gauge voltage and the gauge differential voltage;
An active power calculation unit that calculates active power using the gauge active power, the gauge reactive power, and the rotational phase angle;
An AC electric quantity measuring device comprising: Calculate the gauge voltage obtained by normalizing the voltage amplitude obtained by the square integral calculation of at least three consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is at least twice the frequency of the AC current. A gauge voltage calculation unit;
A gauge current calculation unit for calculating a gauge current obtained by normalizing a current amplitude obtained by a square integral calculation of at least three continuous current instantaneous value data sampled at the sampling frequency;
The voltage instantaneous value data of two points whose measurement time is late among the continuous voltage instantaneous value data of three consecutive points sampled at the sampling frequency, and the same as the voltage instantaneous value of the predetermined three points sampled at the sampling frequency Gauge active power for calculating gauge active power normalized by a predetermined product difference calculation with current instantaneous value data of two points earlier in measurement time out of three instantaneous current value data sampled at time A calculation unit;
The voltage instantaneous value data at two points whose measurement time is early among the three consecutive voltage instantaneous value data sampled at the sampling frequency, and the same time as the voltage instantaneous value at the two points sampled at the sampling frequency A gauge reactive power calculation unit that calculates a gauge reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with current instantaneous value data of two points sampled in
A reactive power calculation unit that calculates reactive power using the gauge voltage, the gauge current, the gauge active power, the gauge reactive power, and the rotational phase angle;
An AC electric quantity measuring device comprising: A gauge voltage obtained by normalizing the voltage amplitude obtained by the square integral operation of at least three consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is twice or more the frequency of the AC voltage is calculated. A gauge voltage calculation unit;
Between tips of adjacent two voltage instantaneous value data in at least four consecutive voltage instantaneous value data including three voltage instantaneous value data sampled at the sampling frequency and used for calculating the gauge voltage A gauge difference voltage calculation unit for calculating a gauge difference voltage obtained by normalizing a value obtained by a square integral operation of three points of differential voltage instantaneous value data representing a distance;
The later of the measurement time 2 of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency 2 The difference voltage instantaneous value data of the point and the current instantaneous value data of two adjacent points in the four current instantaneous value data sampled at the sampling frequency and sampled at the same time as the voltage instantaneous value of the predetermined four points. Gauge difference active power is calculated by normalizing a value obtained by a predetermined product difference calculation with two difference current instantaneous value data of three points earlier in measurement time among three points of difference current instantaneous value data representing the distance between the tips. A gauge difference active power calculation unit;
Two of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data sampled at the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency, the two of which are measured earlier. It is obtained from the instantaneous voltage difference value data of the points and the instantaneous current value data of the three points sampled at the same time as the three instantaneous voltage values sampled at the sampling frequency and based on the two instantaneous differential voltage values. A gauge difference reactive power calculation unit for calculating a gauge difference reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with the difference current instantaneous value data of the two points obtained;
A rotational phase angle calculator that calculates a rotational phase angle in one cycle time of sampling using the gauge voltage and the gauge differential voltage;
An active power calculating unit that calculates active power using the gauge differential active power, the gauge differential reactive power, and the rotational phase angle;
An AC electric quantity measuring device comprising: Calculates the gauge current obtained by normalizing the current amplitude obtained by the square integral calculation of at least three consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is at least twice the frequency of the AC voltage. A gauge current calculation unit;
Between tips of adjacent two current instantaneous value data in at least four consecutive current instantaneous value data including three current instantaneous value data sampled at the sampling frequency and used when calculating the gauge current A gauge difference current calculation unit for calculating a gauge difference current obtained by normalizing a value obtained by square integral calculation of three points of difference current instantaneous value data representing a distance;
The later of the measurement time 2 of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency 2 The difference voltage instantaneous value data of the point and the current instantaneous value data of two adjacent points in the four current instantaneous value data sampled at the sampling frequency and sampled at the same time as the voltage instantaneous value of the predetermined four points. Gauge difference active power is calculated by normalizing a value obtained by a predetermined product difference calculation with two difference current instantaneous value data of three points earlier in measurement time among three points of difference current instantaneous value data representing the distance between the tips. A gauge difference active power calculation unit;
Two of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data sampled at the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency, the two of which are measured earlier. It is obtained from the instantaneous voltage difference value data of the points and the instantaneous current value data of the three points sampled at the same time as the three instantaneous voltage values sampled at the sampling frequency and based on the two instantaneous differential voltage values. A gauge difference reactive power calculation unit for calculating a gauge difference reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with the difference current instantaneous value data of the two points obtained;
A rotational phase angle calculator that calculates a rotational phase angle in one sampling period using the gauge current and the gauge differential current;
An active power calculating unit that calculates active power using the gauge differential active power, the gauge differential reactive power, and the rotational phase angle;
An AC electric quantity measuring device comprising: Gauge voltage calculation that calculates a gauge voltage that normalizes the voltage amplitude obtained by the square integral operation of at least three consecutive voltage instantaneous value data sampled at a sampling frequency that is at least twice the frequency of the AC voltage to be measured And
A gauge current calculation unit for calculating a gauge current obtained by normalizing a current amplitude obtained by a square integral calculation of at least three continuous current instantaneous value data sampled at the sampling frequency;
A three-point difference representing a tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three voltage instantaneous value data used in calculating the gauge voltage. A gauge difference voltage calculation unit that calculates a gauge difference voltage obtained by normalizing the value obtained by the square integral calculation of the voltage instantaneous value data with the amplitude value of the AC voltage;
A three-point difference representing a tip-to-tip distance between two adjacent current instantaneous value data in at least four consecutive current instantaneous value data including the three current instantaneous value data used in calculating the gauge current. A gauge differential current calculation unit that normalizes the value obtained by, for example, square integral calculation of the current instantaneous value data with the amplitude value of the alternating current and calculates it as a gauge differential current;
The later of the measurement time 2 of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency 2 The difference voltage instantaneous value data of the point and the current instantaneous value data of two adjacent points in the four current instantaneous value data sampled at the sampling frequency and sampled at the same time as the voltage instantaneous value of the predetermined four points. Gauge difference active power is calculated by normalizing a value obtained by a predetermined product difference calculation with two difference current instantaneous value data of three points earlier in measurement time among three points of difference current instantaneous value data representing the distance between the tips. A gauge difference active power calculation unit;
Two of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data sampled at the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency, the two of which are measured earlier. It is obtained from the instantaneous voltage difference value data of the points and the instantaneous current value data of the three points sampled at the same time as the three instantaneous voltage values sampled at the sampling frequency and based on the two instantaneous differential voltage values. A gauge difference reactive power calculation unit for calculating a gauge difference reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with the difference current instantaneous value data of the two points obtained;
A rotational phase angle calculator that calculates a rotational phase angle in one cycle time of sampling using the gauge voltage and the gauge differential voltage;
A reactive power calculation unit that calculates reactive power using the gauge differential voltage, the gauge differential current, the gauge differential active power, the gauge differential reactive power, and the rotational phase angle;
An AC electric quantity measuring device comprising: A gauge voltage obtained by normalizing the voltage amplitude obtained by the square integral operation of at least three consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is twice or more the frequency of the AC voltage is calculated. A gauge voltage calculation unit;
A gauge current calculation unit for calculating a gauge current obtained by normalizing a current amplitude obtained by a square integral calculation of at least three continuous current instantaneous value data sampled at the sampling frequency;
A three-point difference representing a tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three voltage instantaneous value data used in calculating the gauge voltage. A gauge difference voltage calculation unit that calculates a gauge difference voltage obtained by normalizing the value obtained by the square integral calculation of the voltage instantaneous value data with the amplitude value of the AC voltage;
A three-point difference representing a tip-to-tip distance between two adjacent current instantaneous value data in at least four consecutive current instantaneous value data including the three current instantaneous value data used in calculating the gauge current. A gauge differential current calculation unit that normalizes the value obtained by, for example, square integral calculation of the current instantaneous value data with the amplitude value of the alternating current and calculates it as a gauge differential current;
The later of the measurement time 2 of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency 2 The difference voltage instantaneous value data of the point and the current instantaneous value data of two adjacent points in the four current instantaneous value data sampled at the sampling frequency and sampled at the same time as the voltage instantaneous value of the predetermined four points. Gauge difference active power is calculated by normalizing a value obtained by a predetermined product difference calculation with two difference current instantaneous value data of three points earlier in measurement time among three points of difference current instantaneous value data representing the distance between the tips. A gauge difference active power calculation unit;
Two of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data sampled at the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency, the two of which are measured earlier. It is obtained from the instantaneous voltage difference value data of the points and the instantaneous current value data of the three points sampled at the same time as the three instantaneous voltage values sampled at the sampling frequency and based on the two instantaneous differential voltage values. A gauge difference reactive power calculation unit for calculating a gauge difference reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with the difference current instantaneous value data of the two points obtained;
A rotational phase angle calculator that calculates a rotational phase angle in one sampling period using the gauge current and the gauge differential current;
A reactive power calculation unit that calculates reactive power using the gauge differential voltage, the gauge differential current, the gauge differential active power, the gauge differential reactive power, and the rotational phase angle;
An AC electric quantity measuring device comprising: The later of the measurement time 2 of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency 2 The difference voltage instantaneous value data of the point and the current instantaneous value data of two adjacent points in the four current instantaneous value data sampled at the sampling frequency and sampled at the same time as the voltage instantaneous value of the predetermined four points. Gauge difference active power is calculated by normalizing a value obtained by a predetermined product difference calculation with two difference current instantaneous value data of three points earlier in measurement time among three points of difference current instantaneous value data representing the distance between the tips. A gauge difference active power calculation unit is provided,
The AC electrical quantity measurement device according to claim 3 or 4, wherein the rotational phase angle calculation unit calculates the rotational phase angle using the gauge active power and the gauge differential active power. The voltage instantaneous value data of two points whose measurement time is late among the continuous voltage instantaneous value data of three consecutive points sampled at the sampling frequency, and the same as the voltage instantaneous value of the predetermined three points sampled at the sampling frequency Gauge active power for calculating gauge active power normalized by a predetermined product difference calculation with current instantaneous value data of two points earlier in measurement time out of three instantaneous current value data sampled at time With a calculator
The AC electric quantity measurement according to any one of claims 5 to 8, wherein the rotational phase angle calculation unit calculates the rotational phase angle using the gauge active power and the gauge differential active power. apparatus. Two of the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data sampled at the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency, the two of which are measured earlier. It is obtained from the instantaneous voltage difference value data of the points and the instantaneous current value data of the three points sampled at the same time as the three instantaneous voltage values sampled at the sampling frequency and based on the two instantaneous differential voltage values. A gauge difference reactive power calculation unit for calculating a gauge difference reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with the difference current instantaneous value data of the two points obtained,
The AC electrical quantity measuring device according to claim 3 or 4, wherein the rotational phase angle calculation unit calculates the rotational phase angle using the gauge reactive power and the gauge differential reactive power. The voltage instantaneous value data at two points whose measurement time is early among the three consecutive voltage instantaneous value data sampled at the sampling frequency, and the same time as the voltage instantaneous value at the two points sampled at the sampling frequency A gauge reactive power calculation unit that calculates a gauge reactive power obtained by normalizing a value obtained by a predetermined product difference calculation with current instantaneous value data of two points sampled in
The AC electrical quantity measurement according to any one of claims 5 to 8, wherein the rotational phase angle calculation unit calculates the rotational phase angle using the gauge reactive power and the gauge differential reactive power. apparatus. Normalize the voltage amplitude obtained by the square integral calculation of at least three consecutive voltage instantaneous value data obtained by sampling the AC voltage to be measured at a sampling frequency that is at least twice the frequency of the AC voltage, and calculate it as a gauge voltage. Steps,
Between tips of adjacent two voltage instantaneous value data in at least four consecutive voltage instantaneous value data including three voltage instantaneous value data sampled at the sampling frequency and used for calculating the gauge voltage Normalizing a value obtained by a square integral calculation of three points of differential voltage instantaneous value data representing a distance and calculating as a gauge differential voltage;
Calculating an amplitude of an alternating voltage using the gauge voltage and the gauge differential voltage;
A method for measuring the amount of alternating current electricity, comprising: Normalize the current amplitude obtained by square integral calculation of at least three consecutive current instantaneous value data obtained by sampling the alternating current to be measured at a sampling frequency that is at least twice the frequency of the alternating current, and calculate it as a gauge current. Steps,
Between tips of adjacent two current instantaneous value data in at least four consecutive current instantaneous value data including three current instantaneous value data sampled at the sampling frequency and used when calculating the gauge current Normalizing the value obtained by the square integral calculation of the differential current instantaneous value data of three points representing the distance and calculating as a gauge differential current;
Calculating an amplitude of an alternating current using the gauge current and the gauge differential current;
A method for measuring the amount of alternating current electricity, comprising:

Images