101

CHAPTER 5

INSTANTANEOUS REACTIVE POWER THEORY

5.1 INTRODUCTION

This chapter presents a novel control strategy for the case of three

phase four wire Unified Power-Quality Conditioner (UPQC) based on the

concepts of instantaneous active and reactive Power theory. Using

instantaneous ac t i ve an d reactive Power theory, current harmonics,

reactive power compensation and voltage c o m p e n s a t i o n have been

simulated and the results are analyzed. The operation and capability of the

proposed system was analyzed through simulations with MATLAB /

SIMULINK.

5.2 REACTIVE POWER THEORY

The Generalized Theory of the Instantaneous Reactive Power in

Three-Phase Circuits also known as instantaneous power theory , or p-q

theory. Instantaneous Reactive Power Theory is based on set of instantaneous

powers defined in the time domain and uses the Park Transform. No

restrictions are imposed on the voltage or current waveforms and it can be

applied to three-phase systems with or without a neutral wire for three-phase

generic voltage and current waveforms. Thus, it is valid not only in the steady

state but also in the transient state. This theory is very efficient and flexible in

designing controllers for power conditioners based on power electronics

devices (Akagi et al 2004).

102

The method offers the technique to calculate the real and reactive

power requirements of the load instantaneously. The method is mostly applied

to calculate the reference current of the shunt and series active filter. The p-q

theory consists of an algebraic transformation (Clarke transformation) of the

three-phase voltages and currents in the a-b-c coordinates to the -0

coordinates, followed by the calculation of the p-q theory instantaneous

power components.

The p-q theory is one of several methods that can be used in the

control active filters. It presents some interesting features, namely,

It is inherently a three-phase system theory

It is based in instantaneous values, allowing excellent dynamic

response

It can be applied to any three-phase system (balanced or

unbalanced, with or without harmonics in both voltages and

currents)

Its calculations are relatively simple (it only includes algebraic

expressions that can be implemented using standard

processors)

It allows two control strategies: constant instantaneous supply

power and sinusoidal supply current

In three-phase circuits, instantaneous currents and voltages are

converted to instantaneous space vectors. In instantaneous power theory, the

instantaneous three phase currents and voltages are calculated as given in

following equations. These space vectors are easily converted into the

orthogonal coordinates (Akagi et al 2004).

103

0

1 1 12 2 2

2 1 11 2 233 30 2 2

a

b

c

V VV VV V

(5.1)

0

1 1 12 2 2

2 1 11 2 233 30 2 2

a

b

c

i ii ii i

(5.2)

The instantaneous active and reactive power in the -0

coordinates are calculated with the following expressions:

IVIVqIVIVp

IVP 000

(5.3)

where p0 = instantaneous zero-sequence power

p = instantaneous real power

q = instantaneous imaginary power

The values of p and q can be expressed in terms of the dc

components plus the ac components, that is,

p p p (5.4)

q q q (5.5)

The power components p and q are related to the same voltages

and currents, and can be written together as given below:

104

iV VpV V iq

(5.6)

V I and V I are instantaneous real and imaginary powers

respectively. Since these equations are products of instantaneous currents and

voltages in the same axis, in three-phase circuits, instantaneous real power is

p and its unit is watt. In contrast V I and V I are not instantaneous powers.

Since these are products of instantaneous currents and voltages in two

orthogonal axes, q is not conventional electric unit like watt or VAr. The

value q is instantaneous imaginary power and its unit is imaginer volt ampere.

These power quantities given above for an electrical system represented in a-

b-c coordinates and have the following physical meaning

p - mean value of the instantaneous real power – It is corresponds to

the energy per time unity which is transferred from the power

supply to the load, through the a-b-c coordinates, in a balanced way

(it is the desired power component). It is the dc component of the

instantaneous power p, and is related to the conventional

fundamental active current.

p - alternated value of the instantaneous real power – It is the energy

per time unity that is exchanged between the power supply and the

load, through the a-b-c coordinates. It is the ac component of the

instantaneous power p, it does not have average value, and is

related to the harmonic currents caused by the ac component of the

instantaneous real power.

q - instantaneous imaginary power – It is corresponds to the power that

is exchanged between the phases of the load. This component does

not imply any transference or exchange of energy between the

105

power supply and the load, but is responsible for the existence of

undesirable currents, which circulate between the system phases

q - dc component of the imaginary instantaneous power q, and is

related to the reactive power generated by the fundamental

components of voltages and currents.

q - ac component of the instantaneous imaginary power q, and is

related to the harmonic currents caused by the ac component of

instantaneous reactive power. This component does not imply any

exchange of energy between the power supply and the load, but is

responsible for the existence of undesirable currents, which

circulate between the system phases

The objective of the p-q theory is to make the source to deliver the

constant active power demanded by the load. At the same time the source

should not deliver any zero sequence active power. The reference source

current in the -0 frame is therefore:

*

* 2 2

1c

c

i v vv vi v v

. (5.7)

Since the zero-sequence current must be compensated, the

reference compensation current in the 0 coordinate is i0 itself

0* iico (5.8)

In order to obtain the reference compensation currents in the a-b-c

coordinates the inverse of the transformation given in Equation (5.2) is

applied.

106

0

* *

* *

* *

1 1 02

2 31 12 223

31 12 22

ca c

cb c

cc c

i i

i i

i i (5.9)

The compensation current for neutral is given by:

****cccbcacn iiii (5.10)

The calculations presented so far are synthesized in Figure 5.1 and

correspond to a shunt active filter control strategy for constant instantaneous

supply power.

Figure. 5.1 Calculation for the constant instantaneous supply power

107

5.3 CIRCUIT CONFIGURATION OF UPQC

The UPQC shown in Figure 5.2 consists of two VSCs (VSC_1 and

VSC_2) that are connected back to back through a common energy storage dc

capacitor . Series converter (VSC_1) is connected through transformers

between the supply and point of common coupling (PCC). Shunt converter

(VSC_2) is connected in parallel with PCC through the transformers. VSC_1

operates as a voltage source while VSC_2 operates as a current source . The

power circuit of VSC_1 consists of three single-phase H-bridge voltage-

source PWM inverters. H-bridge inverters are controlled independently.

The main objective of VSC_1 is to mitigate voltage disturbances

originating from supply side. The ac filter inductor and capacitor are connected

in each phase to prevent the flow of harmonic currents generated due to

switching. The transformers connected at the output of each H-bridge inverter

provide isolation, modify voltage/current levels, and prevent the dc capacitor

from being shorted due to the operation of various switches. The power circuit

of VSC_2 consisting of a three-phase voltage-source PWM inverter is supplied

from dc link . VSC_2 is directly connected through a boost inductor Lsm

which can boost up the common dc link voltage to the desired value.

The objectives of VSC_2 are to regulate the dc link voltage

between both converters and to suppress the load current harmonics. The

switching devices in VSC_1 and VSC_2 are insulated-gate bipolar transistors

(IGBTs) with antiparallel diodes. A three-phase uncontrolled diode-bridge

rectifier with resistive and inductive load is used to produce harmonic current.

The ac reactor Lch placed before the rectifier to enhance the load impedance.

Operation modes of UPQC as follows.

108

Figure 5.2 Schematic diagram of UPQC

1) VSC_1 off and VSC_2 on: When the PCC voltage is within

its operation limits, VSC_1 is closed and VSC_2 works as the

current source . During this operation of UPQC, two lower

IGBTs of each phase H-bridge inverter of VSC_1 remain

turned on while the two upper IGBTs remain turned off,

forming a short circuit across the secondary (inverter side)

windings of the series transformer through Lf.VSC_2

suppresses the load current harmonics and regulates dc-link

voltage during this mode of operation.

2) VSC_1 on and VSC_2 on: When the PCC voltage is outside

its operating range, both VSC_1 and VSC_2 are open.VSC_1

starts to mitigate disturbances using the energy stored in VDC

and VSC_2 continue to suppress the load current harmonics

and to regulate dc-link voltage.

109

5.4 UPQC CONTROL STRATEGY

A UPQC is the extension of the unified power-flow controller

(UPFC) concept at the distribution system. It consists of combined series and

shunt converters for simultaneous compensation of voltage and current

imperfections in a point of common connection (PCC) in the distribution side.

The series and shunt converters connected back-to-back via a common DC

link capacitor. Unlike the UPFC, the series converter is connected to a supply

side and shunt converter is connected load side. This configuration has proved

performance with both supply voltage distortions such as harmonics and

unbalanced line to line voltages as well as load disturbances such as harmonic

current, unbalanced load and reactive power requirement by the load. This

configuration also provides optimum rating for a specific amount of reactive

power compensation.

UPQC is controlled in such a way that the voltage at the load bus is

always sinusoidal with the desired magnitude. Therefore the voltage injected

by series APF must be equal to the difference between the PCC voltage and

the desired load voltage. The series APF acts as a controlled voltage source.

The shunt APF acts as a control source for maintaining the DC link voltage.

The shunt APF also provides required var to the load such that the power

factor at PCC is unity and only fundamental active power is supplied by the

source. The voltage injected by series APF can be varied from 0 to 360

degree.

The control system of the UPQC can be divided into two parts,

namely a shunt APF controller and a series APF controller, in which they

control the shunt current and the series injected voltage respectively. Source

side inverter, called the series inverter is connected through coupling

transformers between the point of common connection and load. The load

110

side inverter, called the shunt inverter is connected in parallel through the

transformers or directly connected.

The series inverter operates as a controlled voltage source, while

the shunt inverter operates as a controlled current source. The method

proposed in the chapter can be used to simultaneously calculate the harmonics

present in current and voltage waveforms, aiming the application in the

control of a UPQC.Therefore, measurement and extraction waveform

compensation components of UPQC are of great significance for its normally

performance. The series injected voltage has to be in phase with PCC voltage

to compensate voltage sag. The series connected inverter injects a voltage in

quadrature with the line current thereby emulating an inductive or a

capacitive reactance in series with the line.

The shunt connected inverter injects a reactive current, thereby also

emulating a reactance at the point of connection. While operating both series

and shunt connected inverters together as UPQC, the reactive power supplied

from source reduces, thus increasing the power factor at PCC. The load

voltage is also compensated against power quality disturbances. The UPQC

controller was designed using the instantaneous power method based on 0

transform and fundamental positive sequence detection.

The UPQC under study in Figure 5.2 is analyzed with p-q-r

instantaneous reactive power theory. In the p-q-r theory proposed,p-q-r

reference frames which rotates according to the voltage space vector of a

three-phase four-wire system .In this theory, the current and voltage in space

coordinate are transformed to p-q-r coordinates. Voltage components only in

p axis, which can simplify the active and reactive current calculation. The

current space vector is transformed into three linearly independent dc based

components, in which p-axis component represents the instantaneous active

111

power when multiplied with the single voltage vector component, where the

q-axis component represents an imaginary current component on plane,

and r-axis component represents an imaginary component which is highly

related to the 0-axis in -0 reference frames.

A control strategy with the combination of voltage detection

method for series active filter and current detection method for shunt active

filter is used, with the reference signal determined by the voltage detection

and current detection method in p-q-r theory. Since the current is

compensated to be a constant length vector that is rotating aligned with the

voltage space vector, when the load voltage cannot fully be compensated to

be balanced and sinusoidal, the current rotating with the voltage space vector

will not be sinusoidal too.

An extra q-axis component is proposed to add to the reference

source current space vector to force it to rotate with a pure sinusoidal

reference. The power supplied by the series active filter and loss in switching

devices is obtained by drawing extra active power from the parallel active

filter. With the aid of p-q-r theory, a control block model of the integration

feedback is formed and the amount of power is determined by an integration

feedback of dc storage power. The equivalent model of integration controller

is proposed by detecting the instantaneous value of dc storage capacitor

voltage. The simulation with MATLAB verifies that the proposed analysis

and control algorithm is valid for the UPQC under three-phase four-wire

system.

The control system of UPQC has three major elements, which are a

positive sequence detector, a shunt inverter control, and a series inverter

control. The positive-sequence detector extracts the positive sequence of

component from the disturbed and unbalanced three-phase source voltage

112

with series of steps as given in the Figure 5.3.The transformed positive

sequence reference voltage V , V , based on the 0 transform are found

out as explained below.

Figure 5.3 Shunt inverter control

The measured source voltage passes through the three phase Phase

Locked Loop(PLL) and the sine wave generator to calculate the fundamental

component of the transformed current are i =sin 1t and i =cos 1t.The

powers corresponds to positive sequence fundamental component are

calculated as active power ps and reactive power qs from the of the source

voltage Vs and fundamental current components i and i .

sc

sb

sa

VVV

VV

232

1

23

21

01

32

(5.11)

'

'

'

'

i

iVV

VV

qp

s

s (5.12)

113

So, the instantaneous value of the positive-sequence component

voltage is,

'

'

'

'

''

''

2'2''

' 1

s

s

s

s

q

pi

iii

iiiiv

v (5.13)

The instantaneous active power loops in the UPQC system and

imaginary power provided by the source should be reduced to a smaller value

such that a larger capacity of power is available to the load side.

5.4.1 Shunt Inverter Control

When there are harmonics and negative sequence components in

the load voltage, the p-q-r reference frames are not rotating at a constant

angular velocity and thus the resulting source current is not sinusoidal. Here, a

compensation method is proposed to control the reference current space

vector to follow the rotation of the sinusoidal reference wave. Since the p-axis

and r-axis are used to compensate the active power harmonics and neutral line

currents respectively, and the remaining y-axis is always located on the

plane, it can be used to move the current space vector to be aligned with the

reference wave, without using extra active power.

For the reference current determination, the load voltage is taken as

the p-q-r rotation reference instead of the reference load voltage since this

guarantees the shunt active filter to compensate the load current harmonics

and to provide the correct amount of power looping in the UPQC, even if the

series active filter cannot fully compensate for the harmonics and unbalance

occurs in the source voltage. Since the p-q-r theory does not require voltage

preprocessing, the control algorithm still works under this case. Unlike a

conventional shunt active filter, it should absorb active power to provide the

114

proper operation of shunt active filter, such that the average of the dc

capacitor voltage is zero.

When the voltage is not balanced and sinusoidal, the instantaneous

frequency of rotation of the p-q-r reference frames is not constant, thus there

is a deviation between the current reference and the ideal voltage reference.

The q-axis component is used to force the original current vector to be

aligned with the balanced and sinusoidal reference wave. The dc component

which corresponds to the average active power component of the load current,

is extracted, and a small amount of r-axis current is added to compensate the

neutral current.

The functions of the shunt inverter are to compensate the current

harmonics, the reactive power, and to regulate the DC link capacitor voltage.

Figure 5.3 shows the configuration of shunt inverter control, which includes

the current control for harmonic compensation and the DC voltage control.

Shunt control calculates the reference value of the compensating current for

the harmonic current and the load reactive power.The instantaneous power is

calculated using components of positive sequence voltage and load

current iL.

L

L

ss

ss

ii

vvvv

qp

''

''

(5.14)

qpP

vvvv

Uii

lossss

ss

c

c''

''

*

* 1 (5.15)

where 2'2'ss vvU

Power corresponds to harmonic content is calculated by separating

oscillating power and fundamental power by passing 5th order butter-worth

high pass filter. Using these active powers (oscillating power and system

115

power loss) and reactive power the reference value of the compensating

current is derived from Equation 5.15.

5.4.2 Series Inverter Control

Figure 5.4 shows the control circuit of series converter. The

function of the series inverter is to compensate the voltage disturbance such as

voltage harmonics, voltage unbalance on the source side, which is due to the

fault and/or line drop because of over load in the distribution line.

Figure 5.4 Control circuit for Series converter

The series active filter power loss, includes the switching loss in the

inverters and the copper loss in the coupling transformers. When there is

voltage flicker, or the voltage is below the rated voltage, ac and dc active

power is needed to draw from the series inverter to the load. The series

inverter control calculates the reference voltage to be injected by the series

inverter, comparing the positive-sequence component Vabc’ with the

disturbed source voltage Vsabc.

The vol tage compensation may involves supplying / absorbing

real power from the supply line, so there must be real power balance

between series and shunt inverters . The instantaneous real power

absorbed / delivered by the series inverter must be equal to the real power

delivered / absorbed by the shunt inverter so as to maintain DC link

capacitor voltage constant. In the Figure 5.4, k=(Vrms/sqrt(3))*sqrt(2) and

G=desired maximum phase voltage value. The reference load voltage of a

116

UPQC system is taken to be balanced and sinusoidal as for the requirement of

sensitive loads, however, the fundamental phase angle between the source

voltage and load voltage can be varied and so as the phase angle of source

current with respect to the load voltage. Varying the phase angles results

approximately same amount of power supplied by the source, however, the

magnitude of the source current and the magnitude of series inverter voltage

varies.

The dc component in r-axis imaginary power refers to the reactive

power component in the load, and the ac component is related to the

harmonics and imbalance. The q-axis imaginary power is mainly produced by

the neutral current imbalance. Reducing the amount of imaginary power

supplied by the source results an increase of capacity of active power

available to the load side. The imaginary power can be fully compensated by

the parallel active filter while the series active filter supplies an imaginary

power with a zero average vector sum to compensate the imbalance and

harmonics in the source voltage.

In order to provide a maximum available capacity for the load side,

the power drawn by the series active filter from the dc link can be reduced by

selecting the reference load voltage to be in phase with the fundamental

positive sequence of source voltage, and the current reference is selected to

eliminate the load current's harmonics, imbalance and reactive power, and

includes an active power for the power given out by the series active filter.

To obtain the voltage and current references as analyzed above,

fundamental positive sequence of source voltage is needed to be extracted,

and the load current components corresponding to the harmonics, imbalance

and reactive power must be extracted. By this algorithm, a balanced and

sinusoidal reference wave can be obtained without time delay, and can be

maintained even if the source voltage is distorted by severe voltage sags.

117

IGBTs are used in the inverter circuits to convert DC power to AC

power. A voltage source inverter is energized by a constant DC voltage

supply of low impedance at the input. The output voltage is independent of

load current. The inverters are then connected in series to the distribution line

through injection transformers. IGBT is a unidirectional conducting device

and hence in most of the applications an anti-parallel diode has to be used.

When IGBTs are used as switching components in an inverter or converter,

freewheeling diodes are needed to sustain the current from the inductive load

such as a motor or transformer.

PWM switched inverters provide superior performance to control

asymmetries and especially over currents during unbalanced faults. Use of

single-phase H-bridge PWM inverters in DVR power circuit makes possible

the injection of positive, negative and zero sequence voltages. The voltage

control is achieved by modulating the output voltage waveform within the

inverter. The main advantage of PWM inverter is including fast switching

speed of the power switches. PWM technique offers simplicity and good

response. Besides, high switching frequencies can be used to improve on the

efficiency of the converter, without incurring significant switching losses.

LC filter suppresses the dominant harmonics produced by inverter

circuit. In this thesis Inverter side filtering is preferred for harmonic

elimination. This scheme has the advantageous of being closer to the

harmonic source and low voltage side thus it prevents the current harmonics

to penetrate into the series injection transformers.

The transformers reduce the voltage requirement of the inverters

and provide isolation between the inverters. This can prevent DC storage

capacitor from being shorted through switches in different inverters

(Ghosh et al 2002). The electrical parameters of series injection transformer

should be selected correctly to ensure the maximum reliability and

118

effectiveness. In normal bypass mode, full load currents pass through

semiconductor switches.

5.5 SIMULATION RESULTS

In this section, MATLAB/SIMULINK software simulation results

are presented to show the performance of UPQC and analyzing the operation

of the UPQC for mitigation of current and voltage harmonic elimination . The

power circuit is modeled as a 3- phase 4-wire system with a non-linear load

that is composed of a 3-phase diode-bridge rectifier with RL load. UPQC uses

common DC link for APF and DVR . The performance of VSC_1 and VSC_2

from the points of view of, voltage compensation, and harmonic suppression

capabilities are investigated. The system circuit parameters adopted are

presented in Table 5.1.

Table 5.1 System parameters of UPQC

System parameters SpecificationsSystem frequency 50 HzDc link capacitance C1=4400 F,C2=4400 FDc-link voltage 600VNon-Linear Load R =20 ohms,

L=15 mH,2.6 KVA

Shunt Inverter Filter L=5.5 mH ,C=12 µF

Series Inverter Filter L=5.5 mH ,C=12 µF

Switching Frequency 9730 HzPWM Control Hysteresis controlCoupling transformer 3.3 KVA

119

5.5.1 Compensation of Current Harmonics

Figure 5.5 (a) Load Current before compensation

Figure 5.5 (b) Source Current after compensation

Figure 5.5 (c)Reference Current of shunt Inverter

Figure 5.5(d) Capacitor voltage of Shunt inverter

The source is selected to be a highly harmonically distorted and

unbalanced. The waveform of load Current before compensation is shown in

Figure 5 . 5 (a ) . When the source voltage is highly distorted by harmonics

which is cannot completely be removed by the series active filter, thus the

waveform of the load voltage is not completely sinusoidal. When the current

is compensated by taking the reference source current in which the q-axis

120

reference source current equals zero, and r-axis component is used to

compensate the neutral line current.

Load harmonics and reactive power required by the load is

compensated by injecting equal magnitude of harmonics but opposite

polarity. The hysteresis current controller is used for synthesizing the

compensating current with the current track band width of 0.018 ampere.

The reference current of shunt inverter consists of harmonic components of

non linear load, reactive current corresponding to load reactive power, power

losses due to inverters and DC voltage regulation current.

Using the reference load voltage wave and the q axis source

current, the source current can be compensated to sinusoidal as shown in

Figure 5 . 5 (b ) . The simulation result verifies that if there is a balanced

sinusoidal reference, with the p-q-r theory the source current can be

compensated to be balanced and sinusoidal. The load absorbs an average

active power of approximately 2.6 kW.Figure 5.5 (c) shows reference Current

of shunt Inverter.

The THD of the distorted three-phase line currents (Ia, Ib & Ic ) are

36.47%, 31.42% and 38.27% respectively. The THD of Source current in

phase A, B and C has reduced to 4.23%, 4.97% and 4.56% respectively. It is

clear from that graph, the response time is less than 5 ms. DC link capacitor

voltage is almost kept constant during voltage unbalance . The results show

that a successful reduction in harmonics of the supply current is obtained. The

PI controlled dc-link capacitor voltage is nearly kept at 600 Vdc. Capacitor

voltage of Shunt inverter under non linear load is shown in

Figure 5.5(d).

121

5.5.2 Compensation of Load voltage

Load voltage with harmonics is shown in Figure 5.6(a). Since theload voltage is compensated to be balanced and sinusoidal, the load voltage inthe p-q-r frames with respect to itself is a constant value. Also, the q and r-axis of the source current is compensated to zero, with a dc value in p-axis,this shows that the current is compensated to be balanced and sinusoidal.Notice that the source voltage have no dc components in the q-axis and r-axis,and since the current is now have a p-axis component only.

Figure 5.6(a) Load voltage with harmonics

Figure 5.6(b) UPQC voltage

Figure 5.6(c) Load voltage after compensation

122

This means that there is no phase difference between the

fundamental positive sequence of the source voltage and the load voltage, and

thus the power looping in the UPQC system has a minimum value.

Load voltage is compensated to be balanced and sinusoidal, thus

there is no influence to the load side even if there is a fault at the source side.

Therefore, series active filter needs more active power from the dc Link and

thus there is an increase in the power drawing from the dc storage. The

integration controller compensates this power with a transient process and the

drop of dc stops after the system reaches its steady state .As expected, the

steady-state dc voltage will be lower if the required power from the series

active filter is larger. The average active power supplied by the source is

approximately the same before and after the fault in steady state, except that

there may be a difference in the loss power. This shows that the power

looping in the UPQC does not consume extra power from the source.

The compensated voltage of series active filter is shown in Figure

5.6(b). Load voltage after compensation is shown in Figure 5.6(c). The Total

harmonic Distortion (THD) of the distorted three-phase load voltages are

51.87%, 48.25% and 49.56 % respectively. The THD of load voltages in

phase A, B and C has reduced to 5.23%, 5.11% and 5.05 % respectively. The

simulation result verifies, the load voltage can be compensated to be balanced

and sinusoidal.

5.6 CONCLUSION

A novel control strategy to generate the reference source current

and reference load voltage under distorted and unbalanced load and source

condition is presented in this chapter. The MATLAB/Simulink based

simulation results show that the distorted and unbalanced load currents and

123

load voltages seen from the utility side act as perfectly balanced source

currents and load voltages are free from distortion.

The drawbacks of the control scheme are uncompensated load

reactive power and failure of control during supply voltage unbalance. When

the load is unbalanced then the p and q powers are time variant quantities that

do not provide instantaneous information on power properties of the load.

Indeed, both powers are involved quantities, dependent at the same time on

two different power phenomena. An additional analysis is required to identify

the active, reactive, unbalanced and apparent powers after the p and q powers

are recorded over the entire period of their variability. Consequently, the IRP

p-q Theory, although it is based on a time-domain approach to power theory,

has no advantages over the frequency-domain approach with respect to the

time interval needed for identification of power properties of three-phase

loads.

According to the IRP p-q Theory, the instantaneous reactive current

can occur in linear circuits without reactive elements and consequently, when

the reactive power is zero. Moreover, the instantaneous active current can

occur when the active power is zero. These conclusions from the IRP p-q

Theory contradict the common meanings of the active and reactive currents.

Moreover, these two currents in systems with sinusoidal supply voltage and

without any loads that generate harmonics are non-sinusoidal. It means, the

IRP p-q Theory misinterprets power phenomena in electrical circuits.

Moreover, it does not reveal the load imbalance as the cause of power factor

degradation. It interprets the load imbalance as a loading that causes only a

change of the active and reactive currents.