DC Side Impedances Research Articles

An Optimized Grid‐Forming Control Strategy for the Flexible Interconnection System in Distribution Transformer Areas

The flexible interconnection system (FIS) in distribution transformer areas can improve the local consumption capacity of high penetration rate distributed photovoltaics and solve the problem of the high loading rate of distribution transformers. This paper presents an optimized grid‐forming control strategy for the FIS in distribution transformer areas. First, the DC side impedance small signal model of the FIS is built, and the reason for the stability difference of the FIS is analyzed when the active power flows in different directions. An optimized control structure is then presented based on the conventional grid‐forming control strategy. The theoretical analysis shows that the optimized grid‐forming control strategy can improve the stability of the FIS. Finally, the controller hardware‐in‐the‐loop experiments based on RT‐LAB confirm the effectiveness of the presented optimized control strategy. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Resonance stability analysis of MMC-based DC grid with coupled multiphase DC lines

The resonance stability of modular multilevel converter (MMC) based high-voltage direct current systems has been extensively researched using the impedance-based stability theory. However, when there are coupled multiphase DC lines (CMDCLs), the DC side stability issues would become more complicated and harder to be analyzed by many well-established stability criteria. To address this challenge, this paper proposes a resonance stability analysis method for MMC-based DC grid with CMDCLs, based on the nodal admittance matrix analysis. First, the DC side impedance models of MMCs with typical control modes are established using the harmonic state-space theory. The parameter matrices of CMDCLs are also introduced and their elements are transformed into the s-domain. Second, the nodal admittance matrix of the DC grid when there are CMDCLs is derived in detail. The resonance mode of the DC grid can then be obtained by solving zeros of the determinant of the s-domain nodal admittance matrix. Finally, the resonance stability characteristics of a bipolar four-terminal MMC-based DC grid are investigated. Simulations in PSCAD/EMTDC verify the effectiveness of the analysis results.

A Comprehensive Survey of HVDC Protection System: Fault Analysis, Methodology, Issues, Challenges, and Future Perspective

The extensive application of power transfer through high-voltage direct current (HVDC) transmission links in smart grid scenarios is due to many factors such as high-power transfer efficiency, decoupled interconnection, control of AC networks, reliable and flexible operation, integration of large wind and photovoltaic (PV)-based off-shore and on-shore farms, cost-effectiveness, etc. However, it is vital to focus on many other aspects like control, protection, coordinated operation, and power management to acquire the above benefits and make them feasible in real-time applications. HVDC protection is needed to focus further on innovative and devoted research because the HVDC system is more vulnerable to system faults and changes in operational conditions in comparison to AC transmission because of the adverse effects of low DC-side impedances and sensitive semi-conductor-based integrated power electronics devices. This paper provides a comprehensive review of the techniques proposed in the last three decades for HVDC protection, analyzing the advantages and disadvantages of each method. The review also examines critical findings and assesses future research prospects for the development of HVDC protection, particularly from the perspective of smart-grid-based power systems. The focus of the review is on bridging the gap between existing protection schemes and topology and addressing the associated challenges and issues. The aim is to inform power engineers and researchers about potential research avenues to tackle the challenges in HVDC protection in smart-grid-based power systems.

A modeling method for the DC side simplified impedance of line commutated converter based on the simplified switching function

With a large amount of new energy access and the wide application of high voltage direct current (HVDC) transmission technology based on line commutated converter (LCC), it is of great significance to study the impedance frequency characteristics of the converter to analyze the stability of the LCC-HVDC system. Due to the complexity and inefficiency of the existing modeling techniques, in this paper, a simplified impedance modeling method for the DC side of LCC based on the simplified switching function is proposed. Firstly, the commutation process of LCC is deduced according to the converter valve opening sequence and circuit principle, and the simplified switching function of LCC is proposed. Next, based on the dynamic phasor method, through the analysis and calculation of harmonic transmission between the AC and DC sides of LCC, the simplified impedance of the DC side of LCC is obtained. Then, a simulation model is established in PSCAD, and the impedance scanning results of the simulation model show that the error is small between the method proposed in this paper and the method without simplification, which verifies the validity of the proposed model. The proposed method can reduce modeling complexity and provide a fast calculation model of the DC side impedance of LCC for analyzing the stability of large complex transmission systems.

Improved virtual synchronous generator control strategy for the flexible interconnection system in distribution transformer areas

• An improved virtual synchronous generator control strategy is proposed for the flexible interconnection system. • The DC side impedance small signal model is built. • The stability of the flexible interconnection system is analyzed mathematically. • The controller hardware-in-the-loop experiment is designed for verification. The flexible interconnection system (FIS) in the distribution transformer areas containing high-penetration distributed photovoltaics plays a significant role in balancing the load and improving new energy consumption. This paper proposes an improved virtual synchronous generator (VSG) control strategy for the FIS. Firstly, the impedance small signal model of the FIS is developed for analyzing the influence of the conventional VSG control strategy on the stability margin of the FIS in the case of bidirectional power flow. Then, the improved VSG control strategy is proposed based on the analysis, which can improve the stability of the FIS in the negative power direction. Finally, the controller hardware-in-loop experiments of the FIS verify the effectiveness of the proposed improved VSG control strategy.

Accurate Impedance Modeling and Control Strategy for Improving the Stability of DC System in Multiterminal MMC-Based DC Grid

This article proposes an accurate dc-side impedance modeling method of modular multilevel converter (MMC) and a control strategy for improving the stability of the dc system in MMC-based dc grid. First, the impedance modeling method based on harmonic linearization is adopted to establish the dc-side small-signal impedance model of MMC, which considers the internal multiharmonic coupling characteristics and the complete control system. Second, an equivalent model is established to analyze the frequency impedance characteristics of the dc ports in MMC-based dc grid, and the stability of dc ports is further analyzed based on the impedance-based stability criterion. Then, considering both the dynamic characteristics and stability of the dc system, a specific design method of controller parameter optimization and additional virtual damping controller is proposed. Based on MATLAB/Simulink, a detailed time-domain simulation model of MMC-based dc grid is established. The simulation results prove the accuracy of the proposed impedance modeling method and the validity of the proposed control strategy.

DC Side Harmonic Resonance Analysis of MMC-HVDC Considering Wind Farm Integration

In a modular multilevel converter (MMC) based wind farm integration system, the wind farm may influence the harmonic resonance characteristics of DC system through the connected MMC. An effective way to assess the harmonic resonances in DC system is the impedance analysis method, in which the key is to develop the DC side impedance model. This paper develops the dc impedance of the wind farm connected MMC by harmonic transfer function (HTF) method that considers both the dynamics of the MMC and wind farm. As a result, the proposed DC impedance model can effectively reveal the impact of the wind farm on the small-signal characteristics of the DC system. Compared to the existing model, the proposed model can improve the accuracy of DC system resonance analysis with consideration of connected wind farm. Therefore, the proposed model can be further used to assist the stability design of wind farm connected MMC-HVDC systems. The time-domain simulations in PSCAD/EMTDC validate the proposed impedance models and stability analyses.

Modeling and Analysis of DC Terminal Impedance of Voltage-Source Converters With Different Control Modes

A dc terminal impedance model of voltage-source converter (VSC) is required to analyze the stability of multiterminal high-voltage direct current system. This article proposes a comprehensive dc terminal impedance model for conventional three-phase two-level VSC under different control modes. The control strategy includes inner decoupled current control and outer control, the latter contains dc voltage control, active/reactive power control, and droop control for grid-connected VSC and ac voltage control for VSC connected to a load. When a VSC is connected to the ac grid, the phase-locked loop (PLL) is also taken into account. The influences of PLL dynamics, control time delay and dead time on the dc-side impedance are explained. Also, how the parameters of the inner current control and outer control affect the characteristics of dc terminal impedance is analyzed in detail. Finally, experimental measurements verify the proposed impedance models and analysis.

Impedance Modeling and Analysis of Three-Phase Voltage-Source Converters Viewing From DC Side

In order to deal with the stability issues in power systems, small-signal impedance models of three-phase voltage-source converters (VSCs) have been well established and widely studied viewing from the ac side. However, with the rapid development of renewable energy sources, the interactions between converters and dc networks need to be further formulated. Hence, dc-side impedance models of three-phase VSCs should be built and examined. In this article, three-phase VSCs are modeled from dc perspective, and several typical control methods are considered, respectively. By using the proposed models, impedance stability analyses are presented. It is shown that the dc-side output impedance has a great influence on the system stability, and the impedance mismatching between dc networks and VSCs can lead to system oscillation. In addition, the influence of controller parameters on the dc-side impedance is disclosed by simulation. Finally, the aforementioned analyses are verified by hardware-in-loop (HIL) tests.

Dynamic modelling and interaction analysis of multi-terminal VSC-HVDC grids through an impedance-based approach

This paper presents an impedance-based interaction and stability analysis of multi-terminal HVDC systems. First, an analytical derivation procedure is presented to obtain the feedback impedance models of a voltage source converter (VSC) as a subsystem, with particular interest on the DC side impedance. Subsequently, in addition to the impedance models of other subsystems, an impedance aggregation method is applied to derive the dynamic closed-loop impedance matrix of the system considering the interconnected structure of the grid. Given the closed-loop impedance matrix, multi-input multi-output (MIMO) relative gain array (RGA) formulation is proposed to analyse nodal interactions between converters and the network. Furthermore, the impedance ratio matrix is proposed for HVDC stability analysis based on impedance models. Remarkably, these formulations are derived compactly without any knowledge of the internal states of any converter and therefore allows the ease of interoperability analysis. Finally, the impact of control architecture and strategy on the dynamic responses, interaction, and stability analysis from an impedance perspective is conducted as a case study. The analysis is done in the frequency domain and validated with the physical model of a three-terminal DC test grid built in SimscapeTM MATLAB/Simulink®.

Review of different fault detection methods and their impact on pre‐emptive VSC‐HVDC dc protection performance

Multi-terminal voltage-sourced converters (VSC) high-voltage direct current (HVDC) transmission system is expected to play a vital role in future power systems. Compared with ac power transmission, dc transmission is more vulnerable to faults due to low dc-side impedances and sensitive power electronics in the converters. Dc protection issues must be tackled before any multi-terminal VSC-HVDC grid can be built. The multi-terminal VSC-HVDC system is studied in detail using switching models for two-level converters, detailed equivalent models for the modular multi-level converters, detailed hybrid circuit breaker switching models and frequency-dependent phase models for dc cables. Using such high-fidelity system models, a systematic study of HVDC fault protection methodologies in more detail than previous studies is conducted. This is the first comprehensive study that includes pre-emptive circuit breaker operation. The results presented in this study underline the benefits of such a detailed treatment of the breaker, and of considering it as part of a fast power electronics system rather than isolated dc equipment. The study identifies the best existing fault detection method and tests it extensively. In order to further improve post-fault system recovery response, which is a key but often neglected part of previous studies, a novel bump-less transfer control has been implemented in the converters.

Impedance Modeling of Three-Phase Voltage Source Converters in DQ, Sequence, and Phasor Domains

This paper presents a modular approach for the impedance modeling of three-phase voltage source converters (VSC) by representing the VSC dynamics using three-by-three transfer matrix in the dq, sequence, and phasor domains. The transfer matrix form simplifies the modeling process by separately modeling the ac and dc side dynamics, and describing the VSC dynamics independent of the ac and dc side networks. It also explicitly captures coupling among the dominant frequency components of the ac and dc side voltages and currents in the off-diagonal elements. Modeling of the VSC ac and dc side impedances, including the effects of the network on the other side of the VSC, is presented using the transfer matrix models. Transfer matrix based impedance modeling in the three domains and several stability analysis case studies are presented for a VSC-based HVDC station in an offshore wind farm. It is shown that the coupling between the ac and dc networks, and between the positive and negative sequence components of the three-phase quantities, play an important role in the low-frequency stability of the VSC. Impedance models and stability analysis predictions are validated using the wind farm simulations.

On DC-Side Impedance Frequency Characteristics Analysis and DC Voltage Ripple Prediction under Unbalanced Conditions for MMC-HVDC System Based on Maximum Modulation Index

In this study, we first briefly introduce the effect of circulating current control on the modulation signal of a modular multilevel converter (MMC). The maximum modulation index is also theoretically derived. According to the optimal modulation index analysis and the model in the continuous domain, different DC-side output impedance equivalent models of MMC with/without compensating component are derived. The DC-side impedance of MMC inverter station can be regarded as a series xR + yL + zC branch in both cases. The compensating component of the maximum modulation index is also related to the DC equivalent impedance with circulating current control. The frequency characteristic of impedance for MMC, which is observed from its DC side, is analyzed. Finally, this study investigates the prediction of the DC voltage ripple transfer between two-terminal MMC high-voltage direct current systems under unbalanced conditions. The rationality and accuracy of the impedance model are verified through MATLAB/Simulink simulations and experimental results.

Harmonic Voltage and Current Transfer, and AC- and DC-Side Impedances of HVDC Converters

This paper presents a set of equations for line commutated HVdc systems that can be used to calculate the main voltages and currents of positive or negative sequence on the ac side of the rectifier or inverter and to calculate the main voltages and currents on the dc side that are related to one ac system background voltage harmonic of positive or negative sequence. Furthermore, the frequency-dependent impedances of a line commutated HVdc system on the ac or dc side can be derived. It will illustrate how the converter impedances on both sides are related via an impedance transformation function, which is the product of the transfer functions for currents and voltages. The equations for the impedances differ from those given in a previous IEEE paper, especially with respect to the representation of the impedance for the converter transformers. It did, however, lead to similar results for the CIGRE benchmark model. In order to distinguish between a monopolar and bipolar scheme, the equations take the numbers of poles into account. Furthermore, six- or 12-pulse arrangements are considered.

Analytical model for assessment of the line harmonic currents generated by a variable speed drive

AbstractWith the widespread use of static power converters in many industrial applications, it requires to characterise more accurately the harmonic content injected on electrical networks. The present paper proposes an analytical method to obtain the model of the harmonic currents produced by a variable speed drive. The bridge rectifier is assumed to operate in the continuous mode. In addition, both the AC and DC side impedances are taken into account. Firstly, the validity of the analytical model is demonstrated by comparison both to the results of the time simulations and experimental measurements. Secondly, a detailed comparative survey between the present modelling and some earlier ones is carried out to define the application fields of the analytical model and to point out its interest in describing the harmonics generated by the rectifier for high DC current ripples.

The frequency dependent impedance of an HVDC converter

A linear and direct method of determining the frequency dependent impedance of a 12 pulse HVDC power converter is presented. Terms are developed for both the DC and AC side impedances of the power converter, including the effect of the firing angle control system, the commutation period, and the variability of the commutation period. The impedance predictions are verified by dynamic simulation. >

An analytical method for calculating harmonic currents of a three-phase diode-bridge rectifier with DC filter

Commonly, three-phase diode bridge rectifiers with an LC filter at the DC side are often used to convert AC input into a DC voltage. It is well known that they generate large amounts of harmonic currents. This paper proposes an analytical method for calculating the harmonic currents for both the continuous and discontinuous current conductions. The equations for the harmonic currents are derived, taking into account the effects of the DC and AC side impedances. All the calculations are conducted only by algebraic calculation with high accuracy. The validity of the proposed method is demonstrated by comparison to the results of time simulation. >

AC/DC harmonic interactions in the presence of GIC for the Quebec-New England Phase II HVDC transmission

During the spring of 1991, several severe geomagnetic disturbances were recorded in North America, and particularly in Northern Quebec, where Hydro-Quebec's La Grande generation complex and transmission system are located. As a result of these disturbances, the Quebec-New England Phase II HVDC system was affected by transformer saturation and harmonic voltage distortion due to geomagnetic induced current (GIC). This paper presents an analysis of the phenomenon observed at Radisson, the northernmost terminal in the system. A central issue which is discussed in the paper is the reflection of the DC side impedance to the AC side for operating converters, and the effect of this reflection on the harmonic impedance as viewed from the AC side.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Calculation of Uncharacteristic Harmonics Generated by Three-Phase Diode-Bridge Rectifier with DC Filter Capacitor.

Three-phase diode-bridge rectifiers are used to convert the AC input into DC voltage. A large capacitor is connected as a filter on the DC side, since in most applications, a low ripple in the DC output voltage is desirable. Unbalance in the supply conditions of a three-phase diode-bridge rectifier with a DC filter capacitor gives rise to uncharacteristic harmonics on both the AC and DC sides.This paper proposes a simplified method for calculating the uncharacteristic harmonic currents generated by the three-phase diode-bridge rectifier under unbalance, taking into account the effects of both the AC and DC side impedances. Analytical expressions for the harmonic currents are derived using the switching functions with overlap period the AC circuit theory. Therefore, the proposed method can be executed only with algebraic computation and its accuracy is quite high. The validity of the proposed method is demonstrated by comparison with the results of time simulation.

Harmonic analysis of a single‐phase rectifier with a DC filter capacitor

AbstractA single‐phase diode bridge rectifier with a filter capacitor on the dc side is often employed to convert ac input into a dc voltage. The input current of the rectifier contains harmonic currents which cause undesirable power line effects. Recently, a method using the time domain analysis has been proposed to calculate the harmonic currents of rectifier considering noninfinite capacitance, i.e., non‐zero dc side impedance. This method is very accurate, but it requires a long computing time and a complicated algorithm.This paper proposes a new method that makes it possible to easily calculate the harmonic currents taking into account the effects of the ac and dc side impedances of rectifier. The proposed method, which is based on the frequency domain method, can be executed only with the algebraic computation, and its accuracy is quite high. The validity of the proposed method is also demonstrated by comparison with the results of time simulation.