RU2629907C1 - Method for measuring reactive power in three-phase symmetric electrical circuit - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: method for measuring reactive power in a three-phase symmetric electrical circuit involves the measurement of instantaneous currents and voltages at each phase. The measured instantaneous values of phase currents and voltages are scaled, then converted from the natural three-phase coordinate system to a two-phase α-β coordinate system. Based on the obtained current projections I_α, I_β and the stresses U_α, U_β at the coordinate α-β system is formed by the current vectors I_s and the voltage U_s:

then the vector product is determined between the vectors I_s and U_s: Q_γ=I_S×U_S. The obtained projections of currents and voltages in αβ the coordinate system are multiplied Q₁=I_α⋅U_β and Q₂=-I_β⋅U_α, then they are added and multiplied by the number of phases:

where

is the estimate of the reactive power of the three-phase circuit. The transformation of phase currents and voltages from the natural three-phase coordinate system to the two-phase system is carried out according to the following expressions:

where I_A, I_B, I_c - instantaneous phase currents; I_α, I_β - the projection of currents in the α-β coordinate system; U_A, U_B, U_C - instantaneous phase voltages; U_α, U_β - the projection of stresses in the α-β coordinate system.

EFFECT: improving the measurement accuracy.

2 cl, 2 tbl, 7 dwg

Description

The invention relates to electrical engineering and can be used in measuring transducers of reactive power for three-phase circuits with a symmetrical load.

A known method of measuring reactive power [SU 1567990 A1, IPC 5 G01R 21/06, publ. 06/30/1990], selected as a prototype, including multiplying the instantaneous values of current and voltage, isolating the variable component of the product and averaging it from the moment zero of one of the input current (voltage) signals during the time interval during which the averaging is performed, complete at the moment of the next zero transition of another voltage (current) signal.

The disadvantage of the proposed method is the need to determine the transition point of the sinusoidal signal through zero, which affects the accuracy of measurement of reactive power.

The objective of the invention is to expand the arsenal of funds for similar purposes.

The proposed method for measuring reactive power, as in the prototype, includes measuring the instantaneous phase values of currents and voltages.

According to the invention, the measured instantaneous values of phase currents and voltages are scaled, then converted from a natural three-phase coordinate system to a two-phase α-β coordinate system. Based on the obtained projections of the currents I _α , I _β and voltages U _α , U _β in the α-β coordinate system, the current vectors I _s and voltage U _{s are formed} :

further define the vector product between the vectors I _s and U _s :

Q _γ = I _s × U _s ,

The obtained projections of currents and voltages in the α-β coordinate system are multiplied by Q ₁ = I _α ⋅ U _β and Q ₂ = -I _β ⋅ U _α , then they are added and multiplied by the number of phases:

- оценка реактивной мощности трехфазной цепи.Where

- evaluation of the reactive power of a three-phase circuit.

The conversion of phase currents and voltages from a natural three-phase coordinate system to a two-phase coordinate system is carried out according to the following expressions:

where I _A , I _B , I _C - instantaneous phase currents;

I _α , I _β — projection of currents in the α-β coordinate system;

U _A , U _B , U _C - instantaneous phase voltages;

U _α , U _β - projection of stresses in the α-β coordinate system.

Thus, the measurement of reactive power is carried out with great accuracy due to the use of the vector product of instantaneous projections of currents and voltages in a two-phase coordinate system α-β.

Table 1 presents the data of phase currents and voltages.

Table 2 presents the parameters of the three-phase circuit.

In FIG. 1 shows a diagram of a device that implements a method for measuring reactive power in a three-phase circuit.

In FIG. Figure 2 shows the waveforms of voltages in a three-phase circuit.

In FIG. Figure 3 shows the waveforms of currents in a three-phase circuit.

In FIG. 4 shows a graph of the signal from the output of the block of the multiplier 16.

In FIG. 5 shows a graph of the signal from the output of the block of the multiplier 17.

In FIG. 6 shows a waveform of reactive power.

In FIG. 7 is a graph of the relative error of reactive power.

The proposed method is implemented using the device (Fig. 1) for determining reactive power in a three-phase symmetrical electric circuit, which contains a normalizing unit 1 (BN), a coordinate converter unit 2 (BOD), and a reactive power calculation unit 3 (BVRM).

The normalizing unit 1 (BN) contains six normalization amplifiers 4 (UN1), 5 (UN2), 6 (UN3), 7 (UN4), 8 (UN5) and 9 (UN6).

The inputs of the first, second and third amplifiers-normalizers 4 (UN1), 5 (UN2) 6 (UN3) are connected to the outputs of the phase current sensors. The inputs of the fourth, fifth and sixth amplifiers-normalizers 7 (UN4), 8 (UN5) and 9 (UN6) are connected to the outputs of the phase voltage sensors.

The coordinate converter unit 2 (BOD) contains two adders 10 (C1), 11 (C2) and four scaling amplifiers 12 (MU1), 13 (MU2), 14 (MU3), 15 (MU4).

The inputs of the first adder 10 (C1) are connected to the outputs of the second 5 (UN2) and third 6 (UN3) amplifiers-normalizers. The output of the first adder 10 (C1) is connected to the input of the second scaling amplifier 13 (MU2). The inputs of the second adder 11 (C2) are connected to the outputs of the fifth and sixth amplifiers-normalizers 8 (UN5) and 9 (UN6). The output of the second adder 11 (C2) is connected to the input of the fourth scaling amplifier 15 (MU4). The output of the first amplifier-normalizer 4 (UN1) is connected to the input of the first scaling amplifier 12 (MU1). The output of the fourth amplifier-normalizer 7 (UN4) is connected to the input of the third scaling amplifier 14 (MU3).

The reactive power calculation unit 3 (BVRM) contains two multipliers 16 (U1), 17 (U2), a third adder 18 (C3) and a fifth scaling amplifier 19 (MU5).

The outputs of the first scaling amplifier 12 (MU1) and the fourth scaling amplifier 15 (MU4) are connected to the inputs of the first multiplier 16 (Y1). The outputs of the third scaling amplifier 14 (MU3) and the second scaling amplifier 13 (MU2) are connected to the inputs of the second multiplier 17 (Y2). The outputs of the first multiplier 16 (Y1) and the second multiplier 17 (Y2) are connected to the inputs of the third adder 18 (C3), the output of which is connected to the input of the fifth scaling amplifier 19 (MU5), the output of which is connected to the reactive power indicator.

As amplifiers normalizers 4 (UN1), 5 (UN2), 6 (UN3), 7 (UN4), 8 (UN5) and 9 (UN6) can be used - LA-UNI4. Adders 10 (C1), 11 (C2) and scaling amplifiers 12 (MU1), 13 (MU2), 14 (MU3), 15 (MU4) can be implemented on the basis of Texas Instruments DSP microcontrollers using standard libraries. The multipliers 16 (U1), 17 (U2), the adder 18 (C3) and the scaling amplifiers 19 (MU5) can be made similarly based on DSP microcontrollers from Texas Instruments.

Measurement of reactive power in a three-phase symmetric electric circuit for one instantaneous value was carried out as follows: when connecting normalization amplifiers 4 (УН1), 5 (УН2), 6 (УН3), 7 (УН4), 8 (УН5), and 9 (УН6) to three-phase current and voltage sensors, the output signals of the instantaneous values of currents I _{A_H} , I _{B_H} , I _{C_H} and voltages U _{A_H} , U _{B_H} , U _{C_H} from these blocks (Figs. 2, 3) were applied to the coordinate transformation unit 2 (BOD), where based on these data (table 1), the projections I _α , I _{β of} currents and voltages U _α , U _{β were} determined. The output signals I _{А_Н} , I _{А_Н} from the amplifiers-normalizers 4 (УH1), 7 (УН4) were converted by scaling amplifiers 12 (МУ1), 14 (МУ3). Using the adder 10 (C1), the output signals I _{B_H} , I _{C_H were added} from the normalization amplifiers 5 (UN2), 6 (UN3). Using the adder 11 (C2), the output signals U _{B_H} , U _{C_H were added} from the amplifiers-normalizers 8 (UN5) and 9 (UN6). The output signals of the adders 10 (C1) and 11 (C2) were converted by scaling amplifiers 13 (MU2) and 15 (MU4):

where I _{A_H} , I _{B_H} , I _{C_H} - normalized instantaneous phase currents;

I _α , I _β — projection of currents in the α-β coordinate system;

U _{A_H} , U _{B_H} , U _{C_H} - normalized instantaneous phase voltages;

U _α , U _β - projection of stresses in the α-β coordinate system.

The output values of blocks 12 (MU1), 13 (MU2) and 14 (MU1), 15 (MU2), which are projections of currents I _α , I _β and voltages U _α , U _β , were submitted to reactive power calculation unit 3 (BVRM) where the output signals were multiplied Q ₁ = I _α · U _β (Fig. 4) and Q ₂ = -I _{β (} U _α (Fig. 5) in the multiplication blocks 16 (U1) and 17 (U2), the products of which Q ₁ and Q _{2 were} then added in the adder 18 (C3) Q ₀ = (Q ₁ + Q ₂ ), the output signal of which was converted in the scaling amplifier 19 (MU5) by multiplying by the number of phases:

- оценка реактивной мощности трехфазной цепи (фиг. 6).Where

- assessment of the reactive power of a three-phase circuit (Fig. 6).

была установлена аналитически на основе определения относительной погрешности Δ:Adequacy of determining reactive power rating

was determined analytically based on the determination of the relative error Δ:

where Q _T is the calculated value of reactive power in an analytical way;

- оценка реактивной мощности в трехфазной цепи.

- assessment of reactive power in a three-phase circuit.

Based on the data from table 2, an analytical calculation of the reactive power Q _{T was} performed. First, the inductive resistances X _A , X _B , X _{C of} phases A, B, C were determined:

X _A = ω⋅L _A = 314.59⋅30⋅10 ^-3 = 9.4 Ohms,

X _B = ω⋅L _B = 314.59⋅30⋅10 ^-3 = 9.4 Ohms,

X _C = ω⋅L _C = 314.59⋅30⋅10 ^-3 = 9.4 Ohms,

where L _A , L _B , L _C inductive resistances; ω = 2⋅π⋅ƒ = 2⋅3.14⋅50 = 314.59 is the cyclic frequency, ƒ is the frequency of the supply circuit.

Next, we calculated the currents I _FA , I _PV , I _FS for each phase:

where U _f - phase voltage.

Then we determined sin (ϕ _A ), sin (ϕ _B ), sin (ϕ _C ):

Next, based on the calculated data, the reactive power in the three-phase circuit was determined:

Q _T = U _F ⋅I _FA ⋅sin (φ _A) + U _F ⋅I _PV ⋅sin (φ _B) +

+ U _Ф ⋅I _FS ⋅sin (ϕ _C ) = 3⋅220⋅16.01⋅0.686 = 7.247⋅10 ³ Var.

Then, the relative error in determining the estimate of the reactive power Q for a three-phase symmetric circuit was calculated:

An analysis of the relative error in the estimation of the reactive power calculation showed that the measurement accuracy for a circuit with a symmetrical load is determined by the accuracy of measuring instantaneous current and voltage and the calculation step (Fig. 7).

Claims (14)

1. The method of measuring reactive power in a three-phase symmetric electric circuit, including measuring the instantaneous values of currents and voltages in each phase, characterized in that the measured instantaneous values of phase currents and voltages are scaled, then converted from a natural three-phase coordinate system to a two-phase α-β coordinate system , based on the obtained projections of the currents I _α , I _β and voltages U _α , U _β in the α-β coordinate system, current vectors I _s and voltage U _{s are formed} :

further define the vector product between the vectors I _s and U _s : Q _γ = I _s × U _s , the obtained projections of currents and voltages in the α-β coordinate system are multiplied by Q ₁ = I _α ⋅ U _β and Q ₂ = -I _β ⋅ U _α , then they are added and multiplied by the number of phases:

Where

- evaluation of the reactive power of a three-phase circuit. 2. The method according to p. 1, characterized in that the conversion of phase currents and voltages from a natural three-phase coordinate system into a two-phase coordinate system is carried out according to the following expressions:

where I _A , I _B , I _C - instantaneous phase currents; I _α , I _β — projection of currents in the α-β coordinate system; U _A , U _B , U _C - instantaneous phase voltages; U _α , U _β - projection of stresses in the α-β coordinate system.

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