Alleviation of Harmonics using Series Power Line Compensator

** Abstract** – This paper proposes series power line compensator which uses a new dual p q theory to effectively eliminate the harmonics in the three phase four wire power system. Further, conventional inverter is replaced with Z source inverter to achieve reduced harmonic levels. Eliminating harmonics reduces the major effects of overheating, malfunctioning, increases the life time of the system. The proposed method is modeled and simulated using MATLAB/SIMULINK environment. Time domain simulations are used to verify the system operations with non linear loads.

*Index Terms***— Harmonics, Dual p-q theory, Series active filter, ZSI, power quality**

**Introduction**

Power quality of the power system deteriorates because of the usage of non linear loads. The presence of non linear load in a utility power transmission system causes harmonic currents which in turn reduces the power quality of the system. [1][2]. Power filters are the special equipments that uses converters to compensate harmonics generated by nonlinear loads. Active power filters are the emerging power quality filters that has numerous advantages compared to classic power filters.[3]

**2.Proposed Method**

Presence of non linear load disturbs the sinusoidal nature of the source voltage and load Voltage waveform. The compensation strategy in this proposing method injects the controlled voltage series into the system so as to maintain the sinusoidal waveform and reduces the THD levels.

Fig.1. Proposed Series Active Filter

Inputs of the reference signal generator are line Currents( I_{la}, I_{lb} ,I_{lc}) and source voltage(V_{sa}, V_{sb}, V_{sc}) which are sensed through current transformer. This block computes the reference signal with the proposed dual p q theory which is given as a gate pulses to the Z source Inverter. Output Voltage from the inverter is injected into the power system by three single phase injecting transformers. This helps to maintain the sinusoidal nature of the waveform there by reducing the THD values and alleviate harmonics.

**3.Mathematical Formulation**

In a three-phase balanced system, the source voltages and the line currents are expressed as

(1)

and

(2)

The three-phase instantaneous active power in three-phase system is given by,

(3)

substituting equations (1) and (2) in equation(3) we get,

Adding equations, we get three-phase instantaneous power as

Thus, for balanced three-phase system, the total instantaneous power is equal to the real power or average active power (P), which is constant and time-independent. The three-phase reactive power can be derived from the imaginary part of the three-phase complex power as

Hence, the three-phase apparent power S3ф is expressed as

3.1 Dual p-q theory

In dual p-q theory, for a three-phase with neutral conductor it is assumed that the currents are known and the real and reactive power are known and the voltage components are calculated or compensated. Thus, dual p-q theory is suitable to perform series voltage compensation instead of shunt compensation done by p-q theory.For a three-phase, four-wired system with neutral connected, no zero-sequence voltage and currents are present. Thus, the αβ0 transformation or the Clarke’s transformation for line voltages neglecting the zero-sequence component are given by

Fig. Flowchart of Dual p-q theory

Similarly, the three-phase source currents ia, ib, and ic can be can be transformed on the αβ axes are given by

The p-q theory for a three phase system with neutral conductor, the instantaneous real and the imaginary power are defined on the αβ axes as

On solving we get,

The oscillatory part of the real and reactive power is eliminated and the average part of real and reactive power is chosen. The αβ voltages will be set as function of currents and the real and reactive powers *pc* *and *qc* *is expressed as

The above equation can be decomposed as

Instantaneous active voltage on α axis Vαp

Instantaneous reactive voltage on α axis Vαq

Instantaneous active voltage on β axis Vβq

Instantaneous reactive voltage on β axis Vβq

The reference voltage signal or the compensated voltages are derived applying the inverse Clarke’s transformation. Thus, the compensating voltages V*ca, V*cb, V*cc from the αβ axes are expressed as

Solving we get,

4. Simulation Results

Fig. Simulink diagram of the proposed system

Fig. Reference signal Generation subsystem

The system shown above has been simulated in the Matlab Simulink platform to verify the proposed control strategy. The power circuit is a three-phase four wire system supplied by a sinusoidal balanced three phase 415 V source with source inductance of 16.56e-3 H and a source resistance of 0.89Ω. ZSI is used because of its inherent advantages. The inverter consists of Insulated Gate Bipolar Transistors (IGBT) Bridge. The compensating voltages from the reference signal block are fed to the gate of the IGBTs. The output voltage from the inverter is fed to the power system by means of three single phase injection transformers with a turn ratio of 1:1.

Two different non linear load types were simulated:

• Non-linear load -1(Diode bridge)

• Non-linear load -2(Induction motor drive)

*CASE 1A: NON-LINEAR LOAD-1 WITHOUT FILTER*

In this case, the non-linear load consists of a three-phase diode bridge with resistance.

Fig.5. The source voltage waveforms for non-linear load-1

Fig.6. Reference and PWM signal for diode bridge rectifier(non-linear load1)

Fig.7. The source voltage THD is 4.00

Fig.8. The load voltage THD is 7.58

Fig.9. The load current THD is 8.09

But the THD caused by ideal diode bridge rectifier is 31.06.

The control strategy is included to compensate, the source voltage THD falls to 4.00, the load voltage THD falls to 7.58 and the load current THD falls to 8.09.

*CASE 1B: NON-LINEAR LOAD-1 WITH FILTER*

Fig. Simulink diagram of nonlinear load without filter

In this case, the non-linear load consists of a three-phase diode bridge with resistance 100e-3Ω. A tuned LC filter is introduced to smoothen the waveform.

Fig.10. The source voltage waveform for non-linear load-1 with LC filter

Fig.11. The source voltage THD is 1.43

Fig.12. The load voltage THD is 4.46

Fig.13. The load current THD is5.08

When the control strategy is included along with a tuned LC filter to compensate, the source voltage THD falls to 1.43, the load voltage THD falls to4.46 and the load current THD falls to 5.08.The waveform is further smoothened sinusoidal waveform.

*CASE 2A: NON-LINEAR LOAD-2 WITHOUT FILTER*

* *

In this case, the non-linear load consists of a three-phase diode bridge and with resistance 100e -3 Ω and an induction motor drive.

Fig.14. The source voltage waveformsfor non linear load-2

Fig.15. The reference and PWM signal for non linear load-2

Fig.16. The source voltage THD is 5.67

Fig.17. The load voltage THD is 5.91

Fig.18. The load current THD is 6.27

But the THD caused by ideal diode bridge rectifier is 36.08.

When the control strategy is included to compensate, the source voltage THD falls to 5.67, the load voltage THD falls to 5.91 and the load current THD falls to 6.27.

*CASE 2B: NON-LINEAR LOAD-1 WITH FILTER*

In this case, the non-linear load consists of a three-phase diode bridge with resistance 100 e-3 Ω and an induction motor drive. A tuned LC filter with L= 25H and C=250milliF is introduced to smoothen the waveform.

Fig. 19.The source voltage and load voltage waveform for non-linear load-2 with LC filter

Fig.20. The source voltage THD is 4.78

Fig.21. The load voltage THD is 5.18

Fig.22. The load current THD is 5.93

When the control strategy is included along with a tuned LC filter to compensate, the source voltage THD falls to 4.78, the load voltage THD falls to 5.18 and the load current THD falls to 5.93. The waveform is further smoothened.

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## V. CONCLUSION

This paper has discussed standard control algorithm dual p-q theory in a series power compensator. This control strategy along with ZSI has reduced the harmonics within the IEEE standards (5%) for various non-linear loads. This paper also presents the results with the inclusion of a LC filter which further reduces the THD values for various non-linear loads and thereby reducing the distortions greatly.

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