Fractional Frequency Transmission Research Articles

Optimal Multiple Wind Power Transmission Schemes Based on a Life Cycle Cost Analysis Model

Due to the high cost and complex challenges faced by offshore wind power transmission, economic research into offshore wind power transmission can provide a scientific basis for optimal decision-making on offshore wind power projects. Based on the analysis of the topology structure and characteristics of typical wind power transmission schemes, this paper compares the economic benefits of five different transmission schemes with a 3.6 GW sizeable onshore wind farm as the primary case. Research includes traditional high voltage alternating current (HVAC), voltage source converter high voltage direct current transmission (VSC-HVDC), a fractional frequency transmission system (FFTS), and two hybrid DC (MMC-LCC and DR-MMC) transmission scenarios. The entire life cycle cost analysis model (LCCA) is employed to thoroughly assess the cumulative impact of initial investment costs, operational expenses, and eventual scrap costs on top of the overall transmission scheme’s total cost. This comprehensive evaluation ensures a nuanced understanding of the financial implications across the project’s entire lifespan. In this example, HVAC has an economic advantage over VSC-HVDC in the transmission distance range of 78 km, and the financial range of a FFTS is 78–117 km. DR-MMC is better than the flexible DC delivery scheme in terms of transmission capacity, scalability, and offshore working platform construction costs in the DC delivery scheme. Therefore, the hybrid DC delivery scheme of offshore wind power composed of multi-type converters has excellent application prospects.

Multi-Objective Optimization and Stable Operation Control Strategy for Fractional Frequency Transmission System Based on Large Signal Stability Analysis

Multi-Objective Optimization and Stable Operation Control Strategy for Fractional Frequency Transmission System Based on Large Signal Stability Analysis

Performance Investigation on PMSG based Fractional Frequency Transmission Systems via XLPE cables for Offshore Wind Power

Presently, the research on Fractional Frequency Transmission System (FFTS) is fastened for the megawatt Offshore Wind Farms (OWF). FFTS has an ability to overcome the problem of charging current presented in the HVAC transmission and will effectively serve as an alternative to the traditional transmission systems. The basic structures and characteristics of a typical PMSG-based FFTS via XLPE cable for offshore wind power system is proposed and described first. Then the technical performance of power transmission through XLPE cable is evaluated by comparing the different cables such as flat and trefoil formation. Simulation results showcase notable enhancements in power transfer capacity, decreased power losses, and improved performance of control schemes. The feasibility studies describe the performance of FFTS (16.67 Hz) via trefoil cable is superior than FFTS flat formation cable transmission.

Large-Signal Stability Analysis Using Takagi-Sugeno Fuzzy Model Theory for Fractional Frequency Transmission System Under Grid Faults

The rapid development of renewable energy requires transmission technology innovation. Fractional frequency transmission system (FFTS) is a promising solution for large-scale renewable energy transmission, and the stability analysis is essential for engineering application. Especially for the grid faults, these large-signal disturbances are inevitable during operation. Thus, the system-level Takagi-Sugeno fuzzy model of FFTS is proposed considering the system parameters, control strategy of modular multilevel matrix converter ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M^{3}C$</tex-math></inline-formula> ) and phase locked loop in this study. Subsequently, the Lyapunov function and the large-signal stability domain of attraction (LS-DOA) are calculated expeditiously based on the proposed fuzzy model. Ultimately, the large-signal stability of FFTS is comprehensively analyzed combining with the different-frequency interaction features under grid fault conditions. Compared with the conventional method, the stability strength and affine angle indexes are proposed for quantitative analysis mathematically. The obtained influence law of the system parameters can guide the parameter optimization of FFTS effectively. The effectiveness of proposed methods is verified by the simulation-based study.

Comprehensive optimization framework for transmission expansion planning with fractional frequency transmission system

AbstractThe Fractional Frequency Transmission System (FFTS) operates with low frequency to decrease the electrical length of AC transmission lines, consequently enhancing transmission capacity. The integration of renewable energy sources via FFTS will significantly impact power system planning. This paper presents a Fractional Frequency Transmission Expansion Planning (FF‐TEP) model, which considers the interaction between FFTS and the industrial‐frequency power grid. This model addresses the challenges posed by the integration of offshore wind power through FFTS, and takes several key factors into account, including the active power coupling of Modular Multilevel Matrix Converter (M3C), inverter capacity, and converter transformer capacity. To address the non‐convexity caused by AC power flow, this paper introduces a Genetic‐Particle Swarm Optimization algorithm (G‐PSO) with dynamic penalties tailored to the M3C structure. This approach incorporates both crossover and mutation operators from Genetic Algorithms (GA) into Particle Swarm Optimization (PSO). The penalty function dynamically adapts according to the M3C structure, resulting in improved global optimization while maintaining computational efficiency. The results of two case studies demonstrate that FFTS can significantly enhance transmission capacity while reducing cable charging power. This reduces investment costs and decreases voltage offset issues.

Analysis of D-Q small-signal impedance of back-to-back frequency converter

The back-to-back frequency converter plays a vital role in the formation of the fractional frequency transmission system Despite their numerous advantages, however, impacted by the unique impedance characteristics of power electronics, the wide-band oscillations occur more frequency as well as more common recently, which have posed great challenges to the system operation and raised great concern over the researchers worldwide. To address this issue and properly investigate the impedance characteristics of the back-to-back frequency converter, this manuscript establishes the small-signal impedance of the back-to-back frequency converter with inner current control loop and outer voltage/power control loop in the synchronous reference (dq) frame. Then, by using the impedance model and determinant-based General Nyquist Criterion (GNC), the stability assessment and instability cause identification are studied. Finally, the analysis presented in this paper is verified based on frequency and time-domain simulations in the MATLAB/Simulink environment.

Large-signal stability analysis for offshore wind power fractional frequency transmission system with modular multilevel matrix converter

Aiming to achieve zero carbon emission, the rapid development of offshore wind power transmission system faces stability challenge. The fractional frequency transmission system (FFTS) with modular multilevel matrix converter (M3C) holds considerable promise among the solutions for large-scale and long-distance offshore wind power transmission. Currently, numerous demonstration projects involving FFTS are being conducted worldwide, necessitating urgent attention to system stability analysis for practical engineering applications. Notably, conventional approaches focusing on small-signal stability are inadequate when confronted with large-signal disturbances. In this study, the Takagi–Sugeno fuzzy model of FFTS is proposed considering the complex control strategy of M3C and the system strong nonlinearity. Subsequently, the Lyapunov function and the large-signal stability domain of attraction (LS-DOA) are constructed expeditiously based on the proposed fuzzy model. When analyzing the system larger-signal stability, the novel stability strength and optimal optimization factor are further introduced to develop a quantitative and efficient methodology for parameter optimization guidance compared with the conventional method. Thus, the FFTS different-frequency interaction features are elucidated from normal and different characteristics parameters mathematically and comprehensively. The effectiveness of proposed methods is verified by the simulation-based study.

Multi-stage stochastic planning for a long-term low-carbon transition of island power system considering carbon price uncertainty and offshore wind power

The characteristics of isolated grids lead island power systems to rely on stable conventional generation, which is not environmentally friendly and has high carbon emissions. This paper proposes a low-carbon transition model for island power systems considering large-scale offshore wind resources and the long-term uncertainty of carbon prices. First, a detailed model for offshore wind power systems is proposed considering the interaction of multiple wind farms and three transmission technologies. Second, a multi-stage power system planning model is established including the upgrading and decommissioning of thermal units. Meanwhile, an improved long-term carbon price uncertainty modeling method based on the binomial tree is proposed. Then, focusing on the uncertainty of carbon prices, a multi-stage stochastic optimization model is established, and the stochastic nested decomposition algorithm is used to solve the problem. Finally, numerical results show that the low-carbon transition develops plenty of offshore wind power as the primary power source and usually adopts a fractional frequency transmission system for offshore wind integration. The uncertainty of carbon prices has a significant impact on the transition: in the high carbon price realization, the annual carbon emissions are only 0.088 Mt, while in the low carbon price realization, the annual emissions are 0.255 Mt.

Research on Slot-pole Combination in High-power Direct-drive PM Vernier Generator for Fractional Frequency Transmission System

Offshore wind energy is an important part of clean energy, and the adoption of wind energy to generate electricity will contribute to the implementation of the carbon peaking and carbon neutrality goals. The combination of the fractional frequency transmission system (FFTS) and the direct-drive wind turbine generator will be beneficial to the development of the offshore wind power industry. The use of fractional frequency in FFTS is beneficial to the transmission of electrical energy, but it will also lead to an increase in the volume and weight of the generator, which is unfavorable for wind power generation. Improving the torque density of the generator can effectively reduce the volume of the generators. The vernier permanent magnet machine (VPM) operates on the magnetic flux modulation principle and has the merits of high torque density. In the field of electric machines, the vernier machine based on the principle of magnetic flux modulation has been proved its feasibility to reduce the volume and weight. However, in the field of low-speed direct-drive machines for high-power fractional frequency power generation, there are still few related researches. Therefore, this paper studies the application of magnetic flux modulation in fractional frequency and high-power direct-drive wind turbine generators, mainly analyzes the influence of different pole ratios and different pole pairs on the generator, and draws some conclusions to provide reference for the design of wind turbine generators.

Upgrading Transmission Capacity by Altering HVAC Into Fractional Frequency Transmission System

Transmission adequacy of power system has been challenged by high investment of new line construction and limit line-corridor space. In this paper, a novel solution to increase transmission capacity by altering HVAC lines into fractional frequency transmission system (FFTS) is proposed. FFTS is a transmission that utilizes a relatively low grid frequency, e.g., 50/3 Hz, to extend the transmission capacity of ac lines. The proposed solution can minimize the construction efforts since the existing HVAC transmission lines can be directly employed by FFTS without any change. The structure and principle of FFTS for transmission line conversion (TLC) are introduced firstly. Then, performance of conventional ac equipment in FFTS is evaluated and comparison with respective counterpart in HVDC is carried out. Next, the economic performance of FFTS for transmission capacity upgrade is conducted based on a typical benchmark, and sensitivity analysis results are presented to determine the economic zone of FFTS. The results show that the uniform annual value (UAV) of TLC into FFTS is 24.9% and 31.6% cheaper than TLC into HVDC and constructing new HVAC lines, respectively. Therefore, FFTS is a superior scheme for transmission capacity boost.

Harmonic characteristics analysis of modular multilevel matrix converter for fractional frequency transmission system

Harmonic characteristics analysis of modular multilevel matrix converter for fractional frequency transmission system

Structure optimization based on phase‐locked loop and controller parameters optimization of Y‐connected modular multi‐level converter for fractional frequency offshore wind power system under weak grid

Based on a practical long-distance large-capacity transmission engineering case, the small-signal stability of fractional frequency transmission system (FFTS) with Y-connected modular multi-level converter (Y-MMC) is mainly researched in this paper. Different from the previous control strategies of Y-MMC, this paper establishes a frequency decoupling mathematical model and proposes the decoupling control strategies. Then, the small-signal model of the Y-MMC system is obtained. Considering the existence of phase locked loop (PLL) will deteriorate the stability of the system under weak grid, this paper applies the short-circuit ratio (SCR) for analysis and proposed a new structure of PLL, called phase-shifted PLL (PS-PLL), to improve the small-signal stability of the system. In addition, for better stability and dynamic response performance of the closed-loop control system, this paper proposes a new parameter optimization objective function for parameters adjustment. Controller parameters optimization is conducted by using the particle swarm optimization (PSO) algorithm and stability evaluation of the system is conducted based on the eigenvalue distribution. Finally, the feasibility and superiority of the proposed strategies and optimization are verified in MATLAB/ Simulink.

An isolated modular multi‐level AC/AC converter with high‐frequency link and pulse flip circuit for fractional frequency transmission system application

Based on the modular topology and the traditional voltage-sourced converter (VSC) model, this paper presents an isolated modular multi-level AC/AC converter with high-frequency (HF) link and pulse flip circuit for fractional frequency transmission system (FFTS) application. The proposed converter uses the HF transformer to realize electrical isolation, omitting the industrial frequency (IF) transformer with large volume and heavy weight. In the primary side of the HF transformer, the power transmission is realized by the rectifier and the inverter. In the secondary side of the HF transformer, the double H-bridges are used to realize the natural freewheeling of the leakage current, which solves the problem of voltage overshoot. On the basis of carrier phase-shifted pulse width modulation (CPS-PWM), an improved modulation strategy is proposed to realize the HF output voltage of the inverter. It has the advantages of easy expansion, no circulation current, good output voltage quality, low cost and no need of offshore converter station, so it has great potential in the field of offshore wind power grid connection. The working principle, natural freewheeling modes, modulation method and overall system control scheme of the proposed topology are introduced in detail, and the feasibility of the proposed topology is verified by simulation in MATLAB/Simulink environment and test through APPSIM platform.

Stability analysis and control optimisation based on particle swarm algorithm of modular multilevel matrix converter in fractional frequency transmission system

Modular multilevel matrix converter (M3C) is a competitive option in the fractional frequency transmission system (FFTS) application. Focusing on stability and power quality issues, this study firstly proposes a new mathematical model and control strategy. Different from the previous research, this control scheme is based on the frequency decoupling model of double dq coordinate transformation and the control of the sub-converter, which implements the frequency decoupling control and solves the frequency leakage problem. Subsequently, a complete state-space model and small-signal model of M3C are built for analysing small disturbance stability. On this basis, the optimisation of M3C in FFTS is studied, and an optimisation method based on particle swarm algorithm is proposed. This method can directly design the adaptive objective function according to the optimisation requirements of system control performance to simultaneously optimise all controller parameters of the system. After optimisation, the stability and dynamic performance of the system have been significantly improved. Finally, the effectiveness of the proposed control and optimisation is verified by the simulation results in MATLAB/ Simulink.

Modeling and Control of Modular Multilevel AC/AC Converter in Y Configuration for Fractional Frequency Transmission System

The modular multilevel AC/AC converter topology in Y configuration, which is called Y‐MMC, suitable for fractional frequency transmission system is proposed in this paper. Y‐MMC can directly connect two three‐phase AC systems of different frequencies and voltage amplitudes with only six equivalent branches, and it has satisfying performance in power quality and characteristics. Y‐MMC enjoys a simple and symmetrical structure with no circulating current problem. The detailed topology and operating principle of Y‐MMC are addressed in this paper. The frequency‐decoupled mathematical model of the Y‐MMC system is deduced. Corresponding control scheme is thoroughly designed, including the inner loop current control, the outer loop control, the individual‐balancing control, and frequency leakage suppression control. The paper also lays emphasis on the optimization of reactive power distribution between the main branches and the assistant branches of Y‐MMC. The validity of the Y‐MMC topology and the effectiveness of the proposed control scheme are verified by the simulation results in MATLAB/Simulink. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Harmonic Analysis of Modular Multilevel Matrix Converter for Fractional Frequency Transmission System

Fractional Frequency Transmission is a competitive technology for offshore wind power transmission. Modular Multilevel Matrix Converter (M3C) plays a key role in a Fractional Frequency Transmission System (FFTS) as the frequency changer. M3C is broadly considered as the AC–AC converter for the future with its attractive advantages in high voltage and high power applications. Due to the lack of a DC link, electrical quantities at different frequencies from two AC systems couple in M3C, resulting in a complex harmonic condition. Harmonics can lead to stability issues and its analysis is of great importance. This paper focuses on the harmonic analysis of M3C. The arm capacitor voltage ripples and the harmonic currents are analyzed at various frequencies. Major factors influencing the harmonics magnitude are discussed. Analysis is conducted on sub-module capacitance and arm inductance selection. A zero-sequence current mitigation controller for M3C is implemented and tested. It is found that for a FFTS, some current harmonics flow into AC systems even though the system is balanced, while the others circulate within the converter. The theoretical harmonic analysis is verified by simulations in Real Time Digital Simulator (RTDS) of a M3C system where each arm consists of forty sub-modules.

A global asymptotical stable control scheme for a Hexverter in fractional frequency transmission systems

A fractional frequency transmission system (FFTS) is the most competitive choice for long distance transmission of offshore wind power, while the Hexverter, as a newly proposed direct AC/AC converter, is an attractive choice for its power conversion. This paper proposes a novel control scheme characterizing the global stability and strong robustness of the Hexverter in FFTS applications, which are based on the interconnection and damping assignment passivity-based control (IDA-PBC) methodology. Firstly, the frequency decoupled model of the Hexverter is studied and then a port-controlled Hamiltonian (PCH) model is built. On this basis, the IDA-PB control scheme of the Hexverter is designed. Considering the interference of system parameters and unmodeled dynamics, integrators are added to the IDA-PB controller to eliminate the steady-state error. In addition, the voltage-balancing control is applied in order to balance the capacitor DC voltages to obtain a better performance. Finally, the simulation results and experimental results are presented to verify the effectiveness and superiority of the IDA-PB controller.

Small Signal Model of Modular Multilevel Matrix Converter for Fractional Frequency Transmission System

Fractional frequency transmission is a promising technology for medium distance offshore wind power transmission. The key component in the fractional frequency transmission system (FFTS) is the modular multilevel matrix converter (M3C). It is regarded as the next generation AC/AC converter for high voltage and high power applications due to various advantages such as high-quality waveforms, scalability, and controllability. It is important to fully study its impact on the power network. The key to the understanding and impact is the development of a suitable model, which is the focus of this paper. A small signal model of the M3C taking into account the dynamics of the capacitor voltage, AC currents, and the control system is developed. Electrical quantities from both AC sides at different frequencies couple in the M3C since there is no DC link. The complicated nonlinear terms in ABC frame are isolated and transformed in DQ frame. The model is convenient to interface with the control system and external AC systems. Small signal analysis is carried out on the influence of the controller parameters and sub-module capacitance. The correctness of the proposed model is verified by comparing to a detailed electromagnetic transient model of the M3C simulated in RTDS.

Multi‐hierarchy control strategy in abc coordinate for modular multilevel matrix converter in fractional frequency transmission system

This paper proposes a multi-hierarchy control strategy in abc coordinate for modular multilevel matrix converter (M3C) in fractional frequency transmission system (FFTS). The proposed control strategy avoids complicated coordinate transformations when the traditional control strategies based on coordinate transformation are adopted. Four hierarchies are designed to balance the capacitor voltages. In different hierarchies, the capacitor voltage ripples have different frequencies. According to this characteristic, different bandwidths of filters are adopted in different hierarchies, resulting in different control speeds among the four hierarchies. This will not only speed up the control but also assure the control accuracy. Simulation results verify the feasibility and effectiveness of the proposed strategy.

IDA‐PB control with integral action of Y‐connected modular multilevel converter for fractional frequency transmission application

Y-connected modular multilevel converter (Y-MMC) is a new topology of direct AC/AC power conversion, with broad application prospects in fractional-frequency transmission system. This study studies the mathematical model of Y-MMC and builds the port-controlled Hamiltonian model. Since vector control scheme can hardly ensure global stability, the interconnection and damping assignment passivity-based control (IDA-PBC) method is applied for controller design of Y-MMC. Three typical IDA-PBC strategies are then proposed, featuring the asymptotical stability of the desired equilibrium. To eliminate steady-state error, integrators are further added to the IDA-PB controller. Different from the previous research, the proposed method enables the decoupling of different-frequency components and the suppression of frequency leakage. Besides, the reactive power distribution coefficients are introduced to characterise the optimisation allocation of reactive power between arms. Finally, the effectiveness and superiority of the proposed control strategy are verified by both the simulation and experiment results.