Evaluation of Power Quality Parameters of Microgeneration Systems Sérgio Lopes, Instituto Superior Técnico, UTL. Abstract - The growing interest and use of microgenerators has brought some attention to the evaluation of their impact on Power Quality, namely to the Total Harmonic Distortion (THD) on the current and on the grid voltage, as well as on the Power Factor and Displacement Factor. Also, the use of microgenerators to mitigate some Power Quality problems, acting as Active Power Filters (APF), is becoming more attractive. This paper presents and evaluates two possible solutions for microgenerators grid connection: through a first order or through a third order filter. For each one of these solutions, linear and nonlinear controllers are designed for the current injected into the low voltage grid. The proposed solutions are simulated in Matlab/Simulink and the obtained results are compared to those obtained for the existing equipment and to the maximum values admissible by international standards. A microgeneration solution with a third order filter in the connection to the low voltage grid and guaranteeing simultaneous reactive power compensation (Active Power Filter) is proposed. Keywords - Microgeneration, Power Quality, Inductive Filter, LCL Filter, Harmonic Distortion, Power Factor. I. INTRODUCTION Usually, microgenerators (µG) have voltage source inverters (VSI) for grid connection. However, due to the high switching frequency of the VSI, it is necessary to use an adequate filter to connect the inverter to the electrical grid, guaranteeing the compliance with international standards. The wide use microgenerators will have an impact on Power Quality (PQ), particularly in the voltage and current total harmonic distortion (THD). The aim of this work is to evaluate the solution - filter topology + controller which introduces less impact on PQ. To meet that goal, two different filters are sized: L filter and LCL filter, and two types of controllers are designed: a) nonlinear control by sliding mode, b) linear Proportional Integral (PI) control and polynomial control. Then it is created a more complete model that allows the compensation of power factor. With this model is intended to inject in the grid the maximum active power consumed by nonlinear loads. With these guidelines, is built a model of a µG which is subsequently included in a model of small test grid. Thus it is possible to analyze the PQ in operating conditions closer to reality. PQ parameters that are compared for the different solutions are: total harmonic distortion of voltage; total harmonic distortion of current; Power Factor. The results are evaluated and compared. II. POWER QUALITY PARAMETERS (PQ) In an electrical system has the power supplied has quality when is guaranteed the proper functioning of electrical equipment without significant changes in performance. The three-phase voltage in Portugal is characterized by three sinusoidal voltages, lagged of 120°, with effective value and frequency defined by the norm NP50160 [1]. When there are significant changes from these features there is a consequent degradation of PQ. In the last decades has been a high growth in the use of electronic equipment, connected to the grid trough power electronic converters, regularly rectifiers with diodes. These devices, while allowing more efficient use of electricity, have a nonlinear behavior, causing distortions in the waveforms of the current, and consequently in the tension, contributing significantly to the decline in quality of power supplied. A. Total Harmonic Distortion - THD Harmonics are voltages or currents with multiple frequencies of the fundamental component (50 Hz). Considering the values of the most significant harmonics, can be calculated one indicator of PQ, the total harmonic distortion (THD) (1). (1) 1 The increase of the THD is reflected in the increase of Joule losses, losses by skin effect, the proximity effect and the increase in neutral currents[1]. the semiconductors command variable γ can take three values, depending on the value of the error: (5) B. Power Factor The harmonics of grid currents and the resulting harmonics of grid voltage produced by nonlinear loads increase losses, usually leading to oversized transformers and equipment connected to the grid. The power factor is defined as the ratio between the Active Power (power delivered to loads) and Apparent Power (installed power) [2] [3]: Considering continuous conduction, the inverter’s output voltage is directly dependent on the semiconductor conduction intervals, so the transfer function of the modulator+inverter association can be write as (6) [3] (2) Fig.2 shows the grid voltage and current when it is used a sliding mode strategy to control the current (6) And can be writhed as a function of the total harmonic distortion: Grid Voltage [V/10] Injected Current [A] 40 30 (3) 20 10 0 III. CONVENTIONAL G -10 The connection of the G to the grid is made through a single-phase inverter and a filter that provides attenuation of high frequency current harmonics the electrical network. In this chapter is introduced the model of the single phase voltage inverter and is dimensioned two types of filter: one of first order (L) and a third order (LCL) filter. For both types of filtering used are sized for sliding mode controllers and linear controllers. -20 -30 -40 0 0.005 0.01 0.015 0.02 time [s] 0.025 0.035 0.04 Fig. 2. Experimental result obtained using sliding mode The current injected into the network can also be controlled using a PI controller (Fig.3): A. G with Inductive Filter RL One approach to control the output filter current is using the sliding mode control (Fig. 1), since it is a robust and easy to implement controller. 0.03 i0ref Linv i0 Amp i + + C(s) Modulator + Inverter - VPWM VR Req i RL i0ref i + e + - Linv Fig. 3. Equivalent diagram of the inverter connected to the network through an inductive filter with PI control. i0 Amp + + Modulator +Inverter VPWM VR i Fig. 1. Equivalent diagram of the inverter connected to the network through an inductive filter with sliding mode control. Considering the effect of non-ideal disturbance introduced by the network voltage, the transfer function of current injected into the grid by the inverter is given by (7): (7) The error of current is given by the difference between the reference current and the inverter output current: (4) Is necessary to design the compensator that guarantees the tracking of reference current. Since it is intended to have a null static error the compensator must have integral action (I). However, if the compensator has only 2 integral action the system becomes sluggish. For this reason is introduced proportional action (P) that enables a faster system response. (8) The transfer function in closed loop of current controller is given by: To control the current to inject into the network, is studied the sliding mode control, control with PI compensator and polynomial control. To dimension the current controller for sliding mode it is assumed that the voltage of the capacitor is approximately equal to the grid voltage. Under these conditions, the design of the controller for sliding mode is identical to that performed for the inductive filter. L1 R1 L2 i1 R2 Amp (9) iref i + Modulator + Inverter + + + - C V12 VPWM VR RC i Grid Voltage [V/10] Injected Current [A] 40 Fig. 6. Equivalent diagram of the inverter connected to the network through an LCL filter with sliding mode control. 30 Fig.7 shows the grid voltage and current when it is used a sliding mode strategy to control the current and a LCL filter 20 10 0 40 -10 30 -20 20 -30 10 -40 Grid Voltage [V/10] Injected Current [A] 0 0 0.005 0.01 0.015 0.02 time [s] 0.025 0.03 0.035 0.04 -10 Fig. 4. Experimental result obtained using a PI control strategy. -20 -30 B. G with LCL filter -40 To obtain a greater attenuation of high frequency harmonics is necessary to consider a higher order filter. In this work was considered an LCL filter that allows a reduction of the THD at lower switching frequencies, which is a big advantage for higher power applications [4]. However, the use of a higher order filter requires the design of a current controller more complex and more susceptible to disruption and distortion in the waveform of the grid. L1 VPWM R1 0.005 0.01 0.015 0.02 time [s] L2 R2 RC 0.03 0.035 0.04 In a second approach is considered to make the current control with a PI compensator. Again, it is considered that the voltage on the capacitor is approximately equal to the network voltage and in this case is controlled the inverter’s output current. The block diagram and layout of the filter are shown in Fig. 8. i2 iC C 0.025 Fig. 7. Experimental result obtained using sliding mode whit a LCL filter. L1 i1 V12 0 R1 L2 i1 R2 Amp iref VR i + C(s) + Modulator + Inverter - C V12 VPWM VR Req RC Req i Fig. 8. Equivalent diagram of the inverter connected to the network through Fig. 5. Schematic of the G filter connected to the grid. an LCL filter with PI control. For the LCL filter, the transfer function is: (10) Assuming that the capacitor’s voltage is approximately equal to the grid voltage, the transfer function is given (11) where is the inverter output current, is the inverter output voltage. (11) 3 (14) is given by (12): (12) Similar to the approach used for the inverter with inductive filter, in this case is also used a PI compensator (8). The transfer function in closed loop of current controller is given by (15): The experimental results obtained using this control strategy is shown in Fig.9. (15) Fig. 11 shows the grid voltage and current obtained with a µG with LCL filter when polynomial control is used. Grid Voltage [V/10] Injected Current [A] 40 30 20 10 0 -10 Fig. 9. Experimental result obtained using PI and a LCL filter. -20 -30 To obtain a compensator a better dynamic response and power factors closer to unity should be considered the dynamics of the 3rd order LCL filter. L1 R1 L2 -40 0 0.005 0.01 0.015 0.02 time [s] 0.025 0.03 0.035 0.04 Fig. 11. Experimental result obtained using polynomial control and a LCL filter. i2 R2 Amp iref i + C(s) + Modulator + Inverter - C V12 VPWM VR Req RC The Power Quality Parameters obtain when these Microgenators are connected to a ideal network are listed in Table I. i TABLE I Fig. 10. Equivalent diagram of the inverter connected to the network through an LCL filter with polynomial control. According to (10), the transfer function of the filter has one zero and three poles e , one real and two complex conjugate (13) . (13) To compensate the effect introduced by the LCL filter, it is assumed that the compensator is polynomial , with three zeros ( e ) to cancel the three filter’s poles and a pole coincident with the filter’s zero. To ensure a null static error in response to the step is considered a pole at the origin. To avoid increasing the excess of zeros/poles of the system, it is introduced a third pole in the compensator with a frequency high enough to not interfere in the dynamics of the system (14). POWER QUALITY PARAMETERS WHEN Gs ARE CONNECTED TO IDEAL GRID Filter L L LCL LCL LCL Controller Slindig Mode PI Sliding Mode PI Polynomial Power Factor 2,97 2,51 0,91 0,45 0,56 0,999 0,999 0,998 0,984 0,998 IV. COMPENSATED µG In the last years the proliferation of power equipment with non-linear load increase the disturbances in PQ, thus is required a more efficient way to mitigate those effects [5]. The Active Power Filter (APF) consists in connecting a capacitor to the VSI in order to reduce the THD and simultaneously compensate the power factor, being a much better solution than conventional approaches. The APF adjusts 4 the amplitude of the inverter’s output voltage o by pulse width modulation or by the control of DC link, and thus cancel the harmonics created by nonlinear loads [6] [7]. L1 CFAP ipv Inverter R1 i1 L2 C V12 VPWM iµG R2 (19) irede icarga VR RC Non-linear Load Fig. 12. Schematic of the G with APF filter. To verify the proposed model are simulated three different cases. In the first case the microgenerator with a LCL filter is connected to the grid with a parallel nonlinear load without the APF. Then is introduced the APF in the model. And in the last case is used an inductive filter instead of the LCL filter. The gird voltage and current of each case is shown in Figs. 15, 16 and 17. And the corresponding THD obtained is listed in Table II. Considering the polynomial current control the controlled system can be represented as a current source. Grid Voltage [V/10] Grid Current [A] 40 30 (16) 20 10 Considering the current source, the simplified model can be represented as: 0 -10 ic VCFAP ipv -20 CFAP -30 i (s) -40 1.9 1.91 1.92 1.93 1.94 1.95 1.96 time [s] 1.97 1.98 1.99 2 Fig. 15. Grid voltage and current, with non-linear load and conventional microgenerator. Fig. 13. Block diagram of the overall system, whereas the current source represents the current control system. Grid Voltage [V/10] Grid Current [A] 40 The capacitor voltage is given by: 30 (17) 20 10 It is used a PI compensator defined as: to control , that can be 0 -10 (18) The block diagram of capacitor voltage in Fig. 14. is represented v + - K Kp i s iref Gi i sTdv 1 i -30 -40 1.9 ipv vcref -20 + - 1 sC vc 1.91 1.92 1.93 1.94 1.95 1.96 time [s] 1.97 1.98 1.99 2 Fig. 16. Grid voltage and current, with non-linear load and compensated microgenerator with LCL filter. v Fig. 14. Voltage controller of the capacitor voltage. The response of the voltage disturbance introduced by the panel is given by: 5 Grid Voltage Grid Current 40 As Table III shows when the number of microgenerators increase, the THD is much higher in cases which the inverter has an inductive filter when compared with the inverters that have a LCL filter. Considering only G with LCL filter it appears that when a PI controller is used the delay of the current’s first harmonic in relation to the supply voltage is much larger than the other cases, and consequently the power factor is never less than 0.984. Nevertheless this value of power factor still conforms to the values defined by the standard [8]. 30 20 10 0 -10 -20 -30 -40 1.9 1.91 1.92 1.93 1.94 1.95 1.96 time [s] 1.97 1.98 1.99 Fig. 17. Grid voltage and current, with non-linear load and compensated microgenerator with L filter. TABLE II THD OF THE GIRD CURRENT WITH CONVENTIONAL AND COMPENSATED MICROGENERATOR Filter LCL L LCL Without APF With APF 20,48 5.34 1,96 Fig.11 and Fig. 12 show that with a use of a compensated microgenerator the grid current is sinusoidal in contrast to what the case without the APF as shown in Fig. 10. The Table II shows that the compensated microgenerator with LCL filter gives a grater attenuation of THD. V. EXPERIMENTAL RESULTS To study the variation of the PQ parameters with the increasing number of the µG in a network is considered the models created in Chapter III and then is created a small low voltage grid with a generator, a Power transformer, a power line and a linear load. TABLE III COMPARATION OF THE 5 CASES STUDIED Filter Controller µG per phase L Slindig Mode 1 5 L PI LCL Sliding Mode LCL PI LCL Polynomial 1 5 1 5 1 5 1 5 Pwer Factor 2,89 5,28 2,61 2,60 0,95 1,23 0,94 0,94 0,98 0,52 1,14 3,48 1,55 1,02 0,05 0,22 0,08 0,12 0,08 0,09 VI. CONCLUSION 2 0,999 0,999 0,999 0,999 0,998 0,998 0,984 0,981 0,998 0,998 This paper aimed to examine some of the indicators of PQ that result from the introduction of Microgeneration in the Low voltage network and suggest strategies to mitigate their effects on quality of the electrical energy, namely in the total harmonic distortion of voltage and current, as well as power factor. The microgenerator connection to the grid is done through a filter, and is analyzed two different topologies for its implementation: first-order filter (inductive) and third order LCL filter. To control the current to inject into the network two types of controllers are designed: nonlinear controllers (sliding mode), and linear controllers – PI and polynomial. For each case the results obtained for the total harmonic distortion of current and power factor to verify the parameters given by manufacturers and do not exceed the maximum values defined by the standards. By making the simulation of a microgenerator connected to a nonlinear load proves the advantage of using the APF filter in a low-voltage network. It allows to greatly reduction of the current THD introduced by nonlinear loads. Comparing the use of an LCL filter with an inductive filter it verifies that the reduction in THD is even more pronounced for the higherorder filter. All the proposed solutions were used in a small test network. The results showed that, in general, for a network with several microgenerators, the third-order filter allows to obtain lower rates of harmonic distortion of current and voltage. And with the increased number of G with LCL filter there is no degradation of power quality parameters studied unlike what happens with inductive filter. REFERENCES [1] [2] [3] Manual da Qualidade da Energia Eléctrica” EDP in collaboration with the ISR, Electrical Engineering Department of Coimbra University, 2005. Grady,W. M.; Gilleskie, R. J., “Harmonics and How They Relate to Power Factor”, Proc of the EPRI Power Quality Issues and Oportunities Conference (PQA’93), San Diego, USA, November 1993. Silva, J. F. A., “Sistemas de Energia em Telecomunicações: Texto de Apoio”, Instituto Superior Técnico, Lisbon, 2008. 6 [4] [5] [6] [7] [8] Shen, G; Xu, D.; Cao, L.; Zhu, X., “An Improved Control Strategy for Grid-Connected Voltage Source Inverters With an LCL Filter”, IEEE Trans. Power Electronics, vol. 23, no.4, pp.1899-1906, 2008. Jalili, K.; Bernet, S., “Design of LCL Filters of Active-Front-End TwoLevel Voltage-Source Converters”. IEEE Trans. Industrial Electronics, vol. 56, no.5, pp. 1674-1689, 2009. Özdemir, E.; Kale, M.; Özdemir, Ş., “Active Power Filter for Power Compensation Under Non-Ideal Mains Voltages”, Proc. 11th Mediterranean Conference on Control and Automation, Rhodes, Greece, June 2003. Morán, L. A.; Dixon, J. W.; Espinoza, J. R.; Wallace, R. R., “USING ACTIVE POWER FILTERS TO IMPROVE POWER QUALITY”, 5º COBEP, Foz do Iguaçu, Brasil, 1999. European Standard EN50438, “Requirements for the Connection of Micro-generators in Parallel with Public Low-Voltage Distribution Networks”, 2007. 7