Stable Operating Region Research Articles

Nonlinear and Transient Stability Analysis of Phase-Locked Loops in Grid-Connected Converters

The undesired nonlinear operation of phase-locked loops (PLL) is one of the main causes of transient instability in grid-connected converters. However, the stable operating region of PLL, knowing which is helpful for protection purposes, is hard to find due to the nonlinear characteristic of the transient process. In this article, the nonlinear characteristic of the PLL control loop relevant to the grid-connected converter operation is identified. The averaging method is applied to derive a time-domain expression for the PLL operation under disturbance. Based on the analytical expression, the transient response and related stability criterion are established, and the PLL design is improved while targeted to focus on various ac grid faults or disturbances. The results, applicable to transient stability enhancement, are verified by circuit simulations and experiments.

An improved methodology for reactive power management in grid integrated solar PV system with maximum power point condition

The grid-integrated solar photovoltaic (PV) inverter is generally used to provide active power (P) support to the distribution grid operated at maximum power point (MPP) condition. Moreover, it should also be capable of providing reactive power support (Q) to the distribution grid. Therefore, an appropriate range of reactive power should be known at MPP condition to ensure satisfactory operation of the grid-integrated PV system (GIPV). In this work, an improved mathematical methodology is proposed to derive the P-Q capability curve of GIPV for managing the reactive power injection into the grid at MPP condition for various environmental conditions. By evaluating all the possible set of working point within the stable region of operation, this methodology is used to obtain reactive power limits of a utility-scale single-stage three-phase PV system connected to the IEEE 33 bus distribution grid. The considered PV system is simulated using software-in-the-loop (SIL) environment based on OPAL-RT OP4510 real-time digital simulator with coordinated closed-loop control of dc-link voltage controller, maximum power point tracking (MPPT) controller, and active and reactive power controller. To validate the effectiveness of the improved mathematical methodology, the reactive power injection to the grid is changed, and the corresponding active power injection to the grid are measured, which are compared with the P-Q values obtained from the improved mathematical methodology.

A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

Rolling-element bearings are widely used in industrial rotating machines, and hence there is a strong need to accurately predict their influence on the response of such systems. However, this can be challenging due to an interaction between the dynamics of the rotor and the bearing nonlinearities, and it becomes difficult to provide a physical explanation for the nonlinear response. A novel approach, combining a Jeffcott rotor supported by a detailed bearing model with the generalised harmonic balance method, is presented, enabling an in-depth study of the complex rotor–stator interaction. This allows the quasi-periodic response of the rotor, due to variable compliance, to be captured, and the impact of clearance, ring and stator compliance, and centrifugal loading of the bearing on the response to be investigated. A strongly nonlinear response was observed due to the bearing, leading to large shifts in frequency as the excitation amplitude was increased, and the emergence of stable and unstable operating regions. The variable compliance effect generated sub-synchronous forcing, which led to sub-resonances when the ball pass frequency coincided with the frequency of one of the modes. Radial clearance in the bearing had by far the largest influence on the unbalance response, the self-excitation due to variable compliance, and the stability. Introducing outer ring compliance was found to slightly soften the system, and centrifugal loading on the bearing elements marginally increased the system’s region of instability, but neither of these effects had a significant impact on the response for the investigated bearing. When the bearing was mounted on a sufficiently compliant stator, the system was found to behave linearly.

A Control Parameter Design Method for Hybrid Multi-Terminal HVDC System

To achieve better control performance, a comprehensive control parameter design method that considers economics, stability and dynamic performance is essential for hybrid multi-terminal HVDC systems. In this paper, a hierarchical model for the control system of Hybrid-MTDC is constructed and the parameters are optimized on two layers. On the system layer, using the normalization processing method, a system-layer objective function that considers both the minimum network loss and the voltage offset is formed for Hybrid-MTDC systems and solved with the proposed penalty interior point method. On the converter layer, using the state-space matrix method, a generic small-signal stability range of each control parameter can be obtained by the traversal calculation of the eigenvalues. Then, to identify the stricter stable operating region for the DC voltage controller under severe conditions, an additional stability criterion based on the mixed-potential theory is deduced, and the design-oriented boundaries are generated and added to the feasible region. Finally, within the design-oriented boundaries, a general dynamic performance evaluation function is constructed to determine the optimal control parameters. Utilizing the proposed method, a typical Hybrid-MTDC system is investigated, and experimental verifications are provided to validate the effectiveness and accuracy.

Integrated characteristic curves of the constant-pressure hydraulic power take-off in wave energy conversion

Power take-off is an indispensable link in wave energy utilization, and its efficiency should be comprehensively investigated at both full load and part load for the effective conversion in variable wave conditions. However, up to now, the research about this issue is still scarce because of its complexity and difficulty. To overcome this obstacle, this paper studies the overall conversion efficiency of the constant-pressure hydraulic power take-off (CPHPTO) of a floating-pendulum wave energy converter, at a wide range of the system pressure, system flow-rate and shaft speed, via the efficiency test and fitting formulas. Furthermore, the integrated characteristic curves, which consist of the characteristic curves and operating curves, are proposed to deal with the four-dimensional data obtained from the experiment or fitting. The results show that the integrated characteristic curves of the CPHPTO are available and play an important role in the optimal design and efficient operation. The stable operating region can also be defined when plotting the operating curves. In general, the integrated characteristic curves are suitable for the preliminary design and further optimization of the similar CPHPTOs for different kinds of oscillating-body wave energy converters.

Investigation of the inerter-based dynamic vibration absorber for machining chatter suppression

This study proposes a novel approach to increase the chatter stability in machining operations. It shows the potential performance improvement when an inerter-based dynamic vibration absorber is employed in a machining operation. Tuned inerter based devices have been employed to decrease the magnitude of the vibrations in applications such as civil engineering structures and vehicle suspension systems but the nature of chatter in machining is different from these applications. Therefore, it requires a different tuning methodology to obtain the optimal design parameters. In this study, the machining operation is modelled as an undamped single degree of freedom system and different configurations of an inerter, a damper and two springs are used to ensure a stable region of operation. Strategies for the tuning parameters are developed both analytically and numerically. Using these techniques the performance improvement in the chatter stability provided by using inerter based devices instead of a traditional dynamic vibration absorber is demonstrated.

Analysis and study of two‐dimensional parameter bifurcation of wind power farms and composite loads

AbstractThis study focuses on the stability of power system based on codimension‐two bifurcation theory. In this paper, we investigate the impact of load modeling on permissible wind power generation margins in distribution networks. The study considers codimension‐two bifurcations of equilibria and limit cycles in wind power systems depending on varying two parameters simultaneously. The principle parameter is the wind power generation, and the other parameter depends on the different types of loads. The types of loads are ZIP, exponential recovery, dynamic induction loads, and composite load models. To study the effects of the induction motor loads, the proportion of the static component in the motor load is changed and assessed with respect to their mechanical loads. Wind generation margin boundaries are traced, and saddle‐node, Hopf, and limit‐induced bifurcation branches are obtained, delimiting the stable and unstable operating regions in the parameter space. The analysis presented in this paper can pave the way for determining methods for improving and monitoring these margins with consideration to the system parameters and load composition.

A Research on Cascaded H-Bridge Module Level Photovoltaic Inverter Based on a Switching Modulation Strategy

The stable operating region of a photovoltaic (PV) cascaded H-bridge (CHB) grid-tied module level inverter is extended by adopting the hybrid modulation strategy. However, the traditional single hybrid modulation method is unable to regulate the DC-side voltage of each module precisely, which may aggravate the fluctuation of modules’ DC-side voltages or even cause the deviation of modules’ DC-side voltages under some fault conditions and, thus, degrade the energy harvesting of PV panels. To tackle this problem, a switching modulation strategy for PV CHB inverter is proposed in this paper. When the CHB inverter is operating in normal mode, the hybrid modulation strategy containing the zero state is adopted to suppress DC-side voltage fluctuation, thereby, improving the output power of PV modules. When the CHB inverter is operating in fault mode owing to failing solar panels, the hybrid modulation strategy without the zero state is utilized to make the DC-side voltages reach the references and, thus, maintain a higher energy yield under fault conditions. Experimental results achieved by a laboratory prototype of a single-phase eleven-level CHB inverter demonstrate both the feasibility and effectiveness of the proposed method.

Analysis of the transient performance of the flashing-driven natural circulation IPWR

The numerous self-regulation mechanisms existing in the flashing-driven natural circulation integrated PWR (NC-IPWR) make its operation characteristics significantly different from typical PWRs or BWRs. This work presents an adequate operation scheme and a corresponding control strategy according to the reactor’s operation characteristics. The thermal-hydraulic characteristics of the flashing-driven NC-IPWR are analyzed under the proposed operation scheme by using RELAP5 code. The effects of different design parameters related to the reactor’s transient performance are revealed. In light of the instability phenomenon occurred at the low load conditions, the OTSG grouping operation scheme and the pressure sliding operation scheme are proposed to extend the reactor’s stable operation region.

A Power Distribution Control Strategy Between Energy Storage Elements and Capacitors for Cascaded Multilevel Inverter With Hybrid Energy Sources

The key technology of a cascaded multilevel inverter with hybrid energy sources lies in the power distribution among different chains. A power distribution control strategy between the energy storage elements and the capacitors is proposed to achieve fault tolerant control. In the cascaded multilevel inverter with hybrid energy sources, the chains with energy storage elements can operate in four quadrants, while the chains with capacitors can only operate in two quadrants. With the proposed control method, the active power distribution is realized by active voltage vector superposition, and the reactive power distribution is achieved by initial operation point selection. This enhances both the system reliability and availability while enabling continuous operation in four quadrants. Meanwhile, the stable operation region and the range of the initial operating point have been derived by the vector analysis to avoid over-modulation. An experimental prototype based on a single-phase link with two series chains has been built in the laboratory. The simulation and experimental results are provided to demonstrate the effectiveness of the proposed control method.

Study on nonlinear dynamic behavior and stable operation region of single-phase photovoltaic inverter

In order to design a photovoltaic inverter with excellent performance, the second-order photovoltaic inverter circuit model under current loop proportional control is established in this paper, the discrete iterative model of system is also obtained. The nonlinear behavior of system is analysed in detail through bifurcation diagram, folding diagram and the phase diagram of output current (i) and output voltage (uc). The simulation model is constructed in Matlab/Simulink, and the correctness of theoretical analysis is verified through time domain waveform and phase-space map. The influence of bifurcation and chaos on system spectrum is analysed from the frequency domain. According to the Jacobian matrix of system, the stable operation region of system is given. The experiment shows that the correct selection of circuit parameters is important for the stable operation of system.

A novel fault-tolerant control for battery-energy-storage system based on cascaded multilevel converter with battery/BMS failure

This paper proposes a novel fault-tolerant method for battery energy storage system (BESS) based on cascaded multilevel converter. During the occurrence of batteries or battery management system (BMS) fault, an asymmetrical cascaded multilevel BESS is formed which includes several batteries and several capacitors. Traditionally, it is challenging to achieve the active power distribution between different cascaded H-bridges with different DC sources. With the proposed fault-tolerant control method, it can distribute active power between batteries and capacitors as well as enables continuous operation in four quadrants. This enhances both system reliability and availability. Meanwhile, the stable operation region has been derived by vector analysis. Simulation results demonstrate the validity and effectiveness of the proposed fault-tolerant control.

A Modified Hybrid Modulation Strategy for Suppressing DC Voltage Fluctuation of Cascaded H-Bridge Photovoltaic Inverter

The hybrid modulation strategy using both low-frequency square-wave modulation and high-frequency pulse-width modulation can extend the stable operating region of a cascaded H-bridge converter. However, it does not control accurately dc voltages of converter but balances them by charging or discharging dc capacitors based on the state of system, which could aggravate fluctuation of dc voltages. If cascaded H-bridge converter is used in photovoltaic field, the aggravated fluctuation on dc capacitor voltages will result in further losses in energy harvesting of solar cells. To address this issue, a modified hybrid modulation strategy is presented in this paper. When dc-bus measured voltages are close to their reference voltages, these H-bridges operate in a zero mode. Adding appropriate zero state can prevent grid current charging or discharging the dc capacitors whose voltages have already reached their control goals. Therefore, the proposed technique is capable of suppressing dc voltage fluctuation, and, thus, improving the output power of solar cells. Simulation and experimental results validate the effectiveness and feasibility of the proposed method.

Application Research of the Improved Overall Temporal and Spatial Economic Operation Model Based on Information Entropy in Large-Scale Hydropower Station

For the high dimensional and complex inner-plant economical operation problem of large hydropower station, an improved ant colony optimization with adaptive ability, inspiring ability and local search ability was proposed. Spatial optimal load distribution model and temporal unit commitment model was combined into an overall temporal and spatial economic operation model, in which an innovative ant colony model of multiple ant colonies, multiple outsets and multiple routes was adopted. Information entropy was applied to adjust the path selection strategy and pheromone updating strategy of ant colonies along with the change of its value during the iteration. Two inspiring factors were applied in the algorithm to guide the ant colonies to search for optimal paths in a more efficient and targeted way. Local search ability was guaranteed by local translation of unit start-stop points of the optimal solution in each iteration. In the optimal load distribution model, optimal distribution table was set in advance using dynamic programming, which only took account of the stable operation regions and avoided the cavitation and vibration areas for the security and stability of units. The proposed method is applied to the Three Gorges Hydroelectric plant. Compared with other methods under different water heads, this method shows optimized result under the premise of both calculation speed and stability.

Short-Term Frequency Response of a DFIG-Based Wind Turbine Generator for Rapid Frequency Stabilization

This paper proposes a short-term frequency-response scheme of a doubly-fed induction generator (DFIG)-based wind turbine generator (WTG) for improving rotor speed recovery and frequency nadir. In the energy-releasing period, to improve the frequency nadir and rotor speed convergence by releasing a large amount of kinetic energy stored in the rotating masses in a DFIG-based WTG, the power reference is increased up to the torque limit referred to the power and reduces along with it for a predefined period which is determined based on the occurrence time of the frequency nadir in a power grid. Then, the reference decreases so that the rotor speed is forced to be converged to the preset value in the stable operating region of the rotor speed. In the energy-absorbing period, to quickly recover the rotor speed, the reference smoothly decreases with the rotor speed and time during a predefined period until it intersects with the maximum power point tracking curve. The simulation results demonstrate that the proposed scheme successfully achieves rapid frequency stabilization with the improved frequency nadir under various wind conditions based on the IEEE 14-bus system.

Behaviour of fractional loop delay zero crossing digital phase locked loop (FR-ZCDPLL)

ABSTRACTThis article analyses the performance of the first-order zero crossing digital phase locked loops (FR-ZCDPLL) when fractional loop delay is added to loop. The non-linear dynamics of the loop is presented, analysed and examined through bifurcation behaviour. Numerical simulation of the loop is conducted to proof the mathematical analysis of the loop operation. The results of the loop simulation show that the proposed FR-ZCDPLL has enhanced the performance compared to the conventional zero crossing DPLL in terms of wider lock range, captured range and stable operation region. In addition, extensive experimental simulation was conducted to find the optimum loop parameters for different loop environmental conditions. The addition of the fractional loop delay network in the conventional loop also reduces the phase jitter and its variance especially when the signal-to-noise ratio is low.

Grid-Forming-Mode Operation of Boost-Power-Stage Converter in PV-Generator-Interfacing Applications

The application of constant power control and inclusion of energy storage in grid-connected photovoltaic (PV) energy systems may increase the use of two-stage system structures composed of DC–DC-converter-interfaced PV generator and grid-connected inverter connected in cascade. A typical PV-generator-interfacing DC–DC converter is a boost-power-stage converter. The renewable energy system may operate in three different operation modes—grid-forming, grid-feeding, and grid-supporting modes. In the last two operation modes, the outmost feedback loops are taken from the input terminal of the associated power electronic converters, which usually does not pose stability problems in terms of their input sources. In the grid-forming operation mode, the outmost feedback loops have to be connected to the output terminal of the associated power electronic converters, and hence the input terminal will behave as a negative incremental resistor at low frequencies. This property will limit the operation of the PV interfacing converter in either the constant voltage or constant current region of the PV generator for ensuring stable operation. The boost-power-stage converter can be applied as a voltage or current-fed converter limiting the stable operation region accordingly. The investigations of this paper show explicitly that only the voltage-fed mode would provide feasible dynamic and stability properties as a viable interfacing converter.

Dissociating two sources of variability using a safety-margin model.

Neurological trauma can have a devastating effect on activities of daily living. One of the consequences is an increased amount of variability in the system, which can challenge individuals to stay within safe and stable regions of operation. There are multiple sources of movement variability; two of these are neuromotor noise and action-tolerance variability. The amount of neuromotor noise that is uncontrollable can impose limitations on reshaping variability. Action-tolerance variability, which can be reshaped through experience, and neuromotor noise, a certain amount of which cannot be altered, are often conflated when discussing motor variability. We attempted to disambiguate the two using an adaptive model, producing distinct "signatures" of neuromotor noise and action-tolerance variability within a task and compare with experimental data on stroke and healthy. Not all stroke survivors could adapt to the task, as predicted for those with greater neuromotor noise. Possible applications of this model can inform us of potential to influence distributions in stroke survivors and other individuals who have had a neurological injury. Additionally, we could design new training environments specifically tailored to the needs of the individual. This technique may also help disambiguate the type of brain injury suffered by stroke survivors.

Position Sensorless Field Oriented Control of IPMSM Under Parameter Uncertainties

Permanent magnet synchronous motors (PMSMs) are widely used in industry due to their high torque per volume ratio, low noise, efficiency and wide stable operation region. Especially in home appliance applications, obtaining high torque using small motors and low audible noise has crucial importance. Therefore, conventional DC motors have been replaced by the permanent magnet synchronous motors in the modern applications. In this study, field oriented sensorless control over wide speed range is carried out under parametric uncertainties. The pole coloring concept is used for the control of a PMSM in an industrial setup for the first time. The design method and experimental results are presented.

Performance of a Nano-CNC Machined 220-GHz Traveling Wave Tube Amplifier

We report on hot test measurements of a wide-bandwidth, 220-GHz sheet beam traveling wave tube amplifier developed under the Defense advanced research projects agency (DARPA) HiFIVE program. Nano-computer numerical control (CNC) milling techniques were employed for the precision fabrication of double vane, half-period staggered interaction structures achieving submicrometer tolerances and nanoscale surface roughness. A multilayer diffusion bonding technique was implemented to complete the structure demonstrating wide bandwidth (>50 GHz) with an insertion loss of about −5 dB achieved during transmission measurements of the circuit. The sheet beam electron gun utilized nanocomposite scandate tungsten cathodes that provided over 438-A/cm2 current density in the 12.5:1 ratio sheet beam. An InP HBT-based monolithic microwave integrated circuit preamplifier was employed for TWT gain measurements in the stable amplifier operation region. In the wide-bandwidth operation mode (for gun voltage of 20.9 kV), a gain of over 24 dB was measured over the frequency range of 207–221 GHz. In the high-gain operation mode (for gun voltage of 21.8 kV), over 30 dB of gain was measured over the frequency range of 197–202 GHz. High-power tests were conducted employing an extended interaction klystron.