XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

Conservative Power Theory Implementation in Shunt Active Power Filtering

Constantin Vlad Suru1, Alexandra Pătrascu2, Mihăită Lincă3; 1University of Craiova, Faculty of Electrical Engineering, Craiova, Romania, vsuru@em.ucv.ro

2University of Craiova, Faculty of Electrical Engineering, Craiova, Romania, apatrascu@em.ucv.ro 3University of Craiova, Faculty of Electrical Engineering, Craiova, Romania, mlinca@em.ucv.ro

Power Electronics - cause and remedy for distortion in distribution systems. Type of presentation: Lecture

Abstract — This paper analyzes the current decomposition, in three-phase, three-wire systems, based on the Conservative Power Theory (CPT), and the application of these components in the active filtering. The CPT current decomposition gives the active component of the current, the reactive component, which can be compensated or not and the void current. It does not give the asymmetry current component, separately. For this reason, the active shunt compensators based on the CPT have the capability of compensating only parts of the non-active current, as needed. The reactive component can be compensated or not, but the void current, which contains the harmonic content, is normally compensated. A problem of the CPT, latter resolved, is the asymmetry current component which was not included in the first definitions. The aim of this paper is to analyze the performance of an experimental active compensator based on the early CPT definitions and a comparative study with the performances of the same compensator based on the improved CPT definitions.

Keywords — Conservative Power Theory, harmonic distortion, current decomposition, active compensator.

I. INTRODUCTION Most of the industrial, commercial and home

consumers have non-linear character, this way harmonic distortion level in power grids has become a serious issue. Another problem that appears in the three-phase networks, which are divided into several one-phase networks, is the current asymmetry.

Negative aspects which could be determined by the high level of harmonics presence in the power grid are well known and there were introduced standards in order to limit these harmonic distortions.

Therefore, customers must limit the harmonic current absorbed from the power grid. Accordingly, they have to insure that harmonics filtering is provided.

Shunt active filters developed once with the new standards imposed to the equipments, in the context of technology evolution and power semiconductor elements performances, but also due to the progress in the DSP, numerical methods and control algorithm domain.

One of the advantages of using an active shunt compensator consists of its capability to compensate not only the current harmonic distortion and reactive component, but also, the current asymmetry. This feature is available only when the compensating current computation algorithm implements the current asymmetry component which can be added if desired to the

compensating current. Regarding the Conservative Power Theory, its first definitions [1-2] did not contain this component. Therefore, the active compensator based on this theory could not compensate only the current asymmetry. The latter definition of this theory [3-5] had resolved this issue, the active, reactive and void components of the non-sinusoidal load current having added an asymmetry component.

II. CURRENT DECOMPOSITION USING THE CONSERVATIVE POWER THEORY

This section presents the orthogonal decomposition of the load current into its active, reactive and void components. Each current term relates to some energy phenomenon, taking into account the supply voltage and load current distortion. This decomposition has two distinct definitions: the first definition is an extension for three-phase circuits of the CPT for one-phase circuits. This means that all the current components are calculated individually for each phase. The second definition takes into account the asymmetry part of each current component, because it considers the three-phase active power and reactive energy.

1. For the classic definition of the CPT, the load current, for one phase is the sum of three components [1-2]:

vraL iiii ++= (1) Where:

uu

Puu

uii22a == (2)

is the active component of the current, i.e. the minimum current which conveys the active power P. It must be mentioned that ||u|| is the RMS value of u(t) and ui is the internal product, which is defined as follows:

dt)t(u)t(iT

uiT

∫=0

1 (3)

Other terms used later in this paper are the homo-integral and the homo-derivative functions of voltage or current, were ω is the angular frequency [1]:

⎟⎟⎠

⎞⎜⎜⎝

⎛ ττ−ττ⋅ω= ∫ ∫∫T tt

dtd)(uT

d)(uu0 00

1 (4)

)t(udtdu ⋅

ω= 1 (5)

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

The reactive component of the load current, for one phase, is defined as:

( ) ( )422

2222

UUUuUQUQuUQUQir

−−+−=

βαβα (6)

As it can be seen the reactive current takes into consideration the integral and derivative power absorption, respectively:

iuiuQ

iuiuQ

r

r

==−

==β

α (7)

The above definitions are valid only for symmetrical loads, but in practice the real industrial loads may have higher or lower asymmetry and the active compensator will not be able to compensate it.

2. To resolve the above issue, the classic CPT theory was improved by defining the required asymmetric components for the current decomposition [3-5]:

vrb

ab

L iiii ++= , (8)

Where, the notation x means the column vector containing the three phase components of x:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

c

b

a

xxx

x (9)

The three-phase balanced active current absorbed from the grid by the unbalanced load is:

uGui bba ==

2UP (10)

Where, P is the three-phase active power of the load:

TSR PPP ++=P (11) and U is the grid voltage norm given by:

222TSR uuu ++=U (12)

The three-phase balanced reactive current absorbed from the grid by the unbalanced load after the compensation, which gives the same reactive energy is:

uBuWi bbr == 2U

(13)

where: TSR WWWW ++= (14) is the three-phase reactive energy absorbed by the load. It must be mentioned that Gb and Bb are the equivalent balanced conductance and susceptance of the unbalanced load.

For the both CPT definitions, the void component of the current is defined as:

raLv iiii −−= (15)

III. COMPENSATING CURRENT COMPUTATION FOR SHUNT ACTIVE FILTERING

Because the shunt active filter acts like a generator, the compensating current must contain the non-active current components which are to be eliminated from the grid current. Thus, the compensating current will be calculated

from the load current depending of the compensation goals, as follows:

- total compensation – in this case, the active filter will compensate the entire non-active current, the compensating current being obtained by:

aL*F iii −= (16)

- partial compensation – in this case the active filter will compensate only the distortion component, the reactive component of the load current being eliminated from the compensating current:

raL*F iiii −−= (17)

The desired filter current was computed for the both CPT definitions, every method having its own implementation for the experimental active filter, using relations (2) and (6) for the first method and (10) and (13) for the other one.

IV. THE EXPERIMENTAL ACTIVE FILTERING SYSTEM For the theoretical and experimental studies conducted in this paper, the classical topology of the shunt filter was adopted. The experimental active filtering system, illustrated in Fig 1, is divided in the following specific components:

- the three-wire power inverter (APF) which consists of six IGBT power transistors (IC = 100 A and VCES = 1200 V) and the corresponding amplification and protection circuitry;

- the 1st order interface filter consisting of three special coils having an inductance of 4.4 mH;

- the DC-link which contains two high voltage capacitors with the rated values C = 2200 µF, UN = 400V

- the control system based on the dSPACE DS1103 acquisition board;

- the control algorithm which, in fact, is a Simulink model compiled and loaded to the DS1103 memory;

- the nonlinear asymmetrical load. The control algorithm implements the following stages found in Fig 1:

o the compensating current computation; o the current hysteresis controller; o the phase locked loop; o the dc-link voltage controller.

The unbalanced nonlinear load used: o a three-phase fully controlled bridge rectifier.

The adopted current controller is a three-phase fixed band hysteresis controller, which is the most simple and robust solution. The hysteresis band is set up to 1 A, considering the maximum current value of 25 A.

The voltage controller is necessary to regulate the dc-link voltage which varies in large amount during the compensation process [6], with negative impact on the compensation efficiency. This is because the generated current dynamic is dependent to the voltage applied to the interface filter inductances, which is the difference between the grid voltage and the dc-link voltage.

The voltage regulation is also necessary in the start-up process, because the normal working dc-link voltage is higher than the maximum grid voltage rectified value.

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

Fig. 1. Schematic diagram of the active filtering system.

The voltage regulator output signal signifies the

amplitude of the current needed to charge the dc-link capacitor and to cover the power inverter losses. So, this value is multiplied with a unitary amplitude three-phase sinusoidal current system obtained by a Phase Locked Loop system. If the model must be simplified (in order to reduce the number of computations and the computation step), the PLL can be replaced with a simple gain block having an amplification factor equal to the inverse of the grid voltage amplitude. This method is less accurate, but the voltage controller compensates the grid voltage

amplitude variations. The command and control section of the system is entirely virtual, i.e. a Matlab/Simulink model using DS1103 specific library blocks (Fig. 2). When in use, this model is compiled and loaded to the DS1103 program memory.

Because the voltage and current transducers outputs are normalized 10 V outputs, the Simulink model must contain gain blocks necessary to obtain the voltage or current actual values.

Fig. 2. The Simulink model which implements the active filter current computation and control algorithm.

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

.

Fig. 3. The active filter virtual front panel.Also, because the power inverter has a three-wire

configuration, all the three-phase voltage and current systems can be acquired using only two transducers. This implies the use of the three-phase reconstruction blocks which computes the third component. The active filter user interface is based on the DS1103 specific software (Control Desk), and consists of the virtual control panel illustrated in Fig 3. The front panel contains all the necessary instruments for the filter manipulation, including check buttons, indicator lamps, etc, and also, the system monitoring devices (virtual panel meters, oscilloscopes, etc). The link between the control panel instruments and the corresponding variables of the Simulink model are also made by the Control Desk software. These links are automatically loaded to the DS1103 memory at the program compilation.

V. EXPERIMENTAL RESULTS The active filter compensation performances were studied for the both definitions of the CPT, based on a specific non-linear and unbalanced load, that is a three phase full wave rectifier. Also, for the compensating current computation both (16) and (17) were used. For this non-linear load, which absorbs from the power grid an unbalanced current of about 15A per phase, the phase current waveforms are illustrated in Fig 4. For the compensating current computation using (10), (13) and (17), the resulted grid current is almost sinusoidal, having a partial harmonic distortion factor (considering the first 51th harmonics) of 4.28%, 4.57%, and 3.40%, respectively, being reduced from the corresponding values of the load current: 23.27%, 25.47%, and 24.45%. This gives filtration efficiency per phase of 5.43, 5.56, and 7.18, respectively, for this nonlinear unbalanced load, and the selected compensation algorithm.

Not only the load current waveform was asymmetric (Fig. 4), but also, the current RMS values were different between the phases: 14.25, 13.98, and 13.04 A. After the compensation, the current RMS value of each phase was modified to the values corresponding to a balanced current system: 13.55, 13.45, 13.93 A, proving the modified CPT capability of efficiently compensating not only the current distortion, but also, the current unbalance (Fig. 5). The calculated asymmetry factor for the grid current gives the value of 5.87% before the compensation and 2.09%, after the compensation, for a grid voltage asymmetry factor of 1.30%. In the case of total compensation, the current computation was based on relations (10) and (16) giving to the active filter the task of compensating all the non-active components of the load current. This gave the grid current waveforms shown in Fig 6.

0 0.01 0.02 0.03 t [s]-40

-20

0

20

40

i Labc

[A]

-400

-200

0

200

400

u Sa [V

]

uSa

iLaiLb iLc

Fig. 4. The three-phase controlled rectifier current.

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

0 0.01 0.02 0.03 t [s]-40

-20

0

20

40

i Sab

c [A

]

-400

-200

0

200

400

u Sa [V

]

uSaiSa iSb iSc

Fig. 5. The grid voltage and the compensated currents

for partial compensation. It can be observed that the compensated current shape is again almost sinusoidal, but the phase shift between the grid phase voltage and the corresponding current was eliminated by the active filter, after the compensation of the reactive component of the current. In this case, the grid current PHD is for each of the phases: 5.70%, 5.31%, and 4.56%, giving a filtration efficiency of: 4.13, 4.85, and 5.41, respectively. The filtration efficiency is slightly lower compared to the partial compensation case because dc-link value was kept constant at 700 V, and for the total compensation mode the necessary voltage is higher [7-8]. This can be concluded not only from the PHD values, but also from the compensated current waveforms in Fig 6, looking at the commutation moments. The actual RMS values of the grid current are: 10.9, 10.89, and 11.25 A. It must be mentioned that the remaining unbalance is due to the grid voltage asymmetry, and not to the compensation method inefficiency. This is shown by the measured grid voltage RMS value asymmetry: Ua = 228.4 V, Ub = 228.1 V, Uc = 232.7 V, giving the grid voltage asymmetry factor of 1.3%. It can be concluded that the grid current system is equilibrated after compensation, considering the initial current asymmetry of 5.755% and the final asymmetry of 2.151%.

0 0.01 0.02 0.03 t [s]-40

-20

0

20

40

i Sab

c [A]

-400

-200

0

200

400

u Sa [V

]

uSa

iSa iSb iSc

Fig. 6. The grid voltage and the compensated currents

for total compensation.

0 0.01 0.02 0.03 t [s]-40

-20

0

20

40

i Sab

c

-400

-200

0

200

400

u Sa [V

]

uSa iSa iSb iSc

Fig. 7. The grid voltage and the compensated currents for partial compensation and classic CPT algorithm.

When using the classic CPT for the current computation (relations (2) and (6)), it’s interesting to study the filtering results, because the classic CPT has no defined asymmetry current component. In the partial compensation mode, for the same non-linear unbalanced load, the compensated grid currents are illustrated in Fig 7.

Because the active filter determines the compensating current independently for each grid phase, the current unbalance is not compensated by the active filter. This is also proven by the compensated current RMS values of: 14.2, 13.4 and 13.08 A. The current PHD drops after compensation from 23.2%, 25.4% and 24.27% to 6.52%, 5.27% and 6.03%, respectively. This gives for this case, a filtration efficiency of 3.55, 4.81, and 4.02. These results can be explained by the compensated current RMS value asymmetry. That is, if the grid current RMS value for one phase is lower than the corresponding symmetric current RMS, the distortion of the first current is higher than for the latter one. The grid current asymmetry factor is 5.46% before the compensation and 5.44% after the compensation, proving that the active filtering has little or no effect on the load current unbalance.

0 0.01 0.02 0.03 t [s]-40

-20

0

20

40

i Sab

c [A]

-400

-200

0

200

400

u Sa [V

]

uSa

iSa iSbiSc

Fig. 8. The grid voltage and the compensated currents

for total compensation and classic CPT algorithm.

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

In the case of total compensation based on relations (2) and (16), the resulted grid currents are the one in Fig 8. The filtration efficiency is 3.42, 4.32, and 3.71, for a compensated current PHD of 6.82%, 5.88%, and 6.55%, respectively. The current RMS values after the compensation are 11.22, 10.49, and 10.85 A. As it can be concluded from the PHD values of the compensated current, the harmonic distortion is higher on all the phases, comparing to the ones obtained with the improved CPT algorithm, and also, the current asymmetry factor is higher, having the value of 3.76%. This proves the active filter incapacity of compensating this kind of distortion, based on the classic CPT, and the results worsen even more as the asymmetry of the load increases. One interesting fact is that only the currents corresponding to the first and the third phase are not compensated correctly, the second phase current is not only having the correct shape (and a PHD of 5.88%), but is having the correct RMS value, comparing with the corresponding current in Fig 6. It must be mentioned that the current asymmetry was obtained by connecting a power resistor in series with the third phase.

VI. CONCLUSION The Conservative Power Theory has proven its

performance in the active filtering current compensation. The obtained experimental results are positive regarding the current harmonic distortion compensation, but also regarding the load current asymmetry compensation when the improved CPT was used. In the case of classic CPT, the current harmonic distortion reduction is comparable to the improved CPT results, but only for symmetric loads, or for load currents with little asymmetry. In this second case, the compensated current keeps its asymmetry, only the harmonic distortion being reduced. In all the cases, the obtained results are dependent of the grid voltage asymmetry, and in the case of asymmetric voltage, the compensated current will take this asymmetry, for the first case, and will add this asymmetry to the already asymmetric compensated current, for the second case.

ACKNOWLEDGEMENT The authors gratefully acknowledge the contributions of Prof.

Alexandru Bitoleanu and Prof. Mihaela Popescu for their work on the original version of this document.

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