Dynamic Load Changes Research Articles

Stability analysis and voltage improvement in DG-integrated distribution networks using VCPI-based critical buses and lines detection considering uncertain power factor

Voltage stability ensures reliable and efficient power transmission to end-users, making it essential for power system efficiency. Dynamic load changes and rising power requirements might cause voltage instability and strain performance. This paper investigates the voltage stability Indicators of distribution systems to address the voltage stability issue in power systems. The uncertain power factor and other numerous technical parameters that affect the voltage drop or voltage collapse are involved in predicting the system’s voltage stability. First, the analysis uses the voltage collapse proximity index (VCPI) technique, which considers bus voltage, impedance, uncertain power factor of load buses, and transmission line impedance at both ends. The applied technique correctly predicts and detects weak buses and transmission lines using different voltage stability indices since technical parameters are correlated with the VCP index. The index and line impedance correspond; consequently, the recommended indication compensates for voltage loss owing to impedance. Therefore, the VCPI is a better index for anticipating voltage collapse and finding network weak busses and lines. The implemented approach is simple, precise, and economical; the index technique detects weak buses and forecasts system collapse. Second, this work introduces EMFO-FPSO, a hybrid metaheuristic that improves voltage stability by combining Fractional-order particle swarm optimization (PSO) and Entropy design mouth flame optimization (MFO). The proposed approach is validated on the IEEE 33 bus system by identifying weak buses and optimizing distributed generation placement in the distribution system. The implemented solution approach based on VCPI and EMFO-FPSO optimization achieves a significant power loss reduction of 71.5% compared to the base case, whereas the reductions for ABC, ACO-ABC, and PSO are 57.3%, 60.7%, and 64.4%, respectively. Moreover, the proposed method attains a stable VCPI Index of 0.90, indicating a 10% enhancement in voltage stability relative to the base case. The study’s results, key findings, and comparisons show the relevance of the proposed method for voltage stability enhancement.

The Impact of Post-Furnace Steel Processing Equipment on Reducing Voltage Fluctuations Caused by Arc Furnaces

Arc devices are among the receivers with the highest power connected to power systems. Due to dynamic load changes, these receivers generate a number of disturbances that affect the quality of electric power. The most important disturbances include voltage fluctuations. It is also worth mentioning the asymmetry and deformation of the supply voltage curve. This article discusses the mutual interaction of receivers operating in parallel, operating stably, and devices with dynamic current consumption. Calculations based on model tests and the results of parameters characterizing the quality of energy, which were recorded in the line supplying the steelworks, are presented. The power supply conditions (power of the short-circuit network) were assessed to influence the degree of suppression of voltage fluctuations by loads with stable current consumption.

SVPWM‐Based Algorithm for Reduced THD and Switching Losses Under Varying Fundamental Frequency and Load in a VSI

ABSTRACTThe present study explores the influence exerted by various pulse width modulation (PWM) techniques upon harmonic distortion and switching losses of a voltage source inverter. In the context of this inquiry, a generalized algorithm for variable frequency operations, inspired by continuous and discontinuous PWM is outlined in this article. The algorithm is explicitly formulated as a function of fundamental frequency and the load power factor angle with the objective of minimizing total harmonic distortion (THD) and switching losses within a specified frequency range. The algorithm is segmented into various regions of frequency, guided by the theory that each region corresponds to a distinct PWM technique that yields reduced harmonic distortion. In this article, a minimum switching loss algorithm is introduced and implemented using both BCPWM and ABCPWM techniques. The algorithm is specifically designed to minimize switching losses across the entire range of load power factor angles. The integration of switching loss algorithm with the selection of the optimal PWM technique across different frequency ranges results in reduced switching losses and harmonic distortion. This leads to a comprehensive PWM algorithm that efficiently reduces both THD and switching losses during dynamic frequency and load changes. Experimental and theoretical evidences demonstrate the efficacy of the proposed algorithm in attaining minimum harmonic distortion and reduced switching loss operation during variations in fundamental frequency and load.

An Investigation into the Impact of Time-Varying Non-Conservative Loads on the Seismic Stability of Concrete-Filled Steel-Tube Arch Bridges

When the arch rib of the mid-bearing through and lower-bearing through arch bridges undergoes out-of-plane deformation, it is usually subject to the resilience force provided by the flexible hanger, which is known as the “non-conservative force effect” of the suspender. In contrast to the static condition, in the dynamic scenario, the time-varying non-conservative force exerted by the flexible suspender becomes more complex due to dynamic changes in external load. Moreover, the difference in fundamental frequency and vibration period between the bridge system and arch rib may influence the stress distribution within the arch rib during ground motion. This paper investigates the impact of time-varying non-conservative forces on the dynamic stability of arch ribs in concrete-filled steel tube (CFST) bridges under seismic loads. Specifically, it examines the influence of different seismic waveforms, frequency disparities between bridge slabs and arch ribs, and suspender stiffness on the non-conservative effect. The results reveal significant disparities in the impact of non-conservative forces exerted by the suspender during seismic events with identical intensity but varying frequency characteristics. The influence of non-conservative forces on the dynamic stability of bridges escalates as deck stiffness increases, while it remains relatively unaffected by changes in suspender stiffness.

Recent progress in the operational flexibility of 1 MW circulating fluidized bed combustion

In this study, various experimental tests were carried out with a 1 MWth circulating fluidized bed pilot plant at the Technical University of Darmstadt to investigate the combustion and co-combustion behaviour of different fuels under load change conditions in air and oxyfuel mode. The combustion tests were carried out with low-calorific lignite and hard coal as reference cases for co-combustion. In the co-combustion experimental tests, straw pellets, and refuse-derived fuels (high and low calorific) were used as co-fuels for coal. In addition, a comprehensive dynamic 1.5-D process simulation model was established for a 1 MWth circulating fluidized bed pilot plant. The model created with the “APROS” software precisely reproduces both the gas/solids and the water/steam side of the 1 MWth pilot plant. The dynamic process simulation model was first validated at various steady-state operation points and, in a second step, at various dynamic load changes. The numerical results, such as the pressure drop and temperature profiles along the fluidized bed riser as well as the flue gas concentrations at the cyclone outlet, were compared with the measurements and showed agreement during the long-term tests of the combustion and co-combustion processes.

Strain modal response and vibration damping optimization of tower for wind power equipment

The safety of wind power equipment under dynamic load is one of the key factors to ensure sustainable energy recovery. In order to effectively improve the reliability of tower structure, the damage identification of flange bolt fracture based on strain mode was studied, and the vibration control and optimization scheme was proposed and verified. The dynamic response of the tower to wind load was calculated using the theory of Davenport spectrum. Combined with computational fluid dynamics, the dynamic load change law of the tower was obtained. Based on ANSYS Workbench, the modal simulation and analysis of the tower were carried out. Under different bolt damage conditions, the distribution characteristics of the strain modal shape of the tower in the axial and radial directions were obtained. The vibration damper was applied to the inside of the tower, and the vibration and stress at different positions under wind load were compared and analyzed to verify the specific vibration reduction and optimization effect. The results show that the strain modal shape of the tower cylinder has a significant peak at the damage site, and the peak height is positively correlated with the damage degree, indicating that the strain modal shape is highly sensitive to the damage. In addition, the vibration and maximum stress of the flange and top position of the tower have been effectively reduced by the shock absorber. The average amplitude of tower top can be reduced by 22.5 %, and the peak stress at the bottom flange position can be reduced by about 38 %.

Building heating load forecasting based on the theory of transient heat transfer and deep learning

Reliable and accurate heating load forecasting can provide comprehensive information for the monitoring and control of Heating, Ventilation, and Air Conditioning (HVAC) in buildings, which reduce uncertainty on the load demand of energy effectively. Data-driven method has demonstrated a potential to forecast heating load, but current methods generally lack the consideration of features on model forecasting performance and applicability. Based on the theory of transient heat transfer and conduction transfer function for building hourly heating load calculation, this study proposes an idea that comprehensively selects physical variables affecting the hourly dynamic changes of the building heating load as features, which enhances the persuasiveness of selecting datasets features. Then we use the deep learning method to build short-term heating load forecasting models, and explore the influence of different feature combinations and time steps on the model forecasting performance. Combining the physical property of building heat gains, we divide the features into external heat gains, internal heat gains and historical heating load and then show their performance of models at different time steps. It is shown that the two-hour data of external heat gains and internal heat gains, the three-hour data of past heat load have the highest value. The best model can achieve a mean absolute error of 0.153 kW and a mean absolute percentage error of 6.2 %. These findings are helpful for researchers to select more relevant features to forecast heating load in buildings and improve their models through physical aspect.

An Implementation of Fuzzy to Minimize Electrical Losses in Induction Machine Vector Control

An induction motor is a motor that is difficult to control so it requires synchronous speed due to dynamic load changes which are controlled by the torque current while the field current is kept constant. Thus, in this paper, we implement an adaptive PID controller method with an induction motor using MATLAB which coordinates the speed of two decoupled loads with a three-phase induction motor, where an adaptive Self Tuning Regulator (STR) PID controller is designed and realized to regulate the speed of a three-phase induction motor. using MATLAB software and AVR Atmega16 microcontroller as input and output from the plant with communication using serial RS232. The results show that after coordinating the system with each motor which is given a neural controller and FOC, the motor speed results are obtained which gradually provide synchronous speed so it can be concluded that this system can work well to slow down the plant response. Keywords: Induction Motor, Motor Speed, neural method, PID controller

Dual‐input step‐up switched‐capacitor multilevel inverter with reduced voltage stress on devices

SummaryThis paper proposes a single‐phase dual‐input step‐up switched‐capacitor multilevel inverter that employs three capacitors, 15 switches, and two diodes to provide 13 voltage levels and triple‐voltage boosting factor in its symmetric form and 37 levels with voltage boosting factor of 3.6 in its asymmetric version. This high boosting factor is accomplished without utilizing any transformer. For each output voltage level, there exists flow paths for both the positive and negative load current directions, which makes the proposed inverter capable of supplying any load type with variety of power factors (zero to unity). The voltage balancing of the capacitors takes place naturally, which tackles the need to auxiliary charge‐balancing circuits or control mechanisms. The proposed inverter can generate negative levels without the end‐side H‐bridge. Moreover, the voltage stress on the semiconductor devices is less than the peak output voltage. The increased number of levels and sinusoidal‐like waveform of the output voltage waveform enhances the quality and lowers the harmonic content of the load voltage and current waveforms, even for resistive loads. As the result, the load‐side filter can be downsized or removed. This paper employs the fundamental frequency method (FFM) as the switching technique, which is simple to implement and also operates the switches at low frequencies, leading to lower switching losses. The ascendancy of proposed inverter over similar counterparts has been investigated through comprehensive comparative analysis. Moreover, the correct performance of the proposed inverter at different modulation indices, and load types as well as during dynamic load changes has been verified by simulation and experimental analysis.

Transformer parameter estimation in distribution network based on deformable transformer

With the large number of distributed power sources and the dynamic change of load, the abnormal parameters of distribution transformers become more and more complicated. So it is particularly important to estimate their parameters accurately. For a low voltage distribution network with a limited number of measuring equipment, a Transformer parameter estimation method based on a Deformable Transformer is proposed in this paper. Firstly, a Transformer parameter estimation model based on a Deformable Transformer network is established by using historical measurement data. Then, a quality evaluation method of parameter estimation is proposed to test the accuracy of parameter estimation. Finally, the effectiveness of the proposed method is verified by practical data.

PSO Training Neural Network MPPT with CUK Converter Topology for Stand-Alone PV Systems Under Varying Load and Climatic Conditions

Temperature and irradiance levels are two examples of environmental variables that affect the power value produced by photovoltaic panels. Therefore, in order to transfer the maximum power value from the PV panel to the load under varying climatic conditions, maximum power point tracking (MPPT) algorithms and DC-DC converter topologies are used. In this study, the performances of boost converter and CUK converter circuit topologies are investigated under variable irradiance and variable load conditions by using a neural network-based MPPT algorithm learning particle swarm optimization (PSO). As the first scenario, it is analyzed assuming that the temperature and irradiance values coming to the panel are constant. As the second scenario, the performance evaluation of the converter topologies according to the current, voltage and power parameters is made for the variable load situation. As the last scenario, the difference in the irradiance value coming to the panel depending on the sun's condition during the day has been examined. Canadian Solar CS6P-250P PV panel is used in the study. 50 kHz is selected as the switching frequency. According to the results obtained, it has been observed that the CUK converter circuit topology reaches the maximum power point faster than the boost converter circuit topology both in dynamic environmental conditions and load change, and the oscillation at this point is less. It is aimed to increase the performance of this method, which uses boost converter topology and MPPT in the literature, by applying CUK converter topology.

Dynamic load modulation predicts right heart tolerance of left ventricular cardiovascular assist in a porcine model of cardiogenic shock.

Ventricular assist devices (VADs) offer mechanical support for patients with cardiogenic shock by unloading the impaired ventricle and increasing cardiac outflow and subsequent tissue perfusion. Their ability to adjust ventricular assistance allows for rapid and safe dynamic changes in cardiac load, which can be used with direct measures of chamber pressures to quantify cardiac pathophysiologic state, predict response to interventions, and unmask vulnerabilities such as limitations of left-sided support efficacy due to intolerance of the right heart. We defined hemodynamic metrics in five pigs with dynamic peripheral transvalvular VAD (pVAD) support to the left ventricle. Metrics were obtained across a spectrum of disease states, including left ventricular ischemia induced by titrated microembolization of a coronary artery and right ventricular strain induced by titrated microembolization of the pulmonary arteries. A sweep of different pVAD speeds confirmed mechanisms of right heart decompensation after left-sided support and revealed intolerance. In contrast to the systemic circulation, pulmonary vascular compliance dominated in the right heart and defined the ability of the right heart to adapt to left-sided pVAD unloading. We developed a clinically accessible metric to measure pulmonary vascular compliance at different pVAD speeds that could predict right heart efficiency and tolerance to left-sided pVAD support. Findings in swine were validated with retrospective hemodynamic data from eight patients on pVAD support. This methodology and metric could be used to track right heart tolerance, predict decompensation before right heart failure, and guide titration of device speed and the need for biventricular support.

Integrated serum pharmacochemistry and investigation of the anti-influenza A virus pneumonia effect of Qingjin Huatan decoction

Ethnopharmacological relevanceQingjin Huatan Decoction (QJHTT) consists of 11 herbal medicines: Scutellaria baicalensis Georgi, Gardenia jasminoides J. Ellis, Platycodon grandiflorus (Jacq.) A. DC., Ophiopogon japonicus (Thunb.) Ker Gawl., Morus alba L., Fritillaria thunbergii Miq., Anemarrhena asphodeloides Bunge, Trichosanthes kirilowii Maxim., Citrus reticulata Blanco, Poria cocos (Schw.) Wolf, and Glycyrrhiza uralensis Fisch. As a traditional Chinese medicinal formula, QJHTT has been used for more than 400 years in China. It has shown promising results in treating influenza A virus (IAV) pneumonia. Aim of the studyTo elusive the specific pharmacological constituents and mechanisms underlying its anti-IAV pneumonia effects. Materials and methodsThe components in QJHTT were analyzed through the use of a serum pharmacology-based ultra high-performance liquid chromatography Q- Exactive Orbitrap mass spectrometry (UHPLC-Q Exactive Orbitrap-MS) method. Simultaneously, the dynamic changes in IAV-infected mouse lung viral load, lung index, and expression of lung inflammation factors were monitored by qRT-PCR. ResultsWe successfully identified 152 chemical components within QJHTT, along with 59 absorbed chemical prototype constituents found in the serum of mice treated with QJHTT. 43.45% of these chemical components and 43.10% of the prototype constituents were derived from the monarch drugs, namely Huangqin and Zhizi, aligning perfectly with traditional Chinese medicine theory. Notably, our analysis led to the discovery of 14 compounds within QJHTT for the first time, three of which were absorbed into the bloodstream. Simultaneously, we observed that QJHTT not only reduced the viral load but also modulated the expression of inflammation factors in the lung tissue including TNF-α, IL-1β, IL-4, IL-6, IFN-γ, and IL17A. A time-effect analysis further revealed that QJHTT intervention effectively suppressed the peak of inflammatory responses, demonstrating a robust anti-IAV pneumonia effect. ConclusionsWe comprehensively analyzed the pharmacological material basis of QJHTT by a highly sensitive and high-resolution UHPLC-Q Exactive Orbitrap-MS method, and demonstrated its efficacy in combating IAV pneumonia by reducing lung viral load and inflammatory factors. This study has significant importance for elucidating the pharmacological basis and pharmacological mechanism of QJHTT in combating IAV pneumonia.

An Extended State Observer Based Adaptive Backstepping Controller for Microgrid

This paper proposes development of a robust distributed secondary control scheme for a photovoltaic (PV) source integrated and inverter-interfaced islanded AC microgrid (MG). The control objective is to regulate the voltage, frequency, and achieve the desired active and reactive power sharing among the distributed generations (DGs) while supporting plug and play operation (PnP) and handling abnormal situations. The above objectives are to be achieved in face of uncertainties in inverter switching pulses, intermittent nature of PV source, dynamic load changes, and disturbances. A backstepping (BS) controller is designed to track the nominal voltage and frequency, whilst an extended state observer (ESO) is designed to estimate the disturbance. The stability of the MG with ESO-BS controller is proved by using Lyapunov stability theory, and graph theory. To verify the effectiveness of the proposed controller, both numerical simulation in MATLAB, and experimentation on OPAL-RT at different operating conditions are pursued. The proposed controller is compared with the distributed averaging based secondary control [15], secondary controller based on MG centralized controller (MGCC) [16]. It is observed that the proposed controller outperforms in terms of enhanced robustness and steady-state performance.

Implementation of the Fuzzy Logic Controlled 31‐Level Diode Switched Multilevel Inverter with Optimal Components for Solar PV‐Fed System

This work presents a novel architecture for the 31‐level asymmetrical DC voltage source configured diode switched multilevel inverter, which has a single phase and fewer components. Using asymmetric DC sources and an H‐bridge, the proposed topology generates a maximum output voltage of 31 levels. This 31‐level topology is suitable for both renewable energy source conversion (RES) and electric vehicle (EV) applications. This topology requires fewer total components, lower cost, and smaller size. Along with the numerous benefits of MLIs, reliability issues are critical due to the larger number of devices required to minimize THD. Several characteristics, such as total standing voltage (TSV), reliability, cost function (CF), efficiency, and overall power losses, are investigated for the developed 31‐level MLIs. The TSV and CF of the proposed MLI are critical factors in demonstrating that the proposed topology is cost‐effective when compared to other recent topologies. Many parameters are thoroughly compared and tabulated, as well as represented graphically. The suggested MLI has lower TSV and component demand. Total harmonic distortion complies with IEEE specifications. The reliability aspects were also calculated and validated. The proposed MLI is controlled by a fuzzy logis controller (FLC) to achieve efficient results. The topology is simulated in MATLAB/Simulink software under a variety of conditions and dynamic load changes, and a prototype with a dSPACE controller is also implemented.

Sonnet: A control-theoretic approach for resource allocation in cluster management

Cluster users expect to minimize the resource costs while ensuring target performance for different applications. It is particularly difficult to reach such a goal, because the applications are diverse with dynamic load changes, and interference exists between them. In addition, the performance of the applications depends on heterogeneous resources with different costs. However, existing works either use simplistic and generalized heuristics that disregard resource-specific characteristics or need suspending service to get expert knowledge to optimize the resource cost for a brand-new application or runtime, which fails to optimize the resource allocation finely.In this paper, we propose Sonnet, a control-theoretic approach to perform efficient resource allocation. Sonnet can efficiently optimize the cost of resources while satisfying the SLO by quickly establishing new application performance models through only online profiling and without affecting service. Experiments on Docker Swarm using various open-source benchmarks demonstrate that Sonnet can decrease the SLO violation rate by 91% while reducing resource costs up to 47% compared with the state-of-the-arts.

A Novel Hybrid IGSA-BPSO Optimized FOPID Controller for Load Frequency Control of Multi-source Restructured Power System

Background: An investigation of Automatic Generation Control (AGC) for a two-area, multi-source, interconnected power system under deregulation is presented in this article. For a more realistic approach, physical constraints namely Generation Rate Constraints (GRC) and Time Delay (TD) are incorporated into the system. Objective: This article proposed a novel hybrid Improved Gravitational Search Algorithm – Binary Particle Search Optimization (IGSA-BPSO) optimized Fractional Order Proportional-Integral- Derivative (FOPID) controller to regulate the frequency of a multi-area multi-source (thermalhydro- gas) interconnected power system in a deregulated environment. Methods: Integral Time Multiplied by Absolute Error (ITAE) is used as the objective function to be minimized by optimization techniques for getting optimum parameters of FOPID controllers installed in each area. Results: To inspect the efficacy of the suggested method, the dynamics of the system are investigated for poolco, bilateral and contract violation cases and the comparative results are also presented and analyzed. The supremacy of the recommended technique is studied by comparing with other well-known techniques namely GSA and PSO. Conclusion: The robustness of the proposed system is examined by sensitivity analysis after variations in different system parameters. In this paper, the AC-DC tie-line model is incorporated for the AGC mechanism. Dynamic load changes condition is also tested and verified. The study found that the proposed controller provides improved system dynamics in all competitive electricity market contract situations under varied system uncertainties.

Comparison of regenerative braking energy recovery of a DC third rail system under various operating conditions

Conducting simulations prior to real-world testing is essential for the planning and development of rail systems. However, accurately representing the train trajectory characteristics resulting from the railway power system and the dynamic load changes based on the train position can be challenging. The power exchange between trains and the fluctuating rail resistance between them add to the computational complexity. Given these challenges, the aim of this study is to develop a comprehensive model of DC third rail systems based on the operational requirements and parameters of the MRT Line 2 Malaysia. Moreover, the simulation method should be adaptable to investigate potential energy savings through regenerative braking systems, thereby maximizing the energy efficiency of electric railways. This study outlines the development of a framework that models the power flow within an electric rail network using a specific case study example. A simulation is presented with 15 trains operating on a double rail track to validate the model for multiple train operations. Notably, the simulation methodology developed in this research is unique compared to other approaches found in relevant literature. It integrates both the power system and train trajectory, incorporating actual system information from a practical DC third rail system to generate precise trajectory outcomes. The results show that implementing a regenerative braking energy recovery system in all traction power substations (TPSSs) has the potential to achieve significant electrical energy savings of up to 55.75% for the entire system.

Optimization of the Relay Coil Compensation Capacitor for the Three-Coil Wireless Power Transmission System

The wireless power transmission (WPT) system, which eliminates the limitation of physical connection and improves the convenience of power transmission, has gradually become a research focus in recent years. However, in the current three-coil WPT system, the power repeater is composed of a coupling coil and a compensation capacitor, and its tuning conditions will affect the power transmission ability of the WPT system. However, the exact impact of compensation capacitor is not clear, which leads to the design of power repeaters being based on experience or trial and error methods, making it difficult to achieve the optimization of the WPT system. Therefore, this paper takes transmission power and transmission efficiency as optimization objectives and obtains the optimal relay coil compensation capacitor model of the three-coil WPT system. The result found that the transmission efficiency of the three-coil WPT system after optimizing the compensation capacitor is 3% higher than before, and the anti-migration ability is enhanced. Meanwhile, in view of the dynamic changes in load and mutual inductance that may occur during the use of the three-coil WPT system, a compensation capacitor design and a relay coil compensation capacitor circuit are proposed, respectively, and the parameter setting scheme of the circuit is proposed. The innovative scheme proposed in this paper can effectively improve the transmission efficiency and stability of the three-coil WPT system.

Voltage Stability and Power Sharing Control of Distributed Generation Units in DC Microgrids

Advancements in power conversion efficiency and the growing prevalence of DC loads worldwide have underscored the importance of DC microgrids in modern energy systems. Addressing the challenges of power-sharing and voltage stability in these DC microgrids has been a prominent research focus. Sliding mode control (SMC) has demonstrated remarkable performance in various power electronic converter applications. This paper proposes the integration of universal droop control (UDC) with SMC to facilitate distributed energy resource interfacing and power-sharing control in DC microgrids. Compared to traditional Proportional-Integral (PI) control, the proposed control approach exhibits superior dynamic response characteristics. The UDC is strategically incorporated prior to the SMC and establishes limits on voltage variation and maximum power drawn from the DC–DC converters within the microgrid. A dynamic model of the DC–DC converter is developed as the initial stage, focusing on voltage regulation at the DC link through nonlinear control laws tailored for Distributed Generation (DG)-based converters. The UDC ensures voltage stability in the DC microgrid by imposing predetermined power constraints on the DGs. Comparative evaluations, involving different load scenarios, have been conducted to assess the performance of the proposed UDC-based SMC control in comparison to the PI control-based system. The results demonstrate the superior efficiency of the UDC-based SMC control in handling dynamic load changes. Furthermore, a practical test of the proposed controller has been conducted using a hardware prototype of a DC microgrid.