A Model Based LCL-Type Grid Connected Converter Under Balanced and Unbalanced Faults in a Micro-Grid Distributed Generation

: This research was conducted to verify the significance of the LCL-filter on the grid current and the impact of variable fault resistance values on the reactive power genereated in a grid-tied inverter. The stability of LCL-type grid connected inverter with capacitor current feedback in active damping state was evaluated in this paper. The effects of balanced and unbalanced grid faults on the active and reactive power was studied through simulation at different fault resistance values of 0.00025Ω and 2.5Ω. The FFT waveforms showed that THD values of 48.56% and 38.45% were achieved for the grid voltage at 0.00025Ω and 2.5Ω fault resistance while THD values of 9.50% and 4.41% were obtained for the grid current at a varied current feedback coefficient (K CP ) of 4.75 and 14.75. Simulation results also showed that a very negligible real and reactive power was gained with a zero grid voltage within the fault zone at 0.00025Ω fault resistance. At a 2.5Ω fault resistance, a voltage sag was produced which accounted for the transient response in the real power generated and reactive power absorbed during the fault period. The result obtained from the root-locus plot showed that the loci for the derived LCL-filter current transfer function intersected at +j 8.734 and -j 8.734 which makes the system marginally stable All simulation procedures were realized in MATLAB/SIMULINK 2015.


Introduction
Micro grid is a small unit of power network which consists of multiple Distributed Generation sources, energy storage devices, and group of loads, that can be operated in either ongrid (grid connected) or off-grid (islanded) mode of operation [1].Maintaining energy balance is essential in either mode of micro grid operation so as to get a better regulation of voltage and frequency level in the network.Any mismatch between the generation and load demand causes deviation in the voltage and frequency level which creates a negative impact on the quality of energy supply, hence affecting the performance of sensitive loads connected in the network.In on-grid mode, regulation of voltage and frequency level can be supported by the utility grid.However, in off-grid mode, all the DG sources are responsible for ensuring power balance and also regulation of voltage and frequency level in the network through active coordinated power management and power sharing control strategies [2][3].Due to the low environmental impact, less maintenance, and high reliability, Solar PV is considered as one of the main Renewable Energy (RE) sources for Micro grid applications.But owing to the intermittent nature of PV power, battery storage can be used to balance the PV power variation and maintain the power balance in PV based Micro grid network [4].A micro-grid usually operates in parallel with the main grid.It is capable of both generating its own electric power with small-scale distributed generation (micro-sources) and also exporting power to the main utility grid [5].Micro grids offer an improved reliability through the islanding process.Islanding implies that the micro grid continues to operate autonomously when disconnected from the grid [6].After islanding, the micro-grid can continue to serve its loads without disruption.Power inverters are usually applied in islanded or stand-alone mode.The control scheme for the micro-source inverter is based on a phase-locked loop (PLL) for frequency and phase detection.The initial step in the control algorithm for the PLL is to transform phase voltages and currents into stationary reference frame (α and β) quantities.The α and β voltage components are applied in the phase locked loop to estimate the frequency and establish the phase reference for the inverter pulse width generator.The PWM generator takes the desired voltage magnitude and phase to create the PWM output signals as shown in Figure 1.This paper focused on the evaluative assessment of an LCLtype grid connected converter under balanced and unbalanced faults in a micro-grid distributed generation.The LCL filter was modeled under a varying capacitor current feedback coefficient while a stability test on the current transfer function was carried out.Simulation was also carried out on the grid tied converter at different fault resistance values of 0.00025Ω and 2.5Ω to assess its effects on the real and reactive power.The FFT waveforms showed that THD values of 48.56% and 38.45% were obtained for the grid voltage at 0.00025Ω and 2.5Ω fault resistance while THD values of 9.50% and 4.41% were gotten for the grid current at current feedback coefficient K CP of 4.75 and 14.75.
The paper is organized as follows: Section 1 Introduction, section 2 literature review of related work, section 3. Methods: modeling of LCL type grid connected converter with capacitor current feedback.Section 4: results and discussion.Section 5: conclusion.

Literature Review
Grid-tied converters have been increasingly deployed to distributed power generation systems as an efficient and flexible interface in the power system operation.To attenuate the switching frequency harmonics, a passive filter is inserted between the converter and the grid.When compared with an Lfilter, an LCL-filter is extensively adopted in grid-tied inverters since it can provide a better harmonic attenuation with reduced inductance [7].Amongst the various available configurations, LCL filter is best suited for the application of grid integration of renewable energy sources.The modeling and control of grid connected inverter with LCL filter has been detailed in the Damping methods and optimal performance of LCL-filters [8][9].The drawback of the LCL filter is the inherent resonance produced which can be overcome through active and passive damping methods [10].An overview assessment of the active damping method for suppressing LCL-filter resonance is presented in a systematic design of active damping using passive elements [11][12].A comparative study between active and passive damping control techniques with different existing topologies have been presented in a research on LCL filter with active damping strategy using active power filter [13][14][15].
However, the resonance effects of the LCL-filter may result in stability difficulty.To keep high performance and obtain strong robustness against grid impedance variation, Pan et al proposed an optimized controller design for gridtied inverters with a specified gain for capacitor current feedback active damping [16].Liu et al adopted a single-loop current control with a hybrid damper for a single phase grid tied inverter particularly with higher order background harmonic voltage at the point of common coupling and when the grid impedance varied [17].Said-Romdhane proposed a systematic design procedure for the capacitor current feedback active damping of voltage-oriented PI control to ensure a stable operation under severe grid inductance variations [18].Adlib et al developed a reduced-order model for grid-tied inverters using the balanced truncation technique while preserving the overall system stability for grid impedance variations [19].
The stability analysis of three-phase grid tied inverter with an L-filter under unbalanced grid impedance can be addressed by the harmonic suppression technique [20].Though the model derivation is complicated when extended to the LCL-filtered grid-tied inverter.A modeling method for a three-phase grid tied inverter with L-filter under unbalanced grid impedance has been presented in three phase grid-connected converters with decoupled transfer functions [21].The stability is analyzed based on the Eigen values of open-loop transfer function using the general Nyquist criterion though it was not easy to apply the proposed modeling to the LCL-filter based grid-tied inverter.Jin et al proved that the unbalanced load would introduce adverse effect on the system stability when the impedance is not matched [22].
This paper therefore presents an analysis of a three-phase grid-tied inverter with LCL-filter under a balanced and unbalanced load based on variable fault resistance and its impact on the real and reactive power.The system stability was succinctly analyzed using the current transfer function and root-locus plots.The result obtained from the root-locus plot showed that the loci for the derived LCL-filter current transfer function intersected at +j 8.734 and −j 8.734 which makes the system marginally stable.

Modeling of LCL-Type Grid Connected Converter with Capacitor Current Feedback
The circuit topology and control block diagram of three phase LCL-type grid connected converter is presented in Figure 1.The LCL filter consists of the converter side inductor L 1 , the filter capacitor C F and the grid side inductor L 2 , the dc-bus voltage U dc and the point of common coupling (PCC) voltage U PC which is used for the synchronous reference voltage of phase locked loop (PLL).I * 2dq is the reference of actual grid current I 2 where I 2 is controlled based on PI-controller in dq frame.In this paper, an ideal grid voltage U g which is in series with the grid impedance is used to emulate the weak grid while the capacitor-current feedback (CCF) active damping is used to suppress the LCL resonance peak.The net impedance and current transfer function of the LCL-grid filter is derived from Figure 2 and presented in equations ( 1) to (4).
Faults in a Micro-Grid Distributed Generation Where: Z = SL , Z 2 = R d + 1 / SC F and Z = SL .Substituting these expressions of Z , Z , Z into equation (1) gives rise to the net impedance expression presented in equation (2).
Based on Figure 2, the voltage across Z net is given by equation (3) while the current transfer function is obtained from equation (4).
Introducing a capacitor current feedback coefficient and converter control delay gives rise to the complete control block diagram presented in Figure 3.The control delay can be expressed as 3 45 %6& and presented in equation ( 5).
3 45 %6& = 78.9:6;< 8.9:6; < (5) where T S is the Sampling time (S) and F S is the Sampling frequency.G *% & K B C .represents the PIcontroller and K CP is the capacitor current feedback coefficient.Further simplification of the closed loop control block diagram of LCL-type grid connected converter in Figure 3 gives rise to the current transfer function equation given in equation (6).

Power Calculation Block
The grid connected inverter generally outputs three phase voltage (Vabc) and current (Iabc) which is in stationary (abc) coordinate form and can be transformed into rotating directquadrature (d-q) system by means of Park transformation.The d-q components of voltage and current are considered as input signals for power calculation block where the active (P) and reactive (Q) power are directly calculated based on the power equations ( 7) and ( 8).
Where V d , i d are the d-axis voltage and current components; V q , i q are the q-axis voltage and current components.In general, the voltage balance equation in d-q frame can be expressed as shown in equation (9).
Where U d , U q are the inverter output voltage reference signals; V d , V q are the inverter output voltage components; i d , i q are the inverter output current components; R and L are the resistance and inductance between inverter and AC network; ω is the network angular frequency (rad/sec).
Total Harmonic Distortion (THD) Analysis: In this paper, current and voltage THD were analysed under fault conditions and variable capacitor current feedback coefficient.This total harmonic distortion is mathematically calculated by the following expression presented in equation (10).
THD = total harmonic distortion, V n = the root mean square value of the nth harmonic component.V 0 = root mean square of the fundamental component which can either be current or voltage.

Results and Discussions
Simulation results were achieved using the parameters presented in Table 1.In Figure 4, the root locus plot of the LCL-filter for the current transfer function gave rise to jω S `j8.784.This implies that the LCL-filter for the grid connected converter based on the above chosen parameters is marginally stable.
In Figure 5 (a), the three phase three level inverter output voltage is presented with a phase displacement of 120 0 and amplitude of 480V.In Figure 5 (b), Grid real and reactive power under pre-fault state is presented.A pronounced transient oscillation was observed at a simulation period of 0-0.2Sec.At steady state, the real power maintained a constant value of 0.015 ( 10 9 kW (15 ( 10 c ) within the simulation period of 0.2-0.5Sec.Similarly, the reactive power value under steady state simulation period of 0.2 to 0.5Sec., settled at 1.5 ( 10 9 kVAR which implies that more reactive was absorbed by the grid under this condition.In Figure 6 (a) the plot of real and reactive power on a balanced three phase to ground fault at a fault resistance value of Ron = 0.00025Ω was presented.It is observed that the initial transient oscillation was obtained between 0 to 0.15 Sec.simulation time.When the fault occurred at 0.15 to 0.3 Sec. the real and reactive power values were entirely grounded to zero.Above 0.3 Sec.post-fault condition, the transient oscillation reemerged and gradually damped to a steady state at 0.435 Sec. while still maintaining 15 ( 10 c kW and 1.5 ( 10 9 kVAR.
In Figure 6 (b), at an increased fault resistance, it was observed that the value of the real and reactive power was not entirely grounded to zero during the fault period.A transient response was observed which is indicative of a fault current remnant on the grid for an increased resistance value of Ron = 2.5Ω.On fault clearance, the transient oscillation gradually decreased until a steady state was attained at 0.425 Sec. with real and reactive power regaining its original value of 15 ( 10 c kW and 1.5 ( 10 9 kVAR. In Figure 7 (a), for an unbalanced fault condition with double line to ground fault (2LG) and a fault resistance of Ron = 0.00025Ω, a close observation showed that the reactive power generated more transient and stiff oscillation within the fault period of 0.15 to 0.3 Sec.The severity of fault on the grid is more pronounced at this stage with the value of the reactive power oscillating between 1.25 ( 10 c and 1.25 ( 10 9 kVAR.Similarly, the real power oscillated between 0.75 ( 10 9 and 0 .75 ( 10 9 kW which is far above the values obtained in Figure 6 (a).On fault removal, the transient oscillation decreased and attained a steady state after 0.475 Sec.
In Figure 7 (b), at an increased fault resistance of Ron = 2.5Ω for a double line to ground fault, it was observed that the transient response of the real power increased within the fault zone with a corresponding decrease in the transient response of the reactive power.This oscillatory transient in real and reactive power reduced gradually at post-fault condition and attained a steady state after 0.425 Sec. with real and reactive power values of 15 ( 10 c kW and 1.5 ( 10 9 kVAR. In Figure 8 (a), the plot of real and reactive power for single line to ground fault for Ron = 0.00025Ω was obtained.It was observed that during the fault period, more reactive power oscillation was produced with a consequential decrease in the magnitude of the real power as compared to Figure 7 (a).This implies that less severity was obtained under this condition.
In Figure 8 (b), it was observed that the level of oscillation was reduced as the fault resistance was increased to Ron = 2.5Ω, a sustained oscillatory transient was maintained throughout the fault period for the real power while a high damping in the reactive power amplitude was achieved during the fault period for Ron = 2.5Ω.
The spectral (FFT) displays for the percentage (%) total harmonic distortion (THD) at different fault resistance values for grid voltage and varying capacitor current feedback coefficient on grid current are presented in Figures 9-13.In Figure 9, it was shown that under a pre-fault or ideal condition, perfect sinusoidal voltage waveform was obtained with a fundamental base value of 13.68 kV and a %THD value of 1.16%.
In Figure 10 a distorted waveform was obtained when a fault occurred at 0.15 to 0.3 sec.the grid voltage was grounded to zero for a fault resistance value of Ron = 0.00025Ω.This accounted for a high rise in the %THD value of 48.56% with a corresponding decrease in the fundamental base value to 9.401kV as against 13.68kV obtained in Figure 9..In Figure 11, when the fault resistance was increased to Ron = 2.5Ω, a voltage sag was observed within the fault zone.This gave rise to a slight increase in the fundamental base value of 10.39 kV as against 9.401 kV obtained in Figure 10.The % THD value also decreased slightly to 38.45% due to the decrease in the voltage magnitude which is in accordance with equation (10).
In Figure 12, the FFT display for the grid current at capacitor current feedback coefficient of K CP = 4.75 was presented.It was observed that due to the capacitor effect, a slight oscillation was obtained between 0 to 0.025 Sec.before steady state.The grid current fundamental base value was 363.3A with %THD value of 9.50%.
In Figure 13, at an increased capacitor current feedback coefficient K CP = 14.75, it was observed that the magnitude of the grid current harmonics appreciably reduced as shown in the %THD value of 4.41% with a slight increase in the fundamental base value of 385.7.Based on this difference in values obtained in Figures 12 and 13, it is obvious that an increased capacitor feedback coefficient (K CP ) affects the rate of grid current harmonics.Therefore the need for a proper choice of K CP .

Conclusion
In this study, a typical LCL-type grid connected inverter with capacitor current feedback in active damping state was evaluated.The effects of balanced and unbalanced grid faults on the active and reactive power was studied through simulation while varying the fault resistance values of 0.00025Ω and 2.5Ω.Based on the results obtained, variation in real and reactive power level was observed around 15 ( 10 c kW and −1.5 ( 10 9 kVAR under balanced condition.However, during the second stage of varying fault resistance and unbalanced fault, pronounced oscillations were observed in reactive power which oscillated from 1.25 ( 10 9 to 1.25 ( 10 9 kVAR and real power from 0.75 ( 10 9 to 0.75 ( 10 9 kW as compared to the values obtained under a balanced condition.Also, a small variation in THD values for the grid voltage (1.16%, 48.56% and 38.45%) and current (9.5% and 4.41%) were obtained under balanced and unbalanced fault condition and at a varying current feedback coefficient (4.75 and 14.75).The research findings have shown that at an increased fault resistance value and capacitor current coefficient a reduced harmonic distortion was obtained across the LCL-type grid connected converter which proffers an efficient performance of a microgrid distributed generation.

Figure 1 .
Figure 1. Circuit topology and control block diagram of LCL-type grid connected converter.

Figure 3 .
Figure 3.Control block diagram of LCL-type grid connected converter with capacitor current feedback.

Figure 9 .
Figure 9. FFT Display of Grid Voltage during Pre-fault condition.

Figure 10 .
Figure 10.FFT Display of Grid Voltage during at a Fault resistance of Ron = 0.00025Ω.

Figure 11 .
Figure 11.FFT Display of Grid Voltage during at a Fault resistance of Ron = 2.5Ω.

Figure 12 .
Figure 12.FFT Display of Grid Current at Capacitor Current Feedback Coefficient of KCP = 4.75.

Figure 13 .
Figure 13.FFT Display of Grid Current at Capacitor Current Feedback Coefficient of KCP = 14.75.