JP3326763B2 - How to measure complex power - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a measuring method for measuring complex power consisting of active power and reactive power.

[0002]

2. Description of the Related Art A conventional wattmeter is an instrument for measuring only active power, but is also used as a reactive power meter by changing a connection method. In the measurement of active power by a conventional wattmeter, the measurement of the positive active power, that is, the power consumption, is negative. The measurement is performed by changing the connection so that

[0003]

In the above-described measurement of reactive power by the conventional wattmeter, the reactive power itself can be measured, but it cannot be determined whether the reactive power is advanced or delayed.
That is, generally, when the complex power is expressed as Pl = Pa + jPr, the active power Pa and the reactive power P
r cannot be measured at the same time, and furthermore, the positive / negative judgment of Pr cannot be made.

In a three-phase power circuit, due to the unbalance of the three-phase power supply or the three-phase load, the complex power shared by the power supplies of each phase and the complex power of each phase load also become unbalanced, and the complex power is accurately measured. Can not do. In particular, when the component values on the three-phase unbalanced load side are unknown, the equivalent circuit viewed from the power supply side must be considered as a black box. In such a case, it is impossible to determine what the three-phase power measurement value physically represents.

Specifically, a three-phase linear motor (LIM)
Is regarded as a black box whose parameter value is unknown from the power supply side due to the end effect caused by the structure. In analyzing this LIM in detail, the calculation of the parameter values of the three-phase equivalent circuit is currently receiving attention, but it is necessary to measure the complex power Pl = Pa + jPr as the power during operation. In particular, complex power measurement is indispensable for the operation control of the LIM, and the actual operation of the LIM uses a low-frequency inverter power supply, and the power measurement at the low frequency increases the error in the conventional power meter. .

The present invention provides a measuring method capable of measuring the above-described complex power, that is, a measuring method comprising only a resistor and a capacitor and calculating the complex power from the effective value measurement of the voltage.

[0007]

The resistor R is connected in parallel with the load Zl.
The first series circuit of _a1 and R _a2, and the resistor Rb and capacitor C
b and the load Zl and the first,
A resistor r is connected between a connection point p on the side of the resistors Ra and Rb of the second series circuit and one end s of the power supply, and the load Zl is connected.
Effective voltage Vl between both terminals of the effective value voltage Va of the resistor R _a1, effective voltage Vb of the resistor Rb, the effective value voltage Vr of the resistor r, end s and the resistor R _a1 and R of the power supply
An effective value voltage Vsa between the connection point a of the power supply _a2 and a connection point b between the one end s of the power supply and the resistor Rb and the capacitor Cb is measured. Vbx and Vby are calculated using Rb and Cb of the above equation, and Vrx and Vby are calculated from the measured values and the calculated values according to equation (1).
Vrx = (Vsa ² −Vr ² −Va ² ) / ² Va (1) Next, for the real part, imaginary part and Vsb of the two voltages Vr and Vb, (Vrx + Vbx) ² + (Vry + Vby) ) ² = Vsb ² (2) holds, and the imaginary part Vry of Vr is calculated from equation (3), and Vry = {(Vsb ² −Vr ² −Vb ² ) / 2−VrxVbx} / Vby. (3) Using these Vrx and Vry, the load current Ir is given by: Ir = Vr / r = Vrx / r + jVry / r (4) Therefore, the load power Pl is Pl = Vl.times.Ir = Vl. Vrx / r + jVl Vry / r (5) The complex power is calculated.

[0008]

As described above, the measurable RMS voltage is measured, and after one measurement, the real part and the imaginary part of the voltage are calculated by a predetermined formula, and the complex power value is calculated from these calculated values. I do.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS As shown in FIG.
The first series circuit of _a1 and R _a2, and the resistor Rb and capacitor C
b, and a resistor r is connected between the load Zl and a connection point p of the first and second resistors R _a1 and Rb on the side of the first series circuit and one end s of the power supply. However, the series impedance of the series resistance and Rb and Cb of a degree that does not affect the load R _a1 and R _a2 are made large, the series resistance r is the value of negligible compared to the load impedance. Each voltage vector at this time can be displayed as shown in FIG. 2 if Va is used as a reference vector.

Now, the voltage vector of the resistor Rb is expressed as Vb =
Vbx + jVby The voltage vector of the resistor r is given by Vr = Vrx +
jVry, the voltage vector between the terminals sa and s and the voltage vector between the terminals sb are respectively Vsa = Vsax + jVsay
, Vsb = Vsbx + jVsby.

The effective values of Va, Vr, and Vsa are represented by Va, V
r, Vsa, the three voltages Va, Vr, Vsa to Vr
Vrx is the real part Vrx using the cosine theorem ^{= (Vsa 2 -Vr 2 -Va 2} ) / 2Va ··· effective measurements from relational expression (1) Vsa, Vr, Va (R a1 and R _a2
Is known, Va is Va = Vl Ral / ( _Ra1 + _Ra2 ) from the measured effective value Vl of the load voltage between the terminals p and q.
Can be calculated and measurement is unnecessary).

Next, with respect to the real part, imaginary part and Vsb of the two voltages Vr and Vb, (Vrx + Vbx) ² + (Vry + Vby) ² = Vsb ^2. 3) calculated from the ^{equation, Vry = {(Vsb 2 -Vr} 2 -Vb 2) / 2-VrxVbx} / Vby ··· (3)

Using the Vrx and Vry, the load current Ir
Is Ir = Vr / r = Vrx / r + jVry / r (4), and the load power Pl is Pl = Vl.times.Ir = V1 Vrx / r + jV1 Vry / r (5), and the complex power is Is calculated.

As a specific example, when the set value is _Ra1 = 1 (k
Ω), R _a2 = 49 (kΩ), Rb = 1 (kΩ), 1 / ωCb
= 30 (kΩ), r = 0.1 (Ω), Vl = 50 (V),
The complex power is calculated as a load impedance Zl = −4−j3 (Ω) (actually, the element value of Zl is unknown, but is assumed to indicate the validity of the theory). The theoretical power is -400 (W) and the reactive power is 3
At 00 (V _ar ), Pl = −400 + j300.

If the effective value of each voltage is four significant digits,
It has the following values: Va = 1.000 (V), Vb = 1.666 (V), V
bx = 0.0555 (V), Vby = 1.665 (V), V
r = 1.000 (V), Vsa = 0.6325 (V), V
sb = 2.384 (V) From equation (1) Vrx = −0.7999 (V) From equation (2) Vry = 0.5996 (V) From equation (5) Complex power Pl = −399.95 + j2
99.8.

[0016]

As described above, it is possible to calculate the complex power with a simple circuit and only by measuring the effective value voltage. For example, by using a thermocouple type instrument, it is possible to measure the equivalent complex power. The effect of use in fields requiring power measurement is extremely large.

In the measurement of power supplied from a low-frequency inverter power supply commonly used as a drive power supply for a motor, a current waveform and a voltage waveform include harmonics and waveform distortion is large. There is no big error.

It is easy to calculate parameter values of a three-phase equivalent circuit of a three-phase linear motor and measure power in real time in operation control.

[Brief description of the drawings]

FIG. 1 is a circuit configuration diagram for implementing a method for measuring complex power according to the present invention.

FIG. 2 is a voltage vector diagram.

[Explanation of symbols]

 E Power supply voltage (V) Vl Load effective value voltage (V) Zl Load impedance (Ω) r Known resistance (Ω) Ra1 Known resistance (Ω) Ra2 Known resistance (Ω) Rb Known resistance (Ω) Cb capacitor (μF) Vr RMS voltage (V) Va RMS voltage (V) Vb RMS voltage (V) Vsa RMS voltage (V) Vsb RMS voltage (V) p, q, a, b, s Terminal symbols Vr, Va, Vb, Vsa, Vsb voltage vector

Claims (1)

(57) [Claims] To 1. A for measuring the complex power consisting of active and reactive power supplied from the power source, a first series circuit in parallel with the load Zl resistor R _a1 and R _a2, and the resistor Rb and capacitor Cb A second series circuit is connected, and a resistor r is connected between the load Zl and a connection point p on the resistors R _a1 and Rb sides of the first and second series circuits and one end s of the power supply. effective voltage Vl between both terminals of zl, the effective voltage Va of the resistor R _a1, effective voltage Vb of the resistor Rb, the effective value voltage Vr of the resistance r, the one end s of the source resistance R
effective voltage Vsa between the connection point between _a1 and R _a2 a, and the effective voltage Vsb between the connection point b between the end s and the resistor Rb and capacitor Cb of the power supply is measured, the from Vl value known Vbx and Vby are calculated using Rb and Cb of the two-series circuit, and Vrx is calculated from the measured value and the calculated value according to the equation (1). Vrx = (Vsa ² −Vr ² −Va ² ) / 2Va (1) Next, for the real part, imaginary part and Vsb of the two voltages Vr and Vb, (Vrx + Vbx) ² + (Vry + Vby) ² = Vsb ² . imaginary part Vry is calculated from equation ^{(3), Vry = {(Vsb 2 -Vr} 2 -Vb 2) / 2-VrxVbx} / Vby ··· (3) this Vrx, using Vry, load current Ir Is: Ir = Vr / r = Vrx / r + jVry / r (4) Therefore, the load power Pl is Pl = Vl.times.Ir = V1 Vrx / r + jVl Vr. y / r (5) A complex power measurement method, wherein the complex power is calculated as follows.