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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.

The papers in this special section examine modeling and simulation methods for the analysis and design of advanced energy conversion systems. Energy conversion lies aEnergyveral fronts including materials, conversion methods, power electronics, and controls have created new opportunities for efficient energy conversion from both the conventional and new sources of energy. Our urgent need to solve many critical problems with regards to the sustainability and security of our energy system as well as the ever-increasing environmental challenges facing humanity have further spurred unprecedented opportunities for creation of innovative solutions to address these challenges.

Grid characteristics have a drastic impact on the stability and control performance of grid-connected systems. Because the grid conditions typically vary over time, online measurements are most desirable for the stability assessment, protection design, and control-system optimization of the systems. Previous studies have presented methods based on Fourier techniques and broadband sequences with which the frequency responses of the grid-connected systems, such as the grid impedance or inverter control loops, can be measured. However, online measurements under unbalanced grids with harmonic voltages have not been comprehensively considered. The present paper demonstrates how the previously applied online-measurement methods fail in the presence of unbalanced grid and voltage harmonics due to the spectral leakage caused by Fourier transform. This work also proposes a simple signal-design method to avoid the leakage. Experimental results based on a high-power grid-connected system are shown to demonstrate the effectiveness of the proposed method. acceptedVersion

The grid-connection point of photovoltaic inverters may exhibit inductive characteristics (i.e., a weak grid) due to long transmission cables as well as multiple transformers. A large grid impedance can arouse impedance-based stability problems, sustained resonances and impose power-delivery limits. This paper discusses an impedance-compensated synchronous reference- frame-PLL-angle-correction method. The method presented in this paper compensates the PLL angle according to estimated or measured grid impedance in order to achieve improved performance in weak grids. Due to the lack of explicit small-signal impedance models around the aforementioned topic, this paper presents a complete small-signal transfer function model to analyze the impedance-based stability of the PLL-angle compensation method. The results are validated with real-time hardware-in-the-loop simulations and laboratory experiments. acceptedVersion

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.

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

This study presents a method to solve the dynamic model of a grid-connected photovoltaic (PV) inverter with battery energy storage. A three-phase grid-connected solar-battery system is studied using small-signal state-space modelling in the synchronously rotating dq-reference frame. The combined effect of a PV generator and a bi-directional dc–dc battery charger (BC) on the inverter dynamic behaviour is analysed. It is shown that the characteristic right-half-plane pole in the PV inverter's dc-link voltage control dynamics shifts to a lower frequency when the BC is connected, which improves the stability of the system and allows a lower bandwidth for the dc-link voltage control. publishedVersion

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

The deadtime is an important factor in the design of power-electronic converters in order to prevent shoot-through faults. The deadtime may also cause a voltage error and an undesired damping effect which, in turn, affect the converter stability. As most effects caused by the deadtime are highly nonlinear, conventional modeling techniques to analyze these effects cannot be straightforwardly applied. This paper proposes a novel frequency-domain approach to model the damping effect caused by the deadtime in single-phase half-bridge inverters. Hardware-in-the-loop (HIL) simulations and laboratory measurements are presented and used to demonstrate the effectiveness of the proposed method. acceptedVersion

AC microgrid is an attractive way to energize local loads due to remotely located renewable generation. The AC microgrid can conceptually comprise several grid-forming and grid-following power converters, renewable energy sources, energy storage and local loads. To study the microgrid dynamics, power-hardware-in-the-loop (PHIL)-based test setups are commonly used since they provide high flexibility and enable testing the performance of real converters. In a standard PHIL setup, different components of the AC microgrid exist as real commercial devices or electrical emulators or, alternatively, can be simulated using real-time simulators. For accurate, reliable and repeatable results, the PHIL-setup should be able to capture the dynamics of the microgrid loads and sources as accurately as possible. Several studies have shown how electrical machines, dynamic RLC loads, battery storages and photovoltaic and wind generators can be emulated in a PHIL setup. However, there are no studies discussing how a three-phase grid-following power converter with its internal control functions should be emulated, regardless of the fact that grid-following converters (e.g., photovoltaic and battery storage inverters) are the basic building blocks of AC microgrids. One could naturally use a real converter to represent such dynamic load. However, practical implementation of a real three-phase converter is much more challenging and requires special knowledge. To simplify the practical implementation of microgrid PHIL-studies, this paper demonstrates the use of a commercial high-bandwidth voltage amplifier as a dynamic three-phase power converter emulator. The dynamic performance of the PHIL setup is evaluated by identifying the small-signal impedance of the emulator with various control parameters and by time-domain step tests. The emulator is shown to yield the same impedance behavior as real three-phase converters. Thus, dynamic phenomena such as harmonic resonance in the AC microgrid can be studied in the presence of grid-following converters. publishedVersion

The utility-scale wind and solar electricity production is typically connected to the power grid through multiple parallel three-phase inverters. One of the main issues in such grid-connected systems is the harmonic resonance caused by interactions between the grid and inverters. A common method for the analysis of these systems has been the impedance-based stability criterion. However, in systems that have multiple parallel inverters, the system complexity and challenges in obtaining the required impedance measurements may deteriorate the accuracy of the impedance-based approach. This paper discusses the aggregation of parallel inverters and the stability analysis of such grid-connected system. A simple method, based on impedance measurements, is shown for defining the allowable number of paralleled inverters so that the system remains stable. Experimental results are shown from power hardware-in-The-loop setup recently developed at DNV GL Flexible Power Grid Lab. acceptedVersion

Grid impedance is an important parameter which affects the control performance of grid-connected power converters. Several methods already exist for optimizing the converter control system based on knowledge of grid impedance value. Grid impedance may change rapidly due to fault or disconnection of a transmission line. Therefore, online grid identification methods have been recently proposed to have up-to-date information about the grid impedance value. This is usually done by perturbing the converter output current and measuring the response in output voltage. However, any parallel converters connected to the same interface point will cause errors, since the measured current differs from the current that is flowing through the grid interface point. This paper points out challenges and errors in grid impedance identification, caused by parallel converters and their internal control functions, such as grid-voltage support. Experimental grid-impedance measurements are shown from the power hardware-in-the-loop setup developed at DNV-GL Flexible Power Grid Lab. publishedVersion

As the share of grid-connected converters increases, potential stability issues in the grid interface of the converters are emphasized. Impedance-based stability criterion can be used to assess the stability of the interface accurately, and the grid conditions should be considered in control design of the converter. However, the grid impedance is often an unknown parameter, and thus, adaptive control is a favorable method for addressing the uncertainties in the control design. This work presents an algorithm, in which the full-order grid impedance is measured during the start-up of the device, and control bandwidth of phase-locked loop and grid-voltage feedforward gains are adjusted to optimize sensitivity function in the grid interface, based on generalized Nyquist criterion. The method can ensure robust control in weak grid conditions, while still achieving good control performance in strong grids. The method is verified with power hardware-in-the-loop experiments with a kW-scale grid-connected three-phase inverter. acceptedVersion

The rapid growth of renewable energy production increases the number of grid-connected inverters in the power system. The interface between the inverter and the grid may face stability issues, which can be assessed using impedance-based stability criterion. The frequency-dependent grid impedance is often an unknown parameter, and vastly simplified grid impedance models are widely used. Most common modeling approach is to use series-connected inductor as the grid impedance. However, measurements on real grids have shown the grid to be more complex, resonant, and time-variant. This paper introduces a grid-impedance model based on aggregation of sub-models, which drastically simplifies complex grid modeling, while still accurately captures resonances and possible time-variant behavior. Numerical sensitivity analysis is carried out for grid parameters to illustrate the significance of separate grid elements. Lastly, impedance measurements are shown for emulated full-order and aggregated impedance models in an experimental power hardware-in-the-loop setup. 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

The internal impedance of a battery has been shown to change as a function of state-of-charge (SOC) and state-of-health (SOH). Therefore, online impedance measurements can provide useful information for SOC- and SOH-estimation algorithms. Broadband injections techniques such as pseudo-random-binary-sequence (PRBS) are attractive alternative for replacing conventional electrochemical-impedance-spectroscopy (EIS) which is very slow for online battery impedance measurements. However, non-linearities of batteries have a negative impact on the measurement results obtained by the PRBS for which the identified system is assumed to be linear. This paper demonstrates the use of ternary-sequence excitation signal for battery impedance measurements. Appropriately designed ternary-sequence can efficiently capture the linear component of the impedance by canceling out the distortion caused by the non-linear parts. The presented method can be used for rapid impedance measurements and thus, as a valuable tool in online SOC- and SOH-estimation algorithms. Experimental measurements are shown from a Lithium-Iron-Phosphate (LiFePO4) battery cell.

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

The grid-forming mode of the voltage source inverters (VSI) is applied in uninterruptible power supplies and micro-grids to improve the reliability of electricity distribution. During the intentional islanding of an inverter-based micro-grid, the grid-forming inverters (GFI) are responsible for voltage control, similarly as in the case of uninterruptible power supplies (UPS). The unterminated model of GFI can be developed by considering the load as an ideal current sink. Thus, the load impedance always affects the dynamic behavior of the GFI. This paper proposes a method, to analyze how the dynamics of GFI and the controller design are affected by the load. Particularly, how the frequency response of the voltage loop gain changes according to the load and, how it can be used to the predict time-domain step response. The frequency responses that are measured from a hardware-in-the-loop simulator are used to verify and illustrate explicitly the load effect. acceptedVersion