Optimal Frequency Response Research Articles

Frequency response coefficient optimal allocation strategy for multi-stacks alkaline water electrolyzer plant

Currently, power discrepancies between stacks are often overlooked when developing frequency response (FR) strategies for multi-stack alkaline water electrolyzer plants (AWEPs), which limits the full utilization of the plant’s FR potential. To address this issue, this paper introduces a stack-level FR coefficient allocation strategy aimed at minimizing post-contingency frequency deviation. Specifically, the quantitative relationship between the operating power of alkaline water electrolyzer (AWE) stacks and steady-state frequency deviation is first derived, followed by the formulation of an optimal FR problem. The solution to this problem is an FR strategy based on the principle of equal frequency deviation, which optimally allocates FR coefficients among AWE stacks according to their operating power, thereby maximizing the plant’s FR support capacity. Equivalent circuit model-based case study demonstrates that, compared to existing strategies, the proposed approach achieves a more balanced power distribution among the stacks during the FR process. This even power allocation not only reduces post-contingency frequency deviation but also enhances productivity and streamlines production management in the AWEP, thereby increasing the plant owner’s willingness to participate in FR. Specifically, the proposed strategy results in a 29.3% reduction in post-contingency frequency deviation, a 1.8% improvement in production efficiency under a 10 MW power imbalance, a 2.3% increase in hydrogen production rate under a 4 MW power imbalance, and more stable operation under a 16 MW power imbalance.

Optimal frequency response coordinated control strategy for hybrid wind‐storage power plant based on state reconstruction

Optimal frequency response coordinated control strategy for hybrid wind‐storage power plant based on state reconstruction

Towards an optimal frequency and time response of singe-tube pressure measurement systems under continuum-flow conditions

The pressure transmission tube, as part of a pressure measurement system, generally has a considerable influence on its dynamic characteristics. The paper deals with the mathematical modelling of the dynamic behaviour of pressure transmission tubes with the aim of providing guidelines for the optimal design of such systems in the frequency and time domains. The mathematical models used are based on linear wave theory and continuum flow mechanics with no-slip and isothermal boundary conditions. The frequency responses were evaluated in terms of frequency bandwidth and the transient step responses in terms of settling and rise times. Following a systematic analysis of these characteristic parameters, we derived an analytically formulated optimisation objective function defining the transition between the low-wavenumber and high-wavenumber pressure waves in the pressure transmission tubes. The demanded dynamic behaviour in the frequency and time domains can be achieved through an appropriate ratio between the actual tube radius and the so-called transition tube radius, which was derived as a function of the tube length, end volume and fluid properties.

Piezoelectric plate generator from consecutive periodic rotary magnetic excitations

The piezoelectric device, connected to the circuit interface and subjected to the consecutive periodic rotary magnetic excitations, is presented for an energy harvesting application. The proposed system consists of a cantilevered piezoelectric plate structure with multiple attached magnets, along with a revolving disc carrying a single magnet. This study sets out to explore the primary development of explicit analytical and finite element formulations that consider magnetic coupling and time-delayed magnetic response. The two theoretical models are used to formulate the optimal power output frequency response equations using Fourier analysis. Due to the asymmetrical magnet locations and time-delayed magnetic response, the consecutive dynamic excitations periodically occur, resulting in dipole–dipole interactions in both spatial and temporal conditions. Consequently, the piezoelectric plate structure, designed to operate higher vibration modes, exhibits a predominant effect of frequency up-converting energy harvesters. The previous work is initially validated by using a single magnetic excitation and examining both cases with and without time-delayed magnetic responses. The analyses of broadband optimal power generations are based on Fourier’s harmonic numbers and frequency domains, including time-tracking magnetic excitations. Finally, various case studies are presented to examine the effects of different physical components, such as magnet numbers, magnet locations and masses, piezoelectric materials and thicknesses, and locations of electrode segments.

Optimizing Load Frequency Control in Standalone Marine Microgrids Using Meta-Heuristic Techniques

Integrating renewable resources into the electrical systems of marine vessels achieves the dual goal of diversifying energy resources and reducing greenhouse gas emissions. The presence of intermittent renewable sources and sudden nonlinear load changes can cause frequency deviations in isolated hybrid marine microgrids. To address this issue, the paper proposes a conventional PID (proportional–integral–derivative)-controller-based LFC (load frequency controller) which is optimized by meta-heuristic optimization algorithms, namely, PSO (particle swarm optimization), GWO (grey wolf optimization) and hybrid PSO-GWO. The proposed LFC was designed using transfer functions of various microgrid components, with ITAE (integral time absolute error) and ITSE (integral time square error) serving as performance indices. The proposed LFC’s validation was performed through HIL (hardware-in-loop) real-time simulation using a DS 1104 R&D controller board, with simulation results showing the better performance of the optimized frequency response compared to the nonoptimized LFC controller in terms of rise time, fall time, slew rate and overshoot. The hybrid PSO-GWO algorithm performs better than the other optimization algorithms. The simulation results demonstrate the stability and robustness of the proposed controller. In summary, the proposed PID-controller-based LFC can regulate frequency deviation in standalone hybrid marine microgrids effectively.

Bayesian Optimization for Microwave Devices Using Deep GP Spectral Surrogate Models

In microwave design, Bayesian optimization (BO) techniques have been widely applied to the optimization of the frequency response of components and devices. The common approach in BO is to model and maximize an objective function over the design parameters, in order to find the optimal spectral response. Such an approach avoids the direct modeling of spectral responses, which is a challenging task for the typical data-efficient surrogate models used in BO. Simple objective functions may lead to a suboptimal solutions, while complicated objectives require more powerful and less data-efficient surrogate models. To resolve this issue, this article proposes to adopt a deep Gaussian process (DGP) to directly model all relevant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula> coefficients over the frequency and the design parameter ranges of interest. Subsequently, an objective probability distribution is retrieved from the DGP model and maximized using a BO scheme. The proposed approach is tested on two suitable microwave examples and compared to the standard BO approach. Results show increased accuracy in identifying the optimal frequency response for the given design parameters and the desired objective, while maintaining high data efficiency.

Optimum frequency response with decentralized drivers in power system

AbstractThis document presents a novel methodology to optimize the power system frequency response based on the implementation of decentralized controllers. The proposed method focuses on the control of the internal rotor angle in the selected generator, which allows its governor to act as a decentralized controller that requires as input local measurements. Through a proposed optimization process, it is first possible to establish a set of optimal parameters for each controller and, second, to determine the required phasor measurement units (PMUs) and their locations that are necessary to be installed in a power system. This comprehensive proposal is based on the time domain evaluation of the frequency response when multiple scenarios of deviations between demand and generation occur. Finally, the new proposal is applied to the IEEE 39‐bus test system to validate its advantages; for this, the test power system as well as the proposed controllers are implemented in DIgSILENT PowerFactory, along with Python to manage the optimization process.

Coordinated Frequency Control of an Energy Storage System with a Generator for Frequency Regulation in a Power Plant

Considering the controllability and high responsiveness of an energy storage system (ESS) to changes in frequency, the inertial response (IR) and primary frequency response (PFR) enable its application in frequency regulation (FR) when system contingency occurs. This paper presents a coordinated control of an ESS with a generator for analyzing and stabilizing a power plant by controlling the grid frequency deviation, ESS output power response, equipment active power, and state of charge (SoC) limitation of the ESS in a power plant. The conventional generator and FR-ESS controllers were investigated and compared. To obtain the optimal frequency and power response, an ESS-based adaptive droop control method was proposed. The proposed control strategy was developed and implemented considering the changes and limitations of the dynamic characteristics of the system, FR requirements, and an ESS using the PSCAD/EMTDC software. The simulation results showed that the proposed method was more effective than the conventional droop-control-based FR-ESS, and the effectiveness of this method was validated.

A Fully Integrated Multi-Phase Buck Converter With On-Chip Capacitor Dynamic Re-Allocation and Fine-Grained Phase-Shedding Techniques

This article presents a fully integrated multi-phase (MP) buck converter for on-chip power management units. A peak-and-valley differential sensing (PVDS) scheme based on a flying capacitor is proposed to evenly balance the multiple inductor currents without significant power overhead even under mismatches in inductances, parasitic series resistances, and control-signal skews among phases. In addition, dynamic re-allocation of on-chip capacitors enables an even more optimal frequency response and output ripple based on the number of activated phases. It also improves the chip area efficiency, resulting in a higher power density. The proposed DLL-based MP clock generation provides high granularity in the phase-shedding control to achieve high efficiency over a wide load range. The proposed fully integrated buck converter using six bond-wire inductors (1 nH) was fabricated in a 28-nm CMOS process. The chip running at a frequency of 400 MHz/phase can finely adjust the number of active phases by an integer step ranging from 1 to 6 through sensing a load current. A maximum power density of 1.23 W/mm2 and a peak efficiency of 83.7% were measured. This work achieved an ultra-fast dynamic voltage scaling (DVS) rate of 75 mV/ns.

Analisis Pemasangan Power System Stabilizer Pada Single Machine Infinite Bus Untuk Kondisi Variasi Beban

Changes in the load on the electric power system suddenly cause dynamic disturbances. The disturbance causes the stability of the generator to be disturbed, because the generator does not respond to the disturbance quickly. This causes oscillations in the generator in the form of oscillations of frequency and rotor angle. One of the additional control equipment that can increase the stability of a generator is the Power System Stabilizer (PSS). With the PSS installation, the optimal frequency response and rotor angle of the SMIB system are obtained, indicated by the minimum system overshot response. The controller is able to provide stability so that overshoot oscillations can be suppressed, as well as faster settling time performance for the system to reach steady state conditions. To test the stability of the SMIB system, a case study of adding and subtracting loads is used, with the proposed control method using PSS.

Particle Swarm Optimization for Optimal Frequency Response with High Penetration of Photovoltaic and Wind Generation

As the installation of solar-photovoltaic and wind-generation systems continue to grow, the location must be strategically selected to maintain a reliable grid. However, such strategies are commonly subject to system adequacy constraints, while system security constraints (e.g., frequency stability, voltage limits) are vaguely explored. This may lead to inaccuracies in the optimal placement of the renewables, and thus maximum benefits may not be achieved. In this context, this paper proposes an optimization-based mathematical framework to design a robust distributed generation system, able to keep system stability in a desired range under system perturbance. The optimum placement of wind and solar renewable energies that minimizes the impact on system stability in terms of the standard frequency deviation is obtained through particle swarm optimization, which is developed in Python and executed in PowerFactory-DIgSILENT. The results reveal that the proposed approach has the potential to reduce the influence of disturbances, enhancing critical clearance time before frequency collapse and supporting secure power system operation.

A Dual-Stage Controller for Frequency Regulation in a Two-Area Realistic Diverse Hybrid Power System Using Bull–Lion Optimization

In this article, a dual-stage proportional integral–proportional derivative with filter (PI–PDF) controller has been proposed for a hybrid two-area power system model having thermal-, hydro-, gas-, wind-, and solar-based power generating sources. Superconductor magnetic energy storage (SMES) units to cope with the transient power deviations have been incorporated in both areas. Governor dead-band (GDB) is considered in the governor model of thermal, and a generation rate constraint (GRC) is considered in the thermal and hydro turbine models to analyze the impact of system nonlinearity. The parameters of the proposed control strategy are optimally tuned by deploying a newly developed bull–lion optimization (BLO) to maintain optimal frequency and power response during system load deviations. Variations in wind speed and PV solar irradiance data have been included to examine the effectiveness of the BLO-based PI–PDF controller with system uncertainties and variability of renewable energy sources. The obtained results are validated by comparison with recently developed existing optimization techniques. The results revealed that the proposed control strategy is efficient for regulating the frequency and tie-line power of renewable integrated power systems. Further, the BLO-based PI–PDF control strategy improved the performance in terms of performance indices like settling time and peak overshoot/undershoot in wide scale.

NIPPF versus ANIPPF controller outcomes on semi-direct drive cutting transmission system in a shearer

Nonlinear integral positive position feedback (NIPPF) and adaptive nonlinear integral positive position feedback (ANIPPF) controllers are used in a shearer's semi-direct drive cutting transmission system, which is powered by a low speed and high torque permanent magnet synchronous motor (PMSM). The transmission system's torsional vibration characteristics were investigated with internal parameter and external cutting load excitation changes caused by harmonic force. In the case of primary and 1:1 internal resonance, an analytic solution is obtained by employing the averaging technique to solve the nonlinear differential equations and modeling the system with NIPPF and ANIPPF controllers. The Poincare portraits were created to imagine how the PMSM would behave around their fixed points. A good match is found when the approximate solutions are compared to the numerical simulations via the Runge–Kutta method fourth-order (RK4). The linearized stability strategy is used to ensure stability near fixed points in the autonomous system. Before and after control, the steady-state amplitude and stability of nonlinear systems were investigated and analyzed. Optimal system operation conditions and frequency response curves (FRCs) were examined at various controller and system parameter values. Numerous system characteristics were found to have an effect after being combined with NIPPF and ANIPPF. The numerical and analytical solutions at time-history and FRCs were compared using the MATLAB program to confirm their comparability. This study's findings were compared to those found in the literature. We conclude from this analysis that the ANIPPF controller provides the best system control. The calculations also revealed that ANIPPF is the most effective controller. Finally, the controls suppress the system's vibration amplitude and chaos motion. The outcomes of this study were used to develop a theoretical foundation for the shearer semi-direct drive cutting transmission system's design and construction.

Optimal frequency response of VPP-based power systems considering participation coefficient

The remarkable presence of renewable resources and the consequent development of virtual power plants (VPPs) in interconnected networks can reduce inertia and spinning reserve in power systems. This issue has created a challenge for power system engineers and analysts to maintain frequency stability in VPPs. Based on the system frequency response (SFR) model and the principal equations of VPPs, this paper presents a new model for the frequency response of a VPP-based interconnected power system. By presenting a method, the optimal reserve amount of generation units of VPP is determined in order to obtain the best frequency response in the frequency recovery for deal with system disturbances. Finally, to analyze the frequency response of the system, various scenarios of the presence or absences of each new resource and its combination with the conventional power networks are simulated. The simulation results indicated the need for the participation of energy storage systems (ESS) and renewable generation resources to safeguard the network frequency stability.

Development and optimisation of low-power magnetic flux leakage inspection parameters for mild steel welds

Magnetic particle and other magnetic flux leakage (MFL)-based methods for the detection and evaluation of surfacebreaking flaws in ferromagnetic materials typically use high-strength (≥0.5 T RMS), low-frequency (≤50 Hz) magnetic fields. The rationale behind this is the ready availability of strong permanent magnets and mains power for high-strength electromagnets. This high field strength is needed to saturate the sample and compensate for the relatively low sensitivity of magnetic particle detection media, silicon Hall sensors, coils and other magnetic transducers used in such methods. Consequently, frequencies greater than 50 Hz and applied magnetic fields less than 100 mT strength have not been widely explored for MFL due to the lack of commercially available sensors capable of detecting the leakage fields (typically in the nT and μT range) with adequate versatility to cope with the variations in inspection parameters, such as changes in liftoff, material properties, etc, which are inherent to non-destructive testing and evaluation (NDT&amp;E) settings. In this study, the MFL response of surface-breaking longitudinal cracks from a ground mild steel weld validation sample, within the DC to 1 kHz and 5 mT to 100 mT RMS applied magnetic field operating range, was explored. This was carried out to determine whether any optimal frequency response exists, better accommodating the inherent sample material properties (for example magnetic permeability and electrical conductivity) and MFL mechanism and attributing phenomena such as electromagnetic skin effect and eddy current contributions. Contrary to previous work published in Insight last year, this study found no particular optimal frequency within this operating range, with explanations to justify the disproval of previously reported conclusions about optimal frequencies within this range. Also, the iteratively developed quantitative analysis performed in this study can be used to help further understand the underlying mechanisms of AC MFL and provide best practice regarding the optimisation of MFL.

Unit Commitment with Tunable Frequency Response from Wind Turbine Generators

Based on the natural inertia on the rotors, wind turbine generators can provide both inertia response and primary frequency response to support the system frequency stability. In this paper, by considering the coordinated optimization of frequency response, a unit commitment with tunable frequency response from wind turbine generators is proposed. The relationship between inertia response and primary frequency response is analyzed. A frequency response correlation constraint is proposed to eliminate the second frequency nadir. Considering the system frequency stability constraints and the feasible region of frequency response provided by wind turbine generators, a security-constrained unit commitment model with tunable frequency response is established. According to the actual operation mode of the power system, a bi-level algorithm is adopted to calculate the frequency response parameters of wind turbine generators. The simulation result of the GB 2030 system demonstrates that the proposed method can reduce operating costs while ensuring system stability.

Frequency Regulation in Isolated Microgrids Through Optimal Droop Gain and Voltage Control

This article presents an adaptive active power droop controller and voltage setpoint control in isolated microgrids for optimal frequency response and stability after disturbances. The control scheme involves an optimal and model predictive control approach that continuously adjusts the active power droop gains and the voltage setpoints of Distributed Energy Resources (DERs) to maintain the frequency of the system within acceptable limits and enhance the primary frequency response of the system, while taking into account the active power sensitivity of the microgrid loads to the system’s operating voltage. The proposed control scheme is tested, validated, and compared with previously proposed techniques using time-domain simulations for a test system based on a CIGRE medium voltage benchmark microgrid under different realistic conditions, demonstrating the advantages of the proposed approach.

Shunted optimal vibration energy harvesting control of discontinuous smart beams

This paper presents an adaptive dynamic analysis of discontinuous smart beam energy harvester systems using a shunt vibration control. The smart structural systems, connected with the shunt and harvesting circuit interfaces, consist of the three types of non-homogeneous structural combinations with different piezoelectric materials. The constitutive coupled dynamic equations with full variational parameters are reduced using the charge type-based Hamiltonian mechanics and the Ritz method-based weak-form analytical approach. Unlike the conventional techniques, this study elaborates the appearance of the two resonances with a wider shift on a specific range of the optimal power output frequencies, using only the first mode of the smart structural systems. Moreover, the two-equal peak of the optimal response may potentially occur to appear not only at the first resonance, but also at the second resonance. This intrinsically represents strong electromechanical effect, depending on the properties and thicknesses of piezoelectric materials and the circuit parameters. The accuracy of the theoretical method is tested using the iterative computational process of the optimal frequency response with full coupled electromechanical system parameters. Further details of the parametric studies are discussed to show the prediction of the energy harvesting with the ability of tuning an adaptive frequency response.

A Grouping-Based Frequency Support Scheme for Wind Farm Under Cyber Uncertainty

The injection of a significant amount of wind power tends to increase the difficulty of the grid frequency control. Therefore, wind farm (WF) has to have the ability to participate in system frequency support. However, during the frequency control process in a large WF, individual wind generators may prone to instability due to possible over-deceleration. In addition, the deeply-intertwined cyber physical power system (CPPS) has gradually replaced the traditional grid due to the development of information and communication technology. However, CPPS also introduces cyber uncertainties that have a significant negative impact on the real-time control of power system. To address above issues, this paper considering possible cyber uncertainty, and proposes a grouping-based hierarchical frequency support scheme for WF. In the proposed scheme, the variable speed wind turbines (VSWTs) are clustered into several groups, according to their wind profiles at first, by dispatching the same control commands to the VSWTs belonging to the same group. As a result, the number of the VSWTs and control variables reduces significantly. Then, a hierarchical control scheme based on virtual inertial control is proposed with consideration of possible cyber uncertainty. The top-layer controller determines whether cyber uncertainty exists, and calculates power increment based on frequency deviation and cyber uncertainty. The bottom-layer controller coordinates the power increment distribution on the basis of ensuring the safe operation of all VSWTs. By do this, it is expected to achieve not only optimal frequency response but also wind generator stability. The effectiveness of proposed scheme is verified on a simulation platform built using MATLAB.

Design of far field beamforming problem by window function

The design of the broadband beam former problem is to find the coefficients vector for all FIR filters such that output fits to a given target spatial directivity pattern in a specified domain. This problem is always very complicated. In this paper, we propose a fast window function method to solve this problem. First, we formulate a simplified optimization problem, where the frequency response function is the decision function. Then an optimal frequency response vector can be obtained by solving this problem. Next we apply the window function to cut off the infinite length of the coefficient. The window function method is efficient and can be applied in real time applications. Numerical example is illustrated to show the efficiency of the method.