Contributions on spectral control for the asymmetrical full bridge multilevel inverter

Las topologías de circuitos inversores multinivel pueden trabajar a tensiones y potencias mayores que las alcanzadas por convertidores convencionales de dos niveles. Además, la conversión multinivel reduce la distorsión armónica de las variables de salida y en algunos casos, a pesar del aumento de elementos de conmutación, también reduce las pérdidas de conversión al incrementarse el número de niveles. La reducción de distorsión alcanzada por el número de niveles puede aprovecharse para reducir las pérdidas de conmutación disminuyendo la frecuencia de las señales portadoras. Para reducir aún más esta frecuencia sin degradar el espectro, nosotros controlamos las pendientes de las portadoras triangulares. Primero se han desarrollado dos modelos analíticos para predecir el espectro del voltage de salida, dependiendo de: el índice de modulación MA, la razón de distribución de voltaje K de las fuentes de alimentación , y las cuatro pendientes de las portadoras{r1, r2, r3, r4}. El primer modelo considera el Muestreo Natural y se basa en Series Dobles de Fourier (SDF) mientras que el segundo modelo, utiliza la Serie Sencilla de Fourier (SSF) introduciendo el concepto de Muestreo Pseudo-Natural, una aproximación digital de la modulación natural. Ambos modelos son programados en Matlab, verificados con Pspice y validados con un prototipo experimental que contiene un modulador digital implementado con DSP.La concordancia entre las modulaciones natural y pseudo-natural, asi como entre sus respectivos modelos, es aprovechada por un algorítmo genético (AG) donde la THD es la función costo a reducir. Después de varios ensayos y de sintonizar el AG, se genera una matriz que contiene conjuntos de portadoras optimizadas dentro un rango específico de las variables {MA,K} y es probada con un segundo prototipo en lazo cerrado. Un lazo lento digital modifica las portadoras creadas por un dsPIC en modulaciones PWM; estas son demoduladas y sus amplitudes corregidas por un lazo de acción anticipada. Estas portadoras se comparan con una referencia sinusoidal que a su vez es modificada por variables de estado, generando finalmente la modulación multinivel en lazo cerrado. Los resultados finales demuestran la fiabilidad de la reducción de armónicos usando la programación de las pendientes de las portadoras. Palabras claves: inversor multinivel, PWM, distorsión armónica, modelo espectral, pendiente de portadora, conjunto de portadoras, distribución de niveles, Serie Doble de Fourier, Serie Simple de Fourier, muestreo natural, muestreo regular, muestreo pseudo-natural , Algoritmos Genéticos.Multilevel inverter (MI) topologies can work at higher voltage and higher power than conventional two-level converters. In addition, multilevel conversion reduces the output variables harmonic distortion and, sometimes, in spite of the devices-count increment, the conversion losses can also decrease by increasing the number of levels. The harmonic distortion reduction achieved by increasing the number of levels, can be used to further reducing the switching losses by decreasing the inverter carrier frequencies. To reduce even more the switching frequency without degrading output spectrum, we control the triangular carrier waveforms slopes. First, to achieve this target, two analytical models have been created in order to predict the inverter output voltage spectrum, depending on diverse parameters: the amplitude modulation index MA, the voltage distribution K of the inverter input sources, and the four carrier slopes {r1, r2, r3, r4}. The first model considers Natural Sampling and is based on Double Fourier Series (DFS) whereas the second model based on Simple Fourier Series (SFS), introduces the concept of Pseudo-Natural Sampling, as a digital approximation of the natural modulation. Both models are programmed in Matlab, verified with Pspice simulations and validated with a first experimental prototype with a DSP digital modulator.The good agreement between natural and pseudo-natural modulations, as well as their respective DFS and SFS models, is exploited by a Genetic Algorithm (GA) application where THD is the cost function to minimize. After testing and properly tuning the GA, a framework matrix containing the optimized carriers set for a specific range of variables {MA,K} is generated and then, tested with a second, closed-loop prototype. A slow digital loop modifies the carrier slopes created by dsPIC microcontroller as PWM modulations, whose amplitude, once demodulated, are affected by a feed-forward loop. These carriers, compared with a sinusoidal reference, state-feedback modified, generate finally the closed-loop multilevel modulation. The final results demonstrates the feasibility of harmonic reduction by means of carrier slopes programming. Keywords: multilevel inverter, PWM, harmonic distortion, spectral modeling, carrier slope, carriers set, level distribution, Double Fourier Series, Simple Fourier Series, natural sampling, regular sampling, pseudo-natural sampling, Genetic Algorithms

Co-design of Security Aware Power System Distribution Architecture as Cyber Physical System

The modern smart grid would involve deep integration between measurement nodes, communication systems, artificial intelligence, power electronics and distributed resources. On one hand, this type of integration can dramatically improve the grid performance and efficiency, but on the other, it can also introduce new types of vulnerabilities to the grid. To obtain the best performance, while minimizing the risk of vulnerabilities, the physical power system must be designed as a security aware system. In this dissertation, an interoperability and communication framework for microgrid control and Cyber Physical system enhancements is designed and implemented taking into account cyber and physical security aspects. The proposed data-centric interoperability layer provides a common data bus and a resilient control network for seamless integration of distributed energy resources. In addition, a synchronized measurement network and advanced metering infrastructure were developed to provide real-time monitoring for active distribution networks. A hybrid hardware/software testbed environment was developed to represent the smart grid as a cyber-physical system through hardware and software in the loop simulation methods. In addition it provides a flexible interface for remote integration and experimentation of attack scenarios. The work in this dissertation utilizes communication technologies to enhance the performance of the DC microgrids and distribution networks by extending the application of the GPS synchronization to the DC Networks. GPS synchronization allows the operation of distributed DC-DC converters as an interleaved converters system. Along with the GPS synchronization, carrier extraction synchronization technique was developed to improve the system’s security and reliability in the case of GPS signal spoofing or jamming. To improve the integration of the microgrid with the utility system, new synchronization and islanding detection algorithms were developed. The developed algorithms overcome the problem of SCADA and PMU based islanding detection methods such as communication failure and frequency stability. In addition, a real-time energy management system with online optimization was developed to manage the energy resources within the microgrid. The security and privacy were also addressed in both the cyber and physical levels. For the physical design, two techniques were developed to address the physical privacy issues by changing the current and electromagnetic signature. For the cyber level, a security mechanism for IEC 61850 GOOSE messages was developed to address the security shortcomings in the standard

Modulation strategies for the neutral-point-clamped converter and control of a wind turbine system

Els convertidors multinivell són topologies de convertidors d’electrònica de potència que poden generar tres o més nivells de voltatge en cadascuna de les fases de sortida. Com a resultat, els voltatges i corrents generats per aquestes topologies presenten una distorsió harmònica baixa. Hi ha diferents configuracions de convertidors multinivell, les quals es basen en connectar dispositius de potència o convertidors en sèrie. El resultat d’aquestes connexions permet obtenir voltatges alts, tant en la part de corrent continu com en la de corrent altern del convertidor. A més, cada dispositiu sols ha de suportar una fracció del voltatge total del bus de corrent continu. Per aquestes raons, els convertidors multinivell són generalment utilitzats en aplicacions d’alta potència. El convertidor de tres nivells amb connexió a punt neutre (neutral-point-clamped) és el més utilitzat. La recerca d’aquesta tesis doctoral està focalitzada en aquesta topologia de convertidor, i el principal objectiu és l’aportació de noves tècniques de modulació. Aquestes tenen en compte diferents aspectes: la velocitat computacional dels algorismes, l’equilibrat de les tensions dels condensadors del bus de contínua, les pèrdues de commutació i les oscil·lacions de baixa freqüència en el punt neutre del convertidor. Totes les estratègies de modulació proposades en aquesta tesis són modulacions d’amplada de polses basades en portadora. En la primera modulació que es presenta, s’injecta un senyal comú (seqüència zero) a totes les moduladores, que es basa en els patrons de la modulació vectorial que utilitza tres vectors dels més propers al de referència (nearest-three-vector modulation). S’estudien i es comparen els resultats d’aquesta modulació amb la seva homòloga, basada en perspectiva vectorial. Una segona proposta és l’anomenada modulació d’amplada de polses de doble senyal (double-signal pulse-width modulation). Aquesta modulació és capaç d’eliminar completament les oscil·lacions de voltatge en el punt neutre del convertidor. No obstant això, es produeix un increment de les pèrdues de commutació en els dispositius de potència i, a més, no hi ha un equilibrat natural de les tensions en els condensadors del bus. Una última estratègia de modulació, anomenada modulació híbrida (hybrid pulse-width modulation), es basa en la combinació de la modulació sinusoïdal (sinusoidal pulse-width modulation) i la de doble senyal. Aquesta presenta una solució de compromís entre reduir les pèrdues de commutació, en detriment d’un augment de l’amplitud de les oscil·lacions de voltatge en el punt neutre. Una segona part d’aquesta tesis es centra en les aplicacions a generació eòlica, ja que els convertidors multinivell estan començant a ser utilitzats en aquest camp. Això es produeix fonamentalment per l’augment continu de les dimensions de les turbines eòliques. En aquesta part de la recerca s’ha considerat la configuració de dos convertidors multinivell connectats a un mateix bus de contínua (back-to-back), tot i que els convertidors han estat estudiats independentment. Inicialment s’ha estudiat el convertidor que va connectat a la xarxa elèctrica i s’ha aplicat l’estratègia de control coneguda com a control orientat a tensió (voltage-oriented control). S’han utilitzat controladors estàndard (proporcional-integral), als quals s’ha afegit un control difús que supervisa i modifica els valors de les constants dels controladors. Aquest supervisor difús millora la dinàmica de la tensió del bus de contínua davant canvis de càrrega quan el convertidor treballa com a rectificador. Per una altra part, s’ha estudiat el control d’una turbina eòlica basada en un generador d’imants permanents. En aquest cas, s’ha aplicat l’estratègia de control coneguda com a control orientat a camp (field-oriented control). S’han avaluat i comparat els avantatges i inconvenients de diferents formes de sintonitzar els controladors.Multilevel converters are power electronic topologies that can generate three or more voltage levels in each output phase. As a result, the voltage and current waveforms generated have lower total harmonic distortion. Multilevel topologies are based on connecting power devices or converters in a series. Consequently, high voltages can be handled on the dc and ac sides of the converter, while each device stands only a fraction of the total dc-link voltage. For these reasons multilevel converters are generally applied to high-power applications. The three-level neutral-point-clamped converter is the most extensively used multilevel topology. This topology is the main focus of research in this dissertation. The main objective is to propose new modulation strategies that are able to meet a compromise solution while considering computational algorithm speed, voltage balance in the dc-link capacitors, switching losses and low frequency voltage oscillations at the neutral point. All the modulation strategies proposed here are based on carrier-based pulsewidth modulation. A new modulation strategy has been implemented using a proper zero-sequence signal injected into the modulation signals. The zero sequence is determined from a space-vector modulation standpoint, particularly the nearest-threevector modulation strategy. The proposed carrier-based technique is compared with its space-vector modulation counterpart. It shows some advantages, such as easier implementation and reduced switching events; however, it still produces oscillations in the neutral-point voltage for some operating conditions. A new modulation strategy able to completely remove such voltage oscillations is also presented. It is called double-signal pulse-width modulation. The main drawback of this strategy is that it increases the switching frequency of the power devices and has no natural capacitor voltage balance. Some balancing strategies are proposed in this dissertation for this specific modulation. Furthermore, a hybrid pulse-width modulation approach is presented which is able to combine sinusoidal pulse-width modulation with doublesignal pulse-width modulation; this represents a compromise solution between switching losses and neutral-point voltage oscillation amplitudes. The second part of this thesis is focused on wind generation applications. Multilevel converters are starting to be used in such a field nowadays, and are expected to be further applied in the near future as the sizes of wind turbines grow. Two back-toback-connected power converters are considered in this application, although they are analyzed independently. First of all, the control of the grid-connected converter is studied. A voltage-oriented control is used with standard proportional-integral controllers. The originality of the method is that a fuzzy supervisor is designed and included in the structure; the fuzzy supervisor is able to modify the proportionalintegral parameters online. It is shown how the control of the total dc-link voltage improves significantly under load changes when the converter is working as a rectifier. On the other hand, a control study is performed on the wind turbine side. The variable speed wind turbine is based on a permanent magnet synchronous generator. A field-oriented control strategy is applied. The controllers are evaluated and compared using different tuning strategies which highlight the advantages and drawbacks of each

Design and Control of Electrical Motor Drives

Dear Colleagues, I am very happy to have this Special Issue of the journal Energies on the topic of Design and Control of Electrical Motor Drives published. Electrical motor drives are widely used in the industry, automation, transportation, and home appliances. Indeed, rolling mills, machine tools, high-speed trains, subway systems, elevators, electric vehicles, air conditioners, all depend on electrical motor drives.However, the production of effective and practical motors and drives requires flexibility in the regulation of current, torque, flux, acceleration, position, and speed. Without proper modeling, drive, and control, these motor drive systems cannot function effectively.To address these issues, we need to focus on the design, modeling, drive, and control of different types of motors, such as induction motors, permanent magnet synchronous motors, brushless DC motors, DC motors, synchronous reluctance motors, switched reluctance motors, flux-switching motors, linear motors, and step motors.Therefore, relevant research topics in this field of study include modeling electrical motor drives, both in transient and in steady-state, and designing control methods based on novel control strategies (e.g., PI controllers, fuzzy logic controllers, neural network controllers, predictive controllers, adaptive controllers, nonlinear controllers, etc.), with particular attention to transient responses, load disturbances, fault tolerance, and multi-motor drive techniques. This Special Issue include original contributions regarding recent developments and ideas in motor design, motor drive, and motor control. The topics include motor design, field-oriented control, torque control, reliability improvement, advanced controllers for motor drive systems, DSP-based sensorless motor drive systems, high-performance motor drive systems, high-efficiency motor drive systems, and practical applications of motor drive systems. I want to sincerely thank authors, reviewers, and staff members for their time and efforts. Prof. Dr. Tian-Hua Liu Guest Edito

Power System Dynamics Enhancement Through Phase Unbalanced and Adaptive Control Schemes in Series FACTS devices

This thesis presents novel series compensation schemes and adaptive control techniques to enhance power system dynamics through damping Subsynchronous Resonance (SSR) and low-frequency power oscillations: local and inter-area oscillations. Series capacitive compensation of transmission lines is used to improve power transfer capability of the transmission line and is economical compared to the addition of new lines. However, one of the impeding factors for the increased utilization of series capacitive compensation is the potential risk of SSR, where electrical energy is exchanged with turbine-generator shaft systems in a growing manner which can result in shaft damage. Furthermore, the fixed capacitor does not provide controllable reactance and does not aid in the low-frequency oscillations damping. The Flexible AC Transmission System (FACTS) controllers have the flexibility of controlling both real and reactive power which could provide an excellent capability for improving power system dynamics. Several studies have investigated the potential of using this capability in mitigating the low-frequency (electromechanical) as well as the subsynchronous resonance (SSR) oscillations. However, the practical implementations of FACTS devices are very limited due to their high cost. To address this issue, this thesis proposes a new series capacitive compensation concept capable of enhancing power system dynamics. The idea behind the concept is a series capacitive compensation which provides balanced compensation at the power frequency while it provides phase unbalance at other frequencies of oscillations. The compensation scheme is a combination of a single-phase Thyristor Controlled Series Capacitor (TCSC) or Static Synchronous Series Compensator (SSSC) and a fixed series capacitors in series in one phase of the compensated transmission line and fixed capacitors on the other two phases. The proposed scheme is economical compared to a full three-phase FACTS counterpart and improves reliability of the device by reducing number of switching components. The phase unbalance during transients reduces the coupling strength between the mechanical and the electrical system at asynchronous oscillations, thus suppressing the build-up of torsional stresses on the generator shaft systems. The SSR oscillations damping capability of the schemes is validated through detailed time-domain electromagnetic transient simulation studies on the IEEE first and second benchmark models. Furthermore, as the proposed schemes provide controllable reactance through TCSC or SSSC, the supplementary controllers can be implemented to damp low-frequency power oscillations as well. The low-frequency damping capability of the schemes is validated through detail time-domain electromagnetic transient simulation studies on two machines systems connected to a very large system and a three-area, six-machine power system. The simulation studies are carried out using commercially available electromagnetic transient simulation tools (EMTP-RV and PSCAD/EMTDC). An adaptive controller consisting of a robust on-line identifier, namely a robust Recursive Least Square (RLS), and a Pole-Shift (PS) controller is also proposed to provide optimal damping over a wide range of power system operations. The proposed identifier penalizes large estimated errors and smooth-out the change in parameters during large power system disturbances. The PS control is ideal for its robustness and stability conditions. The combination results in a computationally efficient estimator and a controller suitable for optimal control over wider range of operations of a non-linear system such as power system. The most important aspect of the controller is that it can be designed with an approximate linearized model of the complete power system, and does not need to be re-tuned after it is commissioned. The damping capability of such controller is demonstrated through detail studies on a three-area test system and on an IEEE 12-bus test system. Finally, the adaptive control algorithm is developed on a Digital Signal Processing Board, and the performance is experimentally tested using hardware-in-the-loop studies. For this purpose, a Real Time Digital Simulator (RTDS) is used, which is capable of simulating power system in real-time at 50 µs simulation time step. The RTDS facilitates the performance evaluation of a controller just like testing on a real power system. The experimental results match closely with the simulation results; which demonstrated the practical applicability of the adaptive controller in power systems. The proposed controller is computationally efficient and simple to implement in DSP hardware

Multilevel inverters for renewable energy systems

Voltage source inverters have become widely used in the last decade primarily due to the fact that the dangers and limitations of relying on fossil fuel based power generation have been seen and the long term effects felt especially with regards to climate change. Policies and targets have been implemented such as from the United Nations climate change conference (COPxx) concerning human activities that contribute to global warming from individual countries. The most effective way of reducing these greenhouse gases is to turn to renewable energy sources such as the solar, wind etc instead of coal. Converters play the crucial role of converting the renewable source dc power to ac single phase or multiphase. The advancement in research in renewable energy sources and energy storage has made it possible to do things more efficiently than ever before. Regular or 2 level inverters are adequate for low power low voltage applications but have drawbacks when being used in high power high voltage applications as switching components have to be rated upwards and also switch between very high potential differences. To lessen the constraints on the switching components and to reduce the filtering requirements, multilevel inverters (MLI's) are preferred over two level voltage source inverters (VSI's). This thesis discusses the implementation of various types of MLI's and compares four different pulse width modulation (pwm) techniques that are often used in MLI under consideration: three, five, seven and nine level inverters. Harmonic content of the output voltage is recorded across a range of modulation indices for each of the three popular topologies in literature. Output from the inverter is filtered using an L only and an LC filter whose design techniques are presented. A generalized prediction algorithm using machine learning techniques to give the value of the expected THD as the modulation index is varied for a specific topology and PWM switching method is proposed in this study. Simulation and experimental results are produced in five level form to verify and validate the proposed algorithm

Assessment of the harmonic behaviour of a utility-scale photovoltaic plant

Thesis (MScEng)--Stellenbosch University, 2017.ENGLISH ABSTRACT: The rapidly increasing deployment of utility-scale solar photovoltaic (PV) plants worldwide presents new technical challenges including the risk of unacceptably high harmonic voltage distortion in the utility network. PV plants affect the harmonic voltage distortion at their point of common coupling primarily by two distinct mechanisms: generation of harmonic currents due to switching action of the inverters and introduction of series and parallel resonances caused by connection of the plant to the network. The objective of this study is to investigate the harmonic behaviour of utility-scale PV plants based on the case-study of a 75 MW PV plant in the Northern Cape province of South Africa. In this work, a harmonic simulation model of a PV plant is developed in DIgSILENT PowerFactory which represents the passive network components with sufficient accuracy to study the frequency response over the harmonic frequency band from 50 to 2500 Hz. 10-minute and 3-second aggregated harmonic measurement data and event-triggered waveform data were captured over a 12-day period using an IEC 61000-4-30 Class A power quality meter installed at the plant’s 132 kV point of connection (POC). A quality assessment of harmonic measurement data shows that the accuracy of harmonic voltage and current measurements are likely to be significantly affected by quantisation and transducer error for even and higher-order harmonics. Analysis of the 3-second aggregated harmonic quantities indicates that their fluctuation during each 10-minute period is sufficiently small that the 10-minute average values adequately approximate the short-term and long-term behaviour of the plant. The harmonic behaviour of the plant is investigated by considering the relationship between harmonic voltage and current emissions and active power, reactive power and time of day. Certain harmonic voltages increase with increasing plant active power output whilst others decrease but all harmonic currents remain constant or increase with increasing active power. It was not possible to quantify the relative impact of active and reactive power variation as the plant operates in voltage control mode. Brief periods of high harmonic current distortion were noted during start up and shut down of the plant. High harmonic currents at the 23rd harmonic order correspond with a series resonance identified in the model thus validating the POC frequency sweep simulation. A comparative analysis of different published methods for assessment of the harmonic emissions contribution of the PV plant is performed. All methods show similar trends in identifying dominant harmonics and general harmonic behaviour but the magnitudes of the calculated emissions differ significantly in some instances. Where accurate frequency sweep data of the utility network and phasor measurement data are both available, the plant model enables application of the harmonic vector method to discriminate between utility and plant contributions. Simulated voltage emissions based using the manufacturer’s quoted inverter current emissions do not closely match measured emissions due to the complexity of active source interactions within the real power system. Comparison of the mean, 75th percentile and 90th percentile emissions assessments demonstrate the effectiveness of percentile assessment in eliminating outlying high distortion periods from the assessed results.AFRIKAANSE OPSOMMING: Die vinnige toenemende implementering van grootskaalse sonkragfotovoltaïese (PV) aanlegte wêreldwyd, bied nuwe tegniese uitdagings, insluitende die risiko van onaanvaarbare hoë harmoniese spanningvervorming in die netwerk. PV aanlegte beïnvloed die harmoniese spanningvervorming by hul punt van algemene koppeling, hoofsaaklik deur twee afsonderlike meganismes: die opwekking van harmoniese strome as gevolg van die skakel aksie van die omkeerders en die inleiding van reeks en parallelle resonansies wat veroorsaak word deur die koppel van die kragstasie aan die netwerk. Die doel van hierdie studie is om die harmoniese gedrag van grootskaalse-PV aanlegte te ondersoek, gebaseer op die gevallestudie van 'n 75 MW PV kragstasie in die Noord-Kaaps provinsie van Suid-Afrika. In hierdie werk word 'n harmoniese simulasiemodel van 'n PV-aanleg ontwikkel in DIgSILENT PowerFactory, wat die passiewe netwerk komponente verteenwoordig met voldoende akkuraatheid, om die frekwensieweergawe oor die harmoniese frekwensieband van 50 tot 2500 Hz te bestudeer. 10-minute en 3-sekonde geaggregeerde harmoniese metingsdata en gebeurtenisgeaktiveerde golfvormdata is oor 'n tydperk van 12 dae opgeneem met behulp van 'n IEC 61000-4-30 klas A kragkwaliteitsmeter geïnstalleer by die substasie se 132 kV punt van verbinding (POC). 'n Kwaliteitsbeoordeling van harmoniese metingsdata toon dat die akkuraatheid van harmoniese spanning en stroommetings waarskynlik aansienlik beïnvloed sal word deur kwantiserings en oorvormer foute vir ewe en hoër-orde harmonieke. Analise van die 3-sekonde geaggregeerde harmoniese waardes dui aan dat hul fluktuasie gedurende elke 10 minute tydperk klein genoeg is, sodat die 10-minute gemiddelde waardes die korttermyn- en langtermyngedrag van die aanleg ‘n voldoende benadering is. Die harmoniese gedrag van die aanleg word ondersoek deur die verband tussen harmoniese spanning en stroom emissies en aktiewe krag, reaktiewe krag en tyd van die dag te oorweeg. Sekere harmoniese spannings verhoog met toenemende aktiewe kraguitset, terwyl ander afneem, maar alle harmoniese strome bly konstant of verhoog met toenemende aktiewe kraguitset. Dit was nie moontlik om die relatiewe impak van aktiewe en reaktiewe kragvariasie te kwantifiseer nie aangesien die aanleg in die spanningskontrolemodus funksioneer. Kort tydperke van hoë harmoniese stroomvervorming is tydens die aanvang en afsluiting van die aanleg opgemerk. Hoë harmoniese strome op die 23ste harmoniek stem ooreen met 'n reeks resonansie wat in die model geïdentifiseer is en dus valideer die POC-frekwensie sweep simulasie. 'n Vergelykende analise van verskillende gepubliseerde metodes vir die assessering van die harmoniese emissie bydrae van die PV-aanleg word uitgevoer. Alle metodes toon soortgelyke neigings in die identifisering van dominante harmonieke en algemene harmoniese gedrag, maar die groottes van die berekende emissies verskil in sommige gevalle beduidend. Waar akkurate frekwensie sweep data van die netwerk en fasor meting data albei beskikbaar is, maak die model dit moontlik vir die toepassing van die harmoniese vektor metode om te onderskei tussen netwerk en PV-aanleg bydraes. Gesimuleerde spanningsemissies gebaseer op die vervaardiger se verklaarde omkeerder-emissies, pas nie noukeurig ooreen met gemete emissies nie as gevolg van die kompleksiteit van aktiewe broninteraksies binne die werklike kragstelsel. Vergelyking van die gemiddelde 75ste persentiel- en 90ste persentielemissiesevaluasies toon die effektiwiteit van persentielassessering om die afgeleë hoë vervormingsperiode uit die geassesseerde resultate te elimineer