Distributed Generation Research Articles

Artificial immune systems (GA-AIS) enabled power loss mitigation in distributed generation: X3PAIS optimization approaches

The distribution network is a crucial component of the power system, with industrialization driving increased energy demand. Traditional power-generating techniques, such as thermal and hydroelectric are not enough to meet this demand, leading to the development of Distributed Generation (DG). DG requires an extensive re-evaluation of the current power system, as it modifies energy losses and line flows. Inadequate integration of DG can cause power outages, disruption of protection coordination, and lead to islanding. AI can help overcome this issue by determining the best system architecture. Researchers have been interested in the Artificial Immune System (AIS) algorithm, which has room for development and lacks a fixed template. In order to improve AIS, X3PAIS, a hybridization strategy that combines clonal selection with a three-parent crossover has been developed within the scope of the study. X3PAIS was pre-tested using applications in a planetary gear train, a wastewater treatment facility, and mathematical calculations, showcasing its robustness and versatility. In the context of power distribution, X3PAIS is used in the multiple DG architecture of the power distribution system, reducing power losses by placing DG units in the best locations and sizing them to match load profiles. The four DGs' experiment results show that X3PAIS can minimize power losses by more than 89 %. To optimize power losses in the power distribution system, X3PAIS may be improved with a three-parent multiple-point crossover operation.

A hybrid optimization for distributed generation and D-STATCOM placement in radial distribution network: a multi-faceted evaluation

The deregulation of the power system, upward growth in electrical energy demand and network expansion have resulted in an increasing integration of distributed generation (DG) and distribution static synchronous compensator (D-STATCOM) into radial distribution systems (RDS). Nonetheless, the optimal allocation of these devices is highly important to derive immense benefits. This investigation narrows down on optimizing DG and D-STATCOM placement in IEEE 33-bus RDS with a view to increase bus voltages, decrease power losses as well as maximize economic gains. The study undertakes a comprehensive analysis comparing the technical, economic and environmental performance of DG and D-STATCOM; thereby enabling power engineers to make informed choices concerning which device will be most advantageous when it comes to delivering power in RDS. A fuzzy enhanced firefly optimization (FEFO) approach is proposed for the optimization and a multifaceted evaluation in terms of technical, financial and environmental is presented for effective decision-making on distributed energy resource deployment. D-STATCOM and wind DG integrations led to notable reductions in power loss and pollutant emissions, highlighting their effectiveness in improving power quality and reducing reliance on fossil fuels. While wind DG incurred a higher installation cost ($3,100,749.2) compared to D-STATCOM ($90,566.6), it achieved greater yearly power loss cost savings ($69,198 versus $47,619). FEFO’s efficiency in optimization stands out, aiding engineers in making informed decisions for optimizing D-STATCOM and wind-DG integration in the IEEE-33 RDS, ultimately enhancing system performance and cost-effectiveness through proactive planning. The integration of D-STATCOM and wind DG led to a significant improvement in distribution system efficiency, with D-STATCOM reducing real power loss by 28.7% and reactive power loss by 27.8%, while wind DG achieved greater reductions of 41.8% in real power loss and 37.5% in reactive power loss, alongside reductions in pollutant emissions of 1.5% and 2.2%, respectively.

Oppositional arithmetic optimization algorithm for network reconfiguration and simultaneous placement of DG and capacitor in radial distribution networks

AbstractThe prime objective of this study is the simultaneous network reconfiguration with distributed generation (DG) and capacitor placement in radial distribution networks (RDN) to get the techno and economic benefits for two separate objectives, which are the minimization of actual power loss and annual economic loss as well as a multi objective combining these two single objectives using an oppositional arithmetic optimization algorithm (OAOA). It is an improved version of the currently suggested arithmetic optimization algorithm (AOA) used in the field of engineering for the optimization task. Though the recently developed AOA shows its efficacy in different optimization tasks but to improve the quality of solutions, convergence behavior, and to avoid the local optima, oppositional behavior is added to AOA. The efficacy and exactness of OAOA are tested on three test systems (33‐bus, 69‐bus, and 118‐bus). For the reduction of power loss and annual economic loss as well as the multi objective optimization, two scenarios with different cases are executed using OAOA in RDNs. In scenario 1, the installation of the capacitor (case 1), the installation of unity power factor (UPF) based DG (case 2), and the placement of optimal power factor (OPF) based DG (case 3) have been executed. In scenario 2, allocation of UPF based DG and capacitors simultaneously (case 1), placement of OPF based DG and capacitors simultaneously (case 2) and simultaneous reconfiguration with installation of OPF based DG and capacitor (case 3) has been executed. This recommended OAOA algorithm provides the percentage improvement in real power loss and yearly economic loss for all cases of 33‐bus, and 69‐bus systems (34.28%, 65.50%, 94.43%, 93.26%, 94.89%, and 95.11%), (28.54%, 56.69%, 83.42%, 79.62%, 83.65%, and 83.71%), and (35.51%, 69.16%, 98.10%, 97.52%, 98.22%, and 98.25%), (30.26%, 61.68%, 88.75%, 85.42%, 88.81%, and 88.98%), respectively. The results and comparative study reveal that the OAOA is better than several optimization algorithms in terms of solution quality and good results. This algorithm has a good speed of response and convergence behavior.

Integrated Optimal Energy Management of Multi-Microgrid Network Considering Energy Performance Index: Global Chance-Constrained Programming Framework

Distributed generation (DG) sources play a special role in the operation of active energy networks. The microgrid (MG) is known as a suitable substrate for the development and installation of DGs. However, the future of energy distribution networks will consist of more interconnected and complex MGs, called multi-microgrid (MMG) networks. Therefore, energy management in such an energy system is a major challenge for distribution network operators. This paper presents a new energy management method for the MMG network in the presence of battery storage, renewable sources, and demand response (DR) programs. To show the performance of each connected MG’s inefficient utilization of its available generation capacity, an index called unused power capacity (UPC) is defined, which indicates the availability and individual performance of each MG. The uncertainties associated with load and the power output of wind and solar sources are handled by employing the chance-constrained programming (CCP) optimization framework in the MMG energy management model. The proposed CCP ensures the safe operation of the system at the desired confidence level by involving various uncertainties in the problem while optimizing operating costs under Mixed-Integer Linear Programming (MILP). The proposed energy management model is assessed on a sample network concerning DC power flow limitations. The procured power of each MG and power exchanges at the distribution network level are investigated and discussed.

Chaos quasi-opposition crayfish based modified new controller designed for hybrid deregulated power environment considering cyber-attack

Frequency security is critical to the stability and dependability of the electrical systems. The integration of renewable energy resources presents new challenges for power networks and frequency security. In order to provide a more reliable control mechanism for improved frequency regulation in multi area deregulated environments with penetrations of renewable energy sources like Solar photovoltaic and wind system has been included considering along with its intermitance nature. Additionally, to get more realistic approach and its analysis, nonlinearities such as generation rate constant and governor dead band has been taken into consideration for the anticipated Load Frequency Control (LFC). A novel modified cascaded Dual-Loop Linear Active Disturbance Rejection based Tilted controller has been proposed for the suggested LFC paradigm. A modified version of the Chaotic Quasi-Opposition Crayfish Optimisation algorithm (CQOCOA) has been offered as a novel optimization approach for optimal parameters of the proposed controller. ITSE has been taken as objective function for optimization purpose. Moreover, a comprehensive detailed examination for the proposed LFC system has been investigated and successfully implemented. The performance has been examined under a variety of operating scenarios, including multiple-step, random load disturbances and Distributed Generation (DG) analysis along with its technical core advancements. This study has been investigated and validated over large multi area power system i.e., IEEE-118 bus system. This work also put forward the deep analysis and implementation of learning-based attack detection and mitigation method for the grid's frequency regulation with cyber-physical model. The effectiveness of the proposed controller has been compared and verified over previous published literature work of international repute. The compressive results analysis provide strong evidence in favour of effectiveness and efficacy of the proposed control methodology. Furthermore, this work also suggests its potential to implement in hybrid multi area power system for enhancing the performance and stability in deregulated power structure.

Improved Harmonic Mitigation and Power Injection Technique for Solar-fed DG System Using GA and PSO

This paper deals with Distributed Generation (DG) system requiring power quality features such as current harmonics, reactive power compensation, and power factor improvement in grid tied operation. The motivation is to combine DG system with the capabilities of shunt active filter to perform real power injection, current harmonics mitigation and power factor improvement. The control algorithm employed in this setup utilizes a reference current generator based on p-q theory together with a pulse width modulation controller for switching pulse generation. The control strategy utilizes PI controller with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) for finding optimal PI controller parameters. The effectiveness of the proposed method is verified using MATLAB/Simulink and experimental model developed for 3kWp inverter. The PI-PSO controller injects 0.588kW active power into the grid results in sharing 54% of load power demand and the current harmonics is reduced from 23.70% to 1.63%. The obtained results demonstrate that the grid tied inverter maintains harmonic standards in accordance with the IEEE-519 standard while injecting maximum possible active power to the line.

Converter-based multi-frequency power transfer system for efficient energy packet transmission in the energy internet

The energy internet concept involves the transmission of energy in discrete packets, akin to the information internet's principle. The energy internet must adopt a decentralized configuration and enable bidirectional and simultaneous power transfer. This raises the problem of congestions during the energy packet dispatching process. To address potential congestion issues, we propose a three-phase multi-frequency power transfer system (MFPTS) where the positive-sequence fundamental frequency component is supplemented with the zero-sequence third and the negative-sequence fifth harmonic components. By using such signals with proper amplitudes, the harmonics are added to the voltage without changing the peak amplitude but increasing the rms value. To exert complete control over the different frequencies employed within the MFPTS, a decoupling method is necessary to separate these frequencies in the control system. This leads to creating three independent channels of power transfer by three frequencies without changing the existing infrastructure as these powers can be transferred within the same lines. This paper explores the feasibility of three-phase three-frequency power transfer by using three parallel power transfer channels, achieved through the utilization of three-phase grid-forming and grid-feeding converters. Using power converters provides the advantage of bidirectional power transfer and facilitates decentralization by serving as an interface between distributed power generation systems and the utility grid. These properties are essential for achieving optimal energy internet performance. The simulation and practical results prove that the proposed MFPTS could solve the energy packet dispatching congestion problem to have a reliable energy internet for the future.

Innovative protection schemes through hardware-in-the-loop dynamic testing.

In microgrid environments, the behaviour of Distributed Generation (DG) during fault conditions varies significantly based on DG types and penetration levels. Conventional Overcurrent Relays (OCRs) with standard time-current characteristics may exhibit limitations during excessive fault scenarios, leading to OCR operating delays and mis-coordination within the microgrid. This study proposes a novel constraint on the maximum Current Multiplier Setting (CMS) and utilizes Water Cycle Algorithm (WCA) and Particle Swarm Optimization (PSO) techniques to optimize the Time Multiplier Setting (TMS). Comparative dynamic analysis through real-time validation shows that the non-standard OCR approach outperforms the standard IEC scheme across all grid operation modes with different type, size and location of DGs. For instance, under F1 conditions, the tripping time of OCR1 was reduced from 0.0226 seconds (IEC) to 0.000981 seconds (non-standard). HIL results further affirm the efficacy of the proposed scheme. The optimization process, implemented in MATLAB and validated using ATP/EMTP simulations and SIPROTEC 7SJ62 relays, demonstrates enhanced microgrid protection coordination, improving system reliability and performance.

Price-based demand response with renewable energy sources and peer-to-peer trading for residential microgrid with electric vehicle uncertainty

This article deals with the impact of demand response (DR) with peer-to-peer (P2P) energy trading for a residential smart home consisting of smart appliances, an electric vehicle, a battery energy storage system (BESS), and renewable energy-based distributed generation (DG) such as solar PV and wind. The proposed work deals with two stages, such as DR implementation and P2P energy trading. The first stage of implementation deals with the optimal scheduling of smart appliances in a residential home using a Binary Dragonfly Algorithm (BDA). Each appliance in the smart home is scheduled based on the slab tariff, Time of Day (ToD), and Real-Time Pricing (RTP) with DR to identify the most economical tariff structure for the residential home. Five different cases are examined to identify the best smart home for effectively utilizing DGs by reducing grid dependency and electricity costs.The RTP tariff is proved to be more beneficial than the slab tariff and ToD tariff because the electricity cost of the smart home is very minimal for all the cases with RTP, especially in case 5 cost is reduced by ₹12.0613 than slab tariff and ₹8.414 than ToD. Hence, the RTP tariff is chosen as the optimal tariff structure for the next stage of the proposed work.The second stage of implementation deals with the P2P trading between the smart homes with a proposed enhanced bidding strategy to reduce the grid dependency and electricity cost of the individual smart homes. The proposed enhanced bidding strategy involves a double auction mechanism to determine the trading decision and trading cost for the benefit of both consumers and prosumers. The electricity cost reduction achieved by consumer 1 and consumer 2 from the enhanced smart bidding strategy are ₹92.7615 and ₹15.1525, respectively. The results also proved that prosumer 1 and prosumer 2 obtained a profit of ₹78.2170 and ₹28.6970, respectively. The EV uncertainty analysis is also examined in smart homes to validate the effectiveness of the proposed bidding strategy. The simulation results proved that the proposed DR-based P2P trading with an enhanced bidding strategy reduces grid dependency and electricity costs, including EV uncertainty conditions.

Optimal Scheduling of the Active Distribution Network with Microgrids Considering Multi-Timescale Source-Load Forecasting

Integrating distributed generations (DGs) into distribution networks poses a challenge for active distribution networks (ADNs) when managing distributed resources for optimal scheduling. To address this issue, this paper proposes a day-ahead and intra-day scheduling approach based on a multi-microgrid system. It starts with a CNN-LSTM-based generation and load forecasting model to address the impact of generation and load uncertainties on the power grid scheduling. Then, an optimal day-ahead and intra-day scheduling framework for ADN and microgrids is introduced using predicted generation and load information. The day-ahead scheduling is responsible for optimizing the power interactions between ADN and the connected microgrids, while intra-day scheduling focuses on minimizing the operational costs of microgrids. The effectiveness of the proposed scheduling strategy is verified via case studies performed on a modified IEEE 33-node ADN. The results show that the network loss of ADN and the operation costs of microgrids are reduced by 17.31% and 32.81% after the microgrid is integrated into the ADN. The peak-valley difference in microgrids decreased by 13.12%. The simulation shows a significant reduction in operational costs and load fluctuations after implementing the proposed day-ahead and intra-day scheduling strategy. The seamless coordination between the day-ahead scheduling and intra-day scheduling allows for the precise adjustment of transfer power, alleviating peak load demand and minimizing network losses in the ADN system.

Highly sensitive protection scheme considering the PV operation control models

The integration of distributed generation (DG) based on inverters into power systems has increased significantly, necessitating a thorough understanding of its impact on fault analysis and the performance of distribution networks' protection mechanisms. This study addresses this issue by examining how various inverter management modes influence protective relay systems within IEEE 9-bus redial and mesh networks, CIGRE and IEEE 33-bus networks featuring Photovoltaic (PV) farms and Battery Energy Storage Systems (BESS), by IEEE1547–2018 and German grid code standards. By analyzing grid-connected scenarios with five distinct PV control modes, the research introduces a novel protection methodology termed the Photovoltaic Overcurrent Relay (PVOCR). This method introduces a current-voltage characteristic to optimally coordinate Overcurrent Relays (OCRs), aiming to reduce their operational time and eliminate mis-coordination events. The proposed PVOCR is evaluated against standard inverse time, SOCR, and modern adaptive voltage, VOCR, relay schemes across various fault scenarios differing in type and location. Furthermore, the PVOCR scheme effectively operates across all PV inverter modes without experiencing miscoordination events, whereas the SOCR and VOCR schemes encountered such issues during the operation of Control 4. These results underscore the potential utility of the PVOCR methodology in enhancing the reliability and efficiency of protection systems in inverter-based DG networks.

Distributed economic control strategy based on reinforcement pinning control for microgrids

Traditional droop control allocates distributed generation (DG) power based on capacity proportion, which leads to high system operating costs. To address this issue, this study proposes a distributed economic control strategy for microgrids based on reinforcement pinning (RP) control. To minimize operating costs, reinforcement learning (RL) continuously updates the Q-value table through reward feedback to obtain the optimal strategy. The optimal action determined by RL is set as the pinning reference value and transmitted to the pinning agent. Other agents achieve marginal cost consistency through the pinning information iteration matrix. To correct frequency deviations, proportional-integral (PI) control is used to ensure frequency stability for the system's operation. Simulations under different scenarios were conducted in MATLAB/Simulink. The results show that the proposed approach can coordinate the output of distributed power sources, reduce the operating costs of the microgrid, and maintain frequency stability.

Current management for charging stations with power coupling items and three charging modes of electric vehicles under DoS attacks

Although the electric vehicle supplied through distributed generators (DGs) as one of the most important methods to reduce carbon emissions has become a research hotspot, the current management for charging stations with power coupling items and three charging modes of electric vehicles under denial of service (DoS) attacks, is rarely studied. Based on this, this paper proposes a new fully distributed consensus fuzzy control to achieve accurate current sharing for charging stations with power coupling items and three charging modes of electric vehicles under DoS attacks. Firstly, the system regarding charging stations with power coupling items and three charging modes is modeled which lays the foundation for the next design. Next, DoS attacks as the common network attacks are taken into consideration and modeled. Meanwhile, in order to reduce the communication burden, the fuzzy logic controller (FLC) is designed in this paper. Then the fully distributed consensus fuzzy control considered DoS attacks is proposed to achieve the current sharing control accurately for charging stations with power items and three charging modes under DoS attacks. Moreover, the system under the distributed consensus fuzzy control strategy is discussed in different situations. Finally, simulation comparisons and experiment results are carried out to verify the performance of the proposed control strategy.

Piecewise affine power flow model for distribution network optimization using CIM aided data-driven approach

Power flow (PF) analysis serves as the basis for power system operation that is extended to the distribution levels integrated with more distributed generations (DG). Solving optimal power flow (OPF)-resembled problems for practical networks is still challenging due to unavailability of accurate PF equations adaptive to systems variations. To solve this issue, we first set up the PF simulations for complex and realistic power networks based on the common information model (CIM). This automates the recognition of network topologies and parameters in the reduced bus-branch form for system simulations and data generations. The non-convexity of OPF imposes an additional challenge, where solving the problem is still difficult for scenarios with intertemporal couplings considering energy storage. We further employ a multi-layer neural network that provides piecewise affine approximations of the PF equations with desired accuracy. The corresponding OPF-resembled problem is then reformulated as a mixed-integer optimization that facilitates fast and optimal coordination of large-scale DGs for various network operational purposes. We demonstrate the proposed framework using real CIM files from system operators, and compare against typical approaches with improved performance for voltage regulation and loss minimization.

Source‐load cooperative frequency regulation based on virtual synchronous/asynchronous machine concept

AbstractDue to the absence of inertia, the high proportion of electronic power equipment is a great threat to the stability of the power system. Previous studies have proposed the virtual synchronous machine (VSM) control method for the inverter‐based distributed generators (DG). However, due to the capacity limitations of DG, the capability of the inverter to provide the inertia action is limited. At the same time, some controllable loads also have the ability to provide inertial support but are still not fully utilised. To get a better grid frequency response, this paper proposes a source‐load coordination strategy based on the VSM and virtual asynchronous machine (VAM) concept. For that purpose, a detailed VAM model is firstly derived for the rectifier on power demand side. Not only the virtual inertia and frequency oscillation damping can be provided, but also the synchronisation units are not needed to obtain the unknown grid frequency. After that, a distributed consensus‐based secondary control is present to regulate the frequency to converge to a reference value based on VSM and VAM. Compared with the existing frequency regulation method, the proposed scheme makes full use of the ability of the load side to participate in frequency modulation. Finally, some numerical simulations are performed to validate the feasibility of the proposed method on MATLAB/Simulink.

Distributed optimization control strategy for distribution network based on the cooperation of distributed generations

AbstractAiming to improve the voltage distribution and realize the proportional sharing of active and reactive power in the distribution network (DN), this article proposes a distributed optimal control strategy based on the grouping cooperation mechanism of the distributed generation (DG). The proposed strategy integrates the local information of the DG and the global information of the DN. Considering the high resistance/reactance ratio of DN, distributed optimization control strategies for node voltage control and active power management are developed with the consensus variable of active utilization rate. And distributed strategy for reactive power management is proposed with a consensus variable of reactive utilization rate. The convergence of the distributed control system for each group is proved. The validity and robustness of the proposed strategy are verified by several simulations in the IEEE 33‐bus system.

An active protection method based on superimposed phase currents for active distribution systems

To enhance the fault current amplitude of active distribution systems during the weak fault period and decrease the influence of the measurement equipment noise, this paper proposes an active protection method based on superimposed phase currents for active distribution systems. This method is shown as follows. First, the reference value of the filter inductor current of each distributed generator (DG) is set as different values when the fault intensity of the active distribution system changes. Second, the superimposed phase current in each relay is obtained by subtracting each sample of phase current from its corresponding sample of phase current in the previous cycle. Third, the fundamental phase angle of the superimposed phase current is extracted. This is because the fundamental current component of the superimposed current cannot be affected by the active control strategy, which is proved in this paper in detail. Meanwhile, the feature direction is built by fundamental phase angles at both ends of the line to detect faulty zone. Finally, the proposed protection method has been validated in a modified IEEE 13-bus test system, and the test results prove the effectiveness of the proposed active protection method that can enhance the faulty feature to detect faults.

Optimal allocation of wind-based distributed generators and STATCOMs using a hierarchical stochastic programming approach

Allocating static synchronous compensators (STATCOMs) to regulate given allotted wind-based distributed generators (W-DGs) during planning stages can provide high investment returns by maximizing the installed W-DGs. Amidst rising global warming concerns, commitments to adopt renewable energy gain international momentum to curb greenhouse emissions and meet environmental targets, reducing reliance on fossil-based resources. Renewable energy's intermittency complicates distribution planning, stressing voltage devices and increasing network losses. This paper presents a new hierarchical stochastic planning model that addresses uncertainties related to W-DGs and generic loads. The model optimizes allocation with voltage constraints and reactive power while incorporating a two-stage mixed-integer nonlinear program (MINLP), maximizing net profit, and adding an economic dimension to promote renewable energy investments. Improved wind power modeling with historical data and collective evaluation metrics for selecting the best-fitted probability distribution function (PDF) enhances the accuracy of wind power integration assessment. The hierarchical approach considers relaxed voltage constraints in Stage I to allow maximum allotment of W-DGs while introducing STATCOMs and DGs' reactive power in Stage II to address voltage violations. Verification on the Canadian 41-bus network demonstrates the advantage of the hierarchical approach in allocating more W-DGs and achieving higher profits than the simultaneous planning approach. These advances significantly enhance renewable energy integration in power systems.

Service restoration in distribution systems considering priority customers and microgrids

Service restoration (SR) consists of automatically generating and executing a plan to restore the service in healthy zones using the least number of maneuvers after detecting and isolating a permanent fault in the distribution system zone. This component is essential to self-healing functionality in smart grids and allows customers to reconnect quickly to the distribution grid after a power outage. Distributed generation (DG) supports the distribution network when there is insufficient capacity to restore all zones out of service or supply the loads locally through microgrids. The power supply must be restored to the highest priority customers in case of partial restoration. Also, most research works use simplified or linearized models to propose restoration algorithms. This paper proposes a complete AC formulation for the service restoration problem in distribution systems considering network reconfiguration (NR), the integration of distributed generation (DG), and priority customers (PCs) into the solution. The optimization problem is solved by a centralized algorithm based on combining the Differential Evolution (DE) and Continuous Population-Based Incremental Learning (PBILc) metaheuristics techniques. Simulation results are presented for three case studies in which the IEEE 33-bus distribution system is tested for different fault scenarios. The numerical results show the robustness and efficiency of the proposed algorithm.

Dynamic partitioning of island smart distribution systems in emergencies

AbstractWhen a severe fault occurs in the distribution network, all or parts of it may be disconnected from the upstream network. Partitioning of these islanded areas is a solution to supplying the affected loads. Due to the variable nature of loads and renewable distributed generation (DG), the static model of partitioning with a fixed nature during island operation cannot be suitable. Therefore, in this article, considering the variable nature of loads and renewable distributed generation, a dynamic model is presented for the island partitioning to restore more valuable loads, which is suitable for quick decision‐making in emergencies. Also, a method for deciding on the mode of charging and discharging storage systems in emergencies is proposed. This model considers time limitation, uncontrollable DGs, controllable DGs and their control, controllability, and priority of loads, tie‐switches, storage systems, simultaneous faults, different situations of unintentional islanding of the distribution network, position of switches, and variable nature of loads and distributed generations. So, it is more comprehensive than the previous methods. Applying the proposed model to the modified IEEE 69‐bus system with controllable and uncontrollable generation and storage systems assuming different scenarios shows the effectiveness of the proposed scheme.