A Lyapunov-Function Based Controller for 3-Phase Shunt Active Power Filter and Performance Assessment Considering Different System Scenarios


3-Phase Shunt Active Power Filter (SAPF) belongs to the class of custom power devices (CPDs) and offers compensation to harmonics originated owing to customer side nonlinear loads, reactive power and unbalance in the distribution power networks functioning in current control mode (CCM). The performance of a SAPF as a harmonic compensator entirely relies on the control technique i.e. the precise detection of the harmonic current components of load that are necessary to be compensated.


Power Filter In the present work, a 3-phase SAPF, inspired by a Lyapunov function based control approach, has been designed for compensation of harmonics resulted in the feeder current owing to the customer side nonlinearity. A control law is determined in the proposed strategy which makes the derivative of the Lyapunov function consistently a negative one for an entire set of stable states. The DC-link capacitor voltage is regulated at constant reference through the proportional-integral (PI) controller. In this method rating of the shunt active power filter is considerably reduced than the other two broadly employed conventional methods.


Furthermore, the harmonic compensation efficacy of the proposed Lyapunov function based SAPF is compared with the one based on other two conventional approaches under four different system scenarios namely a simple nonlinear load with and without utility side voltage distortion, a modified IEEE 13 bus test distribution system loaded with a 3-phase chopper fed direct current (DC) motor drive at a single bus and last especially for increasing the harmonic-constrained penetration level of renewable energy. Results obtained through simulation performed in MATLAB/Simulink shows that total harmonic distortion (THD) of source current and dynamic, as well as steady-state performance with Lyapunov function based controller, is significantly improved than the other two conventional methods. Also, the robust compensation performance of the SAPF empowers it to deal with the high penetration of renewable energy.


  1. SAPF
  2. Lyapunov function
  3. Harmonic compensation
  4.  Hysteresis controller
  5. Renewable energy



Figure 1. Configuration Of Sapf.


Figure 2. Waveforms Of Lyapunov Function Based Control Technique (A-B) Before And (C-E) After Compensation.

Figure 3. Fft Analysis A) Before Compensation, B) After Compensation.

Figure 4. Dynamic Performance Of Sapf Using P-Q Theory With An Unbalanced Or Distorted Source Voltage.

Figure 4. (Continued.) Dynamic Performance Of Sapf Using P-Q Theory With An Unbalanced Or Distorted Source Voltage.

Figure 5. Dynamic Performance Of Sapf Using Srf Theory With An Unbalanced Or Distorted Source Voltage.

Figure 5. (Continued.) Dynamic Performance Of Sapf Using Srf Theory With An Unbalanced Or Distorted Source Voltage.


A control algorithm, based on the Lyapunov function, is proposed for SAPF to mitigate harmonics and reactive power compensation of nonlinear loads. The performance of SAPF has been found satisfactory under all four cases of the study.


The control algorithm is established on the Lyapunov function for achieving global stability in the system. The simulation results validate the control approach for SAPF. A hysteresis controller has been used to generate a switching signal for the voltage source inverter. Based on simulation results following conclusions have been drawn.

1) All the control algorithm’s (p-q theory, SRF theory, Lyapunov function based control theory) performance found satisfactory i.e. THD is less than 5% according to IEEE 519 standards.

2) Under the fully fundamental plus balanced source voltage and purely nonlinear loading condition Lyapunov function-based control algorithm gives the best performance over the other two control algorithms which are commonly used.

3) The THD of the source current under the Lyapunov function based control algorithm is 1.61% in phase a, 2.33% in phase b, 1.99% in phase c when applied on a two-bus system under purely nonlinear load. In the case of a modified 13-bus system, the same with Lyapunov function based control algorithm is 1.59% in phase a, 1.61% in phase b, 1.52% in phase c.

4) In case of distortion and unbalance present in the utility’s voltage, the detection of the reference current is accurately performed by the Lyapunov function-based control algorithm and superiorly in contract to the other two control algorithms.

5) It is also inferred that the dynamic response of the system with the Lyapunov function-based control algorithm to be better than the other two control algorithms.

6) Last but not the least, the harmonic and reactive power compensation offered by Lyapunov function-based SAPF is better also in the case of renewable energy’s penetration. The proposed theory-based SAPF has the potential of enhancing the penetration level of HC-HC of the modern and polluted DPS up to more extent.


[1] X. Zong, P. A. Gray, and P. W. Lehn, “New metric recommended for IEEE standard 1547 to limit harmonics injected into distorted grids,” IEEE Trans. Power Del., vol. 31, no. 3, pp. 963_972, Jun. 2016.

[2] O. F. Kececioglu, H. Acikgoz, C. Yildiz, A. Gani, and M. Sekkeli, “Power quality improvement using hybrid passive _lter con_guration for wind energy systems,” J. Electr. Eng. Technol., vol. 12, no. 1, pp. 207_216, Jan. 2017.

[3] G. K. Singh, “Power system harmonics research: A survey,” Eur. Trans. Electr. Power, vol. 19, no. 2, pp. 151_172, Mar. 2009.

[4] S. S. Reddy and P. R. Bijwe, “Real time economic dispatch considering renewable energy resources,” Renew. Energy, vol. 83, pp. 1215_1226, Nov. 2015.

[5] IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems, IEEE Std 519-2014 (Revision IEEE Std 519- 1992), Nov. 2014, pp. 1_29.

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