An Universal Active Power Line Conditioner

Abstract

The power circuit of a general active power line conditioner
(APLC) is based on series and shunt power converters that share a single
DC link. In the present paper, a generic control concept for these
series and shunt converters is proposed. It is based on the
instantaneous real and imaginary power theory. In fact, the resulting
equipment deals with the custom power and FACTS concepts. This equipment
incorporates not only the compensation functions at the fundamental
frequency like a unified power flow controller (UPFC), but also provides
active harmonic mitigation capabilities. For these reasons, the
compensator proposed here is called the universal active power line
conditioner (UPLC). Simulation and experimental results are presented to
confirm that the new approach has better performance than those obtained
by controllers based on traditional concepts of active and reactive
power

Full text

page 1/8
Active Filters with Control Based on the p-q Theory
João Afonso, Carlos Couto, Júlio Martins
Departamento de Electrónica Industrial
Universidade do Minho
4800 Guimarães – Portugal
tel.: +351 253 510190
fax: +351 253 510189
e-mail: lafonso@dei.uminho.pt
e-mail: ccouto@dei.uminho.pt
e-mail: jmartins@dei.uminho.pt
Introduction
Due the intensive use of power converters and other non-linear loads in industry and by consumers in general, it
can be observed an increasing deterioration of the power systems voltage and current waveforms.
The presence of harmonics in the power lines results in greater power losses in distribution, interference
problems in communication systems and, sometimes, in operation failures of electronic equipments, which are more
and more sensitive since they include microelectronic control systems, which work with very low energy levels.
Because of these problems, the issue of the power quality delivered to the end consumers is, more than ever, an object
of great concern.
International standards concerning electrical power quality (IEEE-519, IEC 61000, EN 50160, among others)
impose that electrical equipments and facilities should not produce harmonic contents greater than specified values, and
also specify distortion limits to the supply voltage. Meanwhile, it is mandatory to solve the harmonic problems caused
by those equipments already installed.
Passive filters have been used as a solution to solve harmonic current problems, but they present several
disadvantages, namely: they only filter the frequencies they were previously tuned for; their operation cannot be limited
to a certain load; resonances can occur because of the interaction between the passive filters and other loads, with
unpredictable results. To cope with these disadvantages, recent efforts have been concentrated in the development of
active filters.
Active Filters
There are basically two types of active filters: the shunt type and the series type. It is possible to find active
filters combined with passive filters as well as active filters of both types acting together.
Fig. 1 presents the electrical scheme of a shunt active filter for a three-phase power system with neutral wire,
which is able to compensate for both current harmonics and power factor. Furthermore, it allows load balancing,
eliminating the current in the neutral wire. The power stage is, basically, a voltage-source inverter with only a single
capacitor in the DC side (the active filter does not require any internal power supply), controlled in a way that it acts
like a current-source. From the measured values of the phase voltages (v
a
, v
b
, v
c
) and load currents (i
a
, i
b
, i
c
), the
controller calculates the reference currents (i
ca
*, i
cb
*, i
cc
*, i
cn
*) used by the inverter to produce the compensation
currents (i
ca
, i
cb
, i
cc
, i
cn
). This solution requires 6 current sensors and 4 voltage sensors, and the inverter has 4 legs
(8 power semiconductor switches). For balanced loads without 3
rd
order current harmonics (three-phase motors, three-
phase adjustable speed drives, three-phase controlled or non-controlled rectifiers, etc) there is no need to compensate
for the current in neutral wire. These allow the use of a simpler inverter (with only three legs) and only 4 current
sensors. It also eases the controller calculations.
Fig. 2 shows the scheme of a series active filter for a three-phase power system. It is the dual of the shunt active
filter, and is able to compensate for distortion in the power line voltages, making the voltages applied to the load
sinusoidal (compensating for voltage harmonics). The filter consists of a voltage-source inverter (behaving as a
controlled voltage source) and requires 3 single-phase transformers to interface with the power system. The series active
filter does not compensate for load current harmonics but it acts as high-impedance to the current harmonics coming
from the power source side. Therefore, it guarantees that passive filters eventually placed at the load input will not drain
harmonic currents from the rest of the power system. Another solution to solve the load current harmonics is to use a
shunt active filter together with the series active filter (Fig. 3), so that both load voltages and the supplied currents are
guaranteed to have sinusoidal waveforms.
Shunt active filters are already commercially available, while the series and series-shunt types are yet at
prototype level.
IEEE Industrial Electronics Society Newsletter
vol. 47, nº 3, Se
p
t. 2000, ISSN: 0746-1240,
pp
. 5-10

page 2/8
Power
Source
Load
Inverter
−
i
ca
*
i
cb
*
i
cc
*
i
cn
*
+
i
ca
i
cb
Shunt Active Filter
Controller
i
s
a
i
s
b
i
s
c
i
s
n
i
a
i
b
i
c
a
b
c
N
v
a
v
b
v
c
v
a
v
b
v
c
V
dc
V
dc
i
a
i
b
i
c
i
n
i
cc
i
cn
Fig. 1 - Shunt active filter in a three-phase power system.
Load
Inverter
v
ca
*
v
cb
*
v
cc
*
+
i
a
i
b
i
c
Series Active Filter
Controller
i
a
i
b
i
c
a
b
c
v
a
v
b
v
c
v
s
a
v
sb
v
s
c
V
dc
V
dc
Power
Source
N
v
ca
v
cb
v
cc
-
v
s
a
v
sb
v
s
c
Fig. 2 - Series active filter in a three-phase power system.
Load
Inverter
1
i
s
a
i
s
b
i
s
c
a
b
c
v
a
v
b
v
c
Power
Source
N
v
ca
v
cc
v
s
a
v
sb
Inverter
2
−
+
i
ca
V
dc
v
sc
v
cb
i
s
n
i
a
i
b
i
c
i
n
Controller
Series-Shunt Active Filter
v
ca
*
v
cb
*
v
cc
*
v
sa
v
sb
v
sc
i
a
i
b
i
c
i
sa
i
sb
i
sc
V
dc
i
ca
* i
cb
* i
cc
*
i
cn
*
i
cb
i
cc
i
cn
Fig. 3 – Series-shunt active filter in a three-phase power system.

page 3/8
The p-q theory
In 1983, Akagi et al. [1, 2] have proposed the "The Generalized Theory of the Instantaneous Reactive Power in
Three-Phase Circuits", also known as instantaneous power theory , or p-q theory. It is based on instantaneous values in
three-phase power systems with or without neutral wire, and is valid for steady-state or transitory operations, as well as
for generic voltage and current waveforms. 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
α
-
β
-0 coordinates, followed by
the calculation of the p-q theory instantaneous power components:
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−−⋅=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−−⋅=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
c
b
a
c
b
a
i
i
i
i
i
i
v
v
v
v
v
v
23230
21211
212121
3
2
23230
21211
212121
3
2
00
β
α
β
α
(1)
000
ivp ⋅= instantaneous zero-sequence power (2)
ββαα
ivivp ⋅+⋅=
instantaneous real power (3)
αββα
ivivq ⋅−⋅≡ instantaneous imaginary power (by definition) (4)
The power components p and q are related to the same
α
-
β
voltages and currents, and can be written together:
⎥
⎦
⎤
⎢
⎣
⎡
⋅
⎥
⎦
⎤
⎢
⎣
⎡
−
=
⎥
⎦
⎤
⎢
⎣
⎡
β
α
αβ
βα
i
i
vv
vv
q
p
(5)
These quantities are illustrated in Fig. 4 for an electrical system represented in a-b-c coordinates and have the
following physical meaning:
0
p = mean value of the instantaneous zero-sequence power – corresponds to the energy per time unity which is
transferred from the power supply to the load through the zero-sequence components of voltage and current.
0
p
~
= alternated value of the instantaneous zero-sequence power – it means the energy per time unity that is exchanged
between the power supply and the load through the zero-sequence components. The zero-sequence power only exists in
three-phase systems with neutral wire. Furthermore, the systems must have unbalanced voltages and currents and/or 3
rd
harmonics in both voltage and current of at least one phase.
p = mean value of the instantaneous real power – 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).
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.
q = instantaneous imaginary power – 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 power supply and the load, but is
responsible for the existence of undesirable currents, which circulate between the system phases. In the case of a
balanced sinusoidal voltage supply and a balanced load, with or without harmonics,
q
(the mean value of the
instantaneous imaginary power) is equal to the conventional reactive power (
11
3
φ
sinIVq
⋅
⋅
⋅
=
).
p
–
p
~
q
p
0
−
p
0
~
LOAD
POWER
SOURCE
a
c
N
b
Fig. 4 – Power components of the p-q theory in a-b-c coordinates.

page 4/8
The p-q theory applied to shunt active filters
The p-q theory is one of several methods that can be used in the control active filters [3-11]. It presents some
interesting features, namely:
- It is inherently a three-phase system theory;
- It can be applied to any three-phase system (balanced or unbalanced, with or without harmonics in both
voltages and currents);
- It is based in instantaneous values, allowing excellent dynamic response;
- 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.
As seen before,
p is usually the only desirable p-q theory power component. The other quantities can be
compensated using a shunt active filter (Fig. 5). As shown by Watanabe et al. [12, 13],
0
p can be compensated without
the need of any power supply in the shunt active filter. This quantity is delivered from the power supply to the load,
through the active filter (see Fig. 5). This means that the energy previously transferred from the source to the load
through the zero-sequence components of voltage and current, is now delivered in a balanced way from the source
phases.
It is also possible to conclude from Fig. 5 that the active filter capacitor is only necessary to compensate
p
~
and
0
p
~
, since these quantities must be stored in this component at one moment to be later delivered to the load. The
instantaneous imaginary power (
q ), which includes the conventional reactive power, is compensated without the
contribution of the capacitor. This means that, the size of the capacitor does not depend on the amount of reactive power
to be compensated.
C
p
~
q
LOAD
POWER
SOURCE
SHUNT
ACTIVE
FILTER
p
~
p
0
~
p
0
~
p
–
p
–
p
0
−
p
0
−
p
0
−
+
−
a
c
N
b
a
b
c
N
p
0
−
Fig. 5 - Compensation of power components
p
~
, q,
0
p
~
and
0
p in a-b-c coordinates.
To calculate the reference compensation currents in the
α
-
β
coordinates, the expression (5) is inverted, and the
powers to be compensated (
0
pp
~
−
and q ) are used:
⎥
⎦
⎤
⎢
⎣
⎡
−
⋅
⎥
⎦
⎤
⎢
⎣
⎡
−
⋅
+
=
⎥
⎦
⎤
⎢
⎣
⎡
q
pp
~
vv
vv
vv
*i
*i
c
c
0
22
1
αβ
βα
βα
β
α
(6)
Since the zero-sequence current must be compensated, the reference compensation current in the 0 coordinate is
0
i itself:
00
i*i
c
= (7)

page 5/8
In order to obtain the reference compensation currents in the a-b-c coordinates the inverse of the transformation
given in expression (1) is applied:
()
*i*i*i*i
*i
*i
*i
*i
*i
*i
cccbcacn
c
c
c
cc
cb
ca
++−=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−−
−⋅=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
β
α
0
232121
232121
0121
3
2
(7)
The calculations presented so far are synthesized in Fig. 6 and correspond to a shunt active filter control strategy
for constant instantaneous supply power. This approach, when applied to a three-phase system with balanced sinusoidal
voltages, produces de following results (Fig. 8):
- the phase supply currents become sinusoidal, balanced, and in phase with the voltages. (in other words, the
power supply “sees” the load as a purely resistive symmetrical load);
- the neutral current is made equal to zero (even 3
rd
order current harmonics are compensated);
- the total instantaneous power supplied,
sccsbbsaas
iviviv)t(p ⋅+
⋅
+⋅=
3
(8)
is made constant.
In the case of a non-sinusoidal or unbalanced supply voltage, the only difference is that the supply current will
include harmonics (Fig 9), but in practical cases the distortion is negligible.
Load
Currents
v
a
v
b
v
c
Phase
Voltages
i
a
i
b
i
c
Calculation
v
α
v
β
v
0
Calculation
i
α
i
β
i
0
Calculation
p
q
p
0
Filter
p
~
p
Filter
0
p
p
0
Calculation
i
c
α
*
i
c
β
*
q
Calculation
i
ca
*
i
cb
*
i
cc
*
i
cn
*
i
0
V
dc
K
Gain
V
dc
V
re
f
+
−
p
reg
~
¯
~
~
¯
¯
Fig. 6 – Calculations for the constant instantaneous supply power control strategy.
The sinusoidal supply current control strategy must be used when the voltages are distorted or unbalanced and
sinusoidal currents are desired. The block diagram of Fig. 7 presents the calculations required in this case. When this
approach is used the results, illustrated in Fig. 10, are:
- the phase supply currents become sinusoidal, balanced, and in phase with the fundamental voltages;
- the neutral current is made equal to zero (even 3
rd
order current harmonics are compensated);
- the total instantaneous power supplied (
S
p
3
) is not made constant, but it presents only a small ripple (much
smaller than before compensation).

page 6/8
v
a
v
b
v
c
i
a
i
b
i
c
Calculation
v
α
v
β
Calculation
i
α
i
β
i
0
Calculation
p
q
p
0
Filte
r
p
~
p
Filte
r
0
p
p
0
Calculation
i
c
α
*
i
c
β
*
q
Calculation
i
ca
*
i
cb
*
i
cc
*
i
cn
*
i
0
p
reg
Calculation
v
a1+
v
b1+
v
c1+
V
dc
K
Gain
Calculation
..AF
p
V
dc
V
re
f
+
−
PI
Calculation
v
0
v
0
Phase
Voltages
Load
Currents
~
¯
~
~
¯
¯
Fig. 7 – Calculations for the sinusoidal supply current control strategy.
The practical implementation of the shunt active filter demands the regulation of the voltage at the inverter DC
side (
dc
V - the capacitor voltage) as suggested in Fig. 6 and Fig. 7, where
ref
V is the reference value required for proper
operation of the active filter inverter.
Figures 8, 9 and 10, present simulation results using Matlab/Simulink [14, 15] for a three-phase power system
with a shunt active filter. They include the following waveforms, corresponding to two-cycles of steady-state operation:
total instantaneous power at load and source, phase voltages, load and source currents (phase and neutral currents). In
the cases with distorted voltages the voltage total harmonic distortion (THD) is equal to 10%, which is a higher value
than what is regulated by any power quality standard.
Load Instantaneous Power:
ccbbaa
iviviv)t(p
⋅
+
⋅
+⋅=
3
Source Instantaneous Power:
sccsbbsaas
iviviv)t(p ⋅+⋅+⋅=
3
Time (s)
p
3
(VA)
p
3s
(VA)
0
Phase Voltages (
v
a
,
v
b
,
v
c
)
Time (s)
v
c
(V)
v
a
(V)
v
b
(V)
Load Currents
(
i
a
,
i
b
,
i
c
,
i
n
)
Time (s)
i
c
(A)
i
a
(A)
i
b
(A)
i
n
(A)
Source Currents (
i
sa
,
i
sb
,
i
sc
,
i
sn
)
Time (s)
i
sc
(A)
i
sa
(A)
i
sb
(A)
i
sn
(A)
Fig. 8 – Simulation results for the constant instantaneous supply power strategy with sinusoidal voltages.

page 7/8
Load Instantaneous Power:
ccbbaa
iviviv)t(p
⋅
+
⋅
+⋅=
3
Source Instantaneous Power:
sccsbbsaas
iviviv)t(p ⋅+⋅+⋅=
3
Time (s)
p
3
(VA)
p
3s
(VA)
0
Phase Voltages (
v
a
,
v
b
,
v
c
)
Time (s)
v
c
(V)
v
a
(V)
v
b
(V)
Load Currents
(
i
a
,
i
b
,
i
c
,
i
n
)
Time (s)
i
c
(A)
i
a
(A)
i
b
(A)
i
n
(A)
Source Currents (
i
sa
,
i
sb
,
i
sc
,
i
sn
)
Time (s)
i
sc
(A)
i
sa
(A)
i
sb
(A)
i
sn
(A)
Fig. 9 - Simulation results for the constant instantaneous supply power strategy with distorted voltages.
Load Instantaneous Power:
ccbbaa
iviviv)
t
(
p
⋅
+
⋅
+
⋅=
3
Source Instantaneous Power:
sccsbbsaas
iviviv)t(p ⋅+⋅+⋅=
3
Time (s)
0
p
3
(VA)
p
3s
(VA)
Phase Voltages (
v
a
,
v
b
,
v
c
)
Time (s)
v
c
(V)
v
a
(V)
v
b
(V)
Load Currents
(
i
a
,
i
b
,
i
c
,
i
n
)
Time (s)
i
c
(A)
i
a
(A)
i
b
(A)
i
n
(A)
Source Currents (
i
sa
,
i
sb
,
i
sc
,
i
sn
)
Time (s)
i
sc
(A)
i
sa
(A)
i
sb
(A)
i
sn
(A)
Fig. 10 - Simulation results for the sinusoidal supply current strategy with distorted voltages.

page 8/8
Conclusions
Active filters are an up-to-date solution to power quality problems. Shunt active filters allow the compensation
of current harmonics and unbalance, together with power factor correction, and can be a much better solution than the
conventional approach (capacitors for power factor correction and passive filters to compensate for current harmonics).
This paper presents the p-q theory as a suitable tool to the analysis of non-linear three-phase systems and for the
control of active filters.
Based on this theory, two control strategies for shunt active filters were described, one leading to constant
instantaneous supply power and the other to sinusoidal supply current.
The implementation of active filters based on the p-q theory are cost-effective solutions, allowing the use of a
large number of low-power active filters in the same facility, close to each problematic load (or group of loads),
avoiding the circulation of current harmonics, reactive currents and neutral currents through the facility power lines.
References
[1] H. Akagi, Y. Kanazawa, A. Nabae, Generalized Theory of the Instantaneous Reactive Power in Three-Phase
Circuits, IPEC'83 - Int. Power Electronics Conf., Tokyo, Japan, 1983, pp. 1375-1386.
[2] H. Akagi, Y. Kanazawa, A. Nabae, Instanataneous Reactive Power Compensator Comprising Switching Devices
without Energy Storage Compenents”, IEEE Trans. Industry Applic., vol. 20, May/June 1984.
[3] Quin, C., Mohan, N., Active Filtering of Harmonic Currents in Three-phase Four-Wire Systems with Three-
Phase and Single-Phase Non-Linear Loads, APEC, 1992, pp. 829-836.
[4] Depenbrock, M., Skudelny, H., Dynamic Compensation of Non-Active Power Using the FBD-Method – Basic
Properts Demonstrated by Benchmark Examples, ETEP - Eur. Trans. Elect. Power Eng., vol. 4, no. 5,
Sept/Oct 1994, pp. 381-388.
[5] Saetieo, S., Devaraj, R., Torrey, D., The Design and Implementation of a Three-Phase Active Power Filter Based
on Slide Mode Control, IEEE Trans. Industry Aplic., vol. 31, no. 5, Sept/Oct 1995, pp. 993-1000.
[6] Delarue, P., Six, J., Ionescu, F., Bogus, C., New Control Method for Active Power Filter, ISIE, Athens, 1995,
pp 427-432.
[7] Divan, D., Lorenz, R., Flux-Based Active Filter Controller, IEEE Trans. Industry Applic., vol. 32, no. 3,
May/Jun 1996, pp. 491-501.
[8] Sonnenschein, M., Winhold, M., Zurowski, R., Shunt-Connected Power Conditioner for Improvement of Power
Quality in Distribution Networks, ICHQP, Las Vegas, 1996, pp. 27-32.
[9] Verdelho, P., Marques, G., An Active Power Filter and Unbalanced Current Compensator, IEEE Trans. Ind.
Electronics, vol. 44, no. 3, June 1997, pp. 321-328.
[10] Chen, Y., O’Connell, R., Active Power Line Conditioner with a Neural Network Control, IEEE Trans. Industry
Applic., vol. 33, no. 4, Jul/Aug 1997, pp. 1131-1136.
[11]
Singh, B., Al-Haddad, K. , Chandra, A., Active Power Filter for Harmonic and Reactive Power Compensation in
Threee-Phase, Four-Wire Systems Supplying Non-Linear Loads, ETEP - Eur. Trans. Elect. Power Eng, vol 8,
no. 2, Mar/April 1998, pp. 139-145.
[12] E. H. Watanabe, R. M. Stephan, M. Aredes, New Concepts of Instantaneous Active and Reactive Powers in
Electrical Systems with Generic Loads, IEEE Trans. Power Delivery, vol. 8, no. 2, April 1993, pp. 697-703.
[13] M. Aredes, E. H. Watanabe, New Control Algorithms for Series and Shunt Three-Phase Four-Wire Active
Power Filters, IEEE Trans. Power Delivery, vol 10, no. 3, July 1995, pp. 1649-1656.
[14] MATLAB: High-Performance Numeric Computation and Visualization Software – Reference Guide, The
MathWorks Inc., April 1993.
[15] SIMULINK: The Dynamic System Simulation Software-User’s Guide, The MathWorks Inc., April 1993.