# HIL-Assessed Fast and Accurate Single-Phase Power Calculation Algorithm for Voltage Source Inverters Supplying to High Total Demand Distortion Nonlinear Loads

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Improving the velocity of the transient response of the averaged power calculation.
- Improving the steady-state accuracy of the averaged power calculation.

## 2. Droop-Based Local Control Techniques against Nonlinear Loads

## 3. Description of the System under Test: VSI Supplying to a Nonlinear Load

_{o}(t) and the current i

_{o}(t) are measured at the PCC when the switches S

_{0}and S

_{1}are open. The averaged active and reactive power, P and Q, are respectively calculated in the “P–Q Power Calculation” block from these measurements. Then a voltage reference v

_{ref}(t) is generated. Later, the inner control loops based on [45] employ this reference and finally generate a pulse-width modulation (PWM) for the switching of the H-Bridge.

_{NL}) consists of an unbalanced diode-bridge rectifier (DBR) that supplies power to a resistive–capacitive (R–C) load, shown in Figure 2. The R–C load parameters are listed in Table 1 and are characterized accordingly to power quality parameters listed in Table 2, based on IEEE std 519-2014 [44]:

_{on}, triggering an abrupt change in the value of P and Q.

_{o}and I

_{o}are the voltage and current amplitudes, respectively; ${\omega}_{o}$ is the fundamental frequency of the system (100π rad/s); ${\phi}_{o}$ is the phase-shift between the fundamental components of the voltage and the current; h is the harmonic index; I

_{h}is the amplitude of the harmonic components of the intensity; and the phase-shift ${\phi}_{h}$ corresponds to each current harmonic component. The term ${I}_{DC}$ corresponds to a DC offset present in the load current.

_{NL}:

## 4. P–Q Calculation Algorithms

## 5. Proposed P–Q Calculation Algorithm

_{1}and h

_{2}coefficients. Those coefficients $\left({h}_{1},{h}_{2}\right)\complement \left[0.05,0.5\right]$ are employed for the attenuation of subharmonics reducing the SOGI1 and SOGI2 LPF cutoff frequencies. Next, Figure 7 shows their magnitude and phase plots. For the sake of simplicity, ${h}_{1}={h}_{2}={h}_{i}$:

_{1}and h

_{2}will lead to a substantial reduction of these components. The next section includes simulations to study the values of ${\xi}_{P}$, ${\xi}_{i}$, h

_{1}, and h

_{2}for a more accurate and faster calculation of the P–Q parameters.

## 6. Simulation Results

_{1}. A similar steady-state ripple for the active power calculation is set as a reference for the analysis. The parameters of the simulations are listed in Table 3.

_{av}plots varying, $0.1\le {\xi}_{i}\le 0.7075$, while keeping constant ${h}_{1}=0.25$ and ${\xi}_{p}=0.7075$. It can be seen that, when increasing the damping factor, the transient response is faster. However, there is an undesired overshoot when ${\xi}_{i}$> 0.2. Therefore, the fastest configuration avoiding the overshoot is the one with ${\xi}_{i}$= 0.2.

_{avM}and a family of P

_{av}calculations, varying ${h}_{1}$from 0.1 to 0.30 and ${\xi}_{i}$= 0.2. It can be observed how the rapidity of the proposed calculation is reduced when h

_{1}is increased. For ${h}_{1}=\left[0.1,0.15\right]$ the Pav transient results slower concerning PavM, and the steady-state ripple results smoother. When ${h}_{1}\ge 0.2$, the velocity of the transient increases, as well the ripple in steady-state. Only for ${h}_{1}=0.25$, it results in being faster, without introducing a remarkable overshoot. At higher values of ${h}_{1}$, it presents an undesired ripple in steady-state and an overshoot that is better to avoid.

_{av}with ${\xi}_{i}$ = 0.2. and ${h}_{1}=0.25$. Figure 9b is the detail of the steady-state ripple, where it can be seen that the fastest algorithm, Pav, shows a similar ripple to the other algorithms. In these conditions, the calculation of Pav results faster than PavM. Therefore, these parameters were chosen for the study of the employed for this last simulation.

_{2}= 0.1, ${\xi}_{p}$ = 0.7075 and with ${\xi}_{i}$ = 0.2. Figure 11 shows the calculation of Qav, QavM, QavT, and QavC when the abrupt load change occurs.

_{1}, keeping ${\xi}_{p}$ = 0.7075. Moreover, when increasing the SOGI1-LPF capability, it maintains a better or similar settling-time while reducing the steady-state ripple. Thus, when Pav reaches a similar settling-time of that of PavM by reducing the h

_{1}parameter, the THD falls from 1.32% to 0.59% (Figure 10). The commented results are shown in Table 4:

_{avM}and 40 ms for P

_{av}. Then, when ${h}_{1}=0.15$, the THD falls drastically down to 0.59% while keeping an 18% shorter settling-time. However, in this last case, the time-delay is higher in 20% for the Pav calculation concerning PavM. For this final reason, the chosen set of parameters for comparing Pav against PavM is are ${\xi}_{i}=0.2,{\xi}_{p}=0.7075,{h}_{1}=0.25$.

## 7. Hardware in the Loop Assessment

_{1}to 0.15 for Pav, to assess the simulation tests achieved in this sense. Figure 13 shows the active power responses during an abrupt load change.

## 8. Experimental Results

## 9. Conclusions

- Active Power: Reduction in 47.78% of the steady-state calculated THD with respect to DC in the simulations for Pav, when the settling-time is similar (Table 4).
- Reactive Power: Reduction in 68.66% of the steady-state calculated THD with respect to DC in the simulations for Qav, when the settling-time is similar (Table 5).

## Author Contributions

## Funding

## Conflicts of Interest

## References

- U.S. Department of Energy. The Smart Grid: An Introduction; DOE: Washington, DC, USA, 2003. [Google Scholar]
- European Commission; Directorate-General for Research. European Technology Platform SmartGrids: Vision and Strategy for Europe’s Electricity Networks of the Future; Office for Official Publications of the European Communities: Luxembourg, 2006. [Google Scholar]
- Sustainable Development Goal 7 (SDG). Available online: https://sustainabledevelopment.un.org/sdg7 (accessed on 4 September 2020).
- Kumar, N.M.; Chopra, S.S.; Chand, A.A.; Elavarasan, R.M.; Shafiullah, G. Hybrid Renewable Energy Microgrid for a Residential Community: A Techno-Economic and Environmental Perspective in the Context of the SDG7. Sustainability
**2020**, 12, 3944. [Google Scholar] [CrossRef] - Manoj Kumar, N.; Ghosh, A.; Chopra, S.S. Power Resilience Enhancement of a Residential Electricity User Using Photovoltaics and a Battery Energy Storage System under Uncertainty Conditions. Energies
**2020**, 13, 4193. [Google Scholar] [CrossRef] - Kumar, S.A.; Subathra, M.S.P.; Kumar, N.M.; Malvoni, M.; Sairamya, N.J.; George, S.T.; Suviseshamuthu, E.S.; Chopra, S.S. A Novel Islanding Detection Technique for a Resilient Photovoltaic-Based Distributed Power Generation System Using a Tunable-Q Wavelet Transform and an Artificial Neural Network. Energies
**2020**, 13, 4238. [Google Scholar] [CrossRef] - Ton, D.T.; Smith, M.A. The U.S. Department of Energy’s Microgrid Initiative. Electr J.
**2012**, 25, 84–94. [Google Scholar] [CrossRef] - Lasseter, R.H. Microgrids. In Proceedings of the 2002 IEEE Power Engineering Society Winter Meeting, New York, NY, USA, 27–31 January 2002; pp. 305–308. [Google Scholar]
- Ali, A.; Li, W.; Hussain, R.; He, X.; Williams, B.W.; Memon, A.H. Overview of Current Microgrid Policies, Incentives and Barriers in the European Union, United States and China. Sustainability
**2017**, 9, 1146. [Google Scholar] [CrossRef] [Green Version] - IEEE Power and Energy Society. IEEE Power and Energy Society. IEEE Standard for the Specification of Microgrid Controllers. In IEEE Std 2030.7; IEEE: Piscataway, NJ, USA, 2017; pp. 1–43. [Google Scholar]
- Cigré. Microgrids 1 Engineering, Economics, & Experience; WG C6.22; Cigré: Paris, France, 2015; ISBN 9782858733385. [Google Scholar]
- Carpintero-Rentería, M.; Santos-Martín, D.; Guerrero, J.M. Microgrids Literature Review through a Layers Structure. Energies
**2019**, 12, 4381. [Google Scholar] [CrossRef] [Green Version] - De Oliveira Costa Souza Rosa, C.; Costa, K.A.; Christo, E.D.S.; Bertahone, P.B. Complementarity of Hydro, Photovoltaic, and Wind Power in Rio de Janeiro State. Sustainability
**2017**, 9, 1130. [Google Scholar] [CrossRef] [Green Version] - Kanase-Patil, A.B.; Saini, R.; Sharma, M. Integrated renewable energy systems for off grid rural electrification of remote area. Renew. Energy
**2010**, 35, 1342–1349. [Google Scholar] [CrossRef] - Shan, Y.; Hu, J.; Liu, M.; Zhu, J.; Guerrero, J.M. Model Predictive Voltage and Power Control of Islanded PV-Battery Microgrids With Washout-Filter-Based Power Sharing Strategy. IEEE Trans. Power Electron.
**2020**, 35, 1227–1238. [Google Scholar] [CrossRef] - Angelopoulos, A.; Ktena, A.; Manasis, C.; Voliotis, S. Impact of a Periodic Power Source on a RES Microgrid. Energies
**2019**, 12, 1900. [Google Scholar] [CrossRef] [Green Version] - Rocabert, J.; Luna, A.; Blaabjerg, F.; Rodriguez, P. Control of Power Converters in AC Microgrids. IEEE Trans. Power Electron.
**2012**, 27, 4734–4749. [Google Scholar] [CrossRef] - Guerrero, J.M.; Vasquez, J.C.; Matas, J.; De Vicuna, L.G.; Castilla, M. Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization. IEEE Trans. Ind. Electron.
**2011**, 58, 158–172. [Google Scholar] [CrossRef] - De Brabandere, K.; Vanthournout, K.; Driesen, J.; Deconinck, G.; Belmans, R. Control of microgrids. In Proceedings of the 2007 IEEE Power Engineering Society General Meeting, Tampa, FL, USA, 24–28 June 2007; pp. 1–7. [Google Scholar]
- Aghaee, F.; Dehkordi, N.M.; Bayati, N.; Hajizadeh, A.; Dehkordi, M. Distributed Control Methods and Impact of Communication Failure in AC Microgrids: A Comparative Review. Electronics
**2019**, 8, 1265. [Google Scholar] [CrossRef] [Green Version] - Zhang, L.; Chen, K.; Chi, S.; Lyu, L.; Cai, G. The Hierarchical Control Algorithm for DC Microgrid Based on the Improved Droop Control of Fuzzy Logic. Energies
**2019**, 12, 2995. [Google Scholar] [CrossRef] [Green Version] - Ranjbaran, A.; Ebadian, M. A power sharing scheme for voltage unbalance and harmonics compensation in an islanded microgrid. Electr. Power Syst. Res.
**2018**, 155, 153–163. [Google Scholar] [CrossRef] - Tavakoli, A.; Sanjari, M.J.; Kohansal, M.; Gharehpetian, G.B. An innovative power calculation method to improve power sharing in VSI based micro grid. In Proceedings of the Iranian Conference on Smart Grids, Tehran, Iran, 24–25 May 2012; pp. 3–7. [Google Scholar]
- Golestan, S.; Joorabian, M.; Rastegar, H.; Roshan, A.; Guerrero, J.M. Droop based control of parallel-connected single-phase inverters in D-Q rotating frame. In Proceedings of the 2009 IEEE International Conference on Industrial Technology, Gippsland, Australia, 10–13 February 2009; pp. 1–6. [Google Scholar]
- Arbab-Zavar, B.; Palacios-Garcia, E.J.; Vasquez, J.C.; Guerrero, J.M. Smart Inverters for Microgrid Applications: A Review. Energies
**2019**, 12, 840. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; Qing, H.; Huang, P.; Zhang, C. Modeling and Stability Analysis of Parallel Inverters in Island Microgrid. Electronics
**2020**, 9, 463. [Google Scholar] [CrossRef] [Green Version] - Kim, J.-H.; Lee, Y.-S.; Kim, H.-J.; Han, B.-M. A New Reactive-Power Sharing Scheme for Two Inverter-Based Distributed Generations with Unequal Line Impedances in Islanded Microgrids. Energies
**2017**, 10, 1800. [Google Scholar] [CrossRef] [Green Version] - Toub, M.; Bijaieh, M.M.; Weaver, W.W.; Robinett, R.D.; Maaroufi, M.; Aniba, G. Droop Control in DQ Coordinates for Fixed Frequency Inverter-Based AC Microgrids. Electronics
**2019**, 8, 1168. [Google Scholar] [CrossRef] [Green Version] - Ren, B.; Sun, X.; Chen, S.; Liu, H. A Compensation Control Scheme of Voltage Unbalance Using a Combined Three-Phase Inverter in an Islanded Microgrid. Energies
**2018**, 11, 2486. [Google Scholar] [CrossRef] [Green Version] - Ma, J.; Wang, X.; Liu, J.; Gao, H. An Improved Droop Control Method for Voltage-Source Inverter Parallel Systems Considering Line Impedance Differences. Energies
**2019**, 12, 1158. [Google Scholar] [CrossRef] [Green Version] - Yang, N.; Paire, D.; Gao, F.; Miraoui, A.; Liu, W. Compensation of droop control using common load condition in DC microgrids to improve voltage regulation and load sharing. Int. J. Electr. Power Energy Syst.
**2015**, 64, 752–760. [Google Scholar] [CrossRef] - Guerrero, J.; Matas, J.; Vicuna, L.G.; Castilla, M.; Miret, J. Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance. IEEE Trans. Ind. Electron.
**2007**, 54, 994–1004. [Google Scholar] [CrossRef] - Yao, W.; Chen, M.; Matas, J.; Guerrero, J.M.; Qian, Z. Design and Analysis of the Droop Control Method for Parallel Inverters Considering the Impact of the Complex Impedance on the Power Sharing. IEEE Trans. Ind. Electron.
**2011**, 58, 576–588. [Google Scholar] [CrossRef] - El Mariachet, J.; Matas, J.; de la Hoz, J.; Al-Turki, Y.; Abdalgader, H. Power Calculation Algorithm for Single-Phase Droop-Operated Inverters Considering Nonlinear Loads. Renew. Energy Power Qual. J.
**2018**, 1, 710–715. [Google Scholar] [CrossRef] - El Mariachet, J.; Matas, J.; Martin, H.; Li, M.; Guan, Y.; Guerrero, J.M. A Power Calculation Algorithm for Single-Phase Droop-Operated-Inverters Considering Linear and Nonlinear Loads HIL-Assessed. Electronics
**2019**, 8, 1366. [Google Scholar] [CrossRef] [Green Version] - Wang, H.; Yue, X.; Pei, X.; Kang, Y. A new method of power calculation based on parallel inverters. In Proceedings of the IEEE EPE-PEMC, Novi Sad, Serbia, 28–30 October 2009; pp. 1573–1576. [Google Scholar]
- Yu, W.; Xu, D.; Ma, K.A. Novel Accurate Active and Reactive Power Calculation Method for Paralleled UPS System. In Proceedings of the APEC, Singapore, 15–16 November 2009; pp. 1269–1275. [Google Scholar]
- Akagi, H.; Watanabe, E.; Aredes, M. Instantaneous Power Theory and Application to Power Conditioning; Wiley-IEEE Press: Piscataway, NJ, USA, 2007; pp. 5–28. [Google Scholar]
- Gao, M.; Yang, S.; Jin, C.; Ren, Z.; Chen, M.; Qian, Z. Analysis and experimental validation for power calculation based on p-q theory in single-phase wireless-parallel inverters. In Proceedings of the 2011 Twenty-Sixth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Fort Worth, TX, USA, 6–11 March 2011; pp. 620–624. [Google Scholar]
- Matas, J.; Castilla, M.; De Vicuna, L.G.; Miret, J.; Vasquez, J.C. Virtual Impedance Loop for Droop-Controlled Single-Phase Parallel Inverters Using a Second-Order General-Integrator Scheme. IEEE Trans. Power Electron.
**2010**, 25, 2993–3002. [Google Scholar] [CrossRef] - Tolani, S.; Sensarma, P. An improved droop controller for parallel operation of single-phase inverters using R-C output impedance. In Proceedings of the 2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Bengaluru, India, 16–19 December 2012; pp. 1–6. [Google Scholar]
- Cardoso, T.D.; Azevedo, G.M.S.; Cavalcanti, M.C.; Neves, F.A.S.; Limongi, L.R. Implementation of droop control with enhanced power calculator for power sharing on a single-phase microgrid. In Proceedings of the 2017 Brazilian Power Electronics Conference (COBEP), Juiz de Fora, Brazil, 19–22 November 2017; pp. 1–6. [Google Scholar]
- Yang, Y.; Blaabjerg, F. A new power calculation method for single-phase grid-connected systems. In Proceedings of the 2013 IEEE International Symposium on Industrial Electronics, Taipei, Taiwan, 28–31 May 2013; pp. 1–6. [Google Scholar]
- IEEE Power and Energy Society. IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems. In IEEE Std. 519-2014 (Revision of IEEE Std. 519-1992); IEEE: Piscataway, NJ, USA, 2014; pp. 1–29. [Google Scholar]
- Guan, Y.; Guerrero, J.M.; Zhao, X.; Vasquez, J.C.; Guo, X. A New Way of Controlling Parallel-Connected Inverters by Using Synchronous-Reference-Frame Virtual Impedance Loop—Part I: Control Principle. IEEE Trans. Power Electron.
**2015**, 31, 4576–4593. [Google Scholar] [CrossRef] [Green Version] - Kullarkar, V.T.; Chandrakar, V.K. Power Quality Analysis in Power System with Non Linear Load. Int. J. Electr. Eng.
**2017**, 10, 33–45. [Google Scholar] - Stošović, M.A.; Stevanović, D.; Dimitrijević, M. Classification of nonlinear loads based on artificial neural networks. In Proceedings of the 2017 IEEE 30th International Conference on Microelectronics (MIEL), Nis, Serbia, 9–11 October 2017; pp. 221–224. [Google Scholar]
- Salam, S.M.; Uddin, M.J.; Hannan, S. A new approach to develop a template based load model that can dynamically adopt different types of non-linear loads. In Proceedings of the 2017 International Conference on Electrical, Computer and Communication Engineering (ECCE), Cox’s Bazar, Bangladesh, 16–18 February 2017; pp. 708–712. [Google Scholar]
- Kneschke, T.A. Distortion and power factor of nonlinear loads. In Proceedings of the 1999 ASME/IEEE Joint Railroad Conference (Cat. No.99CH36340), Dallas, TX, USA, 15 April 1999; pp. 47–54. [Google Scholar]
- Shabbir, H.; Rehman, M.U.; Rehman, S.A.; Sheikh, S.K.; Zaffar, N. Assessment of harmonic pollution by LED lamps in power systems. In Proceedings of the 2014 Clemson University Power Systems Conference, Clemson, SC, USA, 11–14 March 2014; pp. 1–7. [Google Scholar]
- Normanyo, E. Mitigation of Harmonics in a Three-Phase, Four-Wire Distribution System using a System of Shunt Passive Filters. Int. J. Eng. Tech.
**2012**, 2, 761–774. [Google Scholar] - Shahl, S.I. Simulation and Analysis Effects of Nonlinear Loads in the Distribution Systems. Int. J. Sci. Eng. Res.
**2019**, 10, 888–892. [Google Scholar] - Micallef, A.; Apap, M.; Cyril, S.S.; Guerrero, J.M.; Vasquez, J.C. Reactive Power Sharing and Voltage Harmonic Distortion Compensation of Droop Controlled Single Phase Islanded Microgrids. IEEE Trans. Smart Grid
**2014**, 5, 1149–1158. [Google Scholar] [CrossRef]

**Figure 1.**Simplified scheme of a single-phase voltage source inverter (VSI) (Inv. #1) sharing a nonlinear load with a second inverter (Inv. #2), showing the Reference Generator Block that contains the active and reactive averaged powers (P–Q) calculation and the voltage reference generator for the pulse-width modulation (PWM) and control (CTRL) block (PWM + CTRL).

**Figure 2.**Nonlinear load Z

_{NL}, consisting of an unbalanced diode-bridge rectifier that supplies to an R–C load, based on Reference [35].

**Figure 3.**Scheme of a VSI with the existing approaches and the load’s distorted current: (

**a**) block scheme of a single-phase VSI, showing the inner control loops of current and voltage, fed with the voltage reference generated by utilizing the Voltage Reference Generator block, based on References [45,53]; (

**b**) nonlinear current harmonic distribution for Z

_{NL}without filtering, after S

_{0}is turned on.

**Figure 4.**Structure of second-order generalized integrator (SOGI) and bode diagrams with various damping factors: (

**a**) structure of a SOGI with its damping factor, $\xi $, and center frequency, $\omega $, where $V$

_{in}is the input signal, V

_{d}the direct output signal, filtered by a band-pass filter (BPF); V

_{q}the in-quadrature output signal, filtered by a low-pass filter (LPF). (

**b**) Magnitude and phase Bode plots for BPF in (13), varying ξ from 0.1 to 0.9. (

**c**) The magnitude and phase Bode plots for LPF in (14) varying ξ from 0.1 to 0.9.

**Figure 6.**Proposed P–Q calculation algorithm scheme: (

**a**) proposed algorithm scheme consisting of pre-filtering of the current, with only a SOGI, and a SOGI-LPF stage for each of the instantaneous powers calculated; (

**b**) frequency-domain analytical representation for the proposed algorithm.

**Figure 7.**Magnitude and phase bode plots for the LPF capability of SOGI1 and SOGI2, through the variation of h

_{i}.

**Figure 8.**A family of Pav plots after varying its control parameters: (

**a**) plot of the proposed calculation of active power, varying the damping factor of SOGI0 and keeping constant h

_{1}= 0.25 and the damping factors of SOGI1 and SOGI2 at ${\xi}_{p}=0.7075$; (

**b**) Pav varying ${h}_{1}$ from 0.1 to 0.30 with ${\xi}_{i}$ = 0.2 and ${\xi}_{p}$ = 0.7075, PavM in blue dot line, and Pav during the transient step load; (

**c**) steady-state ripple for each calculated Pav, compared with PavM (blue dot line).

**Figure 9.**Active power transient after abrupt load change at t = 5 s, and its detail in steady-state: Pav (red), PavM (blue), PavT (magenta), and PavC (green). (

**a**) Transient after the load step. (

**b**) Steady-state ripple of the calculated active powers.

**Figure 10.**THD with respect DC component calculated, in steady-state, for (

**a**) PavM; (

**b**) Pav with h

_{1}= 0.25; and (

**c**) Pav with h

_{1}= 0.15.

**Figure 11.**Reactive power plots for Qav (red), QavM (blue), QavT (magenta), and QavC (green): (

**a**) transient response detail and (

**b**) steady-state ripple detail after load step.

**Figure 12.**Active and reactive averaged power calculation, when an abrupt load change occurs, through HIL emulation employing a dSPACE-RTI setup at Aalborg Microgrid Laboratory: (

**a**) NLL current; (

**b**) active power calculation, Pav (yellow), PavM (green), PavT (blue), PavC (red), and their steady-state ripple detail; (

**c**) reactive power calculation and its steady-state ripple detail; Qav (yellow), QavM (green), QavT (blue), and QavC (red).

**Figure 13.**HIL active averaged power calculation, when an abrupt load change occurs, through HIL emulation, using a dSPACE-RTI setup at Aalborg Microgrid Laboratory: active power calculation, Pav (green), PavM (red), and its steady-state ripple detail.

**Figure 14.**Experimental setup at the intelligent Microgrid Laboratory in Aalborg University, Denmark: (

**a**) complete experimental setup and (

**b**) detail of the Danfoss© single-phase inverter.

**Figure 15.**(

**a**) Measured current at point of common coupling (PCC) through Fluke Power Analyzer, configured to single-phase employing Channel A; (

**b**) THD of the measured current, calculated using Fast Fourier Transform; (

**c**) PavM Active power calculation and dynamic performance during an abrupt load change, as well as its detail for the steady-state ripple; (

**d**) proposed Pav Active power calculation and dynamic performance during an abrupt load change, as well as its detail for the steady-state ripple.

Parameter | Value |
---|---|

Ron_{D1-D3}/Ron_{D2-D4} | 0.01 Ω/1 Ω |

L_{L}/C1 = C2 | 84 µH/470 µF |

R_{C}_{1} = R_{C}_{2}/R_{L}_{1} = R_{L}_{2} | 37 kΩ/1560 Ω |

Parameter | Value |
---|---|

Individual THDv; Total THD | <5%; <8% |

Individual THDi | >4% for 3 < odd harmonic < 11 >1% for even harmonics |

Total TDD in current | >5% |

Parameter | Value |
---|---|

${V}_{o}$ | 311 V |

${w}_{o}$ | 100 π rad/s |

TDD for i_{o}(t) | 116.41% |

${\xi}_{i}/{\xi}_{p}$ | 0.1 to 0.7075/0.7075 |

${h}_{1}$ | 0.10 to 0.30 (in steps of 0.05) |

${h}_{2}$ | 0.10 |

${\omega}_{C}$; ${\omega}_{CT}$ | 0.74 π rad/s; 2.20 π rad/s |

${\xi}_{v0}/{\xi}_{1}={\xi}_{2}$ | 0.7/1 |

${\xi}_{MV}/{\xi}_{MI}/{\xi}_{A}={\xi}_{B}$ | 0.7/0.14/1 |

C1 = C2/ RC1 = RC2 | 470 µF/37 kΩ |

RL1 = RL2 = RL3 = RL4 | 1.8 mH; 0.01 Ω |

RC BRANCH | 25 µF; 1 Ω |

SWITCHING FREQUENCY, fs | 10 kHz |

Calculated THD | Settling-Time (ms)/% Reduction with Respect to PAVM | Time-Delay (ms)/% Increasing with Respect to PAVM | |
---|---|---|---|

${P}_{avM}$ | 1.13% | 120 | 38 |

${P}_{av}\to $ ${\xi}_{i}=0.2$ ${h}_{1}=0.25$ | 1.32% | 75/32% | 40/5% |

${P}_{av}\to $ ${\xi}_{i}=0.2$ ${h}_{1}=0.15$ | 0.59% | 90/18% | 50/20% |

Reactive Power Calculation Algorithm | Calculated THD | Settling-Time (ms) | Reduction of THD with Respect to Q_{avM} |
---|---|---|---|

${Q}_{avM}$ | 7.85% | 140 | Not applicable |

${Q}_{av}:{\xi}_{i}=0.2{h}_{\mathrm{i}}=0.25;{h}_{2}=0.1$ | 2.46% | 150 | 68.66% |

${Q}_{avT}$ | 3.49% | 250 | 55.64% |

${Q}_{avC}$ | 1.87% | 780 | 76.18% |

Test | ${\xi}_{i}$ | ${\xi}_{p}$ | ${h}_{1}$; ${h}_{2}$ |
---|---|---|---|

HIL TEST-1 | 0.2 | 0.7075 | 0.25; 0.10 |

HIL TEST-2 | 0.2 | 0.7075 | 0.15; 0.10 |

HIL Calculation Algorithm | Settling-Time (ms) | Time-Delay (ms) |
---|---|---|

${P}_{av}$ | 90 | 38 |

${P}_{avM}$ | 140 | 40 |

${Q}_{av}$ | 130 | 50 |

${Q}_{avM}$ | 140 | 45 |

Algorithm | Settling-Time Matlab (ms)/(%Reduction) | Settling-Time HIL (ms)/(%Reduction) | Settling-Time Experimental (ms)/(%Reduction) |
---|---|---|---|

P_{av} | 75/37.5% | 90/(35.7%) | 125/(30%) |

P_{avM} | 120 | 140 | 180 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

El Mariachet, J.; Guan, Y.; Matas, J.; Martín, H.; Li, M.; Guerrero, J.M.
HIL-Assessed Fast and Accurate Single-Phase Power Calculation Algorithm for Voltage Source Inverters Supplying to High Total Demand Distortion Nonlinear Loads. *Electronics* **2020**, *9*, 1643.
https://doi.org/10.3390/electronics9101643

**AMA Style**

El Mariachet J, Guan Y, Matas J, Martín H, Li M, Guerrero JM.
HIL-Assessed Fast and Accurate Single-Phase Power Calculation Algorithm for Voltage Source Inverters Supplying to High Total Demand Distortion Nonlinear Loads. *Electronics*. 2020; 9(10):1643.
https://doi.org/10.3390/electronics9101643

**Chicago/Turabian Style**

El Mariachet, Jorge, Yajuan Guan, Jose Matas, Helena Martín, Mingshen Li, and Josep M. Guerrero.
2020. "HIL-Assessed Fast and Accurate Single-Phase Power Calculation Algorithm for Voltage Source Inverters Supplying to High Total Demand Distortion Nonlinear Loads" *Electronics* 9, no. 10: 1643.
https://doi.org/10.3390/electronics9101643