Automatic Frequency Control Research Articles

A 0.055 mm2 Total Area Triple-Loop Wideband Fractional-N All-Digital Phase-Locked Loop Architecture for 1.9–6.1 GHz Frequency Tuning

This paper presents a wideband fractional-N all-digital phase-locked loop (WBPLL) architecture featuring a triple-loop configuration capable of tuning frequencies from 1.9 to 6.1 GHz. The first and second loops, automatic frequency control (AFC) and counter-assisted phase-locked loop (CAPLL), respectively, perform coarse locking, while the third loop employs a digital sub-sampling architecture without a frequency divider for fine locking. In this third loop, fractional-N frequency synthesis is achieved using a delta-sigma modulator (DSM) and digital-to-time converter (DTC). To minimize area, digital modules such as counters, comparators, and differentiators used in the AFC and CAPLL loops are reused. Furthermore, a moving average filter (MAF) is employed to reduce the frequency overlap ratio of the digitally controlled oscillator (DCO) between the second and third loops, ensuring stable loop switching. The total power consumption of the WBPLL varies with the frequency range, consuming between 8.8 mW at the WBPLL minimum output frequency of 1.9 GHz and 12.8 mW at the WBPLL maximum output frequency of 6.1 GHz, all at a 1.0 V supply. Implemented in a 28 nm CMOS process, the WBPLL occupies an area of 0.055 mm2.

Analysis of Load Frequency Control of Two Area Power System using Different Control Techniques

To maintain stability is a mandatory requirement of any kind of power network. Interconnected power systems have significant advantages in maintaining stability and frequency at their nominal values. The control of the interconnected power systems is performed by Automatic Generation Control (AGC), which has two parts: the Automatic Voltage Regulator (AVR) and Load Frequency Control (LFC). When a disturbance occurs in the system, Load Frequency Control (LFC) acts to re-establish the system into its steady state with zero error as well as the desired transient response characteristics. This paper exhibits the design and implementation of a PID and Fuzzy Logic Controller for two area power systems, taking the steady state error and percentage of overshoot, undershoot, and pre-shoot as comparison parameters. MATLAB/Simulink software was used to bring out the implementation and obtain results. System dynamic performance is observed for PID and Fuzzy Logic Controllers in Simulink. The comparison study indicated that the proposed Fuzzy Logic controller has better performance than the PID controller. IUBAT Review—A Multidisciplinary Academic Journal, 7(1): 62-79

Impact of ABT based control strategies on ALFC and AVR in DFIG-integrated interconnected power systems

To maintain a stable electricity supply in interconnected power grids, effective frequency and voltage regulation are required. Interconnected power systems use Automatic Load Frequency Control (ALFC) and Automatic Voltage Regulator (AVR) for this purpose. The integration of renewable sources, such as Doubly Fed Induction Generators (DFIGs), creates challenges for such control loops. This study investigates the impact of using various Frequency-Linked Pricing (FLP)-based operating strategies under Availability-Based Tariff (ABT) on combined ALFC and AVR in a two-area interconnected power system with DFIGs. FLP-based operating strategies under ABT react to frequency changes through price signals, which can act faster compared to traditional AGC methods that rely on communication between control centers. This quicker response helps maintain frequency and voltage during load disturbances. Most of the earlier research focused mostly on using only a single type of FLP-based operating strategy under ABT within the ALFC loop, neglecting the combined ALFC-AVR interaction. This work addresses this gap by evaluating three FLP-based operating strategies under ABT along with the traditional approach for their impact on frequency and voltage under step load disturbance. Simulation studies conducted in MATLAB 2022a demonstrate the effectiveness of the proposed strategies, providing valuable insights for improving frequency and voltage control in modern power systems. The investigation reveals that the strategy that considers the difference between the actual and reference values of the unscheduled interchange (UI) charge and the marginal cost of generation to produce the control command outperforms the other strategies and restores the frequency and voltage to their nominal values.

Real-time FPGA prototyping of Doppler frequency shift compensation using DSP-assisted automatic frequency control.

This Letter presents a real-time coherent receiver using digital signal processing (DSP)-assisted automatic frequency control (AFC) to compensate for the Doppler frequency shift (DFS). DFS compensation range of ±8 GHz and the frequency shifting rate of 33 MHz/s are demonstrated in an FPGA-based 2.5 Gbaud QPSK coherent optical system. The experimental results indicate that the scheme achieves a sensitivity of -47 dBm at a bit error rate (BER) of 2E-4. The power penalty induced by the DFS compensation is less than 1 dB.

Rapid Switching of a C-Series Linear Accelerator Between Conventional and Ultrahigh-Dose-Rate Research Mode With Beamline Modifications and Output Stabilization

PurposeIn this study, a decommissioned C-series linear accelerator (linac) was configured to enable rapid and reliable conversion between the production of conventional electron beams and an Ultrahigh-dose-rate (UHDR) electron beamline to the treatment room isocenter for FLASH radiation therapy. Efforts to tune the beam resulted in a consistent, stable UHDR beamline. Methods and MaterialsThe linac was configured to allow for efficient switching between conventional and modified electron output modes within two minutes. Additions to the air system allow for retraction of the X-ray target from the beamline when the 10MV photon mode is selected. With the carousel set to an empty port, this grants access to the higher current pristine electron beam normally used to produce clinical photon fields. Monitoring signals related to the automatic frequency control (AFC) system allows for tuning of the waveguide while the machine is in a hold state so a stable beam is produced from the initial pulse. A pulse counting system implemented on a FPGA-based controller platform controls the delivery to a desired number of pulses. Beam profiles were measured with Gafchromic film. Pulse-by-pulse dosimetry was measured using a custom electrometer designed around the EdgeTM diode. ResultsThis method reliably produces a stable UHDR electron beam. Open field measurements of the 16cm (FWHM) gaussian beam saw average dose rates of 432Gy/s at treatment isocenter. Pulse overshoots were limited and ramp up was eliminated. Over the last year, there have been no recorded incidents that resulted in machine downtime due to the UHDR conversions. ConclusionStable 10MeV UHDR beams were generated to produce an average dose rate of 432Gy/s at the treatment room isocenter. With a reliable pulse-counting beam control system, consistent doses can be delivered for FLASH experiments with the ability to accommodate a wide range of field sizes, source-to-surface distances, and other experimental apparatus that may be relevant for future clinical translation.

Анализ возможностей оптимизации выбора ультразвукового оборудования для нанесения функциональных покрытий

To meet the requirements affecting the quality of functional coatings, various technologies are currently being used, one of which is the use of ultrasonics. To form functional coatings, ultrasonics are used both at the stage of surface preparation and at the stage of coating deposition. Thus, at the stage of surface preparation, ultrasonics allow making surface preclean, ensuring the necessary surface roughness due to ultrasonic rolling, as well as preactivation of the surface before nitriding due to surface plastic deformation. In case of coating deposition, ultrasonics contribute to better nitriding and painting. However, ultrasonic equipment used in various preparation and coating deposition processes differs significantly in its characteristics. Thus, the ultrasonic generators vary in alternator capacity, specific material consumption, actual frequency, as well as design features that ensure stable operation, for example, automatic frequency control. The converters differ from each other in accomplishable amplitudes, power and actual frequency. In this regard, the aim of the work is to develop recommendations on the use of ultrasonic equipment in various technical processes for the creation of functional coatings. The paper studies ultrasonic equipment used in surface preparation and functional coating application process. The main process-dependent parameters aimed at choosing the required equipment have been characterized. Recommendations are given on the use of ultrasonic equipment for various functional coatings generation, when a converter-generator couple is found and it meets the requirements for most surface preparation and coating deposition processes.

An Automatic Frequency Control System for Transmission Machinery Based on Back-Propagation Neural Network Algorithm in the Internet of Things Environment

Abstract In order to reduce the error of automatic frequency control of transmission machinery under different disturbances, an automatic frequency control system of transmission machinery based on back-propagation (BP) neural network algorithm is designed. The gradient descent method and Newton method are combined to optimize the BP neural network. Aiming at the periodicity and trend of the actual mechanical vibration frequency time series, the first order backward difference is processed by the difference method, and the autoregressive sequence is derived to obtain the control model. The experimental results show that the system can realize the automatic control of transmission mechanical frequency with small error under different types of interference, and the control effect is ideal.

Generation of transmission wave with low AM noise for sub-GHz CW-EPR spectrometer

This study describes a technique to clean amplitude modulation (AM) noise of RF transmission waves, which is used to observe the sub-GHz CW-EPR spectrum. An RF transmitter amplifier that has the function of cleaning AM noise has been developed. Cleaning of the AM noise was owing to saturation of the output at the amplifier. Three stages of the amplifiers in series could effectively suppress the AM noise to about –176 dBc/Hz and –183 dBc/Hz at offset frequency of 10 kHz and 100 kHz, respectively at the carrier frequency of 750 MHz and the output power of 29 dBm. Since phase modulation (PM) noise is suppressed by phase sensitive detection, the AM noise in the transmission is dominant cause of the noise in the sub-GHz CW-EPR absorption spectrum using a reflection bridge, which depends on the quality factor of the resonator and the power of the RF transmission. The additive phase modulation (PM) noise of this amplifier was –171 dBc/Hz at an offset frequency of 100 kHz, which indicated that the frequency modulation (FM) of the transmission wave was not distorted with this amplifier. Therefore, conventional CW-EPR spectrometers that typically require FM for automatic frequency control or automatic tunning control can use this technique to increase sensitivity.

Providing a Control System for Charging Electric Vehicles Using ANFIS

Frequency control, especially when incorporating distributed generation units such as wind and solar power plants, is crucial for maintaining grid stability. To address this issue, a study proposes a method for controlling the connection status of electric vehicles (EVs) to prevent frequency fluctuations. The method utilizes an adaptive neural-fuzzy inference system (ANFIS) and a whale optimization algorithm to regulate the charging or discharging of EV batteries based on frequency fluctuations. The objective is to minimize and adjust the frequency fluctuations to zero. The proposed method is evaluated using a real microgrid composed of a wind power plant, a solar power plant, a diesel generator, a large household load, an industrial load, and 711 electric vehicles. The ANFIS system serves as the primary controller, taking inputs such as electric vehicle and battery status and generating outputs that determine the charging or discharging of the electric vehicles. Several investigations are conducted to assess the effectiveness of this model, and the results obtained are compared with the normal state where electric vehicles only consume power. By implementing this method, it is expected that the connection status of electric vehicles can be optimized to help stabilize the grid and minimize frequency fluctuations caused by the integration of distributed renewable energy sources. This study highlights the importance of automatic frequency control in smart grids and offers a potential solution using ANFIS and the whale optimization algorithm.

Formation of the Spectral Composition of the Output Voltage of Converters for Nuclear Magnetic Resonance

In this paper, we consider the construction of an asynchronous control system for semiconductor converters for nuclear magnetic resonance. The relevance of research in this direction, main problems that arise during the construction of these systems are shown. Derived the mathematical model of the inverter, on the basis of which a control system with asynchronous pulse-width modulation is constructed. Proposed an equivalent converter circuit with a constant structure, constant parameters, and an equivalent EMF generator. Established correspondence between the equivalent circuit of the converter and its mathematical model in the form of differential equations. On the basis of mathematical equations, a structural diagram of the converter with a control system was developed and the principle of operation of the device was described according to it. To develop an algorithm for the control system, the dependence of the frequency change relative to the resonant frequency on the phase shift between the current through the filter and the voltage on the antenna circuit is determined. For which the model was built in Simulink and the corresponding simulation was carried out. Numerical dependences of reference signal frequency change and phase shift were obtained. The increase in efficiency of device for nuclear magnetic resonance is considered due to the use of multilevel inverters with tuning the frequency of operation to the frequency of the resonant circuit. Simulation of a three-level diode-clamped inverter showed that when the capacitance of the resonant circuit changes and, therefore, the resonant frequency of the circuit, the input current increases. The work obtained specific numerical dependencies. Time diagrams of voltages and currents on the main elements of the converter are given, which illustrate the implementation asynchronous pulse-width modulation in the control system. After working out the automatic frequency control algorithm, the increase in current consumption can be leveled off. The simulation results also show that it is possible to reduce the amplitude of the third harmonic. The disadvantages of the proposed system include the fact that the frequency of the converter is adjusted at each subsequent period of its operation. At the same time, the parameters of the filter can change again, which leads us to believe that adjusting the frequency will never give a 100% result, but will only allow to get as close as possible to the set parameters of the sounding signal. The work also indicates that it is possible to improve the spectral composition of the probing voltage generated by the converter by using more levels of a diode-clamped multi-level inverter. However, increasing the number of levels reduces the action speed of the system and complicates the control system itself. Therefore, the need to maintain a balance between the number of levels of the inverter and the complexity of the system is indicated.

Load Frequency Control and Optimization of Load Allocation for Multi-Area Power System with Electric Vehicle Charging Load

The integration of electric vehicles (EVs) into power systems has introduced new challenges for load frequency control due to the additional charging load they impose. This research article investigates the design and analysis of automatic load frequency control in a two-area power system, considering the presence of EV charging load. The study employs Artificial Neural Network (ANN) based PI control to manage both traditional load demand and the dynamic charging requirements of EVs. Maintaining a stable power system frequency and balancing generation with the EV charging load have become crucial tasks. Automatic Generation Control (AGC) or Load Frequency Control (LFC) systems need to adapt and account for the variability and uncertainty associated with EV charging patterns. The integration of ANN-based PI control provides an intelligent and adaptive approach to address these challenges. Using MATLAB, a power system model is simulated to evaluate the effectiveness of the proposed control scheme. This investigation conducts a comparative analysis of the system's frequency responses under various scenarios, including different EV charging load profiles. It highlights the benefits and challenges of utilizing ANN-based PI control to manage the combined load of traditional demand and EV charging. Moreover, the load distribution among the distribution stations varied from 0.08% to 12.50% when compared between particle swarm optimization and genetic algorithm, respectively. By considering the dynamic interaction between power system operation and EV charging, this research aims to enhance the reliability, efficiency and sustainability of power systems in the context of evolving transportation trends and the increasing electrification of vehicles.

Sliding Mode Without Reaching Phase Design for Automatic Load Frequency Control of Multi-Time Delays Power System

Sliding Mode Without Reaching Phase Design for Automatic Load Frequency Control of Multi-Time Delays Power System

Employment of renewable based sources in amalgamated frequency-voltage control restructured system with TSA trained IPD(1+I) controller

The existing effort explores automatic load frequency control learning and automatic voltage regulator for manifold areas and sources under restructured situations. Sources in Area_1 are bio-diesel and thermal; diesel and thermal plants in Area_2. Thus, each area consists of two generating companies and two distributing companies. A unique attempt has been undergone to perform a deuce phase controller integral-proportional-derivative with one plus integral (IPD(1 + I)) controller. Various examination expresses that IPD(1 + I) is an excellent controller when compared with proportional-derivative (PD) and proportional-integral-derivative-filter (PIDN) from outlook regarding crest overshoot, grade-of-fluctuations, crest undershoot as well as the subsiding period in case of bilateral contacts. In an attempt to secure the controller's attributes bio-enthused meta-heuristic tunicate search algorithm (TSA) is applied. Along with that, renewable source solar energy in the form of solar photovoltaic has been merged in both the operating areas. Action in existence of hydrogen aqua electrolyser – fuel cell (HAE (FC)) has also been examined using IPD(1 + I) controller for bilateral contact, in order to obtain noteworthy outcomes in a dynamic presentation. It is pragmatic that the best responses are obtained for the scheme with the inclusion of both PV and HAE (FC). Also, IPD(1 + I) parameters values at nominal condition has been analyzed to confirm its suitability for varied loading conditions without the need for optimization.

Experience in the Development and Implementation of Modern Systems of Automatic Frequency and Power Control of Large Power Units with Direct-Flow Boilers

Experience in the Development and Implementation of Modern Systems of Automatic Frequency and Power Control of Large Power Units with Direct-Flow Boilers

Technical Infrastructure for Clinical Translation of Electron FLASH

For safe clinical translation of electron FLASH, hardware tools for real-time beam control and software tools for treatment planning are necessary. The purpose of this study is to prototype high-throughput hardware for real-time beam control, along with accurate beam modeling of a modern clinical Linac configured to deliver FLASH dose-rates. For real-time beam current monitoring, a beam current transformer (BCT) was initially coupled to a fast digitizer and its linearity was established by varying dose per pulse. The radiation pulse width was modified, and this change was measured using the BCT. The BCT was then used to measure the variability of dose per pulse and pulse width due to a mistuned linear accelerator system. Next, the BCT was interfaced with a field programmable gate array (FPGA) which provides the ability for high-throughput and deterministic control of the Linac based on dose accumulation. For beam modeling, the program, TOol for PArticle Simulation (TOPAS), was used to obtain beam parameters by using Bayesian optimization of the beam energy, source size, angular, and energy spread via comparison of simulated and representative dose profiles. The beam model would then be employed to calculate 3D dose distribution in a CT scan of a 3D-printed anatomically realistic mouse phantom. The area under the current-time curve from the BCT exhibited excellent linearity (response = 12.80 nC/Gy) up to 2.5 Gy/Pulse (R2 = 0.99). The peak beam current for the electron FLASH beam was measured to be ∼10 mA for an instantaneous dose-rate of ∼5×105 Gy/s. The measured radiation pulse width agreed with the expected value (3.7 μs). The pulse width was then shortened and the measurement by the BCT indicated pulse widths of 1.8 μs and 0.5 μs corresponding to 0.7 Gy/pulse and 0.3 Gy/pulse, respectively. The beamline exhibited a ramp-up in dose per pulse and pulse width when using the automatic frequency controller (AFC). For the first pulse, the dose delivered was ∼0.1-0.3 Gy and the pulse width was 0.6 μs. The output stabilized to nominal values of dose and pulse width after 3-4 pulses. This ramp-up was mitigated by manually tuning the RF resonance with the AFC disabled, after which the BCT exhibited constant output and pulse width. The beam modeling work is in progress. We demonstrated that a BCT can provide real-time measurement of per-pulse output suitable as input for FLASH beam control based on dose accumulation. The next steps are to quantify the accuracy of the dose control mechanism with the FPGA-based hardware. Potential failure modes will be identified and mitigated in parallel with the development of the hardware. A 3D-printed mouse phantom has been constructed to facilitate beam modeling work for treatment planning (in progress). On completion of this work, it is expected that we will have key infrastructure elements needed to move towards an eventual FDA investigational device exemption for clinical trials.

Multi-area load frequency regulation of a stochastic renewable energy-based power system with SMES using enhanced-WOA-tuned PID controller

This paper presents a novel nature-inspired meta-heuristic optimization algorithm known as the Enhanced Whale Optimization Algorithm (EWOA), which imitates humpback whales' social behavior to solve the optimization of multi-area automatic load frequency control (LFC) problems of a stochastic renewable energy-based power system with superconducting magnetic energy storage (SMES). An EWOA algorithm is presented in response to the limitations of the conventional WOA algorithm, including its sluggish convergence time, low accuracy, and propensity to easily enter local optimum. The system model investigated includes some physical constraints such as the time delay (TD), generation rate constraint (GRC), reheat turbine (RT), and the dead band (DB). The impacts of these physical constraints on the dynamic performance of the proposed controller were investigated. The EWOA algorithm is utilized to dynamically optimize the parameters of the PID controller for optimal system performance. The effectiveness and dynamic performance of the proposed controller are compared with the conventional WOA using some performance metrics. The system model also includes superconducting magnetic energy storage (SMES) units in both areas and their impacts on the system performances are also investigated. The effects of the changes of two different parameters of the system (frequency bias parameter, B, and the governor speed regulation, R) on the frequency deviation responses and the controller's robustness are examined. It is evident from the results that the dynamic performance of the proposed controller is better than that of the conventional WOA and it is more robust and stable to changes in system loading, parameters, and step load perturbation.

Enhancing of the power system resilience through the application of micro power systems (microgrid) with renewable distributed generation

The power sector plays a critical role in the functioning of the economy and the security of a country, being closely interconnected with other vital infrastructures, such as gas supply, water supply, transportation, and telecommunications. Ensuring a stable power supply is crucial for the uninterrupted operation of these systems. One way to enhance the resilience of the power system is by integrating local networks with distributed renewable generation into the overall energy infrastructure. The flexibility, stability, controllability, and self-healing capabilities of microgrids make them an effective solution for improving the resilience of the power system. The power grid is susceptible to disturbances and disruptions that can cause large-scale power outages for consumers. Statistical data indicates that approximately 90% of outages occur due to issues in the distribution system, thus research focuses on local microgrids with distributed renewable generation. This study analyzed the role of microgrids with renewable generation in enhancing the resilience of power systems. Additionally, functions of microgrids that contribute to enhancing power system resilience, such as service restoration, network formation strategies, control and stability, as well as preventive measures, were summarized. It was found that local microgrids have significant potential to enhance power system resilience through the implementation of various strategies, from emergency response planning to providing reliable energy supply for quick responses to military, environmental, and human-induced crises. The concept of local distributed energy generation, storage, and control can reduce reliance on long-distance power transmission lines, reduce network vulnerabilities, and simultaneously improve its resilience and reduce recovery time. It has been determined that the most necessary and promising approaches to enhance the resilience of the power system include developing appropriate regulatory frameworks, implementing automatic frequency and power control systems, ensuring resource adequacy (including the reservation of technical components), promoting distributed generation, integrating energy storage systems into the energy grid, and strengthening cyber security. Keywords: resilience, local power systems, MicroGrid, distributed generation, renewable energy sources.

A low-noise X-band microwave source with digital automatic frequency control for electron paramagnetic resonance spectroscopy

We report a new design of microwave source for X-band electron paramagnetic resonance spectrometer. The microwave source is equipped with a digital automatic frequency control circuit. The parameters of the digital automatic frequency control circuit can be flexibly configured for different experimental conditions, such as the input powers or the quality factors of the resonator. The configurability makes the microwave source universally compatible and greatly extends its application. To demonstrate the ability of adapting to various experimental conditions, the microwave source is tested by varying the input powers and the quality factors of the resonator. A satisfactory phase noise as low as −135 dBc/Hz at 100-kHz offset from the center frequency is achieved, due to the use of a phase-locked dielectric resonator oscillator and a direct digital synthesizer. Continuous-wave electron paramagnetic resonance experiments are conducted to examine the performance of the microwave source. The outstanding performance shows a prospect of wide applications of the microwave source in numerous fields of science.

Load Frequency Control and Automatic Voltage Regulation in Four-Area Interconnected Power Systems Using a Gradient-Based Optimizer

Existing interconnected power systems (IPSs) are being overloaded by the expansion of the industrial and residential sectors together with the incorporation of renewable energy sources, which cause serious fluctuations in frequency, voltage, and tie-line power. The automatic voltage regulation (AVR) and load frequency control (LFC) loops provide high quality power to all consumers with nominal frequency, voltage, and tie-line power deviation, ensuring the stability and security of IPS in these conditions. In this paper, a proportional integral derivative (PID) controller is investigated for the effective control of a four-area IPS. Each IPS area has five generating units including gas, thermal reheat, hydro, and two renewable energy sources, namely wind and solar photovoltaic plants. The PID controller was tuned by a meta-heuristic optimization algorithm known as a gradient-based optimizer (GBO). The integral of time multiplied by squared value of error (ITSE) was utilized as an error criterion for the evaluation of the fitness function. The voltage, frequency, and tie-line power responses of GBO-PID were evaluated and compared with integral–proportional derivative (GBO-I-PD), tilt integral derivative (GBO-TID), and integral–proportional (GBO-I-P) controllers with 5% step load perturbation (SLP) provided in each of the four areas. Comprehensive comparisons between GBO-PID and other control methodologies revealed that the proposed GBO-PID controller provides superior voltage, frequency, and tie-line power responses in each area. The reliability and efficacy of GBO-PID methodology were further validated with variations in the turbine time constant and speed regulation over a range of  ± 25%. It is evident from the outcomes of the sensitivity analysis that the proposed GBO-PID control methodology is very reliable and can successfully stabilize the deviations in terminal voltage, load frequency, and tie-line power with a shorter settling time in a four-area IPS.

Dandelion Optimizer-Based Combined Automatic Voltage Regulation and Load Frequency Control in a Multi-Area, Multi-Source Interconnected Power System with Nonlinearities

Frequency, voltage, and power flow between different control zones in an interconnected power system are used to determine the standard quality of power. Therefore, the voltage and frequency control in an IPS is of vital importance to maintaining real and reactive power balance under varying load conditions. In this paper, a dandelion optimizer (DO)-based proportional-integral-proportional-derivative (PI-PD) controller is investigated for a realistic multi-area, multi-source, realistic IPS with nonlinearities. The output responses of the DO-based PI-PD were compared with the hybrid approach using artificial electric field-based fuzzy PID algorithm (HAEFA), Archimedes optimization algorithm (AOA)-based PI-PD, learning performance-based behavior optimization (LPBO)-based PI-PD and modified particle swarm optimization (MPSO)-based PI-PD control schemes in a two-area network with 10% step load perturbation (SLP). The proposed strategy was also investigated in a two- and three-area IPS in the presence of different nonlinearities and SLPs. The simulation results and the comprehensive comparison between the different control schemes clearly confirm that the proposed DO-based PI-PD is very effective for realistic, multi-area multi-source IPS with nonlinearities.