This article presents a primary-side dual-loop hysteresis control method for series-series (SS) compensated inductive power transfer (IPT) systems. One of the two parallel hysteresis loops is designed to achieve fast transient response, while the other ensures accurate steady-state power control and suppression of power oscillations in battery charging applications with constant voltage load (CVL) characteristics. Since the transferred power is accurately regulated by introducing individually skipped voltage pulses, zero voltage switching (ZVS) can be achieved across the entire operating range. The method also prevents the skipped pulses from exciting the poorly damped oscillation mode that can appear in IPT systems with CVLs. The closed-loop control is exclusively implemented on the primary side, eliminating the need for high-speed communication while allowing for steady-state correction through a low-bandwidth communication link. In addition to fast dynamic response, the proposed implementation enables high efficiency in a wide range of power and coupling while providing accurate power reference tracking. The proposed method is validated by simulations and results from a small-scale laboratory prototype, confirming its effectiveness and practicality.

This paper presents an analysis of small-signal stability and parametric sensitivity in the isolated ac network of a large-scale offshore wind farm with two HVDC terminals. The wind farm is assumed to be based on Type-4 wind turbines with grid-following (GFL) control organized in two clusters, each associated with a HVDC converter terminal. The two parts of the wind farm are interconnected with an ac cable, and the HVDC converters are controlled as Virtual Synchronous Machines (VSMs) to provide grid-forming (GFM) functionalities and ensuring shared frequency and voltage control in the islanded ac grid. Two different approaches for the small-signal analysis have been considered, based either on explicit analytical modeling or on numerical analysis in Matlab/Simulink, and the advantages or disadvantages of both approaches are discussed. Sensitivity analysis is conducted to examine the influence of key internal parameters of the VSM implementations, especially considering the virtual impedance required for parallel operation. While the analysis confirms that sufficient small-signal stability margins can be ensured in a wide range of parameters and operating conditions, it is also shown how too high or too low values of the virtual impedance can cause stability issues depending on the VSM implementation.

This paper presents a simulation-based investigation of compatibility between grid forming converters with different control system implementations when operating in the islanded ac-grid of an HVDC-connected offshore wind farm. A system configuration with two HVDC-terminals connected to separate clusters of a large-scale offshore wind farm with an internal ac-connection is assumed. Both HVDC converters operate in grid forming mode and share the responsibility for voltage and frequency control within the islanded offshore ac grid. Grid forming functionality is assumed by applying the general framework of Virtual Synchronous Machine (VSM)-based control. Three different VSM-implementations are considered and all their combinations are investigated. The intention is to evaluate the compatibility of the different implementations for parallel operation in an islanded system and to reveal if any specific combinations of grid forming control schemes have advantages or disadvantages in terms of interoperability-friendliness. Simulation studies are conducted in Matlab/Simulink, and the results demonstrate that all the investigated implementations can operate safely in the same system. However, there are differences in the sensitivity to key parameters, which implies that different parameter values might be required to ensure good dynamic response for different combinations of VSM implementations.

This paper presents an iterative algorithm for tuning of converter control loops by utilizing parametric eigenvalue sensitivities. The tuning algorithm is designed to affect the eigenvalues representing poorly damped oscillations or slow responses that significantly impact the system outputs. The critical eigenvalties to be addressed by the algorithm are identified by weighting their real part and their corresponding Hankel Singular Values (HSV). For this purpose, a simple procedure is proposed to associate each eigenvalue to an HSV. The functionality of the proposed algorithm is illustrated by a numerical example showing the tuning of a grid-connected voltage source converter with a grid-forming control strategy. The results show how the dynamic response of a system can be significantly improved by utilizing the proposed tuning algorithm for moving the location of the identified critical eigenvalues. Moreover, it is highlighted how identification of critical modes by considering both the real part of the eigenvalues and the corresponding HSV produces a more efficient and effective iterative tuning

In recent years, transmission system operators have started requesting converter-interfaced generators (CIGs) to participate in grid services such as power oscillation damping (POD). As power systems are prone to topology changes because of connection and disconnection of generators and lines, one of the most important requirements in the design of POD controller is to account for these changes. This can be done by either adjusting the controller structure during the operation or applying a fixed structure designed to address changes in the system. The fixed structure is usually preferred by transmission system operators since it is easier to determine its impact on the system. In this paper, a design procedure is proposed for network-reconfiguration-aware POD controller with fixed structure for CIG-based power plants that considers network configurations with any one line disconnected. The design procedure is based on frequency-response techniques, so it is suitable for application in CIG-based power plants, even in cases when a detailed small-signal model of the system is not available. Designs of a POD controller for the damping of critical system modes can be obtained by using active power, reactive power, or both power components simultaneously. The application to the design of a POD controller for a CIG-based power plant connected to the IEEE 39-bus system is presented as an example. Simulations performed in MATLAB and SimPowerSystems are used to validate the proposed design procedure. The validation includes an analysis of system performance with changes considered in the proposed designed procedure. Also, the system performance under unconsidered changes is examined, covering variations in load and inertia values, as well as disconnection of synchronous generators.

This paper presents a feed-forward control method for improving the power reference tracking performance of Virtual Synchronous Machines (VSMs) without compromising their main features in terms of grid forming capability and inertia emulation. The proposed approach acts directly on the phase angle used for reference frame transformations in the control system and can be generally applied to all VSM-based control schemes relying on a virtual swing equation. A small-signal model of a selected VSM implementation with the proposed feedforward control is derived. This model is utilized to assess the impact of the power reference feedforward on the operational characteristics of the VSM. The improvement of the power reference tracking capability is demonstrated by analysing the transfer function from the power reference to the power injected to the grid, as extracted from the small-signal model. The frequency domain analysis also demonstrates how the oscillation modes of the VSM and the inertial response to grid frequency perturbations remain unaffected by the proposed feed-forward control. Finally, the findings from the frequency domain analysis are verified by time domain simulations.

This paper proposes a universal Shore-to-Ship Charging (S2SC) concept for multi-vessel onshore power supply and charging of onboard batteries. One of the main challenges of existing S2SC systems is the lack of interoperability between shore-side charging systems and onboard power system configurations. To address this issue, the proposed S2SC concept is designed to provide charging to multiple ships with various onboard configurations and vessel missions. To reduce the impacts of grid outage events and grid capacity limitations on the charging performance, an On-Shore Battery (OSB) unit is considered. This OSB is connected directly to a common dc bus, without a dedicated OSB converter to ensure a cost-effective solution. Furthermore, the power converters are designated to serve multiple functions while forming an integrated configuration. This can enable increased utilization of the infrastructure. Moreover, a charging management system is introduced as a high-level controller to deliver stable, controllable, and prioritized shore power to multiple vessels. This high-level controller regulates the OSB power and State-of-Charge (SoC) while ensuring the charging service during grid outages and limited grid capacity conditions. As a proof of concept, the complete model of a S2SC designed for supplying four different vessels is simulated and the control performance is validated via a series of case studies.

Abstract Power system stability characteristics are typically evaluated in terms of small‐ and large‐signal (transient) stability. Access to the time‐varying A‐matrix of a state‐space‐based power systems model during transient conditions can be utilized to apply linear time‐varying system concepts for large‐signal stability analysis. In linear time‐varying system analysis, the differential Riccati equation (DRE) plays a vital role when the power system is subjected to a severe disturbance. The Möbius transformation is proposed in this paper to solve the DRE with singularity issues. It is shown that the solution of the DREs follows a specific mathematical pattern when the power system is stable but does not follow this pattern when the system progresses toward instability. The proposed method can be used in large‐signal stability analysis to predict instability and make the stability analysis more efficient. Additionally, the vector‐DRE is proposed to generalize the index in a large‐scale power system. Results show that analyzing the corresponding Riccati equation's behaviour can help researchers predict a power system's performance and improve the control and management of the system.

This article identifies the critical conditions of bifurcation and frequency splitting phenomena in inductive power transfer (IPT) systems used for battery charging, considering a constant voltage load (CVL) model. While prior studies covered these phenomena for IPT systems with constant resistance loads, their application to battery-loaded systems is limited due to the variation of equivalent load resistance with the operating frequency. By using the CVL model and analyzing the output power peak points, this article calculates the critical conditions for the frequency splitting phenomenon. This enables determining the power's monotonic range and peak in the frequency-control system. Moreover, by analyzing the monotonicity of the system's input impedance angle, the critical condition for bifurcation can be identified for determining the operating region that achieves zero-voltage switching or designing zero-phase angle IPT systems. To avoid bifurcation and achieve zero-voltage switching across the entire operational range, boundary conditions for frequency detuning design in systems with resistance or voltage loads are identified. The proposed analysis is validated through experimental measurements, and an example illustrating the impact of critical conditions on IPT system design for battery charging is provided.

The foundation for a passivity-based screening method is introduced with the objective of narrowing the scope of interaction studies for converter interoperability assessment to only those locations where stability issues may arise. With the growing prevalence of renewable energy sources and converter-based generation in the power system, converter interoperability studies are becoming increasingly important. Ensuring that a new converter will not negatively interact with other converters and grid elements can be a challenging and time-consuming undertaking. Screening methods to reduce the effective area to consider in interaction studies can provide a tool to reduce the complexity. However, established methods rely on empirical observations and experience to determine interaction likelihood. The proposed method provides a way to screen for converter interoperability issues using the concept of passivity to provide stability guarantees. Although presently limited to converter interactions with a passive system, it provides the basis for a full screening method between any two systems. The method is tested in Simulink by simulation of a 39-bus system with a 2-level converter, demonstrating the validity of the proposed approach.

This paper demonstrates how the internal virtual impedance in virtual synchronous machines (VSM) can be chosen to ensure stability and robustness against grid impedance variations. Three VSM implementations are considered: a current controlled VSM with dynamic electrical model (CC DEM) VSM, a current controlled VSM with quasi stationary electrical model (CC QSEM) VSM, and a voltage controlled (VC) VSM with cascaded voltage and current control loops. Eigenvalues analysis is applied to demonstrate how the virtual impedance requirements for ensuring stability are different for the three studied VSM implementations. Moreover, it is shown how tuning of the virtual impedance can ensure stability for all three VSM implementations under all combinations of grid resistance and inductance in the interval r(g) is an element of (0, 0.2] p.u. and l(g) is an element of (0, 1] p.u. The results from the small signal analysis are validated using time domain simulations.

This paper presents an approach and a corresponding laboratory infrastructure for multi-hardware-in-the-loop (M-HiL) testing of power converters and intelligent electronic devices (IEDs) with wide area features for power system monitoring and control. The basis for the testing environment is a digital real-time simulation (RTS) platform which can be utilized for phasor-based or hybrid phasor and electromagnetic transient (EMT) power system simulation. A high-bandwidth power amplifier is used for interfacing the real-time simulated power system to the power hardware. The necessary elements and their interfaces required for realizing the M-HiL testing are highlighted in the paper. Finally, a complete example of an M-HiL test based on real-time simulation of the Nordic 44 (N44)-bus power system model is presented. The test setup includes two phasor measurement units (PMUs) with their corresponding communication layers and a converter configuration for scaled emulation of the HVDC transmission system of an offshore wind farm. The configuration also includes a grid forming converter unit operated in parallel to the grid-side HVDC terminal. The presented test demonstrates how a grid forming converter operated as a Virtual Synchronous Machine (VSM) can provide frequency support to the Nordic power system and how this support would be recorded by the PMUs.

State-space models are useful for a wide range of power system analyses relying on eigenvalue-based small-signal stability assessment. However, state-space models for detailed analysis of power converter dynamics are typically not provided to third-parties due to intellectual property (IP) concerns. This work illustrates how diagonalization of a state-space model will effectively obscure sensitive information about the system structure and parameters. Thus, diagonalization can be utilized as a safe method for providing black-boxed state-space models. The process is performed on an example system to clearly demonstrate that the information revealed in a diagonalized model is no more than what can be determined from system identification of a black-boxed time-domain model. A practical method of implementing this technique to provide linearized small-signal models across the full range of operating points in a compiled application is presented.

This paper discusses how an Active Power Filter (APF) can be utilized for system-wide harmonic mitigation in a microgrid with multiple sources of harmonic distortion located at different buses. A two-bus microgrid system with independent nonlinear loads at both buses is first investigated analytically, and it is demonstrated that it is possible to derive a harmonic current injection from the APF that will minimize the harmonic distortion at both buses. However, analytical optimization of the APF current will be sensitive to parameter variations, will deteriorate when the APF reaches current saturation and cannot be easily extended to larger systems with many loads at different buses. A more practically applicable method for calculating the APF current references, by using the framework of Model Predictive Control (MPC) is instead proposed for the investigated system. Under realistic operating conditions, this approach can obtain further improvement in the system-level harmonic mitigation. The characteristics and performances that are obtained with the analytical solution and the MPC-based control are assessed by time domain simulations in the Matlab/Simulink environment. The results clearly indicate how an MPC-based system-oriented compensation can maximize the utilization of a single APF in a multi-bus Microgrid.

This paper presents a sending-side gain-scheduled controller for improving the dynamic response of Inductive Power Transfer (IPT) systems with sub-resonant frequency control. The presented method is intended for inductive battery charging in high-power transport applications which are required to operate under highly variable conditions, including a wide range of coupling and output power. For such applications, the use of fixed controller gains selected to ensure the system stability in the full range of operation causes a slow response under low coupling or light load conditions. For implementing the gain-scheduling, the output power and coupling coefficient of IPT systems with the sub-resonant frequency control are estimated in real-time by using only sending-side information. The parameters of the gain-scheduled controller are then determined by the output power value and the estimated coupling, to ensure the rapid response and stability of the system. Moreover, the bandwidth limitations and risks of instability caused by dual-side communication in closed-loop power control is avoided. Effectiveness and feasibility of the proposed method are validated by time-domain simulations and experimental results from a small-scale laboratory prototype.

In this work we address the modeling of multi-port subsystems with unknown inner dynamics by utilizing vector fitting to identify state-space models for performing eigenvalue-based analysis. Vector fitting is used to characterize frequency responses obtained from frequency domain analysis, for example, from Fourier transformation of time domain data. The intended use is for interconnection with other models in system stability analysis, where the use of compact state-space models is desirable. Typically, vector fitting of a multiple-input/multiple-output (mimo) system leads to a large state-space model where each column (input) is fitted by a common pole set using a predefined model order. An alternative vector fitting process based on a pole collapsing scheme is proposed which can find suitable poles for a more compact state-space model. Additionally, a method for simpler, more automated order determination is introduced. The use of the presented approach for obtaining a fully compacted model (without pole repetitions) is examined and compared against a previously proposed method based on singular value decomposition. Application to an example system representing a 2-level power electronic converter demonstrates that the proposed method gives a model with improved accuracy of eigenvalue identification and model compaction, while retaining the essential information in terms of system dynamic behavior.

This letter proposes a conditional pulse density modulation (PDM) method for inductive power transfer (IPT) systems, which can automatically adapt the generated output patterns to effectively suppress current/power ripples. The proposed conditional PDM introduces a sending current limitation as an additional condition to skip pulses, which modifies the output patterns generated by conventional delta-sigma-based PDM. Thus, the PDM pulse pattern is continuously adapted to attenuate any excited current/power oscillations. The presented modulator is simple to implement and well-suited for IPT systems with poorly damped constant voltage load characteristics. Simulations and experiments demonstrate the effectiveness of the proposed modulation method.

This paper presents an approach for representing nonlinear operating point dependencies in small-signal state-space modelling of power electronic converters. The intended application is for unifying a set of small-signal models identified from black-box simulation models or physical measurements into a single operating point dependent model. The approach is based on a polynomial fitting of the operating point dependency of the matrix elements in a state-space modal representation. The fitted expressions for the matrix elements provide a single model that can be utilized for small-signal analysis in a wide range of operating conditions and prevents the need for investigation of individual models at each operation point. Two different cases are discussed for evaluating the applicability of the presented approach, including a grid-forming converter with a Virtual Synchronous Machine (VSM)-based control and a conventional grid-following converter with dc-link voltage control. The results show that a quadratic fitting of the matrix elements can provide acceptable model accuracy in most cases.

This paper introduces a methodology for abstraction of photovoltaic (PV) technologies by parametrization of relevant PV module characteristics. The proposed approach is utilized to evaluate PV projects integrated with the road infrastructure. The silicon monocrystalline and polycrystalline PV modules are selected as examples of technologies for illustration of the proposed meta-parametrization methodology and the calculated meta-parameters for these two PV technologies are reported. The proposed methodology can be applied to evaluate PV projects based on general PV technology characteristics instead of individual PV module parameters. An example of a PV system design next to a road is analyzed to illustrate how the proposed methodology can enable comparison of PV technologies in a general way. The example also shows how different trade-offs can be identified from the meta-parametrization compared to comparison based on individual modules. It has been found that the polycrystalline technology performs better for the considered case study.

This paper proposes a dc-voltage control design for a dc-dc converter with saturation nonlinearity. The suggested implementation is only slightly altered from the traditional structure of cascaded PI-controllers for handling the nonlinearity introduced by the input voltage limitation. Singular Perturbation Theory (SPT) is used to justify time-scale separation between the outer loop voltage control implementation and the inner loop current control. Furthermore, it is proved by SPT and Lyapunovs direct method that the proposed dc-voltage control system is globally asymptotically stable with input voltage saturation nonlinearity. Simulation results are presented to illustrate how the voltage saturation can influence a regular dc-voltage control loop and how the proposed implementation can ensure a stable and smooth response when reaching the saturation limit.