Loss Of Energy Expectation Research Articles

Planning renewables in distribution system with electric vehicles to improve hosting capacity and energy losses: Two-stage stochastic optimization framework

Excessive penetration of renewables in distribution system can create several operational issues. One of the technologies that can maximize accommodation of renewables is electric vehicles (EVs). However, along with EVs additional measures are required while maximizing hosting capacity (HC) to avoid negative impact on system and account for uncertain parameters. In this regard, this paper proposes a two-stage stochastic optimization approach for planning of renewables in distribution system integrated with EVs. In the first stage, capacity of renewables is determined while maximizing HC whereas in the second stage operating strategy of EVs, renewables and grid power is evaluated to minimize expected energy losses. The proposed framework includes uncertainties in load demand, renewables and EVs characteristics through stochastic programming approach. The optimization problem is formulated as second order cone programming problem. The proposed model is tested on modified IEEE-33 bus and real-life 108-bus Indian distribution systems with different charging/discharging patterns and penetration rates of EVs. Moreover, an economic based cost analysis to compare planning cost and EV charging cost is also provided. Simulation results reveal that in 33-bus system with 500 EVs, the HC with vehicle-to-grid capability (V2G) is higher as compared to uncoordinated and coordinated charging by 29.86% and 6.36% respectively, while in 108-bus system with 1000 EVs, it is higher by 18.51% and 5.69% respectively. Further, the energy losses with V2G are 27.54% and 1.36% less in 33-bus system and 7.31% and 3.22% less in 108-bus system as compared to uncoordinated and coordinated charging respectively.

Multi-objective placement and sizing of energy hubs in energy networks considering generation and consumption uncertainties

This paper presents the placement and sizing of energy hubs (EHs) in electricity, gas, and heating networks. EH is a coordinator framework for various power sources, storage devices, and responsive loads. For simultaneous modeling of economic, operation, reliability, and flexibility indices, the proposed scheme is expressed as a three-objective optimization in the form of Pareto optimization based on the sum of weighted functions. The objective functions of this problem respectively minimize the planning cost of EHs (equal to the total cost of construction of hubs and their expected operating cost), the expected energy loss of the mentioned networks, and the expected energy not-supplied (EENS) of these networks in the case of an N − 1 event. The problem is constrained by power flow equations and operation and reliability constraints of these network together with the EH planning and operation model, and flexibility constraints of the EHs. Then, to achieve unique optimal solution in the shortest possible time, a linear approximation model is extracted for the proposed scheme. Moreover, scenario-based stochastic programming (SBSP) is employed to model uncertainties of load, energy cost, renewable power, and accessibility of the mentioned network equipment. Finally, the obtained numerical results indicate the capability of the proposed scheme in enhancing the economic and flexibility situation of EHs and improving the reliability and operation status of energy networks along with achieving optimal planning and operation for EHs.

Frequency regulation with storage: On losses and profits

Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future frequency deviation trajectories as functional uncertainties in a receding horizon robust optimization problem. We constrain the expected terminal state-of-charge to be equal to some target to allow storage operators to make good decisions not only for the present but also the future. Thanks to this constraint, the amount of electricity traded on day-ahead markets is an implicit function of the regulation power sold to grid operators. The implicit function quantifies the amount of power that needs to be purchased to cover the expected energy loss that results from providing frequency regulation. We show how the marginal cost associated with the expected energy loss decreases with roundtrip efficiency and increases with frequency deviation dispersion. We find that the profits from frequency regulation over the lifetime of energy-constrained storage devices are roughly inversely proportional to the length of time for which regulation power must be committed.

Energy management of distribution network with inverter‐based renewable virtual power plant considering voltage security index

AbstractVirtual power plants (VPP) with resources and storages are able to control the active power of the network. They are also connected to the network through an inverter, which is capable of controlling reactive power. Therefore, it is expected that the optimal use of inverter‐based VPP can play an effective role in improving the economic and technical status of the distribution network. So, the operation of a smart distribution system is presented in this paper by considering inverter‐based VPPs constrained to the operator's measures. The weighted sum of expected energy loss (EEL) and voltage security index (VSI) is minimized while considering AC optimal power flow equations, restrictions of network's security, and operating model of the inverter‐based VPPs. Uncertainties with an origin of the amount of demand, renewable energy, and parameters of mobile energy storage are also discussed. The uncertainties are modelled using a stochastic optimization approach relying on the unscented transformation (UT). Evaluating inverter‐based VPP performance, providing models of flexible resources such as responsive loads and mobile storages, checking network voltage security status, and modelling uncertainties using the UT method are among the innovations of this study. According to the results, it is demonstrated that the technical situation of the distribution system is improved with the help of optimal management of the VPP. With energy management of the inverter‐based VPP, the suggested design has succeeded to enhance the operating status (voltage security) of the system by approximately 33–73% (12%) in comparison to power flow studies.

Stochastic Coordinated Management of Electrical–Gas–Thermal Networks in Flexible Energy Hubs Considering Day-Ahead Energy and Ancillary Markets

This paper presents an optimal operation framework for electrical, gas, and thermal networks in the presence of energy hubs (EHs), so that EHs can benefit from day-ahead ancillary and energy markets. Therefore, to consider the goals of network operators (optimal operation of networks) and EHs (optimal operation in markets), the proposed model is developed in the form of a bi-level optimization. Its upper-level formulation minimizes the expected energy loss in the proposed networks based on the optimal power flow constraints and technical limits. At the lower-level problem, maximizing the expected profit of EHs in day-ahead energy and ancillary markets (including reactive and reserve regulation) is formulated based on the operational model of resources, storage devices, and responsive load in the EH framework, and the flexible constraints of EHs. This scheme includes the uncertainties of load, market price, renewable energy resources, and mobile storage energy demand, which uses the point estimation method to model them. Karush–Kuhn–Tucker is then used to extract the single-level model. Finally, by implementing the proposed scheme on a standard system, the obtained numerical results confirm the capability of the proposed model in improving the network’s operation and economic status of EHs. As a result, the proposed scheme is able to decrease operation indices such as energy losses, voltage drop, and temperature drop by approximately 28.5%, 39%, and 27.8%, respectively, compared to load flow analysis. This scheme can improve the flexibility of EHs, including non-controllable sources such as renewable resources, by nearly 100% and it obtains considerable profits for hubs.

Optimal Defensive Strategy for Power Distribution Systems Against Relay Setting Attacks

Improving the cyber security of critical protection devices is of paramount importance for reducing the impact of cyber attacks on power distribution system. This paper proposes a game-theoretic approach to identify the optimal defensive strategy and scheme to minimize the impact of relay setting attack on power distribution systems. To this end, two types of attacks, namely active and passive relay setting attacks (RSA), are introduced and modeled as the potential threats to the protection relays. The active RSA impacts the distribution system immediately, while passive RSA disrupts the relay coordination and escalates the outages resulted from future system faults. The optimal budget allocation problem for strengthening the security of relays is modeled by formulating the interaction between the defender, the attacker and the distribution system operation as a tri-level optimization problem, which is then cast into a single-level operation and a bi-level defender-attacker problem. The bi-level problem is further reduced to an expected energy loss minimization problem using an auxiliary constrained parameter. The proposed approach is tested on the IEEE 123-node test feeder, the results of which exhibit the effectiveness of the proposed model on determining the most vulnerable relays and reducing the expected energy not served.

Wholesale and retail energy markets model for the energy networks in the presence of the energy hubs

In this paper, the formulation of the energy market in two wholesale and retail models for different energy networks such as electric, gas and thermal networks in the presence of energy hubs according to the two-layer energy management system is presented. In the first layer of EMS, the coordination of resources and ALs with the operator of EHs is considered, and in the second layer of EMS, the coordination of the operator of EHs with ENOs is considered. In the proposed design, the mentioned networks have participated in the wholesale market as private distribution companies or DisCo and then buy energy from it. These companies have shared the purchased energy in the retail energy market environment between consumers and EHs connected to itself. This design is expressed in the form of two-level optimization, the upper level of which is the minimization of the expected energy cost of ENs in the mentioned markets, and the other level is the minimization of the expected energy losses of ENs in the retail market. In the following, the Karush–Kuhn–Tucker (KKT) method and Pareto optimization technique based on epsilon constraint method were used to derive the single-level and single-objective problem. Then, the unscented transformation (UT) method was used to model the uncertainties of load, energy price, renewable power and EV energy demand. Finally, based on the numerical results, it was observed that the proposed plan achieves the highest profit for EHs in proportion to the time-varying energy price. Also, with the optimal energy management of EHs, it has been able to reduce the energy cost of ENs by about 12% compared to load flow studies.

Optimal traffic operation for maximum energy efficiency in signal-free urban networks: A macroscopic analytical approach

The integration of artificial intelligence and wireless communication technologies in communicant autonomous vehicles (CAVs) enables coordinating the movement of CAV platoons at signal-free intersections. The capacity of signal-free intersections can be significantly improved by adjusting traffic variables at a macroscopic scale; however, the resulting improvement in the capacity does not necessarily have a positive impact on the energy consumption of CAVs at the network level. In this research, we develop an analytical model to enhance energy efficiency by optimizing macroscopic traffic variables in signal-free networks. To this end, we adopt a macroscopic modeling approach to estimate the operational capacity by accounting for the stochasticity resulting from the error in synchronizing the arrival and departure of consecutive platoons in crossing directions at intersections. We also develop a macrolevel analytical model to estimate expected energy loss during the acceleration/deceleration maneuver required for resynchronization at intersections as a function of synchronization success probability. We then maximize energy efficiency by minimizing expected energy loss and maximizing expected capacity in a biobjective optimization framework. We solve the energy efficiency problem using an analytical approach to derive a closed-form solution for the optimal traffic speed and the length of the marginal gap between the passage of consecutive platoons in crossing directions through intersections for a (general) normal distribution of the operational error. Having the closed-form solution of the energy efficiency problem, we balance the trade-off between energy loss and operational capacity at a large scale by extending the analytical model to the network level using the Macroscopic Fundamental Diagram (MFD) concept. The results of our two-ring simulation model indicate the accuracy of the proposed analytical model in estimating the macroscopic relationship between the expected energy loss at intersections and the vehicular density in signal-free networks. Our numerical results also show that optimizing the traffic speed and marginal gap length can improve energy efficiency by 31% at the cost of a 16% decrease in maximum capacity.

Optimal Reactive Power Compensation in Distribution Networks with Radial and Meshed Structures Using D-STATCOMs: A Mixed-Integer Convex Approach.

This paper deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) in electrical distribution networks to minimize the expected total annual operating costs. These costs are associated with the investments made in D-STATCOMs and expected energy losses costs. To represent the electrical behavior of the distribution networks, a power flow formulation is used which includes voltages, currents, and power as variables via incidence matrix representation. This formulation generates a mixed-integer nonlinear programming (MINLP) model that accurately represents the studied problem. However, in light of the complexities involved in solving this MINLP model efficiently, this research proposes a mixed-integer convex reformulation. Numerical results regarding the final annual operating costs of the network demonstrate that the proposed mixed-integer convex model is efficient for selecting and locating D-STATCOMs in distribution networks, with the main advantage that it is applicable to radial and meshed distribution grid configurations. A comparative analysis with respect to metaheuristic optimizers and convex approximations confirms the robustness of the proposed formulation. All numerical validations were conducted in the MATLAB programming environment with our own scripts (in the case of metaheuristics) and the CVX convex disciplined tool via the Gurobi solver. In addition, the exact MINLP model is solved using the GAMS software.

Impact Assessment of Diverse EV Charging Infrastructures on Overall Service Reliability

A higher penetration of EVs may pose several challenges to the power systems, including reliability issues. To analyze the impact of EVs on the reliability of power systems, a detailed EV charging infrastructure is considered in this study. All possible charging locations (home, workplace, public locations, and commercial fast chargers) and different charging levels (level 1, level 2, and DC fast charging) are considered, and seven charging infrastructures are determined first. Then, the reliability impact of each charging infrastructure is determined using the two widely used reliability indices, i.e., the loss of load expectation (LOLE) and the loss of energy expectation (LOEE). The impact of mixed charging infrastructure portfolios is also analyzed by considering two different cases, which included the equal share of all charging infrastructure and charging infrastructure share based on consumer preferences. The performance is analyzed on a well-known reliability test system (Roy Billinton Test System) and different penetration levels of EVs are considered in each case. Test results have shown that fast-charging stations have the worst reliability impact. In addition, it was also observed that mixed charging portfolios have lower reliability impacts despite having a fair share of fast-charging stations.

A hybrid probabilistic information gap decision theory based energy management of an active distribution network

The optimal operation of an active distribution network requires proper coordination between multiple entities like renewable energy sources, storage units, power electronic devices, demand response implementation, and network reconfiguration. In this context, this paper proposes optimal energy coordination and management scheme among various entities with different ownership in a reconfigurable active distribution network. The distribution system operator manages the coordinated energy procurement scheme from multiple sources to maximize the expected hourly profit of operation. Uncertainties of load, renewable generation, grid energy price, and the charging power of hybrid electric vehicles are modelled using a probabilistic “Hong’s 2m point estimate” approach. On the other hand, the uncertainty of the demand response is modelled using information gap decision theory. The optimization problem is solved in a hybrid framework encompassing probability and information gap decision theory. Simulation studies on a thirty-three-node distribution network validate the efficacy of the proposed method. With the proposed energy management and coordination scheme, the daily expected operating cost reduces by ∼6.66% while the daily expected energy loss reduces by ∼26.05%. Implementing a risk-averse strategy to hedge against the risk of uncertain demand response participation reduces the profit by ∼3.21% for a tolerance limit of 5%.

Application of the SSA for Optimal Reactive Power Compensation in Radial and Meshed Distribution Using D-STATCOMs

This paper deals with the problem regarding the optimal placement and sizing of distribution static compensators (D-STATCOMs) in radial and meshed distribution networks. These grids consider industrial, residential, and commercial loads within a daily operation scenario. The optimal reactive power flow compensation problem is formulated through a mixed-integer nonlinear programming (MINLP) model. The objective function is associated with the minimization of the expected energy losses costs for a year of operation by considering the investment costs of D-STATCOMs. To solve the MINLP model, the application of a master–slave optimization approach is proposed, which combines the salp swarm algorithm (SSA) in the master stage and the matricial backward/forward power flow method in the slave stage. The master stage is entrusted with defining the optimal nodal location and sizes of the D-STATCOMs, while the slave stage deals with the power flow solution to determine the expected annual energy losses costs for each combination of nodes and sizes for the D-STATCOMs as provided by the SSA. To validate the effectiveness of the proposed master–slave optimizer, the IEEE 33-bus grid was selected as a test feeder. Numerical comparisons were made against the exact solution of the MINLP model with different solvers in the general algebraic modeling system (GAMS) software. All the simulations of the master–slave approach were implemented in the MATLAB programming environment (version 2021b). Numerical results showed that the SSA can provide multiple possible solutions for the studied problem, with small variations in the final objective function, which makes the proposed approach an efficient tool for decision-making in distribution companies.

Participation of Grid-Connected Energy Hubs and Energy Distribution Companies in the Day-Ahead Energy Wholesale and Retail Markets Constrained to Network Operation Indices

In this paper, the optimal scheduling of energy grids and networked energy hubs based on their participation in the day-ahead energy wholesale and retail markets is presented. The problem is formulated as a bilevel model. Its upper level minimizes the expected energy cost of electricity, gas, and heating grids, especially in the form of private distribution companies in the mentioned markets, in the first objective function, and it minimizes the expected energy loss of these networks in the second objective function. This problem is constrained by linearized optimal power flow equations. The lower-level formulation minimizes the expected energy cost of hubs (equal to the difference between sell and purchase of energy) as an objective function in the retail market. Constraints of this model are the operation formulation of sources and active loads and the flexibility limit of hubs. The unscented transformation approach models the uncertainties of load, renewable power, energy price, and energy demand of mobile storage. Then, the Karush–Kuhn–Tucker approach and Pareto optimization technique based on ε-constraint are adopted to extract the single-level single-objective formulation. Finally, obtained results verify the capability of the present method in improving the economic status of hubs and the economic and operation situation of the mentioned networks simultaneously so that the proposed scheme by managing the power of energy hubs compared with power flow studies has been able to reduce operating costs by 8%, reduce energy losses by 10%, and improve voltage profile and temperature by 36% and 30%.

Reliability Analysis of Wind Energy Generation System Using Stochastic Method

Operators of renewable energy systems (RESs) must always manage uncertainty to some extent to ensure the reliability and the security of the electric power supply source. The guiding principle in this regard is to ensure service reliability and quality by balancing load variations with the variable renewable energy (VRE) sources. If the power generated by these VRE sources is not properly managed in conjunction with the varying load, the power grid may fail to achieve the required balance. To ensure its reliable operation, reliability analysis is vital for wind energy generation system (WEGS). This paper evaluated and assessed the reliability of WEGS and a proposed varying load by first using a stochastic approach to model the WEGS and the proposed varying load after which power generation indices were used to evaluate and assess the performance of the model. The WEGS and the varying load were modelled separately after which the two were combined into one model. Full availability, partial availability, the expected energy not supplied (EENS) or loss of energy expectation (LOEE), the mean or average instantaneous electric power generation and mean instantaneous generation deficiency were the indices used for the evaluation of the WEGS. The results indicated that the electric power generation will meet the power demand during most of the transition states of the WEGS with the expectation that the variation in the load will not be at fast pace and in large quantum.

Reducing conventional generation dependency with solar Pv power: A case of Delhi (India)

ABSTRACT In several Indian cities, the governments is planning to reduce excessive air pollution due to fossil fuel used by traffic and local industries. This is done by encouraging greater use of renewable energy resources. One such city that has come under this observation is the Metropolis of Delhi, the capital of India. The Government of Delhi NCR has initiated corrective policy moves that promote the use of solar photovoltaic energy for minimizing dependency on fossil-fueled generation. However, it is well known that renewable energy has its limitations in relation to steady availability and desired quantity for bulk applications. Thus, at best, renewable energy can partially replace conventional fossil-fueled energy resources. The extent to which solar photovoltaic (SPV) energy can replace conventional-fueled generation is broadly referred to as capacity credit or capacity value of the concerned SPV. This paper is an attempt to compute the sizing of the optimum solar PV installation for a satisfactory level of capacity credit. The analysis employs the state sampling approach. The system adequacy is evaluated in terms of the reliability indices Loss of Energy Expectation (LOEE) and Loss of Load Expectation (LOLE). The Monte Carlo simulation technique is applied for the reliability evaluation, on account of its simplicity and better relative accuracy as compared with other available techniques. It is observed that for a solar penetration level of 30%, the increment in capacity contribution shows dissimilar trends with the increment in installation capacity. The optimum installation is witnessed for the 200 W and 400 W for the reliability criteria of LOLE and LOEE indices, respectively.

Probabilistic indices for analysing the impact of penetration of distributed energy resources on system reliability

Recent years have seen a steep increase in penetration of renewable energy sources (RES) based generators and storage devices; collectively referred as distributed energy resources (DERs). The traditional reliability indices used by utilities such as loss of load expectation, loss of energy expectation and loss of load probability are suitable for systems with conventional generators. However, they fail to acknowledge stochastic behaviour of RES based generators and energy limited capabilities of storage appropriately. In this study, new probabilistic reliability indices for investigating impact of penetration of DERs on system reliability have been proposed. In order to provide effective assessment, a reliability index referred as expectation of failure in grid connected mode (EFG) and three reliability indices viz. expectation of complete success in islanded mode, expectation of partial failure in islanded mode, expectation of complete failure in islanded mode have been proposed in grid connected mode and islanded mode, respectively. The mathematical formulation for proposed indices has been developed in probabilistic framework. The formulation has been implemented on a 33-bus distribution feeder. Different penetration levels have been investigated to provide adequate justification for proposed indices. Parametric analyses with storage integration have also been carried out. The proposed reliability metrics will assist system planners to choose optimum penetration level with greater efficacy.

A Distributed Lumped Parameter Model of Blood Flow.

We propose a distributed lumped parameter (DLP) modeling framework to efficiently compute blood flow and pressure in vascular domains. This is achieved by developing analytical expressions describing expected energy losses along vascular segments, including from viscous dissipation, unsteadiness, flow separation, vessel curvature and vessel bifurcations. We apply this methodology to solve for unsteady blood flow and pressure in a variety of complex 3D image-based vascular geometries, which are typically approached using computational fluid dynamics (CFD) simulations. The proposed DLP framework demonstrated consistent agreement with CFD simulations in terms of flow rate and pressure distribution, with mean errors less than 7% over a broad range of hemodynamic conditions and vascular geometries. The computational cost of the DLP framework is orders of magnitude lower than the computational cost of CFD, which opens new possibilities for hemodynamics modeling in timely decision support scenarios, and a multitude of applications of imaged-based modeling that require ensembles of numerical simulations.

Stochastic Optimization for Discrete Overcurrent Relay Tripping Characteristics and Coordination

The inverse-time operating characteristic of overcurrent relays is the primary protective element in distribution system protection schemes and has been utilized for several decades. As the distribution system becomes increasingly complex due to the growth of distributed generation, the protection task based on existing methodologies will become more difficult. Faster relay operating times while maintaining selectivity is critical. In this paper, a stochastic mixed-integer linear program is formulated to minimize a relay’s tripping time at discrete fault current intervals and considers the cost of tripping a relay as the objective function. The formulation takes into account the probabilistic nature of the fault current observed at each relay, which can be impacted by fault location, fault resistance, device failure, and DG output. Monte Carlo simulation is used to determine the empirical probabilities of each relay observing a particular fault current. Probabilistic fault scenarios are simulated on the IEEE 34-node test feeder. The proposed approach shows a decrease in expected energy loss due to faults up to 11.5% compared to conventional TCC curves for 10 000 Monte Carlo fault scenarios.

Multi-Timescale Coordinated Voltage/Var Control of High Renewable-Penetrated Distribution Systems

This paper proposes a multi-timescale coordinated stochastic voltage/var control method for high renewable-penetrated distribution networks. It aims to utilize multiple devices to counteract uncertain voltage fluctuation and deviation. In the hourly timescale (first stage), capacitor banks and transformer tap changers are scheduled before stochastic renewable output and load variations are realized. In the 15-min timescale (second stage), inverters that interface the renewable energy resources provide var support to supplement the first-stage decision after uncertainty is observed. The coordination is model as a two-stage stochastic programming problem with scenario reduction. It is then converted to a deterministic mixed-integer quadratic programming equivalence model and solved by commercial solvers combined. Compared with existing methods, the proposed volt/var control can achieve lower expected energy loss and can sustain a secure voltage level under random load demand and renewable power injection. The proposed method is verified on the IEEE 33-bus distribution network and compared with existing practices.

A Two-stage Stochastic Programming Model for Optimal Reactive Power Dispatch with High Penetration Level of Wind Generation

The increasing of wind power penetration level presents challenges in classical optimal reactive power dispatch (ORPD) which is usually formulated as a deterministic optimization problem. This paper proposes a two-stage stochastic programming model for ORPD by considering the uncertainties of wind speed and load in a specified time interval. To avoid the excessive operation, the schedule of compensators will be determined in the first-stage while accounting for the costs of adjusting the compensators (CACs). Under uncertainty effects, on-load tap changer (OLTC) and generator in the second-stage will compensate the mismatch caused by the first-stage decision. The objective of the proposed model is to minimize the sum of CACs and the expected energy loss. The stochastic behavior is formulated by three-point estimate method (TPEM) to convert the stochastic programming into equivalent deterministic problem. A hybrid Genetic Algorithm-Interior Point Method is utilized to solve this large-scale mixed-integer nonlinear stochastic problem. Two case studies on IEEE 14-bus and IEEE 118-bus system are provided to illustrate the effectiveness of the proposed method.