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Design Method of Multi-sine Signal for Broadband Impedance Measurement
Abstract
With the increasing penetration of renewable energy, it is important to analyze the impedance characteristic of renewable energy grid-connected system (REGS) to implement the stability analysis of the grid connection operation. In order to further improve the accuracy of the broadband impedance measurement, this paper proposes a design method for the multi-sine signal considering both the signal-to-noise ratios (SNR) of the perturbation signal and the response signal in the impedance measurement. By quantitatively analyzing the mathematical relationship between the SNRs and the measurement error, the principle to select the minimum SNR requirement of the perturbation and response signal can be obtained so as to guide the amplitude design of the perturbation signal, which can further improve the broadband impedance measurement accuracy. The multi-sine signal is adopted in this paper to realize the proposed design method. In the application of the multi-sine signal, in order to limit the peak value of the multi-sine signal to avoid over-modulation, an improved phase design method for the multi-sine signal based on crest factor reduction algorithm is proposed. Finally, experiments based on Typhoon Control-hardware-in-loop platform (CHIL) are carried out to verify the effectiveness of proposed design method for the multi-sine signal in the impedance measurement.
... In the design of a multisine excitation signal, there is an inherent trade-off between the number of excited frequency points in the spectrum, the available power that limits the excitation amplitude, and the required SNR for accurate impedance measurements. Many works have discussed this problem [19][20][21]. ...
... The available degrees of freedom when designing the excitation signal include the amplitudes A i , frequency f i , and phase ϕ i of each individual component, along with the total number N T of frequency components. Given this definition and the number of parameters involved, the multisine signal can be properly designed to concentrate the excitation power into selected frequency components and achieve specified SNR values for each frequency [20]. ...
... Guillaume [33] proposed another method where Lp norms of the time-domain multisine signal are used as an optimization objective for the Gauss-Newton algorithm. Various attempts have been made to improve the results of the Schroeder and VDO algorithms by also utilizing combinations of the analytical formula and/or numerical iteration methods [20,34,35]. However, the optimization was carried out for a relatively low number of sinusoidal components. ...
Multisine electrochemical impedance spectroscopy (EIS) represents a highly promising technique for the online characterization of battery functional states, offering the potential to monitor, in real-time, key degradation phenomena such as aging, internal resistance variation, and state of health (SoH) evolution. However, its widespread adoption in embedded systems is currently limited by the need to balance measurement accuracy with strict energy constraints and the requirement for short acquisition times. This work proposes a novel broadband EIS approach based on a multiband multisine excitation strategy in which the excitation signal spectrum is divided into multiple sub-bands that are sequentially explored. This enables the available energy to be concentrated on a limited portion of the spectrum at a time, thereby significantly improving the signal-to-noise ratio (SNR) without substantially increasing the total measurement time. The result is a more energy-efficient method that maintains high diagnostic precision. We further investigated the optimal design of these multiband multisine sequences, taking into account realistic constraints imposed by the sensing hardware such as limitations in excitation amplitude and noise level. The effectiveness of the proposed method was demonstrated within a comprehensive simulation framework implementing a complete impedance measurement system. Compared with conventional excitation techniques (i.e., the sine sweep and the classical single-band multisine methods), the proposed strategy is an optimal trade-off solution both in terms of energy efficiency and measurement time. Therefore, the technique is a valuable solution for real-time, embedded, and in situ battery diagnostics, with direct implications for the development of intelligent battery management systems (BMS), predictive maintenance, and enhanced safety in energy storage applications.
... The impedance characteristic of the RPGE can be obtained by means of analytical impedance modeling [6]- [9] or impedance measurement [10]- [28]. The impedance nianheng@zju.edu.cn; ...
... johniej@zju.edu.cn). measurement method can be categorized into passive methods [10] and active methods [11]- [28]. The passive methods use the voltage and current harmonics that already exist in the system under test [10]. ...
... The passive methods use the voltage and current harmonics that already exist in the system under test [10]. Active methods adopt a small-signal perturbation injection to perturb the system and calculate the impedance by signal processing in frequency domain [11]- [28]. Passive methods have been proved to be ineffective if power system disturbances are not strong enough and, consequently, active methods have become more popular in the practical application [24]. ...
Impedance measurement is an effective method to obtain the impedance characteristic of renewable power generation equipment (RPGE) for stability analysis. Frequency-coupling characteristic of RPGE will bring about difficulty to measuring the impedance in a wide frequency band based on broadband signals. In order to guarantee the accuracy of the broadband impedance measurement considering the frequency-coupling characteristic, this paper explores the method to accurately measure the frequency-coupling characteristic of the RPGE. The signal-to-noise ratio (SNR) issue in view of the measurement of the frequency-coupling characteristic is also investigated. Accordingly, an evaluation method for the measurement accuracy is proposed. The evaluation results will be adopted to guide the design for the perturbation amplitudes. The redesigned multi-sine signal will be used in another group of measurement so as to achieve targeted accuracy level. Finally, experiments based on Typhoon Control-hardware-in-loop (CHIL) platform are carried out to verify the reliability of proposed evaluation method and the effectiveness of proposed design method for the perturbation amplitudes.
... It should be noted that the external noise introduced by the volatge/current sensors in the real prototype is the main factor which may interfere the measurement precision [15]- [20]. Therefore, in order to emulate the noise brought about by the sensors, a noise genertaor is adopted to generate random noise signal which will be superimposed with the volatge and current signals [25] [28]. The parametres of the type-IV wind turbine are shown in Table I. ...
... For the sake of revealing the limitation on the perturbation amplitudes, the measurement results obtained while perturbation amplitudes are 10 V are shown in Fig. 6. In order to reveal the accuracy of the measurement results, the admittance obtained by frequency scan is presented as a reference [28], which is depicted by the red solid lines. According to Fig. 6, the average magnitude error is 3.7 dB and the maximum magnitude error is 14 dB, which indicates that the measurement accuracy is poor since the measurement points are seriously deviated from the reference admittance. ...
Impedance measurement is a practical method to obtain the impedance characteristic of the power electronic equipment (PEE), which is important for the small-signal stability analysis. In the impedance measurement, the measurement results may be influenced by the external noise. Therefore, it is essential to study how to avoid the measurement errors caused by the noise. To address this issue, this paper analyzes the method of suppressing the noise interference by enhancing signal-to-noise ratio (SNR) and concludes that there is limitation on improving the measurement accuracy by merely enhancing SNR due to the practical limitation on the perturbation amplitudes. And then this paper proposes an improved impedance measurement method, by which the measurement errors caused by the noise can be decreased effectively. By investigating the influence mechanism of the noise on the impedance measurement results, the measurement error can be divided into average component and fluctuant component. The average component can be eliminated by averaging two groups of measurement results with the phase difference of π rad while the influence of the fluctuant component can be minimized by employing complex-linear fitting algorithm. Finally, experiments are conducted to verify the effectiveness of proposed impedance measurement method.
... Most of these algorithms focus on optimizing the phase of each frequency component in a multisine signal to reduce its CF value. Some algorithms simultaneously consider the amplitude and phase of each frequency component to optimize the CF value [46]. For simplicity, this article assumes equal amplitudes for each component in a multisine signal and solely concentrates on optimizing the phases. ...
Electrochemical impedance spectroscopy (EIS) is a widely employed non-invasive detection technique for battery state estimation and fault diagnosis. This article introduces a novel multi-sinusoidal pulse-width modulation (MSPWM) excitation for the purpose of online battery impedance spectroscopy identification. The introduced excitation is a unique form of broadband binary excitation that enables precise design of the amplitude and phase for every fundamental component, which can meet customized measurement requirements. Furthermore, the article proposes a method to inject the MSPWM excitation into cells and conduct online EIS measurements using reconfigurable battery systems (RBSs). Through modulation of the battery pack’s charging or discharging current during regular operations, without the need for an additional external programmable power supply, the MSPWM excitation can be injected into the RBS cells, facilitating impedance measurement without interrupting the normal operation of the system. To validate the proposed method, a DC RBS consisting of 16 lithium-ion battery cells was constructed. The experimental results show strong consistency between the EIS measurements conducted using the proposed method and those obtained from a commercial electrochemical workstation.
... The approach in [10] viewed the signal design from the perspective of optimizing an input trajectory that maximizes parameter identifiability. The signal-to-noise ratio (SNR) was utilized to guide the amplitude spectrum shaping in [11]. Signal design for kernel-based identification was considered in [12], where a two-step procedure using quadratic transformation was applied. ...
This paper considers the shaping of amplitude spectra of perturbation signals for the identification of a thermostat system. The current approach in control engineering practice utilizes flat spectrum signals, which may not result in the highest possible accuracy. This research aims to investigate the effectiveness of optimal signals with amplitude spectra designed using two state-of-the-art software approaches, namely the model-based optimal signal excitation 2 (MOOSE2) design and the optimal excitation (optexcit) design, in improving estimation accuracy. Such a comparison on a real system is currently lacking. In particular, there exists a research gap on how the combined choice of signal and model structure affects performance measures. In this research, two model structures are used, which are the autoregressive with exogenous input (ARX) and the output error (OE) model structures. Four performance measures are compared, namely the determinant of the covariance matrix of the parameter estimates and the minimum error, mean error and maximum error in the frequency response. Results show that the optimal signals are effective in reducing the determinant of the covariance matrix and the maximum error in the frequency response for the thermostat system, when applied in combination with the ARX model structure. The flat spectrum signal remains very useful as a general broadband perturbation signal as it provides a good overall fit of the frequency response. The findings from this work highlight the benefits of applying optimal signals especially if the identification results are to be used for control, since these signals improve key performance measures which have direct implications on controller design.
... As a summary, Table I compares the features of the abovementioned existing noncontact in-circuit impedance measurement setups with the proposed SPS. There are reported works based on the multisine excitation for multifrequency in-circuit impedance measurement with good performance [32], [33], [34]. Their measurement setups are based on the V-I approach, which require some form of direct electrical contact with the energized SUT, and may impose electrical hazards, especially for high operating voltage. ...
The single-probe setup (SPS) based on the inductive coupling approach is a promising candidate for in-circuit impedance measurement of an energized electrical system due to its non-contact characteristics and simple configuration. However, the conventional SPS performs the measurement with a frequency-domain measuring instrument via stepped swept-sine excitation. It measures in-circuit impedance at only single frequency at a time while sweeping across frequencies of interest, which is not only inefficient but also not fast enough to capture in-circuit impedance with time-variant characteristics. To overcome these limitations, this paper proposes a novel SPS with a time-domain measuring instrument via multi-sine excitation. The proposed SPS can perform multi-frequency simultaneous measurement of in-circuit impedance without direct electrical contact. By combining it with a short-time Fourier transform (STFT) algorithm, in-circuit impedance with time-variant characteristics can be captured. Experimental case studies validate the capability and accuracy of the proposed SPS.
... And the controllers of DFIG are implemented in a TMS320F28335/Spartan6 XC6SLX16 DSP+FPGA control board. Applying the CHIL to analyze the stability of megawatt DFIG-grid interconnected system has been proposed in [30]- [32]. The parameters of the system are listed in Table I and Table II in section APPENDIX. ...
With the increasing applications of grid-connected voltage source converters, it is important to analyze the impedance characteristic of the grid-connected system to implement the stability analysis of the grid connection operation. Compared with the three-phase three-wire system, an additional zero-sequence path exists in the three-phase four-wire system. Therefore, it is necessary to consider the influence of the zero sequence when analyzing the stability of the system. In this paper, an impedance model including positive-sequence, negative-sequence and zero-sequence impedance of the three-phase four-leg grid-connected inverter is established. Through impedance characteristic analysis, the relationships between zero-sequence impedance and positive-sequence, negative-sequence impedance can be found which are decupled. Based on the developed zero-sequence impedance model, the main factors affecting the zero-sequence impedance model are revealed. Then, the system stability consisting of the grid and three-phase four-wire inverter is investigated, and the experimental results validate the theoretical analysis.
Impedance measurement is an effective method to obtain the dynamic characteristics of a renewable energy generator (REG). Signal-to-noise ratio (SNR) is an important index to analyze the noise resistance of measurement and to ensure measurement accuracy. Existing research on SNR primarily focuses on single-input single-output (SISO) impedance models. Frequency coupling characteristics make the impedance multiple-input multiple-output (MIMO) models. Measuring frequency coupling characteristics involves the intertwinement of eight measurement signals. As a result, solely relying on the SNR of each individual measurement signal cannot accurately reflect measurement accuracy, nor can it provide a theoretical basis for improving measurement accuracy. In this paper, considering the intertwinement of eight measurement signals and frequency coupling characteristics, a generalized-SNR (GSNR) index is proposed to evaluate the accuracy and depicted as error bars in Bode diagram. Moreover, a GSNR-based accuracy enhancement method, including quantitative design of perturbation amplitudes and overlap extraction of multiple error bars, are proposed to realize the broadband accurate measurement. Finally, control-hardware-in-loop (CHIL) experiments are carried out to verify the effectiveness of the proposed method.
Accurate identification for the frequency-coupling admittance of the grid-connected converters is a key factor in impedance stability analysis. However, not all information about the grid-connected converters is available, which results in the “black/grey-box” phenomenon. It is challenging to identify the frequency-coupling admittance of black/grey-box devices under all operating conditions. An accurate identification method of the frequency-coupling admittance under all operating conditions is proposed in this paper, which can be used for grey-box devices. The influence of the transmission power on frequency-coupling admittance is quantified, which can be used to analyze the amplitude and phase characteristics. A capacitor identification method based on voltage disturbance is proposed, which can be used to accurately solve the actual capacitor parameter. Therefore, the impact of capacitance parameter mismatch on frequency-coupling admittance can be eliminated. In addition, the frequency-coupling admittance under all operating conditions is modeled, which can quantify the impact of capacitor parameter mismatch. Finally, a hardware prototype of the grid-connected converter is built; the accurate identification method of frequency-coupling admittance for the grid-connected converter under all operating conditions is verified by simulation and experimental results.
Perturbation injection device has become a key tool for obtaining impedance information by administering a perturbation signal to the system under investigation. It is important to reasonably design the injected perturbation signals in order to obtain impedance curves quickly and accurately. This paper proposes a multi-stage design strategy for a broadband perturbation signal (BPS) intended for impedance measurement. Firstly, initial BPS is designed considering various factors affecting the measurement accuracy, including peak, selectable frequencies, and frequency coupling. Then, an error estimation technique is introduced to assess measurement precision, with the ensuing findings applied to the subsequent BPS design stage. The iterative application of these stages allows for the continuous approximation of the real impedance curve. The paper concludes with a series of simulations demonstrating both the practicality and precision of the proposed technique.
Lithium-ion batteries have extensive usage in various energy storage needs, owing to their notable benefits of high energy density and long lifespan. The monitoring of battery states and failure identification are indispensable for guaranteeing the secure and optimal functionality of the batteries. The impedance spectrum has garnered growing interest due to its ability to provide a valuable understanding of material characteristics and electrochemical processes. To inspire further progress in the investigation and application of the battery impedance spectrum, this paper provides a comprehensive review of the determination and utilization of the impedance spectrum. The sources of impedance inaccuracies are systematically analyzed in terms of frequency response characteristics. The applicability of utilizing diverse impedance features for the diagnosis and prognosis of batteries is further elaborated. Finally, challenges and prospects for future research are discussed.
The increasing use of inverter-based resources (IBRs) in power systems highlights the need for a deep understanding of their stability and dynamics. Traditional analytical models, limited by the black-box nature of IBRs, underscore the importance of frequency-domain methods through measured admittance. Facing challenges in real-world admittance measurement, such as the absence of ideal voltage or current sources, the use of measurement inverters as perturbation sources has emerged as a promising approach, despite drawbacks like reduced system stability and increased measurement time. This article introduces a novel control strategy for measurement inverters, elucidating the impact of abc/dq and dq/abc transformations on admittance measurement. The key advancements are an analysis of the admittance contributions from these transformations and the implementation of double phase-locked loops in the measurement inverters, aimed at improving stability and decreasing measurement duration.
Under the weak grid conditions, the number of oscillation accidents caused by the impedance mismatch between the power grid and the grid-tied inverters are on the rise, which makes the accurate identification of the broadband impedance characteristics of the power grid that can sense the current operating state of the system an urgent problem to be solved. In this paper, theoretically analyzing the discrepancy between the impedance characteristics of the conventional purely inductive grid impedance and the generalized grid impedance by comparing the amplitude-phase characteristic curves of both, which in turn affects the analytical results of stability. Subsequently, in order to accurately recognize the GGI, a signal-to-noise ratio (SNR) design scheme based on the active impedance identification technique is proposed, which investigates the impact of signal-to-noise ratio on the identification accuracy from the perspective of a grid-tied inverter, with the GGI including transmission lines and grid-tied devices external to the inverter as the identification target. Moreover, current disturbances at different characteristic harmonic frequency points are injected into the grid in MATLAB/Simulink platform to verify the accuracy of the SNR design scheme with the help of the sweep results of GGI. Finally, the significance of generalized grid impedance as the main form of the grid is further revealed through comparative experiments on the RT-BOX platform.
We evaluate the feasibility of spectral (STDR) and spread spectrum time domain reflectometry (SSTDR) as a new modality for impedance measurement to test energized/noisy systems over a very broad frequency spectrum (near DC to GHz) as well as multiple channels in parallel. We simulate how the S/SSTDR signal parameters (SNR frequency and length of the PN signals) affect the accuracy and usable frequency band for reflection coefficient and impedance measurement. An initial measurement validation is included. We conclude with a recommendation of what will be required for a viable multi-channel impedance (and reflection, transmission coefficient) measurement system for either energized or non-energized systems, in noisy environments, and that can test multiple channels simultaneously.
In order to achieve the major strategic goal of carbon peaking by 2030 and carbon neutralization by 2060, a new power system with new energy should be built to create a clean, low-carbon, safe and efficient energy system, and further promote the construction of the power market. It is necessary to build a peaking capacity market to ensure the safe and stable operation of the power grid. In the paper, a peaking capacity market mechanism is designed to encourage thermal power units to strengthen equipment transformation, operation and maintenance, and reduce the unscheduled shutdown of thermal power units. Key processes of the market including market demand evaluation, bidding, clearing, settlement are introduced. Based on the market operation, the power generation capacity of thermal power resources is expected to be fully enhanced during peaking periods of power system to ensure the system-wise capacity adequacy.
Frequency-domain impedance or admittance model is widely applied to analyze harmonic stability of power electronic converters. Conventionally, the converter impedance is modeled holistically, without exhibiting the sole effect of different control and phase-locked loop (PLL). Besides, harmonic voltage or current injection external to the converter is usually adopted, which involves dedicated equipment and introduces unexpected inner impedance. In this paper, the response of voltage perturbation upon AC-DC power converter along various voltage signal flow paths is analyzed, based on superposition principle. Each part of admittance and its effect on stability can therefore be quantified explicitly. By injecting harmonic perturbation through the identified paths within the converter controller, each part of admittances, with and without the concerned control or PLL blocks, are measured and summed to be the total admittance. Harmonic voltage mitigation control implemented on a grid-forming converter creates an ideal grid with constant voltage and nearly zero inner impedance at the injected harmonic frequency. The proposed admittance analysis and measurement is successfully applied to power converter with different PLL, voltage feedforward, output power control, DC voltage control and grid-forming cascaded control. Effectiveness of the analysis and the proposed admittance measurement approach are validated by comprehensive simulation and hardware test.
Impedance measurement is an effective method to obtain the impedance characteristic of the renewable power generator (RPG). Discrete Fourier transformation (DFT) is commonly used to extract measurement signals. However, when there is slight fundamental frequency deviation (FFD), the frequency resolution of DFT may be insufficient due to spectral leakage (SL). Under this circumstance, the measurement signals will be overlapped with the fake spectra caused by the SL and unable to be extracted precisely. Besides, when frequency coupling characteristic exists, FFD will also lead to the change of coupling frequencies. Thus SL will also happen at the coupling frequencies which make it more difficult to extract measurement signals. Targeting this issue, this paper analyzes the mechanism of SL and grasps the characteristics of fake spectra caused by SL. Accordingly, a Hann-window (HW)-based method is proposed to accurately extract the measurement signals during FFD. The superiority of proposed method is none of the requirement to extend the original measurement time. Finally, the experiments based on Control-hardware-in-loop (CHIL) are carried out to verify the effectiveness of proposed method.
Broadband battery impedance spectroscopy brings valuable information that facilitates states estimation and fault diagnosis, which are of extensive research interests at present. pseudo random sequence (PRS) provides a promising tool for realizing online battery impedance measurements, yet it suffers from an insufficient signal-to-noise ratio (SNR). Motivated by this, this paper proposes a novel hybrid pseudo random sequence (HPRS) to boost the signal power in the low-frequency region, where the measurement data is exceptionally robust against noise corruption. The disturbances are further suppressed by applying a specially designed adaptive bilateral impedance filter (ABIF), which considers signal power content and impedance measurements' distribution enabling a nearly unbiased result. The feasibility of the proposed HPRS signal is verified experimentally by comparing it with the typical PRS signal and step signal. The results suggest superior broadband impedance measurements' accuracy and robustness under different ambient temperatures and state of charges (SOCs) and the maximum normalized root mean square error (NRMSE) is limited to 0.77 .
Increasing penetration of grid-connected renewable energy systems and smart loads based on power electronics converters (such as solar inverters, wind turbines, and variable speed motor drive systems) has been increasing in low- and medium-voltage power networks. High penetration of power electronics converters has the potential to degrade the power quality of grids introducing strong resonances in grids, waveform distortion (e.g., harmonics), transients, or flicker, which pose severe risks to the distribution networks and connected equipment. Especially waveform distortion above and below 2 kHz, as well as fast transients, can cause failures in grid communication, degradation of equipment such as distribution transformers, and losses of energy, and can affect system protection. This further faces the community with challenges in the measurement of voltage and current as well as in maintaining the requirements of the electricity codes and contractual obligations between network operators and users. The automobile industry is going through an incredible transformation from internal combustion engines (ICEs) to all-electric vehicles (EVs). Some European countries have decided to ban all petrol-powered cars in the next 25–40 years. The fast-growing penetration of EVs charger will result in new challenges in distribution networks and connected loads. For example, grid impedance and its variation have a significant impact on grid-connected power converter behavior, interaction, stability, and harmonic emission and immunity. Thus, grid impedance modeling and estimation are required for existing and future analysis of distribution networks with a high number of grid-connected inverters. This Special Issue aimed to emphasize and document the latest research that addresses the abovementioned emerging challenges. In response to the call for articles, the total number of manuscripts received was 53, and 15 articles were accepted for publication. The submitted manuscripts came from 19 different countries, covering most of IEEE regions, i.e., Australia, China, Hong Kong, India, Bangladesh, Iran, Turkey, Finland, Sweden, Denmark, Belgium, France, Germany, the U.K., the United States, Canada, South Africa, Mexico, and Chile. From the accepted articles, all 15 articles address issues directly relevant to this Special Topic. Broadly, the articles can be categorized as follows: control and stability, assessment of frequency-dependent impedance, power quality aspects in distribution networks, and grid distortion impacts on power converters.
Online measurements of the battery impedance provides valuable information on the battery state-of-charge and state-of-health which can be utilized for improving the safety and the performance of the associated system. The electrochemical-impedance- spectroscopy (EIS) is widely used for battery impedance measurements but it is not the most applicable solution for online measurements due to its slowness and complexity. These drawbacks can be improved using broadband signals, such as, pseudo-random-sequences (PRS), which are fast and easily implementable. However, the non- linear behavior of batteries have significant effect on the impedance measurements and the selection of the PRS signal. Majority of the PRS signals are applicable for measurements of linear systems but also signals for non-linear system identification do exist. Moreover, the reduced accuracy and signal-to-noise ratio of the PRS signals compared to the EIS make the filtering of the results as well as the amplitude design important aspects. This paper demonstrates the use of two PRS signals, the pseudo-random-binary-sequence (PRBS) and a ternary- sequence with better toleration to battery non-linear effects, with comprehensive amplitude and filtering design for battery impedance measurements. The results are referenced and validated to practical EIS measurements in various operating conditions for lithium-iron-phosphate cell.
The accurate information of the wide-bandwidth impedance versus frequency is urgently needed for evaluating the system resonances, instabilities and operations of the railway traction power system (TPS), and to avoid/control the harmonic resonance and oscillation issues. As the system topology and detailed parameters of the TPS are not fully known even timely varying, we have to obtain the detailed wide-bandwidth impedance information through exciting harmonic disturbance into the system and then calculating the response information. Therefore, a controlled wide-bandwidth impedance measurement approach is presented here. In which, a butterfly-type disturbance circuit and chirp-pulse width modulation (PWM) signal model are cooperated to generate the desired controlled-bandwidth harmonics with a high aggregation as well as the average amplitude. Impedance measurement results of the proposed approach have been validated through both simulation and experiment. Considering the measured errors, the proposed method is efficient in testing the wide-bandwidth impedance of the single-phase railway traction system.
Electrochemical Impedance Spectroscopy (EIS) is a valuable tool for the characterization of electrical, thermal and aging behavior of batteries. In this paper, an EIS measurement technique to acquire impedance spectra with high time resolution is examined, which can be used to gather impedance data during dynamic operating conditions. A theoretical analysis of the used multi-sine excitation signals is performed in detail and a practical measurement system is presented and validated. Afterwards, EIS measurements during the charging process of a lithium-ion battery are performed and discussed.
The operation of more electric aircraft is dependent on the embedded power grid. Therefore, the on-board power-distribution system must be reliable, having a high level of survivability, and promptly respond to any change in aircraft's operation. Recent studies have presented a number of frequency-response-based tools with which to analyze both single- and multi-converter systems. The methods can be efficiently applied for on-board system analysis, stability assessment and adaptive control design. Most often, wideband measurement techniques have been applied to obtain the frequency response from a specific converter or a subsystem required for the analysis. In the methods, a broadband excitation such as a pseudo-random binary sequence (PRBS) is used as an external injection, and Fourier techniques are applied to extract the spectral information. This paper presents implementation techniques of the wideband methods using power-hardware-in-the-loop measurements based on OPAL-RT real-time simulator. The presented methods make it possible to modify the system characteristics, such as impedance behavior, in real time, thereby providing means for various stability and control design tools for on-board power distribution systems. Experimental measurements are shown from a high-power energy distribution system recently developed at DNV GL, Arnhem, Netherlands. OAPA
DC distribution systems typically consist of several feedback-controlled switched-mode converters forming a complex power distribution system. Consequently, a number of issues related to stability arise due to interactions among multiple converter subsystems. Recent studies have presented methods such as passivity-based stability criterion where the stability and other dynamic characteristics of an interconnected system can be effectively analyzed using bus-impedance measurement. Studies have presented online measurement techniques where the bus impedance is obtained by combining together the measurements of input and output impedances of single converters in the system. Since the converters are coupled, the presented measurement techniques require several measurement cycles in order to sequentially measure the individual impedances to be combined to obtain the overall bus impedance. This paper presents a measurement technique based on injection of orthogonal binary sequences. Applying this method, all the impedances in the system can be simultaneously measured during one measurement cycle. Therefore, the overall measurement time of the bus impedance is reduced compared to conventional measurement techniques. Furthermore, the method guarantees that the system dynamics do not change between measurements, and therefore, the computed bus impedance is not distorted. Experimental results are presented and used to demonstrate the effectiveness of the proposed method.
The large-scale integration of power electronic based systems poses new challenges to the stability and power quality of modern power grids. The wide timescale and frequency-coupling dynamics of electronic power converters tend to bring in harmonic instability in the form of resonances or abnormal harmonics in a wide frequency range. This paper provides a systematic analysis of harmonic stability in the future power-electronic-based power systems. The basic concept and phenomena of harmonic stability are elaborated first. It is pointed out that the harmonic stability is a breed of small-signal stability problems, featuring the waveform distortions at the frequencies above and below the fundamental frequency of the system. The linearized models of converters and system analysis methods are then discussed. It reveals that the linearized models of ac-dc converters can be generalized to the harmonic transfer function, which is mathematically derived from linear time-periodic system theory. Lastly, future challenges on the system modeling and analysis of harmonic stability in large-scale power electronic based power grids are summarized.
This paper analyzes the small-signal impedance of three-phase grid-tied inverters with feedback control and phase-locked loop (PLL) in the synchronous reference (d-q) frame. The result unveils an interesting and important feature of three-phase grid-tied inverters – namely, that its q–q channel impedance behaves as a negative incremental resistor. Moreover, this paper shows that this behavior is a consequence of grid synchronization, where the bandwidth of the PLL determines the frequency range of the resistor behavior, and the power rating of the inverter determines the magnitude of the resistor. Advanced PLL, current, and power control strategies do not change this feature. An example shows that under weak grid conditions, a change of the PLL bandwidth could lead the inverter system to unstable conditions as a result of this behavior. Harmonic resonance and instability issues can be analyzed using the proposed impedance model. Simulation and experimental measurements verify the analysis.
Multisine signal with a low crest factor (CF) can bring a high signal-to-noise ratio for fast frequency response function (FRF) estimation. Synthesis of a low CF multisine with the given amplitude spectrum depends on optimum selection of the initial phases of its cosinusoidal components. The solutions investigated can be generally divided into two branches: (1) the analytical method based on direct formula calculation; and (2) the numerical method based on iterative computations. The analytical method works well only for an equidistant and flat amplitude spectrum, while the numerical method can generally output better results, even for a sparse or non-flat spectrum, but the number of iterations might be huge. This paper presents an improved CF minimization algorithm to synthesize multisine signals based on the combination of the previous Schroeder analytical method and the Van der Ouderaa (VDO) iteration procedure. The improved algorithm adopts the Schroder phases as the iterative initial phases, and employs a logarithmic clip function of the iterative index i in the VDO iteration procedure. Comprehensive experiments of multisine synthesis on three types of cosinusoidal amplitude spectra are performed, and the resulting CFs remain the lowest level in all cases compared with the earlier methods. The proposed algorithm provides a fast and efficient solution to synthesize multisine with the lowest CF for an arbitrary user-prescribed spectrum.
This paper addresses the harmonic stability caused by the interactions among the wideband control of power converters and passive components in an ac power-electronics-based power system. The impedance-based analytical approach is employed and expanded to a meshed and balanced three-phase network which is dominated by multiple current- and voltage-controlled inverters with LCL- and LC-filters. A method of deriving the impedance ratios for the different inverters is proposed by means of the nodal admittance matrix. Thus, the contribution of each inverter to the harmonic stability of the power system can be readily predicted through Nyquist diagrams. Time-domain simulations and experimental tests on a three-inverter-based power system are presented. The results validate the effectiveness of the theoretical approach.
The maximum amplitude of a waveform corresponding to a particular harmonic spectrum depends on the phases of its harmonic components. A waveform with a low peak-to-rms ratio is desirable in situations requiring a maximum signal-to-noise ratio. This paper introduces a genetic algorithm-based method for selecting the phases that produces better results than previously described methods. Results for four different amplitude spectra are given. For the case of a flat spectrum with up to 40 harmonics, the genetic algorithm finds peak factors peak/& rms ranging from 0.98 to 1.24. © 1996 Acoustical Society of America.
The dq-frame impedance model is increasingly employed to analyze the grid-converter interactions in three-phase systems. As the impedance model is derived at a specific operating point, it is required to connect the converter to actual power grids during the impedance measurement. Yet, the non-zero grid impedance causes cross-couplings between perturbation and response signals, which consequently jeopardize the accuracy of impedance measurement. This paper analyzes first the coupling effect of the grid impedance on the measured impedance, and then proposes a multiple-input multiple-output (MIMO) parametric impedance identification method for mitigating the effect. Instead of using the Fast Fourier Transform (FFT), the method allows for obtaining the parametric impedance model directly from the time-domain data. Further, with the simultaneous wideband excitations, only a single measurement cycle is needed. The effectiveness of the method is verified in both simulations and experimental tests.
Impedance-based method is an effective method to analyze the system stability. Based on the impedance stability theory, a doubly fed induction generator (DFIG) based wind power generation system can be decoupled into a positive- and a negative-sequence subsystem. Then, under small-signal operation, each subsystem is assumed to have linear characteristic in the frequency domain. Therefore, a single-in-single-out stability criterion can be applied for each subsystem to analyze the stability of the interconnected system consisted of the DFIG system and the grid. However, when there is frequency coupling in the DFIG system, this linear assumption may lead to wrong conclusion of the system stability analysis. The frequency coupling of DFIG can be caused by the PLL and the asymmetric rotor current control. In this paper, the frequency coupling characteristic of DFIG caused by these two causes will be studied, and an analytical model that describes the frequency coupling of DFIG will be developed and validated by simulations. Based on this derived model, the system stability and the influencing factors of frequency coupling will be analyzed.
Sequence impedance models are presented for type-III wind turbines that use doubly-fed induction generators (DFIG) and back-to-back voltage source converters. The models, presented in analytical form for both positive and negative sequence impedances, include the effects of the induction machine, both the stator and rotor side converters as well as their controls, and the phase-locked loop (PLL) used for synchronizing converter control with the grid voltage. The models are valid from subsynchronous frequency up to 1/3 of the switching frequency of the converter, making them useful for the analysis and mitigation of both subsynchronous and supersynchronous resonances and control interactions of type-III turbines with different types of grid.
This paper deals with damping of resonance between grid-connected inverters and the power grid. This paper proposes a narrow-band digital filtering technique to resolve the resonance problem by shaping the inverter output impedance at selected frequencies without affecting the characteristics of the inverter outside the selected frequency range. A frequency-sampling method is used to implement the narrow-band digital filter which allows direct control of the filter's amplitude and phase response in accordance with damping requirements. The experimental results are presented to demonstrate the performance of the proposed method.
Grid impedance is an important parameter for the operation and control of grid-connected inverters used for the integration of solar, wind, and other distributed generation resources. Since the grid impedance usually varies over time and with grid operation conditions, online measurement is required for adaptive control of grid-connected inverters. Existing online measurement methods based on impulse perturbation and Fourier analysis require large current or voltage injection that may interfere with normal operation of the inverter. This paper proposes the use of maximum-length binary sequence (MLBS) injection and averaging Fourier techniques to overcome the drawbacks of impulse injection. Experimental results based on a three-phase grid-connected inverter are presented and used to demonstrate the effectiveness of the proposed methods.
This paper presents small-signal impedance modeling of grid-connected three-phase converters for wind and solar system stability analysis. In the proposed approach, a converter is modeled by a positive-sequence and a negative-sequence impedance directly in the phase domain. It is further demonstrated that the two sequence subsystems are decoupled under most conditions and can be studied independently from each other. The proposed models are verified by experimental measurements and their applications are demonstrated in a system testbed.
AC distributed power systems (DPS) can be found in several new and emerging applications. Similar to dc distributed power systems, an ac DPS relies on power electronics and control to realize its functions and achieve the required performance. System stability and power quality are important issues in both types of systems due to the complex system behavior resulted from active control at both the source and the load side. Traditional small-signal analysis methods cannot be directly applied to an ac DPS because of the periodically time-varying system operation trajectory. Possible solutions to this problem include transformation into a rotating ( dq ) reference frame, modeling using dynamic phasors, reduced-order modeling, and harmonic linearization. This paper reviews these small-signal methods and discusses their utilities as well as limitations. Compatibility of each type of models with state-space and impedance-based system analysis approaches will also be discussed. Problems related to the linearization of phasor-based models and their use in impedance-based system analysis are highlighted in particular.
Recent progress in the identification of switching power converters using an all-digital controller has granted network analyzer functionality to the control platform. In particular, the cross-correlation technique provides a nonparametric identification of a converter's small-signal control-to-output frequency response. The literature shows the viability of this technique as well as a few improvements to the basic technique. This online network analyzer functionality allows new flexibility in the areas of online monitoring and adaptive control. In this paper, several improvements to the cross-correlation method of system identification are proposed that aim to further improve the accuracy of the frequency response identification, particularly at high frequencies near the desired closed-loop bandwidth frequency. Additionally, an extension to the cross-correlation method is proposed that allows measurement of the control loop gain without ever opening the feedback loop. Thus, performance and stability margins may be evaluated while maintaining tight regulation of the output. Simulation and experimental results are shown to verify the proposed improvements and extension.
Grid-connected inverters are known to become unstable when the grid impedance is high. Existing approaches to analyzing such instability are based on inverter control models that account for the grid impedance and the coupling with other grid-connected inverters. A new method to determine inverter-grid system stability using only the inverter output impedance and the grid impedance is developed in this paper. It will be shown that a grid-connected inverter will remain stable if the ratio between the grid impedance and the inverter output impedance satisfies the Nyquist stability criterion. This new impedance-based stability criterion is a generalization to the existing stability criterion for voltage-source systems, and can be applied to all current-source systems. A single-phase solar inverter is studied to demonstrate the application of the proposed method.
In this paper, a new control algorithm is proposed to achieve optimal dynamic performance for dc-to-dc converters under a load current change and for a given set of circuit parameters, such as the output inductor, output capacitor, switching frequency, input voltage, and output voltage. Using the concept of capacitor charge balance, the proposed algorithm predicts the optimal transient response for a dc-to-dc converter during a large signal load current change. During steady state operation, conventional current mode proportional-integral-derivative (PID) is used. During large signal transient conditions, the new control algorithm takes over. The equations needed to calculate the transient time and the required duty cycle series are presented. By using the proposed algorithm, the optimal transient performances, including the smallest output voltage overshoot/undershoot and the shortest recovery time, is achieved. In addition, since the large signal dynamic response of the power converter is successfully predicted, the large signal stability is guaranteed. Experimental results show that the proposed method produces superior dynamic performance over a conventional current mode PID controller.
In this paper, a technique is presented for measuring the harmonic
impedances of an unbalanced three-phase distribution feeder. The
technique uses transients in bus voltages and feeder currents generated
by several close-trip operations of the shunt capacitor bank. The work
is based on the assumption that the impedance of the feeder does not
change over time during which the switching operations are performed.
Mathematical development of the technique is verified with the
laboratory and the field tests. The technique provided good measurements
of the harmonic impedances up to 1.5 kHz for the given capacitor sizes.
Statistical indices were developed to assess the accuracy of the
estimated impedance values
Inexpensive portable instrumentation is used to measure the
impedance of an example utilization-voltage power system, With the power
system in normal operation, line-to-neutral, line-to-ground and
neutral-to-ground impedances are measured over a bandwidth of 20 Hz-24
kHz. The measured impedance is presented as resistance and inductance,
which vary with frequency. Based on the measurements, additional
calculations are performed to find the resistance and inductance of
every conductor in the system. This complete wide-band characterization
of power system impedance provides valuable data for power quality
calculations
Low crest-factor of excitation and response signals is desirable
in transfer function measurements, since this allows the maximization of
the signal-to-noise ratios (SNRs) for given allowable amplitude ranges
of the signals. The authors present a new crest-factor minimization
algorithm for periodic signals with prescribed power spectrum. The
algorithm is based on approximation of the nondifferentiable Chebyshev
(minimax) norm by l p-norms with increasing values of
p , and the calculations are accelerated by using FFTs. Several
signals related by linear systems can also be compressed simultaneously.
The resulting crest-factors are significantly better than those provided
by earlier methods. It is shown that the peak value of a signal can be
further decreased by allowing some extra energy at additional
frequencies
An algorithm is presented to minimize the peaks in the time domain
of bandlimited Fourier signals. This method has the ability to compress
signals effectively without disturbing their spectral magnitudes. A
computationally efficient algorithm is presented that leads to strongly
compressed signals (crestfactors of 1.41 compared to 1.67). The method
is applicable not only to flat spectrum magnitudes but to any frequency
domain energetic distribution
This correspondence considers the problem of how to adjust the phase angles of a periodic signal with a given power spectrum to minimize its peak-to-peak amplitude. This "peak-factor problem" arises in radar, sonar, and numerous other applications. However, in spite of the wide-spread interest it has evoked, the peak-factor problem has so far defied solution except in cases where the number of spectral components is small enough to permit an effectively exhaustive search of all phase angle combinations. In this correspondence, a formula for the phase angles is derived that yields generally low peak factors, often comparable to that of a sinusoidal signal of equal power. A formula is also derived for the case in which the phase angles are restricted to 0 and pi . The latter formula is applicable to the problem of constructing binary sequences of arbitrary length with Iow autocorrelation coefficients for nonzero shifts.
Online measurement of three-phase AC power system impedance in synchronous coordinates
- Shen
Online grid impedance measurement using discrete-interval binary sequence injection
- T Roinila
- M Vilkko
- J Sun