Dq Impedance Research Articles

Analysis of high frequency oscillations based on MMC-HVDC system

Modular multilevel converter is widely used in new energy grid-connection and power grid asynchronous interconnection by virtue of its advantages of flexible and easy to expand structure and no commutation failure problem. In recent years, high-frequency oscillations have been observed in several flexible DC transmission projects at home and abroad, while the internal harmonic dynamic characteristics and control system of the MMC system are complex and the mechanism of high-frequency oscillations has not been sufficiently analysed at present. In this paper, the detailed DQ impedance model and the equivalent circuit impedance model on the AC side are firstly derived based on the state-space model of the MMC system, and the impedance sweeping method with superimposed small perturbations is proposed. Meanwhile, the dynamic characteristics of the detailed DQ impedance model are compared with those of the electromagnetic transient model. The amplitude-frequency characteristics of the system impedance under different system delays are further compared, and the mechanism of the high-frequency oscillation of the MMC-HVDC system is revealed.

Stability Assessment of a High-Voltage DC Transmission System Using MIMO- and SISO-Based Impedances

Grid-connected inverters used in High-Voltage Direct Current (HVDC) transmission systems, which have become increasingly popular worldwide in recent years, employ a variety of control methods for each frequency band, and resonances can occur between multiple control devices within a device or between multiple devices placed in close proximity. Practical impedance-based data-driven methods, rather than linear approximation models, are becoming widely used for these stability analyses. On the other hand, HVDC transmission systems require multiple domain transformations between synchronous and stationary reference frames. Therefore, in this study, both Multiple-Input Multiple-Output (MIMO) analysis using impedances on the direct-quadrature (dq) synchronous frame and Single-Input Single-Output (SISO) analysis using positive and negative sequence impedances on the stationary reference frame were performed. Consequently, the two unstable frequencies identified in the eigenvalue trajectories for the dq impedance were also identified within a single Nyquist plot for the sequence domain impedance, validating both the unstable frequencies observed in the dq domain. These frequencies suggest that weak AC systems on the generation side of the HVDC transmission system may be causing instability in the DC transmission lines and AC systems on the demand side. Additionally, the results of this study also suggest that the introduction of an advanced inverter control method, called the Virtual Synchronous Generator (VSG) control method, in the grid-connected inverter on the receiving side may mitigate the effects of having weak AC systems on the generation side.

Sequence Impedance Measurement of Utility-Scale Wind Turbines and Inverters – Reference Frame, Frequency Coupling, and MIMO/SISO Forms

Sequence impedance responses are increasingly used for the stability analysis of converter-grid systems; however, many aspects of the sequence impedance measurement process, particularly those resulting from the frequency coupling between the positive- and negative-sequence impedances, are not yet fully explored. Existing methods for measuring sequence impedance with frequency coupling are complicated, not suitable for large wind turbines and inverters, and they can measure the sequence impedance in only one of the MIMO and SISO forms. This paper shows that the sequence impedance has a reference frame similar to the dq impedance and presents a method for measuring the sequence impedance with frequency coupling. The proposed method aligns the sequence impedance reference frame based on the estimation of the grid voltage angle and obtains the impedance response in both MIMO and SISO forms. The paper also demonstrates the impact of the fundamental frequency on the accuracy of the impedance measurements. The proposed method and practical issues associated with the impedance measurement of utility-scale wind turbines and inverters are demonstrated on a 1.9-MW Type III wind turbine and a 2.2-MVA inverter using an impedance measurement system built around a 7-MW/13.8-kV grid simulator and a 5-MW dynamometer.

General‐purpose computation of two‐axis frequency characteristics of power converter circuit for stability analysis controlled in αβ frame

AbstractFrequency characteristics for a converter are necessary to design circuit and control parameters and they are utilized, for example, for stability analysis by the impedance method. This paper proposes an automatic formulation and analysis method, which are based on a general‐purpose simulation algorithm for the frequency analysis of an averaged power converter, based on node‐connection and model characteristic information of circuit and control elements. The general equation formulation method is extended to be able to include circuits controlled in αβ frame and characteristic expressions with αβ or dq frame. As the first application example, a three‐phase grid‐following inverter with a digital sinusoidal controller based on the complex vector theory in αβ frame is analyzed for the frequency characteristics of the output admittances. The characteristics are utilized for stability analysis by the impedance method and the inverter is assured to have passive characteristics and to be stable. As the second example, a three‐phase inverter is analyzed for its αβ and dq impedances. The proposed method is investigated for the computed results and it is validated.

A Multi-Frequency DQ Impedance Measurement Algorithm for Single-Phase Vehicle-Grid System in Electrified Railways

Dq impedance measurement is of great importance as a part of the impedance-based analysis. At present, impedance of objects in single-phase vehicle-grid system are mainly obtained by injecting the voltage or current disturbance of one single frequency into the system circularly. However, as the number of measurement frequency points increases, there will produce much time-consuming of measurement. In this paper, a quick dq impedance measurement algorithm for single-phase vehicle-grid system based on multi-frequency sweep is proposed. First, pseudo-random binary sequences (PRBS) and ternary sequences are modified as the driving signals rather than directly injecting into the control link. Then three types of disturbance with specific frequency characteristics are introduced into the system and their parameters setting principle are given for the first time. According to the different characteristics of measurement objects, the proposed algorithms are also different to ensure the maximum specificity and sensitivity. Finally, for different objects in vehicle-grid system like traction network, single-phase converter and dual-interleaved converter, simulation and experimental results based on the hardware in the loop real-time simulation platform both show the correctness of the proposed algorithm, and the possible causes of errors are also analyzed in detail. Moreover, the proposed algorithm makes it possible to quickly measure the dq impedance of the single-phase vehicle-grid system, and the correctness of the theoretical and measured value can be judged and used for the stability analysis of electrical systems.

Impedance-Based Stability Analysis of Less Power Electronics Integrated Electric Shipboard Propulsion System Considering Operation Mode, PLL, and DC-Bus Voltage Control Effect

A doubly-fed induction machine (DFIM) is a promising choice for the shipboard propulsion system (SPS) of a more-electric ship (MES) to increase the system safety level by employing less power electronics. In this paper, the detailed impedance model of DFIM-SPS is established, with a salient-pole synchronous generator (SPSG) acting as the power source and a DFIM functioning as the propulsion load. The impedance modelling of DFIM is carried out from the aspect of ac coupling between the stator and rotor circuits, which is easy for physical understanding. In addition, the back-to-back power converter (BTBPC) is regarded as controlled voltage sources with impedances in the equivalent circuit. The phase-locked loop (PLL) is a key element in influencing the system stability, and it is integrated to upgrade the system dq impedance model. Moreover, the impedance shaping effect caused by dc-bus voltage control is investigated. Nyquist stability criterion is employed for system small-signal stability analysis, which is implemented with respect to the DFIM operation mode and PLL controller effect, and the time-domain simulations are carried out to verify the stable operation of a 5 MW DFIM-SPS in Matlab/Simulink. Furthermore, the experimental verification is done on a 1.5 kW DFIM electric drivetrain platform.

Input–Output Small-Signal Stability Analysis of a PLL-Free Direct Power-Controlled Partially Power-Decoupled More-Electric Shipboard Propulsion System

With the partially power-decoupled system architecture, a doubly fed induction motor-based shipboard propulsion system (DFIM-SPS) has the potential of increasing the system safety level by decreasing the penetration of power electronics. In this article, a phase-locked-loop-free (PLL-free) direct power control (DPC) strategy is proposed for a DFIM-SPS to increase the system dynamic performance. The system small-signal stability analysis is carried out based on the source-load structure, where a salient-pole synchronous generator supplies power to the DFIM electric drivetrain. A detailed dq impedance model of DFIM-SPS is established with the power controller gains of the back-to-back power converter (BTBPC) considered. The proposed source-load dq impedance model of PLL-free DPC-based DFIM-SPS can easily reflect the equivalent impedance produced in the stator and rotor circuits. The effects on system stability caused by the equivalent impedance variations due to power controller gain changes are evaluated in detail. The frequency response of the elements in the DFIM impedance matrix is investigated first, and then, the minor loop gain matrix is obtained. The system input-output small-signal stability is analyzed based on the Nyquist stability criterion. Time-domain simulations are carried out in MATLAB/Simulink to validate the effectiveness of the proposed PLL-free DPC strategy for DFIM-SPS.

DQ Impedance Stability Analysis for the Power-Controlled Grid-Connected Inverter

For a grid-connected inverter requiring the ac voltage magnitude and the active power control, both vector control and power synchronization control can be applied. The stability comparison based on the dq impedance stability analysis between both control are carried out via three factors including the grid impedance, the inner current loop and the virtual impedance. The dq impedances of the inverter based on both control are derived. The determinant of the impedance ratio matrix is used for the stability analysis. The bode plot of the grid impedance and the inverter impedance are present to assist the stability analysis and explain their interactions. It is found that increasing the grid impedance and the cut-off frequency of the current loop stabilize the inverter with the power synchronization control, which is converse to the vector control. Furthermore, the inverter with the power synchronization control may suffer the instabilities when connecting to a strong grid. The virtual inductor and resistor are proposed to enhance the stability for the vector control and the power synchronization control respectively. The simulation validation using Matlab/Simulink is performed.

DQ impedance‐decoupled network model‐based stability analysis of offshore wind power plant under weak grid conditions

This study presents a dq impedance-decoupled network modelling method of offshore wind power plant (OWPP) for stability analysis. DQ impedance frequency responses of grid-connected inverters (GCIs) and long transmission cables (LTCs) are first measured by frequency scanning method, which are fitted as transfer function matrices using matrix fitting algorithm. Then, the GCIs are modelled as Norton equivalent circuits. In addition, per-unit-length electrical parameters of the LTCs are extracted from the measured dq impedance frequency responses of a specific LTC, based on which dq impedance-decoupled two port network models of the LTCs are established. DQ impedance-decoupled network model of the whole OWPP is then established based on connection relationships of these GCIs and LTCs. Finally, generalised Nyquist criterion (GNC) is performed in all the dq impedance-decoupled subsystems, and the subsystems where the GNC is not satisfied are identified as instability sources. Compared with conventional impedance-based stability analysis methods of OWPP, the proposed dq impedance-decoupled modelling method is able to facilitate the application of GNC and further instability source identification based on partitioning the whole OWPP into several decoupled subsystems. The effectiveness of the network modelling method is validated based on time-domain simulation results in Matlab/Simulink and real-time verification results in OPAL-RT.

Effect of Reactive Power Characteristic of Offshore Wind Power Plant on Low-Frequency Stability

Oscillation phenomena of offshore wind power plant (OWPP) in a wide frequency range can be caused due to impedance interactions between grid-connected inverters (GCIs) and transmission cables. In this article, impedance model of GCI with outer power control loop, inner current control loop and phase-locked loop is first established in dq reference frame. The correctness is validated by frequency scanning method. Then, the effects of active and reactive power/current references on dq impedance characteristics of GCI with/without consideration of power control loop are investigated using complex space vectors and complex transfer functions. Furthermore, RLC circuit model of transmission cable considering frequency-dependent characteristics is also established for dq-domain IBSC. On the basis of them, it's found that low-frequency oscillation phenomena of OWPP under power control mode may occur if active power reference exceeds a certain threshold value, which can be mitigated by injecting a certain amount of negative reactive power. Impacts of PLL parameters, length of transmission cable and number of paralleled GCIs on required negative reactive power for low-frequency stabilization are further investigated. Both Matlab/Simulink-based simulation and OPAL-RT-based real-time verification are implemented in an OWPP with four permanent magnet synchronous generators to validate the correctness of the reactive power characteristic analysis results and the feasibility of mitigating low-frequency oscillation phenomena by negative reactive power injection.

Analysis of transforming dq impedances of different converters to a common reference frame in complex converter networks

Analysis of transforming dq impedances of different converters to a common reference frame in complex converter networks

Modelling and Stability Analysis of Wind Power Plants Connected to Weak Grids

It is important to develop modelling tools to predict unstable situations resulting from the interactions between the wind power plant and the weak power system. This paper presents a unified methodology to model and analyse a wind power plant connected to weak grids in the frequency-domain by considering the dynamics of the phase lock loop (PLL) and controller delays, which have been neglected in most of the previous research into modelling of wind power plants to simplify modelling. The presented approach combines both dq and positive/negative sequence domain modelling, where a single wind turbine is modelled in the dq domain but the whole wind power plant connected to the weak grid is analysed in the positive/negative sequence domain. As the proposed modelling of the wind power plant is systematic and modular and based on the decoupled positive/negative sequence impedances, the application of the proposed methodology is relevant for transmission system operators (TSOs) to assess stability easily with a very low compactional burden. In addition, as the analytical dq impedance models of the single wind turbine are provided, the proposed methodology is an optimization design tool permitting wind turbine manufacturers to tune their converter control. As a case study, a 108 MW wind power plant connected to a weak grid was used to study its sensitivity to variations in network short-circuit level, X/R ratio and line series capacitor compensation (Xc/Xg).

Coupling Influence on the dq Impedance Stability Analysis for the Three-Phase Grid-Connected Inverter

The dq impedance stability analysis for a grid-connected current-control inverter is based on the impedance ratio matrix. However, the coupled matrix brings difficulties in deriving its eigenvalues for the analysis based on the general Nyquist criterion. If the couplings are ignored for simplification, unacceptable errors will be present in the analysis. In this paper, the influence of the couplings on the dq impedance stability analysis is studied. To take the couplings into account simply, the determinant-based impedance stability analysis is used. The mechanism between the determinant of the impedance-ratio matrix and the inverter stability is unveiled. Compared to the eigenvalues-based analysis, only one determinant rather than two eigenvalue s-function is required for the stability analysis. One Nyquist plot or pole map can be applied to the determinant to check the right-half-plane poles. The accuracy of the determinant-based stability analysis is also checked by comparing with the state-space stability analysis method. For the stability analysis, the coupling influence on the current control, the phase-locked loop, and the grid impedance are studied. The errors can be 10% in the stability analysis if the couplings are ignored.

Analysis and controller design for stand‐alone VSIs in synchronous reference frame

The common practice for controlling the stand-alone voltage source inverters (VSIs) is to transform abc voltage and current signals to DC signals using the dq transformation, which makes it possible to control the new DC voltage and current signals just using simple proportional-integral controllers with a zero steady-state tracking error. However, the transformation causes coupling terms between d- and q-axis components in both current control loops and voltage control loops, which deteriorate the dynamic and steady-state performance of the control system. This study presents a step-by-step graphical analysis and design approach for a three-phase stand-alone VSI system in the dq reference frame, which provides a clear systematic decoupling process to design the inner- and outer-loop current and voltage controllers, respectively. The closed-loop d- and q-axis output impedances of the stand-alone VSI system by considering the coupling effects between axes are also formulated, modelled, and evaluated. The study investigates how the decoupling and compensating terms added in the current and voltage controllers affect the dynamic performance and output dq impedances of the VSI system. Simulation and hardware results verify the effectiveness of the graphic design and analysis strategy.