Energy Management Problem Research Articles

Smart building energy management with renewables and storage systems using a modified weighted mean of vectors algorithm

With the advancement of automation technologies in household appliances, the flexibility of smart home energy management (EM) systems has increased. However, this progress has brought about a new challenge for smart homes: the EM has become more complex with the integration of multiple conventional, renewable, and energy storage systems. To address this challenge, a novel modified Weighted Mean of Vectors algorithm (MINFO) is proposed. This algorithm aims to enhance the performance of smart building EM by overcoming the limitations of conventional approaches, such as low solution accuracy and inadequacy in handling complex problems. MINFO operates on two key principles. Firstly, it employs the Elite Centroid Quasi-Oppositional Base Learning (ECQOBL) approach to improve the exploitation capabilities of conventional algorithms. Secondly, it utilizes an Adaptive Levy Flight Motion (ALFM) technique to enhance exploration. The EM problem tackled involves optimizing the scheduling of multiple energy sources, including diesel generators, PV units, and batteries, within a smart building context. Additionally, it incorporates time-of-use-based demand-side response (DSR) to manage shiftable loads, thereby reducing electricity costs and peak-to-average ratio (PAR) simultaneously and independently. The effectiveness of MINFO is demonstrated through comprehensive evaluations, comparing its performance with other optimization methods across 33 benchmark functions from basic and CEC-2019 test suites. Results indicate that MINFO significantly improves smart building EM, achieving a reduction of 53.20% in electricity costs (cost only), 53.19% in PAR (PAR only), and 50.84% in combined cost and PAR compared to the base case. These findings underscore the robustness of MINFO as an optimizer for smart building energy management.

Automated multi-dimensional dynamic planning algorithm for solving energy management problems in fuel cell electric vehicles

Automated multi-dimensional dynamic planning algorithm for solving energy management problems in fuel cell electric vehicles

Reliable Data Delivery and Load Balancing in Improved Energy Efficient RPL Routing Protocol for Low Power and Lossy Networks

ABSTRACTThe energy‐constrained nodes and tree‐like topology of Low‐Power and Lossy Networks (LLNs) frequently result in serious problems when energy bottlenecks occur. This occurrence affects the network performance in terms of node failure, lower connectivity, and higher energy consumption. This paper proposes a novel solution to these problems by integrating an Energy Efficient Multipath Routing Protocol (EM‐RPL) with a Load‐Based Energy Efficient RPL (LBEE‐RPL) protocol. To address energy bottlenecks, the proposed EM‐RPL protocol initiates the crucial mechanisms as subnode switching mechanism and an improved Trickle timer. The network's energy load is balanced by the subnode switching mechanism, which redistributes traffic away from overloaded nodes. The enhanced Trickle timer guarantees prompt identification and response to energy shortage conditions. This method enhances overall network performance while addressing the issue of data imbalance in energy consumption. An extensive simulation shows the proposed EM‐RPL significantly increases network lifetime and energy efficiency. Specifically, integrating these protocols leads to a notable reduction in power consumption and a rise in the network's operational lifespan. The important problem of energy management in LLNs is effectively resolved by this work, which offers improved performance and sustainability for a range of Internet of Things (IoT) and related fields applications.

Energy Management Strategies for Hybrid Propulsion Ferry with Different Battery System Capacities

The International Maritime Organization (IMO) has been continuously strengthening environmental regulations to reduce greenhouse gas emissions from ships, which has led to increased attention on hybrid ship propulsion systems combining hydrogen fuel cells and batteries. This study analyzes the energy management strategy of a hybrid ship propulsion system in relation to changes in the battery system’s energy capacity. The target vessel was set as a 500 kW-class ferry operating for 24 h, and the maximum current rate (C-rate) and effects of the equivalence factor, which are key elements of the energy management problem, in relation to changes in energy capacity were investigated. The results show that while changes in the battery system’s energy capacity do not significantly affect the optimal operating point of the hybrid ship propulsion system, they are highly influenced by the response speed of the hydrogen fuel gas supply system and fuel cells, as well as the maximum C-rate required by the battery system. Furthermore, the equivalence factor, one of the key parameters in the optimization problem, tends to vary depending on the degree of charging and discharging, as it affects the equivalent fuel consumption of the battery system.

Towards the integration of interconnected microgrids to deregulated electricity markets

In response to rising energy consumption and its adverse environmental impact, there is an urgent need to integrate innovative technologies in intelligent energy management systems (EMS). This work develops sophisticated systems to optimize energy management enabling Microgrids (MGs) to participate optimally in Peer-to-Peer (P2P) electricity markets. MGs under examination comprise residential buildings, including thermal and electrical loads, renewable energy sources (RES), and plug-in electric vehicles (PEVs). It presents a comprehensive framework for the economic operation of interconnected MGs, combining two strategies: 1) MG energy management and 2) MG participation to P2P electricity market. The energy management problem is solved at MG level to minimize its operation cost over a time horizon. P2P electricity market participation is achieved through a non-cooperative game where each MG can have its distinct objectives, which is a vital characteristic for liberalized markets. Within this framework, each MG adapts its operations to market dynamics, aligning with economic goals and operational efficiency. Notably, during P2P electricity market participation, MGs share information only about the offered energy and price, maintaining the highest possible confidentiality.

A Performance Survey and Simulated Residual Energy of Sensor Nodes in a Typical Wireless Sensor Network

This paper is a performance survey on the residual energy of nodes in a wireless sensor network (WSN). Wireless sensor nodes are limited in application due to constraints in energy of nodes’ battery and addressing the problem of energy management is essential to lengthen the life of a deployed network of wireless sensors. In the method used, Sensor nodes were equally distributed on the complete border of the network field. An exclusive cluster, six hierarchical, and eighteen hierarchical clusters were formed based on even partition of the border of the network field. The choice of Cluster Head (CH) within each cluster formed was based on selection of a sensor node with minimal transmission distance to the Base Station. A comparison of the various hierarchical scenarios was simulated in MATLAB. The mean residue energies (MREs) after the network lifetime are 3%, 52%, and 35% of the initial node energy for single, six and eighteen hierarchical clusters respectively. The residual energies of sensor nodes above the recorded MREs were taken on a class interval of 50’s of the node identity (nid) and respective averages of residual energies of sensor nodes (AEr) of each selected class interval were evaluated. Based on the result, certain categories of sensor nodes at a section of the network field indicated that the battery energy of the affected nodes was not maximally utilized thereby leading to enormous residual energy. It was concluded that the residual energy of nodes in a WSN could be optimized to extend the lifetime.

Privacy‐Preserving Optimization Algorithm for Distributed Energy Management Over Time‐Varying Graphs: A State Decomposition Method

ABSTRACTThe rapid advancements of intelligent technologies have brought about the potential vulnerability of confidential gradient information linked to cost functions when solving distributed optimization and its related problems. Within the context of distributed energy management, safeguarding such private information has risen to paramount importance. This article investigates a distributed energy management problem (DEMP) to minimize cost while simultaneously satisfying multiple local constraints and protecting the private gradient information of the cost function. To this end, a new privacy‐preserving distributed optimization algorithm under the framework of gradient tracking over time‐varying graphs is proposed for solving the DEMP. Specifically, the auxiliary variables are designed for each node in the algorithm to update the gradient while the original state variables are responsible for the interaction with original neighbors and auxiliary variables. Consequently, the devised algorithm can protect the confidentiality of private cost gradient information, even in the presence of eavesdroppers within the network. In contrast to the homomorphic encryption, signal masking method, and some other algorithms without utilizing the state decomposition, the designed algorithm does not require extra information or computing resources. Moreover, it is proven that the designed algorithm could theoretically converge to the exact optimum of the DEMP at a rate of under some mild assumptions.

A Cooperative Multi-Agent Q-Learning Control Framework for Real-Time Energy Management in Energy Communities

Residential and commercial buildings are responsible for 35% of the EU energy-related greenhouse gas (GHG) emissions. Reducing their emissions is crucial for meeting the challenging EU objective of the agenda for becoming a net-zero continent by 2050. The diffusion and integration of distributed renewable energy sources (RESs) and energy storage systems (ESSs), as well as the creation of energy communities (ECs), have proven to be crucial aspects in reducing GHG emissions. In this context, this article proposes a multi-agent AI-based control framework to solve the EC’s energy management problem in the presence of distributed RESs and ESSs as well as considering a shared ESS. The objectives of the proposed control framework are to satisfy the EC members’ load demand to maximize self-consumption and to manage ESSs charging and discharging processes, to enforce cooperative behavior among the EC members by adopting fair and personalized strategies and to maximize EC members’ profits. The proposed control procedure is based on three sequential stages, each solved by a dedicated local RL agent exploiting the Q-Learning algorithm. To reduce the computational complexity of the proposed approach, specifically defined state aggregation criteria were defined to map the RL agents’ continuous state spaces into discrete state spaces of limited dimensions. During the training phase, the EC members’ profiles and the ESSs’ and RESs’ characteristics were randomly changed to allow the RL agents to learn the correct policy to follow in any given scenario. Simulations proved the effectiveness of the proposed approach for different costumers’ load demand profiles and different EC configurations. Indeed, the trained RL agents proved to be able to satisfy the EC members’ load demands to maximize self-consumption, to correctly use the distributed and shared ESSs, to charge them according to respective personalized criteria and to sell the energy surplus, prioritizing sales to the EC. The proposed control framework also proved to be a useful tool for understanding EC performance in different configurations and, thus, for properly dimensioning the EC elements.

A two-layer strategy for sustainable energy management of microgrid clusters with embedded energy storage system and demand-side flexibility provision

The intermittent nature of renewable energy generation and the fluctuating demands pose persistent challenges in microgrid operations. In response, stakeholders and operators have turned to clustering the geographically adjacent microgrids as a solution. In this context, this paper introduces a novel two-layer energy management strategy for microgrid clusters, utilizing demand-side flexibility and the capabilities of shared battery energy storage (SBES) to minimize operational costs and emissions, while ensuring a spinning reserve within individual microgrids to prevent load-shedding. In the lower layer, the proposed approach devises optimal day-ahead operation policies, while the upper layer employs a cooperative strategy to further optimize the operational efficiency across the entire cluster. The energy management problem is accurately formulated as a mixed integer quadratic programming (MIQP) optimization, which incorporates linear terms in the problem's constraints. The formulation accounts for operational costs associated with SBES including expenses of charging/discharging and changes in operating states (CiOS). Real-world case studies with a cluster of three microgrids in Australia validate the effectiveness of this approach. Results show a reduction in operational costs for the base case scenario by 6.96 % compared to conventional microgrid management strategies. Sensitivity analyses further demonstrate the economic benefits of varying SBES capacity and flexibility pricing, with savings ranging from 6.5 % to 8.1 %. The proposed strategy also reduces CO2 emissions by up to 11.6 %, while improving system reliability. This strategy holds promise for integration into distributed energy systems with high renewable penetration and clustered local grids, offering significant advantages for utility operators and end-users through improved energy efficiency and reduced emissions.

An energy trade-off management strategy for hybrid ships based on event-triggered model predictive control

This paper addresses the energy management problem of hybrid ships by proposing an event-triggered model predictive control (ET-MPC) method. The novelty in this work lies in the establishment of an event-triggered mechanism and a state prediction model for energy management of hybrid ships. First, torque models of the internal combustion engine (ICE) and electric machine (EM) are developed using a data-driven approach, followed by the construction of fuel consumption and carbon emission models. Second, an event-triggered mechanism, dependent on state prediction error, is introduced and updated at each time step based on the system’s current state. Additionally, a cubature Kalman filter (CKF) is employed to estimate and correct the state prediction error, minimizing inaccuracies. A trade-off coefficient is incorporated to optimize the balance between fuel consumption and carbon emissions. The ET-MPC method results in a 0.68% difference in fuel consumption and 3.43% increase emissions compared to the traditional MPC method. However, ET-MPC significantly reduces computational overhead by 56.66. The ET-MPC method effectively allocates the ship’s energy according to the varying trade-off coefficient, achieving optimal energy management under different constraints.

Mixed‐Integer Optimal Control via Reinforcement Learning: A Case Study on Hybrid Electric Vehicle Energy Management

ABSTRACTMany optimal control problems require the simultaneous output of discrete and continuous control variables. These problems are typically formulated as mixed‐integer optimal control (MIOC) problems, which are challenging to solve due to the complexity of the solution space. Numerical methods such as branch‐and‐bound are computationally expensive and undesirable for real‐time control. This article proposes a novel hybrid‐action reinforcement learning (HARL) algorithm, twin delayed deep deterministic actor‐Q (TD3AQ), for MIOC problems. TD3AQ leverages actor‐critic and Q‐learning methods to manage discrete and continuous action spaces simultaneously. The proposed algorithm is evaluated on a plug‐in hybrid electric vehicle (PHEV) energy management problem, where real‐time control of the discrete variables, clutch engagement/disengagement and gear shift, and continuous variable, engine torque, is essential to maximize fuel economy while satisfying driving constraints. Simulation results show that TD3AQ achieves near‐optimal control, with only a 4.69% difference from dynamic programming (DP), and outperforms baseline reinforcement learning algorithms for hybrid action spaces. The sub‐millisecond execution time indicates potential applicability in other time‐critical scenarios, such as autonomous driving or robotic control.

Practical solutions for microgrid energy management: Integrating solar forecasting and correction algorithms

Nowadays, the shift towards renewable energies is happening at an exponential pace. Microgrids are an integral part in integrating renewable energies into the global energy mix. Due to the volatility of renewables, such as solar or wind, proper energy management is needed to avoid generation or load curtailment. This issue is addressed throughout the literature using a wide variety of strategies, ranging from classical linear to nature inspired metaheuristic optimization algorithms. This paper goes beyond the simulation phase of different optimization algorithms and addresses the optimal energy management problem by proposing a novel framework to integrate optimization strategies into the daily operation of microgrids. The proposed framework showcases 3 practical methods for controlling the distributed generators, as well as a communication scheme which facilitates the data transfer between the machine running the optimization strategy and the energy management system of the microgrid. The framework is demonstrated on a small-scale islanded microgrid setup, located at the Technical University of Cluj-Napoca. The microgrid setup consists of a photovoltaic array, a battery energy storage system and two dispatchable generators. A two-stage optimization strategy is used, consisting of a day-ahead stage, which uses the solar forecast provided by the Global Forecast System, prior to each day, to issue a working plan for the dispatchable generators, and an intra-day stage, which uses hourly solar forecasts, issued during the day, to adjust the operation of the microgrid and minimize the error between the day-ahead solar forecast and the actual weather conditions. Mixed integer linear programming is used to solve the optimization problem and validate the correct operation of the proposed framework over two case studies. The results show that the microgrid works as intended, in both scenarios, as well as the benefits of using an intra-day correction stage.

Economic management of microgrid using flexible non-linear load models based on price-based demand response strategies

Demand response programmes are used in microgrid research without considering the different price elasticity of distinct load types. To evaluate the impacts of demand response efforts, it is necessary to utilise a mix of nonlinear and linear models for creating load-responsive models in a manner that is realistic. With an aim to address this gap in research, an exhaustive technoeconomic investigation is being conducted to determine the effect that price-dependent demand response programmes have on the optimal scheduling of microgrids when linear and nonlinear load models are present. The flexible elasticity model is used to accurately describe how customers respond to changes in electricity price. Four load models, including exponential, hyperbolic, linear, and logarithmic, were constructed for each demand response programme. Rime is a newly created physics-based algorithm that has been deployed to handle the anticipated energy management problem that the microgrid may be experiencing. To evaluate the efficacy of the proposed strategy, four case studies based on grid price and participation scenarios have been carried out. The findings from our research are notably impactful, revealing an 8 % reduction in energy consumption when applying the critical peak price (CPP) load demand model. This efficiency gain translates into a notable enhancement in the load factor, increasing from 0.83 to 0.86, and a significant drop in overall generation costs from $25,463 to $21,823 under optimal conditions. These results vividly illustrate the practical value of our proposed research work, showcasing their ability to generate substantial energy savings and cost efficiencies in microgrid operations. The improvements in operational efficiency and cost-effectiveness underscore the potential of these models to refine microgrid management, delivering both economic and performance gains that are crucial for advancing sustainable energy solutions.

Real-time analytical solution to energy management for hybrid electric vehicles using intelligent driving cycle recognition

For series hybrid electric vehicles, due to the limitation of engine operating characteristics, speed regulation is usually performed using discrete operating points. This leads to the problem of mixed integer programming when solving energy management problem. In this paper, an analytical method with strong real-time performance and small computational load is proposed. First, an intelligent cycle recognition system is designed. It can cluster driving cycles offline based on the probability distribution of the required power and efficiently recognize unknown driving cycles online. Then the analytical expression of power distribution is derived, and the selection scheme of engine operating point is given. Finally, the required power information obtained from the clustering is substituted into the analytical expression. The specific values of the corresponding analytical solutions for each type are computed offline. When facing unknown conditions, this method can match the power distribution scheme quickly once the driving cycle is recognized. The results of the simulation and hardware-in-loop experiments demonstrate that this method can effectively control the SOC trajectory and allocate power more optimally. Compared to the benchmark method, the proposed strategy improves the fuel economy by 5.52 % and 7.49 % in two cases, and the computational efficiency is significantly enhanced.

Optimization of Distributed Energy Resources Operation in Green Buildings Environment.

Without a well-defined energy management plan, achieving meaningful improvements in human lifestyle becomes challenging. Adequate energy resources are essential for development, but they are both limited and costly. In the literature, several solutions have been proposed for energy management but they either minimize energy consumption or improve the occupant's comfort index. The energy management problem is a multi-objective problem where the user wants to reduce energy consumption while keeping the occupant's comfort index intact. To address the multi-objective problem this paper proposed an energy control system for a green environment called PMC (Power Management and Control). The system is based on hybrid energy optimization, energy prediction, and multi-preprocessing. The combination of GA (Genetic Algorithm) and PSO (Particle Swarm Optimization) is performed to make a fusion methodology to improve the occupant comfort index (OCI) and decrease energy utilization. The proposed framework gives a better OCI when compared with its counterparts, the Ant Bee Colony Knowledge Base framework (ABCKB), GA-based prediction framework (GAP), Hybrid Prediction with Single Optimization framework (SOHP), and PSO-based power consumption framework. Compared with the existing AEO framework, the PMC gives practically the same OCI but consumes less energy. The PMC framework additionally accomplished the ideal OCI (i-e 1) when compared with the existing model, FA-GA (i-e 0.98). The PMC model consumed less energy as compared to existing models such as the ABCKB, GAP, PSO, and AEO. The PMC model consumed a little bit more energy than the SOHP but provided a better OCI. The comparative outcomes show the capability of the PMC framework to reduce energy utilization and improve the OCI. Unlike other existing methodologies except for the AEO framework, the PMC technique is additionally confirmed through a simulation by controlling the indoor environment using actuators, such as fan, light, AC, and boiler.

Deep reinforcement learning based adaptive energy management for plug-in hybrid electric vehicle with double deep Q-network

The equivalent consumption minimization strategy (ECMS) with pre-calibrated constant equivalence factor (EF) can ensure near global optimal solution for certain driving cycle and enable good real-time capability, but it is difficult to adapt to a wide range of driving conditions. To this end, aiming at the optimal energy management problem of a plug-in hybrid electric vehicle (PHEV), this paper proposes a deep reinforcement learning (DRL) based adaptive ECMS by combing the double deep Q-network (DDQN) and the driving cycle information. The DDQN is applied to correct the EF of the ECMS in a feed-forward manner with the battery state-of-charge (SOC) and the periodic predicted driving cycle information as inputs, and the ECMS is utilized to calculate the engine torque and gear ratio of the powertrain. The driving cycle information is represented by the average velocity, which is predicted by the historical velocity sequence based on the back-propagation (BP) neural network, and the difference of the average velocity between two continuous time windows. The hardware-in-the-loop (HIL) platform is constructed to test the performance of the proposed strategy. It is shown that the future average velocity can be well predicted by the historic velocity sequence. Both simulation and HIL test results demonstrate that the proposed adaptive ECMS based on DDQN exhibits superior performance in improving the vehicle fuel economy.

Digital Twin-Enhanced Control for Fuel Cell and Lithium-Ion Battery Hybrid Vehicles

With the development of lithium-ion batteries and fuel cells, the application of hybrid power systems is becoming more and more widespread. To better optimize the energy management problem of fuel cell hybrid systems, the accuracy of system modeling and simulation is very important. The hybrid system is formed by connecting the battery to the fuel cell through an active topology. Digital twin technology is applicable to the mapping of physical entities to each other with high interactivity and fast optimization iterations. In this paper, a relevant model based on mathematical logic is established by collecting actual operational data; subsequently, the accuracy of the model is verified by combining relevant operating conditions and simulating the model. Subsequently, a three-dimensional visualization model of a hybrid power system-based sightseeing vehicle and its operating environment was established using digital twin technology to improve the model simulation of the fuel cell hybrid power system. At low speeds, the simulation results of the hybrid power system-based sightseeing vehicle have a small error compared with the actual running state, and the accuracy of the data related to each internal subcomponent is high. In the simple interaction between the model display vehicle and the environment, the communication state can meet the basic requirements of the digital twin model because the amount of data to be transferred is small. This study makes a preliminary attempt at digital parallelism by combining mathematical logic with visualization models and can be used as a basis for the subsequent development of more mature digital twin models.

An enhanced jellyfish search optimizer for stochastic energy management of multi-microgrids with wind turbines, biomass and PV generation systems considering uncertainty

The energy management (EM) solution of the multi-microgrids (MMGs) is a crucial task to provide more flexibility, reliability, and economic benefits. However, the energy management (EM) of the MMGs became a complex and strenuous task with high penetration of renewable energy resources due to the stochastic nature of these resources along with the load fluctuations. In this regard, this paper aims to solve the EM problem of the MMGs with the optimal inclusion of photovoltaic (PV) systems, wind turbines (WTs), and biomass systems. In this regard, this paper proposed an enhanced Jellyfish Search Optimizer (EJSO) for solving the EM of MMGs for the 85-bus MMGS system to minimize the total cost, and the system performance improvement concurrently. The proposed algorithm is based on the Weibull Flight Motion (WFM) and the Fitness Distance Balance (FDB) mechanisms to tackle the stagnation problem of the conventional JSO technique. The performance of the EJSO is tested on standard and CEC 2019 benchmark functions and the obtained results are compared to optimization techniques. As per the obtained results, EJSO is a powerful method for solving the EM compared to other optimization method like Sand Cat Swarm Optimization (SCSO), Dandelion Optimizer (DO), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and the standard Jellyfish Search Optimizer (JSO). The obtained results reveal that the EM solution by the suggested EJSO can reduce the cost by 44.75% while the system voltage profile and stability are enhanced by 40.8% and 10.56%, respectively.

Gas emission optimization and optimal energy management of a microgrid operating by renewable and sustainable generation systems

The economic operation of electric energy generating systems is one of predominant problems in energy systems. Due to the need for better reliability, high energy quality, lower losses, lower cost and clean environment, the application of renewable and sustainable energy sources such as wind energy, solar energy, fuel cells, etc. in recent years has become more widespread mainly. In this work, one of most general of all swarm intelligence algorithms inspired by collective intelligent behavior of natural or artificial systems called the Particle Swarm Optimization (PSO) is applied to solve the Gas emission Optimization (GEO) and the Optimal Energy Management (OEM) problems of a micro-grid (MG) operating by Renewable and Sustainable Generation Systems (RSGS). Our main goal is to minimize nonlinear objective function of an electrical micro-grid taking into account of equality and inequality constraints. The PSO approach was examined and tested on a standard MG system composed of different types of RSGS such as wind turbines (WT), photovoltaic systems (PV), fuel cells (FC), micro turbine (MT), diesel generator (DEG) and loads with energy storage systems (ESS). The results are promising and show the effectiveness and robustness of proposed approach to solve the GEO and the OEM problems. The results of proposed method have been compared and validated with those known references published recently.

Robust economic–environmental dispatch problem for BESS and PV generators in MT-HVDC systems: A MI-MPC approach

The research addresses the energy management problem (EMP) in multi-terminal high-voltage direct current (MT-HVDC) systems using a mixed-integer model predictive control (MI-MPC). The MT-HVDC system consists of conventional thermal generation plants (fossil sources), renewable generation sources (solar photovoltaic plants), and battery energy storage systems (BESS). This combination creates a complex nonlinear EMP, as it introduces the power losses of the transmission networks through B-coefficients. The main contributions of this research can be summarized in three elements: (i) the formulation of a measurement- or simulation-based approach to determine B−coefficients in MT-HVDC systems for calculating power losses; (ii) the convexification of the EMP model through MI-MPC approaches, allowing to minimize economic and environmental objective functions; and (iii) the inclusion of uncertainties through the robust convex method. Numerical validations in the 11-bus grid, including the linear transportation model for the MT-HVDC system, confirm the multi-objective nature of the EMP when considering economic and environmental indices. In addition, the effect of uncertainties on generation and demand causes significant variations in the optimal Pareto front when compared to the deterministic scenario.