Probability Distribution Of Load Research Articles

Two-stage distributionally robust optimization operation of virtual power plant considering the virtual energy storage of electric vehicles

Virtual Power Plant (VPP) is a key to aggregate various distributed energy sources. With the vigorous rise of various distributed energy sources, the direct access of large-scale electric vehicle load will increase the complexity of VPP coordinated operation. Hence, this paper proposes a VPP optimization method for Electric Vehicle Virtual Energy Storage (EV-VES). Firstly, the travel characteristics of electric vehicles are analyzed, and EV-VES model is established to coordinate and manage the charge-discharge behavior of EV. Secondly, the “carbon charge rate” model of energy storage (ES) is introduced to establish the relationship between carbon emission and electricity price, and the VPP operation model considering the “carbon charge rate” of energy storage is established. Finally, the two-stage robust optimization operation model of VPP is constructed, Wasserstein distance is used to describe the confidence set of uncertain probability distribution of wind power generation and load, and the uncertainty of system source and load are described by the confidence set. The Column and Constraint Generation (C&CG) algorithm was used to determine the optimal operational benefit solution. The effectiveness of the proposed VPP optimal operation model was validated through case study.

Short-term stochastic multi-objective optimization scheduling of wind-solar-hydro hybrid system considering source-load uncertainties

Uncertainties in energy outputs (source side) and load side are simultaneously present and cannot be ignored in the actual operation of multi-energy systems. Adopting a reasonable uncertainty modeling method and understanding the impact of source-load uncertainties on optimization scheduling are key to formulating accurate and effective multi-energy scheduling plans. To address the uncertainties on both the source side and the load side in wind-solar-hydro hybrid systems, this paper proposes a multi-objective optimization scheduling model based on stochastic programming theory. The model aims to maximize the net profit of the system's power generation and minimize the fluctuation of the remaining load. It employs Vine-Copula coupled with Monte Carlo simulation and the deep learning method TimeGAN to generate joint wind and solar power output and load scenario sets. The generated source-load uncertainty scenarios are then reduced to representative scenarios using the K-Means clustering method, which are used as inputs for the scheduling model. The proposed model is applied to a wind-solar-hydro energy base in China, and the results show that: 1) The Vine-Copula-based source-side scenario generation method can quantitatively consider the correlations among meteorological factors. The relative errors of the generated scenarios' statistics compared to the original data are all less than 5%, and the relative errors of the correlation coefficients are less than 10%. 2) The TimeGAN-based load-side scenario generation method avoids the presupposition of the load probability distribution. Compared to the original data, the generated scenarios have R2 and Pearson correlation coefficients of 0.77 and 0.87, respectively. Additionally, TimeGAN shows significant advantages over traditional random sampling methods in simulating extreme scenarios. 3) Both source-side and load-side uncertainties significantly impact the optimization scheduling results of multi-energy systems, leading to increased fluctuation of the remaining load and decreased net profit. 4) The combined source-load uncertainties have a synergistic negative impact on the multi-objective optimization scheduling results. 5) The Pareto front of the optimization results is a concave function with low marginal benefits. Decision-makers should adopt a compromise solution as a guide for the operation of multi-energy systems.

Consequences of the Improved Wave Statistics on a Hull Girder Reliability of Double Hull Oil Tankers

This paper investigates the change in hull girder failure probabilities and partial safety factors caused by the implementation of the new procedure for direct computation of wave loads recommended by the International Association of Classification Societies (IACS). Differences between new and previous procedures are primarily related to the different associated scatter diagrams, and secondarily due to the assumptions on wave spectrum, wave energy spreading, and ship speed. This study performs a comparative structural reliability analysis of the global longitudinal bending of five oil tankers of different sizes between two procedures for wave load computation. Firstly, failure probabilities are compared, and secondly, modified partial safety factors are proposed, resulting in similar failure probabilities according to two separate procedures. It is found that implementation of the new revision of the IACS procedure for direct computation of wave loads results in a reduction of the minimum required ultimate vertical bending capacity of a ship hull by 10%. In addition to the novel investigation of the safety of oil tankers using a revised wave scatter diagram, this study offers a new rapid method for calculation of extreme vertical wave bending moments based on the regression of the parameters of the Weibull function, used for the long-term probability distribution of wave-induced loads.

Probabilistic analysis of operational ice damage for Polar class vessels using full-scale data

To ensure the safety of maritime operations in polar waters, the IMO enforced the International Code for Ships Operating in Polar Waters (Polar Code) in 2017. To address ice navigation related risks, the Polar Code refers to a set of guidelines known as the Polar Operational Limit Assessment Risk Indexing System (POLARIS). Following POLARIS, operational limits for ice navigation are defined based on the Risk Index Outcome (RIO) value, which takes into account the prevailing ice conditions and the ice class of a ship.Recent studies indicate that the POLARIS guidelines are well-founded. However, no direct relationship between RIO values and the probability of an ice-induced hull structural damage has been established. To enable a more accurate analysis of ice navigation risks, this article addresses this issue by (i) relating measured ice-induced loads to RIO values corresponding to the ice conditions in which the loads were measured, (ii) calculating the load limits for plastic deformation and rupture of the ice belt of hull structures representing different ice classes, and (iii) defining the probability of structural damage for different load limits. The study utilizes long-term full-scale ice load measurements carried out onboard Polar Supply and Research Vessel (PSRV) S.A. Agulhas II in the Antarctic Ocean. The load limits were calculated for ice class standards, PC3, PC4, PC5, PC6, and PC7 in accordance with the Unified Requirements of the International Association of Classification Societies (IACS).On a general level, the results are consistent with earlier findings indicating that the POLARIS guidelines are well-founded. If a ship operates mainly at ‘normal operation’ level, the probability for fracture at hull are at probability levels of 10-3 and 10-4 for ice classes PC3 to PC5. The probability levels for PC6 and PC7 are higher that is possibly a result from conservative load probability distributions. When the portion of operations at ‘special consideration’ level becomes significant, the probability of fracture at the hull increases significantly. However, large ice thicknesses and the largest load magnitudes may be associated with positive RIO values. Some inconsistencies are recognized, and the uncertainty and limitations of the analysis are discussed.

Day-Ahead Peak Load Probability Density Forecasting Based on QRLSTM-DF Considering Exogenous Factors

High-precision peak load forecasting is the guarantee of dispatching and decision-making in power systems. It is difficult to predict the peak power demand accurately and robustly due to many unstable factors that affect power loads. In order to solve this problem, this paper proposes quantile regression long-short term memory based on decoupling features (QRLSTM-DF) for probability density forecasting of the day-ahead peak load. This method reduces the possibility of mutual influence among characteristics by decoupling factors in different branches of neural network. Then, kernel density estimation (KDE) is used as a post-processing technique to generate probability density curves, which can give the comprehensive probability distribution of future peak loads and effectively quantify the uncertainty. Experimental results on three datasets show that the model outperforms several existing prediction models. In particular, the prediction results of the maximum daily peak power load and the peak load beyond the sample maximum boundary are also accurate and robust.

A data-driven multi-energy economic scheduling method with experiential knowledge bases

The high penetrability of renewable energy and the increasing demand for hydrogen energy pose challenges to system scheduling and the accommodation of photovoltaic and wind power. Therefore, a data-driven multi-energy economic scheduling method with experiential knowledge bases is proposed to enhance system operational efficiency and economic performance. Firstly, the Wasserstein generative adversarial network is used to enhance wind power and photovoltaic historical samples. The K-medoids clustering algorithm and ϕ-divergence are applied to achieve scenario reduction and acquire fuzzy sets, eliminating the need for assumptions about their probability distributions. Secondly, a kernel density estimation is used to improve the accuracy of characterizing the probability distribution of energy loads. Based on fuzzy sets, the distributionally robust optimization is used to achieve optimal scheduling in an integrated electricity-hydrogen-heat system. This technique enhances the accommodation capacity of photovoltaic and wind power while reducing operational costs. Finally, a decision-making technique based on an experiential knowledge base is studied, aiming to swiftly match corresponding decision variables by evaluating the similarity of labeled state variables. Simulation results show that the proposed method improves the decision-making speed by about 0.8 times and reduces operating costs and photovoltaic or wind power curtailment by at least 1%. The method can provide fast and efficient day-ahead economic scheduling for digitized integrated energy systems.

Estimation of the Ice-Induced Fatigue Damage to a Semi-Submersible Platform under Level Ice Conditions

This study presents a fatigue analysis procedure for inclined structures operated in level ice fields. Three methods for calculating the local ice load causing fatigue damage, namely the direct method, simplified method, and semi-analytical method, were introduced and compared. The direct method uses finite element analysis to simulate the continuous breaking of ice, while the simplified method and the semi-analytical method estimate the probability distribution of local ice loads based on theoretical equations and empirical data. The fatigue damage ratio at the target location was calculated by applying the ice load calculated by each method to a deformable finite element model of the structure. The results obtained from each method indicate that they provide a reasonable estimation of the local ice load causing fatigue damage in level ice fields. The direct method offers high accuracy but requires significant computational time, while the simplified method and semi-analytical method offer a faster analysis time and are more suitable for long-term time domain analysis. The semi-analytical method requires empirical data to supplement theoretical formulas due to the complex natural phenomena involving various environmental conditions that must be modeled. The findings of this study provide valuable insights into the prediction of fatigue damage in ice-going ships due to long-term ice impacts. The methods proposed in this study can aid in the design of Arctic ships exposed to various conditions and provide a more cost-effective and time-efficient approach to evaluating fatigue damage compared to field measurement. Future research in this field could investigate the application of these methods to other types of structures and further refine the methodology to improve accuracy and reduce computational costs.

Risk assessment method of gas explosion based on quantification of margins and uncertainties (QMU):a case study on beam structures in buildings

Combustible gas explosions are common accidents in residential areas. Key building structural components, such as beams, slabs and columns, can be quickly damaged and destroyed by explosive overpressure loads, which may also result in continual collapse. Risk of interior gas explosions in buildings should be assessed to analyze the ability of structures to withstand disasters, which can also offer a theoretical basis for improving the structural design and construction of buildings. In this study, reinforced concrete beams in buildings were selected as the research object, and the risks to beam structures under mixed methane and air explosions were assessed using the quantification of margins and uncertainties (QMU) method. First, the uncertainty of the existing methods to calculate gas explosion and beam bending loads was analyzed. Through an influence regularity analysis, the expansion factor of combustible gas combustion products in enclosed explosion chamber, the initial density of the gas mixture in the explosion chamber before deflagration, the compressive strength of concrete, and the tensile strength of reinforcement were selected as the key uncertainty parameters. Furthermore, the Monte Carlo method was used to create 5000 samples of the selected uncertainty parameters, and statistical analysis was conducted to obtain the probability distribution of the gas explosion overpressure load and reinforced concrete beam bending load. Based on the sampling results, the beam structure’s safety margin and uncertainty analysis were analyzed to determine the probability of structural failure at the 90% confidence level. Finally, this paper provides guidelines for determining structural failure under different boundary value conditions of combustion explosion overpressure loads and reveals the sensitivity of different uncertainty parameters to structural safety margins using stepwise regression analysis. Compared to previous methods, this work includes the uncertainty features of disasters and disaster-bearing items when analyzing combustible gas explosion accidents; we anticipate it offers a fresh perspective on the quantitative assessment of gas explosion risks in buildings.

An effective two-stage optimization method on aerodynamic measures to mitigate wind loads considering uncertainties in wind direction and velocity

At present, deterministic optimization methods on aerodynamic measures are usually employed to mitigate wind loads at one certain wind direction, ignoring the effects of the uncertainties in wind direction and velocity on wind loads. The uncertain optimization method with the consideration of the joint probability distribution (JPD) of wind speed and direction is hardly to conduct because it is very time-consuming and costly. In order to overcome these shortcomings, this study proposes an effective two-stage uncertain optimization method considering uncertainties in wind direction and velocity to achieve a considerable reduction of wind loads. In the first stage, the exceedance probability distribution of wind loads is determined based on the JPD and the wind load coefficients on the building, and the wind loads in the most unfavorable range of wind directions are chosen as the optimization objective. In the second stage, the optimal values of the design variables are determined by an interval optimization algorithm using the surrogate model and non-dominated sorting genetic algorithm II in the most unfavorable range of wind directions, where the surrogate model is constructed by the radial basis function method to relate the wind load coefficients to the design variables of aerodynamic measures, and can significantly improve the efficiency of the optimization algorithm. To validate the effectiveness of the proposed method, a flat-roof building with four spoilers is investigated and the rotation angles of spoilers are set as the design variables. The results show that the proposed method reduces the uplift wind loads with a 50-years return period up to 15.48% compared to the deterministic optimization method for one certain wind direction.

Chance-constrained optimization of distributed power and heat storage in integrated energy networks

Energy storage is widely recognized as an effective alternative to match the instantaneous imbalance between distributed renewable energy sources and loads. However, suitable installation sites and capacities are necessarily determined in integrated energy networks. This paper constructs a two-layer optimization model of integrated power and heat networks to obtain the optimal installation nodes and capacities of electric energy storage (EES) and thermal energy storage (TES) units. In the optimization model, the interchange of power to heat with storage units is collaborated to unitize distributed renewable energy sources and decrease comprehensive costs, including investment cost of storage units and operation cost. A chance-constrained optimization model is proposed to transform the uncertain variables of electric and heat loads into a deterministic optimization problem. The impacts of confidence levels involved in load probability distributions on the optimal nodes and capacities are analyzed. The results demonstrate that the optimal installation nodes are determined by the distributions of distributed power sources and load ratios in networks. The increased confidence level globally raises the optimal installation capacities of EES and TES. When the confidence level increases from 0.50 to 0.99, the utilization rate of wind power increases by 3.91 %, whereas the comprehensive cost increases by 22.34 %. The hybrid integrations of EES and TES consume more uncertain renewable power and improve the economic performances by the interchange of power to heat.

Probabilistic load forecasting using post-processed weather ensemble predictions

Probabilistic forecasting of electricity demand (load) facilitates the efficient management and operations of energy systems. Weather is a key determinant of load. However, modelling load using weather is challenging because the relationship cannot be assumed to be linear. Although numerous studies have focussed on load forecasting, the literature on using the uncertainty in weather while estimating the load probability distribution is scarce. In this study, we model load for Great Britain using weather ensemble predictions, for lead times from one to six days ahead. A weather ensemble comprises a range of plausible future scenarios for a weather variable. It has been shown that the ensembles from weather models tend to be biased and underdispersed, which requires that the ensembles are post-processed. Surprisingly, the post-processing of weather ensembles has not yet been employed for probabilistic load forecasting. We post-process ensembles based on: (1) ensemble model output statistics: to correct for bias and dispersion errors by calibrating the ensembles, and (2) ensemble copula coupling: to ensure that ensembles remain physically consistent scenarios after calibration. The proposed approach compares favourably to the case when no weather information, raw weather ensembles or post-processed ensembles without ensemble copula coupling are used during the load modelling.

Time-Dependent Reliability Assessment Method for RC Simply Supported T-Beam Bridges Based on Lateral Load Distribution Influenced by Reinforcement Corrosion

The safety and reliability of bridges gradually decrease over time under the influence of disadvantageous environmental factors, primarily due to reinforcement corrosion caused by chloride ingress. The traditional lateral load distribution (LLD) theory does not consider the influence of corrosion, which degrades the accuracy of bridge performance and reliability calculation. A time-dependent reliability assessment method for simply supported T-beam bridges is proposed in this paper, which considers the influence of reinforcement corrosion on LLD. Firstly, the steel corrosion process and degree are predicted based on the chloride ingress model, into which the water/cement ratio and concrete strength are innovatively introduced in order to improve the prediction accuracy. Secondly, the effective stiffness calculation method for corroded reinforcement bridges is established with the moment of inertia and section crack condition employed. Thirdly, the modified eccentric compression method is improved by the effective stiffness and iterative algorithm, which is suitable for the LLD calculation of corroded reinforcement bridges. The time-dependent vehicle load effect can be computed combined with the probability distribution of live load. Finally, the time-dependent reliability of the flexural bearing capacity is obtained by the Monte Carlo method and Bayesian theory without prior information. A simply supported bridge with five T-beams is taken as an example for analysis. It is indicated that the results calculated by the traditional reliability method are conservative, which cannot make a true and accurate evaluation. The method proposed in this paper can effectively reduce the assessment error caused by model uncertainty while considering the interaction between reinforcement corrosion and vehicle live load effect.

Method of constructing stochastic near-extreme daily weather data for efficient calculation of probabilistic load in air-conditioning system design

To solve the oversizing problem of the air-conditioning systems caused by the deterministic method of calculating design load, the probabilistic method has been proposed, in which the design load is selected based on the load probability distribution. In the probabilistic method, obtaining the probabilistic load based on the annual weather scenarios is time-consuming. Thus, it seems more efficient to determine the design load by obtaining the probabilistic near-extreme load directly through stochastic simulation. Therefore, a refined stochastic near-extreme daily weather (SNDW) model, in which the coupling of weather parameters was considered, was proposed to quantify the uncertainty of weather parameters in the stochastic simulation of near-extreme load. Taking Tianjin in China as an example, the SNDW model was established, and the probabilistic design loads of three types of buildings were calculated on this basis. The results showed that compared to the benchmark method, the application of the SNDW model could ensure about 1.5% of the relative error of the design load selected, and the average simulation time was reduced to 1/23 of the benchmark. Finally, the adaptability of the SNDW model to different climatic zones was verified.

Probability Distribution and Determination of Blast Loading during Structural Blast Resistant Study

Explosion overpressure and its duration are important parameters describing blast loading. However, their values obtained using the currently available methods differ significantly. To address this problem, we simulated the overpressure reflection coefficient (i.e., the ratio of reflection overpressure to incident overpressure) and fitted the analytical expressions to the test data. We then collected a large amount of theoretical and experimental blast loading data from literature and studied the probability distribution of blast loading for different scaled distances. The results show that the probability density function of explosion overpressure obeys an exponential distribution when the scaled distance is between 0.1 m / kg 1 / 3 and 0.5 m / kg 1 / 3 . On the other hand, it obeys a normal distribution when the scaled distance is greater than 0.5 m / kg 1 / 3 . The coefficient of variation reaches the maximum value of 1 when the scaled distance is between 0.1 m / kg 1 / 3 and 0.5 m / kg 1 / 3 , while it is between 0.13 and 0.2 when the scaled distance is from 1.5 m / kg 1 / 3 to 6 m / kg 1 / 3 . The coefficient of variation of reflected overpressure is slightly bigger than that of incident overpressure. Nevertheless, the coefficient of variation of proportional duration (i.e., the ratio of actual duration to cubic root of charge mass) is generally smaller, between 0.408 and 1.017. It was also found that there is no clear probability distribution for the blast loading duration. Finally, formulas for the explosion overpressure and proportional duration were determined together with their 95% confidence level bounds.

Wheel forces estimation with an Augmented and Constrained Extended Kalman Filter applied on a nonlinear multi-body model of a half vehicle

The design of a vehicle suspension requires the knowledge of wheel loads due to road unevenness. These loads can be identified from measurements acquired during vehicle rolling on roads or tracks. Different off-line methods are used to identify them. Most of these methods use some transfer functions between points of measurements and hypothesis of linear dynamic behaviour of the vehicle. This leads to miss-estimation of end-tail load probability distribution. We propose here an approach based on a nonlinear multi-body model of the half-vehicle and an Augmented and Constrained Extended Kalman Filter for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. This half vehicle model lies in a 2D plane and allow the description of pitch behavior but not the yaw neither the roll behavior. The specificities of our work are that 1) the Kalman state vector is composed of positions and velocities of each solid in the multi-body system, 2) the state model of the multi-body system is based on the Newmark explicit integration scheme, 3) the road/tracks loads are unknown and 4) the state prediction is constrained by kinematic links between bodies. Finally, this method provides an estimation of wheel center forces for a multi-body car model.

Ice loads and ice-induced vibrations of offshore wind turbine based on coupled DEM-FEM simulations

The drifting sea ice is a significant factor affecting the structural design and operation of offshore wind turbine (OWT) in cold regions. The extreme load and ice-induced vibration produced by sea ice can cause significant harm to the structures of OWT. In this study, a “strong” coupled model of the discrete element method (DEM) and finite element method (FEM) was adopted to investigate the impact of ice load and ice-induced vibration on the monopile foundation of OWT during the crushing process of sea ice. The sea ice and OWT were simulated through spherical particles in a parallel bonding mode and the Euler–Bernoulli beam element, respectively, and a “coupling” bridge was built to handle and transfer the DEM and FEM calculation parameters to achieve the “strong” coupling between the two methods. Subsequently, to examine the validity of the coupled DEM-FEM method in calculating the ice load on OWT, the ice load history and probability distribution obtained from a test in a 3-MW OWT model at Tianjin University as well as numerical simulation were compared and analyzed. In several simulations of the interaction between a 3.3-MW OWT and sea ice under various drifting speeds and thickness, some numerical results, such as ice load form, ice-induced vibration response of various parts, and mode of sea ice failure, were analyzed in several simulations. The simulation results obtained in this study primarily describe the phenomenon of the overall structural response of OWT to first-order vibration frequency and the conditions required for their generation. Therefore, the method and conclusions of this study provide a useful reference for the anti-icing design and anti-icing performance evaluation of monopile OWT in icy regions.

Transferability of weakest link model parameters of polysilicon from indentation fracture to failure of MEMS structures

Polysilicon weakest link model parameters obtained from indentation fracture are used to predict failure in MEMS structures. Plain and notched polysilicon micro-cantilevers were fabricated using surface micro-machining and bending tests were carried out till the structure failed catastrophically. To estimate the failure probability of fabricated samples, numerical studies were carried out on models closer to the actual experimental condition, by estimating and incorporating fabrication details such as undercut and roughness. Initially, the undercut inherent to fabrication process was estimated on plain cantilevers by comparing the elastic behavior with experiments. The geometry of open cavities in the sidewall, formed as a consequence of etching, were characterized using SEM micrographs. The stress field obtained from 3D FEM analysis of the notched geometries, including these geometric details, showed great sensitivity to the positioning of cavities in the sidewall relative to the top surface. Applying weakest link theory based local criteria, the probability distribution of failure load of tested structures was generated using weakest link parameters from indentation fracture. Failure loads, thus predicted, were validated with experimental data.

Reliability analysis of mixer structure under mixing simulation

When the forced two-horizontal shaft mixer is used to mix concrete, the mixing drum and the mixing components are subjected to random loads of the mixture. Structural static analysis usually ignores the randomness of the load, resulting in a large calculation error. Based on the EDEM software, this paper simulates the mixing process of the mixture, obtains the random load data of the mixture on the mixing drum and the mixing parts, and describes the variation law of the random load with a probability distribution, establishes the stress-strength interference reliability model of the mixer structure, and Monte Carlo simulation method is used to solve the structural reliability of the mixer. The results show that the load distribution of the mixing arm is the same as the mixing blade, the load distribution follows the gamma distribution, and the mixing shaft also follows the gamma distribution; the load distribution of the mixing drum follows the normal distribution. After calculation, the above load probability distribution and its intensity distribution do not interfere, and the structural reliability of the mixer meets the requirements, which can ensure the safe operation of the mixer. This method solves the reliability calculation error caused by random loads.

A Bottom-up Method for Probabilistic Short-Term Load Forecasting Based on Medium Voltage Load Patterns

Load forecasting has always been an essential part of power system planning and operation. In recent decades, the competition of the market and the requirements of renewable integration lead more attention to probabilistic load forecasting methods, which can reflect forecasting uncertainties through prediction intervals and hence benefit decision-making activities in system operation. Moreover, with the development of smart grid and power metering techniques, power companies have collected enormous load data about electricity customers and substations. The abundant load data allow us to utilize medium voltage measurement data to achieve better accuracy in high voltage transmission substation load forecasting. In this paper, a bottom-up probabilistic forecasting method is proposed for high voltage transmission substation short-term load forecasting, in which the probability distributions of medium voltage day-ahead load forecasting values are estimated and added up to form high voltage load predictions. Two bottom-up frameworks based on load patterns collected from medium voltage outgoing lines and substations are proposed respectively, in which mismatches between load data at different levels are estimated for correcting high voltage predictions. The comparison of predictions obtained by traditional and bottom-up methods demonstrates that the proposed method obtains high voltage load forecasting more accurately and give narrower prediction intervals.

Mobility-Aware Electric Vehicle Fast Charging Load Models With Geographical Price Variations

We study the traffic patterns as well as the charging patterns of a population of cost-minimizing EV owners traveling and charging within a transportation network equipped with fast charging stations (FCSs). Specifically, we study how the charging network operator (CNO) can influence where EV users charge in order to optimize the utilization of FCSs. These charging decisions of private EV owners affect aggregate congestion at stations (i.e., waiting time) as well as the aggregate EV charging load across the network. In this work, we capture the resulting equilibrium wait times and electricity load through a so-called traffic and charge assignment problem (TCAP) in an FCS network. Our formulation allows us to: 1) study the expected station wait times as well as the probability distribution of aggregate charging load of EVs in an FCS network in a mobility-aware fashion (an aspect unique to our work) while accounting for heterogeneities in users' travel patterns, energy demands, and geographically variant electricity prices; 2) analytically characterize the special threshold-based structure that determines how EV owners choose where to charge their vehicle at equilibrium, in response to the FCS's charging price structure, users' energy demands, and users' mobility patterns; and 3) provide a convex optimization problem formulation to identify the network's unique equilibrium. Furthermore, we illustrate how to induce a socially optimal charging behavior by deriving the socially optimal plug-in fees and electricity prices at the charging stations.