Control of a Three Phase Inverter Mimicking Synchronous Machine with Fault Ridethrough

Transcription

1 2017 Ninth Annual IEEE Green Technologies Conference Control of a Three Phase Inverter Mimicking Synchronous Machine with Fault Ridethrough Capability Vikram Roy Chowdhury, Subhajyoti Mukherjee, Pourya Shamsi, Mehdi Ferdowsi Missouri University of Science and Technology Electrical and Computer Engineering, Department Rolla, MO. Abstract Due to high penetration of renewable energy systems in the distribution grid, it has become an extreme challenge to maintain synchronous stability of the grid. During asymmetrical faults the major challenge is to limit the inverter current and keep it within limits so that the inverter relay does not trip. Such a control methodology ensures seamless power to the consumers without damaging the inverter. In this paper a second order generalized integrator based inverter control operating like a virtual synchronous machine is proposed. The calculations for the inverter control states are performed on a per phase basis and the control algorithm is developed. The dynamic equations describing the proposed control algorithm with its analyses is presented in this paper. Numerical simulations based on MATLAB/Simulink are performed to verify the efficacy of the proposed control technique on a three phase grid connected inverter. Keywords- Virtual inertia; three phase inverter; second order generalized integrator (); active power; reactive power; phase locked loop (PLL); line to ground (LG) fault; point of common coupling (PCC); I. INTRODUCTION With a focus on reducing emissions, power production via renewable energy resources gained immense importance in recent years [1-3]. However, higher penetration of renewable resources make it immensely difficult to maintain the synchronous stability of the grid. Efficient control technique has been proposed to deal with this problem by researchers in many literatures. It is termed as virtual inertia based control [3-4] of grid connected inverters where an inverter is controlled to mimic an alternator with significant amount of inertia to cater for the stability problem. Such a control methodology takes care of the absence of any inertia for renewable energy system within the control architecture of the inverter in a virtual sense. The advantage of such a control technique lies in the fact that as the inertia is virtual so it can be adjusted as per the requirements of the system. During normal operating conditions, the virtual inertia based control of inverters stabilizes the system frequency and also provides a methodology to connect the inverter to the grid without a dedicated synchronization unit or PLL [5-6]. This feature of the inverter control along with inertia emulation makes the system more stable [7-9] and proper setting of the inertia makes it possible to optimally utilize the dedicated control unit. This feature enables to connect more renewables to the distribution system and still maintain the synchronous stability of the grid. It is also possible that few of the several inverters connected to a grid can be controlled in virtual inertia mode and the rest can be controlled in traditional current control [10-12] mode. So overall such a control technique gives flexibility to choose which inverter(s) should be controlled for stability improvement. It is well known that distribution grids are prone to unbalanced faults. It becomes a challenge to keep the inverter currents within limit during such faults. In this paper a distribution grid is considered and the most commonly occurring fault, i.e., line to ground (LG) fault is considered. A per phase control technique based on second order generalized integrator () [13] is proposed to control the inverter and keep the currents within safe operating limits. A three phase four wire system is considered for the analysis purpose. The rest of the paper is organized as follows. Section II presents the overall control architecture of virtual inertia emulation by an inverter. Section III presents the basics of structure and its application to calculate the active and reactive powers in this paper. Section IV presents a closed loop control architecture to keep the currents within limits. Section V presents simulation results based on MATLAB/Simulink for the system verification. Section VI presents the conclusion and scopes for future work for the proposed control technique. II. V dc VIRTUAL INERTIA BASED CONTROL OF A THREE PHASE INVERTER v pa vpb Figure 1 : Three phase grid connected inverter with a first order filter A three phase grid connected inverter with a first order filter is presented in figure 1. The governing equations for controlling the inverter in virtual inertia mode of operation is presented in this section. The philosophy of control of the inverter like a synchronous machine lies in the fact that the swing equation of the machine has to be implemented in the control architecture of the inverter. The details of the equations are presented in this section. power of a virtual inertia based three phase inverter are presented by equations (1) and (2), respectively. ( )= = v pc r 1a r 1b r 1c + L 1a L 1b L 1c (1) (2) v a v b v c /17 $ IEEE DOI /GreenTech

2 Equation (1) presents the well-known swing equation for a synchronous machine where J is the virtual inertia and B is the friction coefficient of the machine. Therefore the active power is controlled via equation (1) for the three phase grid connected inverter thereby emulating a virtual synchronous machine. Equation (2) presents the reactive power transferred from the inverter to the grid. The grid voltage is not under the control of the user, the inverter voltage is. As a result of which the inverter voltage is controlled to change the reactive power that is transferred to the grid. Normally the current at the grid is kept at minimum and the reactive power pushed by the inverter is nearly zero apart from the losses in the PCC inductor that consumes a little reactive power. Such a control methodology ensures that the inverter voltage magnitude is controlled to achieve reactive power control whereas the active power control is achieved via controlling the inverter phase angle like a synchronous machine. The simplified block diagram of the control architecture is presented in Figure 2. P* δ + - 1/(Js+B) 1/s structure is presented by equations (3) and (4) respectively for the in phase and quadrature components. () = (3) () () = (4) () The Bode plots of the transfer functions of (3) and (4) are presented in figure (3) respectively. Pout PWM Modulator To Inverter Q* + - Kp+Ki/s + + Vinverter Q Vgrid Figure 2. Simplified block diagram for the control architecture Figure 2 presents the control architecture utilized to control the inverter mimicking a synchronous machine. Such control architecture takes care of the system inertia mathematically by making the inverter response towards frequency change sluggish like a synchronous machine. Next the focus is turned on to compute active and reactive powers from current and voltages on a per phase basis utilizing a architecture. III. AND ITS APPLICATION TO CALCULATE ACTIVE AND REACTIVE POWER Second order generalized integrator () is a structure which becomes highly useful while applying d-q transformation for a single phase system. For a single phase system it is not possible to apply Park s transformation to calculate the equivalent d-q components. For this reason two bandpass filter structures are utilized to generate two signature waveforms in a pseudo two phase stationary frame. These two waveforms can then be utilized to calculate the active and reactive power for the three phase inverter system on a per phase basis. Utilizing those values for active and reactive powers the inverter voltage reference can be generated to control the inverter. During normal operating conditions, such a control architecture may not be useful. However during abnormal operating condition like an L-G fault this control architecture can be utilized to control the inverter on a per phase basis and keep the grid currents balanced. This hinders any faulty tripping of the inverter overcurrent relay and seamless power supply to the grid/local load is ensured. Transfer function of the Figure 3. Bode Plot of the structure Bode plot of Figure 3 shows that the gain of the α axis controller increases from -40 db to 0 till 60 Hz whereas the β axis controller gain remains nearly constant at a small negative value with change in the oscillation frequency till 60 Hz. This indicates that the generation of α axis component will have higher settling time compared to the waveform of β axis. This is clarified by the simulation result presented in Figure 5. Figure 4 presents the single phase sinusoidal waveform or the grid voltage from which the component waves are to be generated. Figure 4. Grid Voltage of phase a for the three phase system 2

3 components making the computed powers to be oscillatory. Thereby the currents at the PCC becomes oscillatory and have high overshoots. This will in effect trip the protective relay of the inverter and power transfer to the grid/local load is hampered. The next section presents a case study where an L-G fault in phase a is considered. The methodology to generate the active power reference in that case for the faulted phase is discussed. Figure 5. Output voltage signal obtained from the structure It is observed from Figure 5 that with such a transfer function structure it is possible to generate two sinusoidal signals in quadrature as shown. Also from the Bode plot of Figure 3 it is observed that the settling time of the α axis controller is higher compared to the β axis controller. This is also evident from the simulation result presented in Figure 5. So the output of the can be considered as an equivalent two phase system on which d-q transformation can be easily applied. The details of the design of the can be obtained in [10]. This structure is utilized in this paper over a three phase inverter and the voltage of each phase is reconstructed into its α-β components. Similar component reduction is also carried out on currents. Utilizing this structure the active and reactive power supplied by the inverter is calculated on a per phase basis. The simplified block diagram is presented in Figure 6; V a V b V c I a I b I c V aα V aβ V bα V bβ V cα V cβ I aα I aβ I bα I bβ I cα I cβ x x x + + 3/2 P a x - + 3/2 Q a Figure 6. Calculation of active and reactive power on a per phase basis Figure 6 shows the calculation of active and reactive power on a per phase basis. For simplicity only the power calculation of phase a is presented. Similar calculations are carried out for the other phases and the active and reactive powers are computed. The power on a per phase basis is utilized to control each leg of the inverter separately. During normal balanced conditions, such calculations are not required. But during faulted conditions (LG fault in this case), the voltage of the faulted phase suffers a sag. This makes the system to become unbalanced. In that case if the power calculations are carried out on a three phase basis there will be negative sequence and zero sequence IV. CLOSED LOOP CONTROL FOR ACTIVE POWER REFERENCE GENERATION FOR THE FAULTY PHASE In this section the active power reference generation for the faulted phase is discussed. Generally grid connected inverters are operated to supply active power at minimum current at the PCC, i.e., at unity power factor (UPF). In this case UPF operation is considered and a closed loop control design to generate active power producing current is only considered. The major concern during a fault is the voltage sag of that phase which thereby creates an unbalanced current flow having huge overshoots. This section presents a closed loop control methodology to generate the active power reference for the faulty phase based on the currents of the healthy phases. The simplified block diagram of the control architecture is presented in Figure 7. I b I a * Average + I c - Figure 7. Active power reference generation for faulted phase The average of the healthy phase currents are taken over the magnitude of the healthy phase currents obtained from the components of the structure utilized. This is presented by equations 5 and 6 for phases b and c respectively. = = + + I a PI P a * The block diagram of Figure 7 shows the methodology utilized for reference generation of the faulted phase (phase a in this case). The healthy phases supply same amount of active power whereas the unhealthy phase active power is reduced so that the currents at the PCC remain balanced. This methodology generates unbalanced modulating signals for the inverter and thereby operates the inverter for balanced grid currents. The proposed technique is verified via numerical simulations based on MATLAB/Simulink to check the efficacy of the proposed technique. V. SIMULATION RESULTS The proposed system is modeled in MATLAB/Simulink. The most commonly occurring fault for distribution grid is considered in this case, i.e., LG fault in phase a. To simulate the fault, the voltage of the phase is reduced by 30% of its nominal value. The other two phases were kept at their nominal values. Comparative results with power calculation on a three (5) (6) 3

4 phase basis and with the proposed control technique is presented in this section. The parameters utilized for simulation is presented in table 1. Table I SIMULATION PARAMETERS Parameters Values J B 0.5 Switching Frequency 5 khz The results for the grid currents with power calculation on a three phase basis and with the proposed control technique is presented respectively in Figures 8 and 9. Figure 10. Active Power reference and actual for the healthy phases(s) with three phase based power calculation Figure 8. Grid currents for faulted condition with three phase based power calculation Figure 11. Active power reference and actual for the healthy phase From Figure 10, it is observed that due to unbalance in grid voltage the power calculation on a three phase basis incorporates negative sequence components in the power and oscillations are more in the computed power. However with the proposed control technique with power computation on a per phase basis it is possible to keep the power oscillations minimum as presented in Figure 11. Similar results are observed for the reactive power as shown in Figures 12 and 13 respectively with three phase based power calculation and with the proposed control technique. Figure 9. Grid current for faulted condition with proposed control technique From Figures 8 and 9, it is observed that when the power calculations are carried out on a three phase basis with unbalanced grid conditions, the peak current is higher whereas with the proposed control architecture balanced current can be supplied to the grid even during unbalanced grid voltage conditions. The results for the active power for the healthy phase(s) with calculation on a three phase basis and with the proposed control technique is presented in Figures 10 and 11, respectively. Figure 12. Reactive Power reference and actual with three phase based power calculation 4

5 Figure 13. Reactive Power reference and actual with the proposed control technique From Figures 12 and 13, it is again observed that the oscillations in the reactive power with the proposed control technique is lower compared to the three phase based power calculations. The result for the active power reference and actual generated by the controller architecture of Figure 7 for the faulted phase is presented in Figure 14. Figure 16. Current of the PCC with the proposed control technique From the results it is observed that with the proposed control technique it is possible to control the three phase inverter and keep the currents within limits even during unbalanced grid voltage conditions. Also the results for reactive power indicating the transient change in active power of the healthy phase is presented in Figure?15. Figure 14. Active power reference and actual for the faulted phase The transient response for active power is observed from Figure 14 for the faulted phase when the power reference of the healthy phase is changed. The transient response for the active power of the healthy phase and the PCC current is presented respectively in Figures 15 and 16. Figure 17. Reactive Power of the healthy phase Figure 17 shows the transient response in reactive power when the active power reference is changed for the healthy phase. The proposed control technique shows successful control of the three phase inverter even during unbalanced grid conditions. VI. CONCLUSION AND SCOPES FOR FUTURE WORK The control technique proposed in this paper enables to operate the inverter even during faulty conditions. The proposed control technique not only keeps the grid currents within the limits but also reduce the oscillations in the active and reactive powers. Also, by such a control technique it is possible to cater for the non-idealities on a per phase basis for the inverter. Figure 15 Active Power reference and actual for the healthy phase REFERENCES [1] J. Morren, S. de Haan, and J. Ferreira, Contribution of DG units to primary frequency control, in Future Power Systems, 2005 International Conference on, Nov. 2005, pp [2] H. P. Beck and R. Hesse, Virtual synchronous machine, in Electrical Power Quality and Utilisation, EPQU th International Conference on, Oct. 2007, pp [3] K. Visscher and S. De Haan, Virtual synchronous machines for frequency stabilisation in future grids with a significant share of 5

6 decentralized generation, in SmartGrids for Distribution, IET- CIRED. CIRED Seminar, Jun. 2008, pp. 1 4 [4] J. Driesen and K. Visscher, Virtual synchronous generators, in Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE, Jul. 2008, pp [5] Saeed Golestan, Mohammad Monfared, Francisco D. Freijedo, Josep M. Guerrero, Second Order Generalized Integrator Based Reference Current Generation Method for Single-Phase Shunt Active Power Filters Under Adverse Grid Conditions. 4th Power Electronics, Drive Systems & Technologies Conference (PEDSTC2013), Feb 13-14, 2013, Tehran, Iran. [6] Prabha Kundur et al, Definition and Classification of Power System Stability, IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, IEEE Transactions On Power Systems, Digital Object Identifier /TPWRS m, IEEE [7] Johan Morren, Sjoerd W.H. de Haan and J.A. Ferreira, "Contribution of DG Units to Primary Frequency Control", Future Power Systems 2005, Amsterdam, November [8] J. Ekanayake, N. Jenkins, Comparison of the Response of Doubly Fed and Fixed-Speed Induction Generator Wind Turbines to Changes in Network Frequency, IEEE Trans. Energy Conversion, Vol. 19, No. 4, pp , [9] G. Lalor, J. Ritchie, S. Rourke, D. Flynn, M.J. O Malley, Dynamic Frequency Control with Increasing Wind Generation, in. Proc IEEE PES General Meeting, Denver, Co., 6 10 June [10] J. Ekanayake, L. Holdsworth, N. Jenkins, Control of DFIG wind turbines, Power Engineering Journal, Vol. 17, No. 1, pp , Feb