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Due to potential dynamic interactions among dc microgrid power converters, the performance of some of their control loops can vary from the designed behavior. Thus, online monitoring of different control loops within a dc microgrid power converter is highly desirable. This paper proposes the simultaneous identification of several control loops within dc microgrid power converters, by injecting orthogonal pseudo-random binary sequences (PRBSs), and measuring all the loop gains in one measurement cycle. The identification results can be used for different purposes such as controller autotuning, impedance shaping, etc. Herein, an example of output impedance estimation and shaping based on locally-measured loop gains is presented. The proposed identification technique and its application in output impedance shaping are validated on an experimental dc microgrid prototype, composed of three droop-controlled power converters.

Power electronic converters used in a dc microgrid environment are usually equipped with several control loops. When many converters are connected to a common dc bus, the performance of some loops can be different from the behavior designed for the stand-alone converter, depending on the number, topology, and control of the interconnected converters. In order to establish the performance of each loop in real-time, it is important to continuously monitor the loop gains. This article presents the application of an online identification technique in rapid and simultaneous measurement of several control loops in dc microgrid power converters. To this end, multiple orthogonal pseudorandom binary sequences (PRBSs) are simultaneously injected into different loops of power converters. Since the frequency components excited by each PRBS are unique and different from any other, multiple PRBSs can be injected at the same time. This will allow to measure all the loop gains in only one measurement cycle. Hence, the operating condition of the system is kept unchanged during the measurement, which is an important factor to achieve accurate monitoring. The online identification method is applied to an experimental dc microgrid prototype, composed of three droop-controlled converters. After identifying different control loops, an adaptive tuning algorithm is implemented to adjust the digital compensator of each loop, in order to reach the desired dynamic performance. The reported experimental results confirm the accuracy and the applicability of this technique.

Grid impedance affects the stability and control performance of grid-connected power-electronics devices, such as inverters, used to integrate wind and solar energy. Adaptive control of such inverters, to guarantee stability under different grid conditions, requires online measurement of the grid impedance performed in real time. Wideband frequency-response-measurement techniques based on the pseudo-random binary sequence (PRBS) or impulse injection have been often applied for grid-impedance measurements. However, while using the PRBS or impulse, it is assumed that the system under study is linear. Because such an assumption does not typically hold for grid-connected systems, the measured impedances are usually prone to distortions caused by nonlinearities. This paper proposes the use of periodic ternary sequences for online grid-impedance measurements. Using appropriately designed periodic ternary signals, the linear component of the grid impedance can be identified, eliminating errors from even-order nonlinear distortions. In addition, the ternary sequences can be designed for a much wider range of sequence length compared to the conventional PRBS, enabling more efficient optimization of computing power and frequency resolution. Experimental measurements are shown from a grid-connected photovoltaic inverter.

Grid impedance has a major effect on the operation of inverter-connected systems, such as renewable energy sources. Stability of such system depends on the ratio of the inverter output impedance and the grid impedance at the point of common coupling. Because the grid impedance varies over time with many parameters, online grid-impedance measurement acquired in real time is most preferred method for observing the stability. Recent studies have presented methods based on multiple-input-multiple-output (MIMO) identification techniques, where the stability of grid-connected system is rapidly assessed in the dq domain. In the methods, orthogonal injections are used with Fourier techniques, and the grid impedance d and q components are measured. The Nyquist stability criterion is then applied to assess the stability. This paper extends previous studies, and presents a real-time implementation for the online stability analysis using MIMO-identification methods. The practical implementation is discussed in detail and experimental results based on a grid-connected three-phase inverter are provided to demonstrate the effectiveness of the methods.

Grid impedance and the output impedance of grid-connected inverter are important parameters for the operation of grid-connected systems, such as solar, wind, and other distributed-generation resource systems. The impedance mismatch between the grid and the interfacing circuit often generates harmonic resonances that lead to reduced power quality and even instability. Since the impedances usually vary over time as a function of many parameters, online measurements are required for stability assessment and adaptive control of the inverters. Several methods have been proposed for quick, accurate measurements of impedances, but the use of multiple-input multiple-output (MIMO) identification techniques have not been considered. Applying the MIMO techniques, different components of the inverter output impedance or grid impedance can be simultaneously measured during a single measurement cycle. Therefore, the operating conditions of the system can be kept constant during the measurements, and the overall measurement time is significantly reduced. This paper shows the use of orthogonal binary sequences to simultaneously measure the “d” and “q” components of grid-connected inverter output impedance and/or grid impedance. Experimental results based on a three-phase grid-connected inverter are presented and used to demonstrate the effectiveness of the proposed methods.

Power electronic inverters are devices that are used to interface renewables, such as photovoltaic panels or wind turbines, with the electrical power system. The inverter should control its output current to follow a sinusoidal reference to avoid distorting the voltage waveform of the power system. However, in real inverters dead-time is used in the control signals which causes unwanted harmonics, leading to lower power quality. The amount of harmonics is difficult to predict due to nonlinear nature of the dead-time. Moreover, the harmonic distortion depends on many variables, such as inverter control parameters and power system impedance. This paper shows that frequency response from inverter control signal (duty ratio) to grid current is linked to the detrimental dead-time effect and poor power quality. The frequency response is identified by perturbing the inverter control signal with a maximum length binary sequence (MLBS). The magnitude of the identified frequency response is shown to follow the same trend as the amount of current distortion. Therefore, the effect of dead-time on power quality could potentially be modeled using a linearized model allowing optimal control design in the presence of dead time.

As the amount of renewable energy increases rapidly, power systems will face novel challenges to maintain power quality. Power quality issues, which usually arise from the grid connection through power-electronic devices, can be reduced by proper control strategies. Grid-connected devices are conventionally optimized into a single operating point, but real performance is affected by the interfaced grid conditions. As the grid conditions change over time, the control performance varies, as does the quality of the power produced. To tackle this issue, the adaptive grid-voltage feedforward is introduced to the control system. The adaptive method, applying a perturb-and-observe algorithm, improves the produced power quality in real time by taking the control system characteristics and the grid conditions into account. The results show the improved power quality in various grid conditions when comparing the adaptive grid-voltage feedforward and the conventional implementations. acceptedVersion

The impedance of a Li-ion battery is an important parameter for the battery's state-of-charge (SOC) and state-of-health (SOH) estimation. Battery impedance is typically modeled by an equivalent-circuit-model (ECM) in which the variations in the specific model parameters can be used for estimating the SOC and the SOH. However, the fact that the battery impedance is highly non-linear complicates the parameterization of the model. The model is traditionally obtained by a complex non-linear least-squares fitting algorithm which comes with high complexity. This paper proposes a novel approach to extract all the ECM parameters of the battery impedance obtained with online-capable pseudo-random-sequence (PRS) measurements. Although the algorithm has low complexity, it still captures the desired variations in the ECM parameters as a function of SOC. The algorithm is validated for the impedance data from a lithium-iron-phosphate cell. acceptedVersion

Battery Energy Storage Systems (BESSs) play an important role in grid-connected renewable energy systems as they provide great flexibility in the energy production. For photovoltaic (PV) energy applications, the BESS may be connected to the dc-link of the converter system to inject the deficit or to absorb the surplus of generated power. One of the main issues in such systems is the voltage variation at the dc-link, especially under grid imbalance, distorting the current fed to the grid. This paper studies a method to control the BESS to emulate a capacitance, thus mitigating the dc-link voltage fluctuation, for example, under heavy imbalance. The derived model initiates impedance-based analysis at the output of the battery charger. acceptedVersion

Frequency-response measurements at high frequencies have been shown to provide a valuable design tool in various fields of electronics. These measurements are often challenging when using most commercially available measurement tools due to their relatively low maximum sampling frequency and long measurement time. This effectively prevents frequency-response-based low-cost applications where fast and reliable measurements are required. This paper proposes the use of a combined frequency mixer applied with pseudo-random sequences. In this method, the applied pseudo-random excitation is upconverted to high frequencies by the mixer, and once injected into the device being tested, the system response is downconverted to lower frequencies. The method provides a low-cost solution that can be applied for rapid high-frequency measurements by using only modest data-acquisition tools. Experimental results based on a high-frequency resonator are presented and used to demonstrate the effectiveness of the proposed methods.

The amount of photovoltaic inverters connected to the electrical grid is increasing. In order to control the power fed to the grid, the inverter must be controlled, and many different approaches for small-signal modeling have been proposed to facilitate the controller design. However, a solar panel cannot be modeled by an ideal current source and the photovoltaic inverter is not connected to an ideal grid on the load side. This paper proposes a generalized method to include the load and source effects to the dynamic model of a photovoltaic inverter. The method can be used to include the source impedance of the photovoltaic generator and impedance of the distribution line in the small-signal model of the photovoltaic inverter. acceptedVersion

Utilization of renewable energy sources such as solar and wind power requires affordable, reliable and efficient methods for grid connection. Most often, grid-parallel inverters are applied. As the number of inverter-connected resources in the power grid increases, they start to have a significant effect on the dynamics of the power system. The inverters have been shown to produce harmonic oscillations. To avoid producing or amplifying the harmonic content in the power grid currents and voltages, sensitivity of the inverter against external distortion should be analyzed. This paper provides a method for sensitivity analysis of the inverter. The sensitivity is analyzed by applying a forbidden region in the complex plane, which is based on the maximum-peak criterion that is often applied in the field of control engineering. The system is defined to have robust stability if the minor-loop gain formed by the inverter output impedance and the grid impedance stays out from the forbidden region.

Several stability and power quality problems have been reported recently in power systems, which experience a high penetration of power electronics converters, such as renewable energy inverters. The problems are often caused by the interaction between the converter and the grid impedance. Stability monitoring tools have been presented to gain insight into the stability margin of the power system. Online methods are most favorable since the power system has many parameters that vary with time. However, the online methods that have been presented may produce inaccurate estimate of the stability margin due to several simplifications, such as using reduced-order impedance models. This paper introduces an improved dq-domain stability analysis that takes into account the time-varying grid impedance in real time and also the multivariable inverter output impedance, including the crosscouplings.

Power quality problems caused by grid-connected renewable energy inverters have been reported in recent literature. Excessive harmonics and interharmonics may arise when the inverter starts to interact with the grid impedance. Small-signal impedance models have been proven to be useful tools to analyze the stability margins. However, most often the grid voltage feedforward loop employed by the inverter is not included in impedance-based analysis. To fill this gap, this paper presents an impedance model, which includes the effect of feedforward, to analyze impedance-based stability in the presence of large grid impedance. The model is verified by impedance measurements from a laboratory prototype. The model is shown to give accurate prediction of small-signal stability when the Nyquist stability-criterion is applied. Thus, the model can be used to re-shape the inverter impedance to avoid stability problems. The developed impedance model will also provide a useful tool to monitor stability margins online, which necessitates adaptive impedance-shaping of grid-connected inverters.

The internal impedance of a battery has been shown to vary as a function of state-of-charge (SOC) and state-of-health (SOH) which are important parameters defining the battery conditions in Li-Ion batteries. Therefore, the online monitoring of the internal impedance can be used as a useful SOC- and SOH-estimation parameter in battery management systems. Recent studies have shown methods based on broadband injections which make it possible to perform rapid Li-Ion battery impedance measurements. The studies have not, however, fully considered the properties of the applied injections nor the applied computation methods. This work extends the studies, and presents systematic steps for designing an excitation signal for battery internal impedance measurements. A pseudo-random binary sequence (PRBS) is applied and the internal impedance is obtained through Fourier techniques. The presented methods can be used for rapid and accurate impedance measurements, and thus, as a valuable online tool in SOC- and SOH-estimation algorithms. Practical measurements are shown from a commercial nickel-manganese-cobalt (NMC) Li-Ion battery.

Time-varying grid impedance has a major effect on the stability and operation of grid-connected systems. The stability of such systems can be assessed by impedance- based stability analysis. Recent studies have shown methods for online stability assessment and adaptive control of grid- connected inverters to ensure the system stability in varying grid conditions. This paper extends the previous studies, and presents a method in which a grid-voltage feedforward is adaptively controlled by applying real-time grid-impedance measurements. The measurements are performed by using pseudo-random binary sequences and Fourier techniques. In parallel with the adaptive control, the system stability is assessed in real-time. Experimental results based on a three-phase grid-connected inverter are presented and used to demonstrate the effectiveness of the proposed methods.

Interaction of grid-connected inverter and power grid can be analyzed through their impedances. The impedances can be used to evaluate stability at the point of common coupling and to define how the system reacts to harmonic distortion. Because the grid conditions have capacitive characteristics and vary over time a voltage source connected through inductors is not sufficient. Power-hardware-in-the-loop method can be used to produce a controlled research environment. The power grid is simulated on a real-time digital system simulator (RTDS) and emulated using voltage amplifier. However, the method causes issues with accuracy and stability of the test bench. Instability can be hazardous as large overcurrent and voltages may appear. In this paper the reliability of the test bench is evaluated. Stability and accuracy of the test bench are tested by simulation and experiments. Suitability of the test bench for performing experiments is evaluated.

Harmonic resonance and power quality problems have been reported in grid-connected photovoltaic and wind power systems. The AC-side impedance of three-phase converter is an important characteristic, which can be effectively used as a design parameter to avoid instability and excessive harmonics. A number of methods to measure the three-phase AC impedance have been reported. However, solutions for high power applications such as wind and photovoltaic converters with a power rating of several megawatts, have not been discussed. This paper introduces a new method to measure the impedance from high power three-phase converter. The impedance is identified by perturbing the converter first by voltage-type injection utilizing high-power grid-forming inverter, and subsequently by current-type injection by utilizing low-power grid-parallel converter. The main benefit of the proposed setup is the possibility to measure the converter impedance online in its natural operating point both at high and low frequencies. The paper presents a proof-of-concept by validating the method using a switching model. acceptedVersion

Grid-parallel inverters are typically used to connect renewable energy sources to a power grid. The impedance mismatch between the grid and the interfacing circuit can generate harmonic resonances which may lead to reduced power quality. The impedance mismatch can be mitigated by applying an inverter that employs feedforward control. This paper presents a novel DQ-domain technique, based on pseudo-random sequences, for acquiring the impedance information and verifying the effectiveness of the feedforward control. The results can be used for tuning the feedforward control and as a method to perform fast on-line stability analysis of grid-connected systems in the DQ domain.

Voltage-type sources such as storage battery, ac grid, and constant-output-voltage-regulated converters have dominated as input sources for power electronic interfaces for a long time, leading to the development of different power stages dedicated to voltage-type input sources. Recent penetration of renewable energy sources has initiated the use of current-type sources as well as input voltage regulated converters as input sources for power electronic interfaces. While the power electronic converter topology remains unchanged in both the cases, steady state and dynamic properties of the coupled source-converter system are quite different. Moreover, the voltage/current nature of the load contributes to the complex dynamics as well. This paper investigates the factors determining the dynamic properties of a power electronic converter in a specific arrangement. The findings show that the open-loop converter (without any internal or external feedbacks) automatically adapts its dynamic properties to the properties stipulated by source and load if certain terminal constraints are satisfied. If internal or external feedback is activated, the dynamic properties of the converter may be varied as desired; however, the control design process is substantially different for each source/load arrangement. The findings presented in this paper have not been presented in the literature by far. A buck-power-stage converter is used as an illustrative example. Experimental results are given to validate the analytic investigation outcomes.

The increasing use of grid-connected inverters to connect renewable energy sources to a power grid will have globally important effect on grid performance. A mismatch between the grid and inverter impedance may cause harmonic resonances, which can lead to instability of the grid and disruption of inverter operation. The grid dynamics vary over time, so the inverter should adapt to the varying conditions to ensure system stability. Recent studies have presented online methods to adaptively control the grid-connected inverters in the sequence domain. This paper extends those previous studies, and presents an online method to adaptively control the inverters in the dq domain. In the method, the grid impedance is measured online using a pseudo-random-binary-sequence (PRBS) injection and Fourier techniques. The inverter control parameters are then adaptively adjusted based on the measurements. This paper presents experimental results based on a three-phase photovoltaic inverter using power hardware-in-the-loop (PHIL) setup.

Electric drives are a key technology for reducing energy consumption of industrial processes, for wind power generation and for enabling electric transportation. It has been observed that almost half of the global electrical energy is consumed by electric motor drives. The university course about modeling and control of electric drives must give the required knowledge to the students hence they are capable of working with the drives during their future career. The implemented problem based learning (PBL) method encourages the students towards the attitude required in their future career and supports increased motivation for learning. The paper describes the educational strategy, course objectives and the exercises including the developed laboratory setup. The number of the enrolled students and the course grades increased compared to the previous course implementations without the use of the PBL method. Moreover, the feedback from the students was more positive.

Grid interfacing of photovoltaic generators using three-phase inverters offers the advantage of constant power flow allowing smaller capacitance values to be used in the dc-link compared to single-phase inverters. Electrolytic capacitors, used in the dc-link, are often considered to decrease reliability. Reliability could be improved by using film capacitors, but their usage is limited by high cost and low capacitance. Much research has been done to minimize the dc-link capacitance value, particularly, in the field of drives and wind turbines. It has been shown that motor drive in regenerative mode contains a right-half-plane (RHP) pole in its control dynamics having a significant effect on the required dc-link capacitance. The RHP pole can cause instability as has been observed in wind turbine applications. Photovoltaic inverters have been reported to suffer from instability of the dc-link-voltage control, but the origin of the observed problems is poorly understood. This paper shows explicitly that an RHP pole is present in the control dynamics also in photovoltaic inverters affecting the minimum required dc-link capacitance. The paper proposes a minimum value for the dc-link capacitance that is required for stable operation. Design rules are given for single- and two-stage inverters. Moreover, it is shown that a source having constant power output effectively removes the RHP pole from the dc-link-voltage control dynamics.

Renewable energy-based generation of electrical energy is currently experiencing rapid growth in electrical grids [...]

Impedance-ratio-based interaction analyses in terms of stability and performance of DC-DC converters is well established. Similar methods are applied to grid-connected three-phase converters as well, but the multivariable nature of the converters and the grid makes these analyses very complex. This paper surveys the state of the interaction analyses in the grid-connected three-phase converters, which are used in renewable-energy applications. The surveys show clearly that the impedance-ratio-based stability assessment are usually performed neglecting the cross-couplings between the impedance elements for reducing the complexity of the analyses. In addition, the interactions, which affect the transient performance, are not treated usually at all due to the missing of the corresponding analytic formulations. This paper introduces the missing formulations as well as explicitly showing that the cross-couplings of the impedance elements have to be taken into account for the stability assessment to be valid. In addition, this paper shows that the most accurate stability information can be obtained by means of the determinant related to the associated multivariable impedance ratio. The theoretical findings are also validated by extensive experimental measurements.

A photovoltaic (PV) generator is internally a power-limited nonlinear current source having both constant-current- and constant-voltage-like properties depending on the operating point. This paper investigates the dynamic properties of a PV generator and demonstrates that it has a profound effect on the operation of the interfacing converter. The most important properties an input source should have in order to emulate a real PV generator are defined. These properties are important, since a power electronic substitute is often used in the validation process instead of a real PV generator. This paper also qualifies two commercial solar array simulators as an example in terms of the defined properties. Investigations are based on extensive practical measurements of real PV generators and the two commercial solar array simulators interfaced with dc-dc as well as three- and single-phase dc-ac converters.

LCL-filter is commonly used as an output-side filter in a grid-connected converter due to its good attenuation capability at the switching harmonic frequencies. LCL-filter creates several resonances in the converter dynamics which shall be damped for ensuring robust performance of the converter. The resonant behavior introduced by the LCL-filter can be attenuated with active damping (AD) instead of passive damping to improve system efficiency. Moreover, the active damping affects especially the output impedance of the converter and the output impedance should be accurately predicted in order to perform impedance-based stability analysis. This paper presents the smallsignal model for inverter-current-feedback (ICF) converter as well as output impedance properties using only the inverter-side inductor current feedback for both control and active damping. Furthermore, traditional feed-forward (FF) from the grid-voltages combined with the active damping scheme is analyzed since their simultaneous effect of is not yet discussed in the literature. Experimental measurements with 3-kW prototype are presented to verify the analysis.

Three-phase converters are common in modern power systems in interfacing of renewable sources and for improving power quality. A three-phase converter, whether operating as an inverter or active front-end, produces a varying common-mode voltage when conventional sinusoidal PWM is used. Frequency components of the common-mode voltage are located at the switching frequency which ranges usually from few kilohertz to tens of kilohertz and its multiples. The high-frequency AC component produces common-mode current which depends on the magnitude of common-mode impedance seen by the power converter. The common-mode current is usually mitigated by using common-mode chokes, complex passive filter topologies or active methods. The design of these filters is not straight-forward since the common-mode impedance is often unknown and may exhibit resonances. Therefore, an accurate method for measuring common-mode impedance is needed to enable deterministic filter design. Moreover, the common-mode impedance should be measured online, i.e., in the normal operating environment of the converter. In this paper an online method for measuring the common-mode impedance is proposed. The method can be implemented by using a converter which is able to achieve high switching frequency, such as an inverter based on SiC-switches.

Grid impedance and the output impedance of grid-connected inverter are important parameters for the operation of grid-connected systems, such as solar, wind, and other distributed-generation resource systems. The impedance mismatch between the grid and the interfacing circuit often generates harmonic resonances that lead to reduced power quality. Since the impedances usually vary over time with many parameters, online measurements are required for adaptive control of the inverters. Several methods have been proposed for quick, accurate measurements of impedances, but the use of multiple-input multiple-output (MIMO) identification techniques have not been considered. Applying the MIMO techniques, different components of the inverter output impedance or grid impedance can be simultaneously measured during a single measurement cycle. Therefore, the operating conditions of the system can be kept constant during the measurements, and the overall measurement time is significantly reduced. This paper shows the use of orthogonal binary sequences to simultaneously measure the d- and q-components of grid-connected inverter output impedance. Experimental results based on a three-phase grid-connected inverter are presented and used to demonstrate the effectiveness of the proposed methods.

LCL-filter is commonly used as an output-side filter in a grid-connected converter due to its good attenuation capability at the switching harmonic frequencies. LCL-filter creates several resonances in the converter dynamics which shall be damped for ensuring robust performance of the converter. The resonant behavior introduced by the LCL-filter can be attenuated with active damping (AD) instead of passive damping to improve the conversion efficiency. The active damping affects the output impedance of the converter, and the impedance should be accurately predicted in order to allow analyzing impedance-based stability of power electronics-based power systems. This paper presents the small-signal model for inverter-current-feedback (ICF) converter using only the inverter-side inductor current feedback for both control and active damping. Additionally, the output impedance properties are comprehensively analyzed. Experimental measurements from 3-kW prototype are presented to verify the analysis.

Grid-connected three-phase inverters are increasingly used to interface renewable energy sources to distribution networks. From the perspective of power quality the output impedance of the inverter should be as large as possible since inverters are usually operated under output-current control mode. Feedforward from grid voltages has been demonstrated to improve power quality which is an indicator for better impedance behavior. However, the effect of feedforward has not been verified by accurate impedance measurements in the literature. This paper demonstrates the effect of grid voltage feedforward on the output impedance of a three-phase inverter with LCL-filter and proposes an accurate small-signal model to predict the shape of inverter output impedance in the dq-domain. The model can be used in impedance shaping and for evaluating instability caused by impedance-based interactions. Moreover, the ideal feedforward transfer functions are derived and it is shown that the proposed method has the potential to increase the inverter output impedance significantly at the LCL-filter resonant frequency.

This paper proposes a multivariable small-signal model of a three-phase grid-connected renewable energy inverter in dq-domain. The model allows predicting the shape of inverter output admittance with an arbitrary power factor and includes the dynamic effects of DC-voltage control, AC-current control, phase-locked-loop and decoupling terms. There is no need to simplify the model by neglecting any cross-couplings between d and q-components because the model is developed by recognizing the multiple-input multiple-output (MIMO) nature of the inverter. The output admittance matrix of the inverter including the crosscoupling admittances can be accurately predicted which allows precise evaluation of small-signal stability with finite grid impedance. It is shown that neglecting the crosscoupling admittances gives inaccurate predictions on small-signal stability and the full admittance matrix should be used in stability analysis instead.

Three-phase photovoltaic inverters are usually equipped with an LCL-type output filter to reduce cost and size of the converter compared to a simple L-type output filter. However, an LCL-filter has an inherent resonance which has to be damped by a passive or active method to avoid instability. This paper presents an accurate small-signal model of the three-phase VSI-based photovoltaic inverter with LCL-type output filter using transfer matrices. Additionally, the effect of active damping on the output impedance is analyzed. The developed small-signal model has been verified by extracting frequency responses from a simulation model and a scaled-down prototype inverter. The model is shown to accurately predict the shape of inverter transfer functions such as the output impedance. Furthermore, it allows deterministic control design and accurate tuning of the active damper as well as performance evaluation of the control system.

Three-phase photovoltaic inverters are usually equipped with an LCL-type output filter to reduce cost and size of the converter compared to a simple L-type output filter. The LCL-filter has an inherent resonance which has to be damped by a passive or active method to avoid instability. This paper presents an accurate full-order small-signal model of the three-phase VSI-based photovoltaic inverter with LCL-type output filter. The model is developed in the dq-domain, where the steady-state operating point can be solved. The developed small-signal model has been verified by extracting frequency responses from a scaled-down prototype. The model is shown to give accurate predictions on the shape of inverter transfer functions such as control loop gains and output impedance. Thus, the model can be used for control design, impedance shaping and impedance-based stability analysis.

Voltage-type sources such as grid, constant-voltage-regulated power supplies, and storage batteries have dominated as input sources for power electronic converters leading to development of multitude of different power stages dedicated for such input sources. The growing application of renewable energy sources has revealed that there are also current-type input sources such as e.g. photovoltaic generator requiring different kind of power electronic converters for interfacing them to practical usage. There are persistent assumptions that the power stage itself determines the steady-state and dynamic properties of the corresponding converter. This paper introduces the decisive factors determining the properties of specific power stages. The findings are supported with comprehensive experimental measurements.

In this paper the small-signal model of a three-phase photovoltaic inverter is upgraded to include the grid-voltage feedforward. The feedforward is shown to increase d and q-components of the inverter output impedance which makes the inverter more insensitive to impedance-based interactions and explains the reported improvement in the output current harmonics. However, using a low-pass filter in the feedforward path is shown to deteoriate the effectiveness of the feedforward already at the frequencies one decade below the cut-off frequency of the low-pass filter. The effect of the feedforward is verified by extracting frequency responses from a switching model and from a prototype inverter operating at reduced voltages.

This paper introduces a simple method to measure the output impedance of a three-phase grid-connected inverter in dq-domain. The impedance measurements are most often used for model verification purposes but they can be also utilized to study impedance-based interactions between three-phase converters and the utility grid. Therefore, the methods to model and measure three-phase impedances can provide to the inverter manufacturers valuable information about their products. Implementation of the proposed method requires a three-phase voltage source, a digital signal processor, and a frequency response analyzer which are equipment typically available in most power electronic laboratories. The algorithms used in the method are explained, and the performance of the method is verified by means of frequency response measurements from a small-scale laboratory prototype.

Photovoltaic generator is often interfaced with the utility grid using a two-stage inverter. The two-stage inverter comprises of a dc-dc boost power-stage converter and a three-phase inverter. The duty ratio of the dc-dc converter can be given directly by a MPPT-algorithm or, alternatively, by a controller which regulates the voltage of the PV generator. It is shown in this paper that the two-stage inverter has a RHP-pole in its dc-link-voltage control dynamics with the first control option but the RHP-pole is effectively removed when the voltage of the PV generator is controlled. The RHP-pole introduces a minimum value for the required dc-link capacitance. The minimum value of the dc-link capacitance can be solved when the maximum power of the PV generator is known. Too small capacitance values in the dc-link make the dc-link-voltage control of the inverter unstable leading to subharmonic ac current components. The existence of the RHP-pole is inherent to the power stage and, thus, does not depend on the power or voltage level. The results are verified using a low-power prototype operating at reduced voltages and a switching model operating at grid voltage levels.

Z-source inverter (ZSI) is a recently proposed buck-boost type inverter topology that has wider input voltage range compared to a commonly used voltage-source inverter (VSI). In photovoltaic (PV) applications, the wide input voltage range increases maximum power point tracking efficiency of the interfacing converter and makes it more suitable for different photovoltaic generator configurations. This paper presents a method to derive detailed small-signal model for a grid-connected three-phase ZSI and furthermore describes how a non-linear behavior of a photovoltaic generator (PVG) can be included in the model. It is shown that a right-half-plane (RHP) zero appears in grid current control related transfer function when the PVG is operating at voltages below the maximum power point voltage. The effect of the zero can be mitigated using properly designed input voltage control and without the input voltage control the inverter is prone to instability. The appearance of the RHP zero and its effect to control dynamics is verified by simulations and experimental measurements.

Photovoltaic power has to be converted from DC into AC in grid-connected applications. The conversion is done by using a single or three-phase inverter. Phase angle and frequency of the injected current and the grid voltage have to match to achieve unity power factor. This has been commonly accomplished by using a phase-locked-loop (PLL). The PLL has a tendency to make the output impedance of the inverter to appear as a negative resistor which can introduce harmonics in the grid current or even make the inverter-grid interface unstable. This paper presents a general small-signal model of a PV inverter in the synchronous reference frame which includes the PLL. Due to the negative resistance, the inverter can become unstable when the grid has high inductance. The derived small-signal model can be used to predict the exact conditions where the instability will take place by utilizing the impedance ratio and Nyquist stability criterion.

A photovoltaic (PV) generator is internally a power limited non-linear current source having both constant current and voltage like properties depending on the operating point. This paper investigates the dynamic properties of a PV generator and demonstrates that it has a profound effect on the operation of the interfacing converter. The most important properties an input source should have in order to emulate a real PV generator are defined. These properties are important, since a power electronic substitute is often used in the validation process instead of a real PV generator. This paper also qualifies one commercial solar array simulator as an example in terms of the defined properties. Investigations are based on extensive practical measurements from dc-dc as well as three- and single-phase dc-ac converters.

Dc-dc interfacing of photovoltaic (PV) modules into the downstream system is usually done by using a boost-power-stage converter with an added input capacitor. Its dynamic properties are often assumed to be equal to those of a conventional boost converter. The input voltage of the converter is most often feedback controlled to achieve maximum power transfer in PV applications, which actually changes the converter to be a current-fed converter. This paper will show that the boost-power-stage converter with an added input capacitor has thoroughly different dynamic properties than those of the conventional voltage-fed boost converter. The effect of input-side control on the output impedance and the mode of the output port are also discussed.