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Electric systems are experiencing fast development, mainly motivated by the carbon reduction policies in the energy sector and the technological developments that introduce new elements and processes. The transition to active distribution networks (ADNs) represents a significant technological advancement in this ever-evolving context. Accurate models for each device present in ADNs are crucial for adequately representing their dynamics; however, load modeling poses challenges due to the vast diversity of load components, variations over time, and dependence on several factors. Despite these challenges, understanding load behavior is fundamental for efficient planning and operation of ADNs. Therefore, precise load models are indispensable for conducting preventive and forensic studies. This paper analyzes various scientific documents from the most relevant scientific databases, explicitly focusing on the challenge of measurement-based load modeling in ADNs. The main contribution of this document lies in enhancing the representation and understanding of loads in ADNs through the analysis of current approaches, challenges, and measurement-based modeling strategies. Additionally, it serves as a reference for future research in the field of load modeling. [ABSTRACT FROM AUTHOR]

Fast and accurate power-flow methods are of great importance, especially in near real-time optimal operation of power systems. This importance will be even more highlighted in the presence of more repetitions of power-flow calculations, which cause more computational complexities in optimization problems. As a solution, in this paper, a novel fast and accurate approach of linear power-flow formulation is proposed. Principles of the proposed approach are based on dividing power-flow calculations into base and variable parts. To this aim, at first, system modeling of base and variable parts are presented. For the base-part modeling, utilizing a nonlinear power-flow, an accurate base power-flow (BPF) is extracted. Afterwards, by linearizing the power system around the BPF, variable-part model which is the result of a linear fitting process, is obtained. Then, it is shown that the variable-part of the operating point is always a function of the obtained base-part and variable-part models. In this paper, by focusing on the stochastic application of the proposed approach, different uncertainties in a distribution system are considered. Finally, numerical results carried out in the Matlab environment, for a IEEE 34-bus standard distribution system and then a 1486-bus case study, verify the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is devoted to electric arc furnace (EAF) modeling using a random differential equation based on the power balance equation. The proposed approach broadens and improves the model through the introduction of stochastic processes in place of existing coefficients. The paper presents a method which enables the estimation of EAF model coefficients with the help of measurement data - voltage and current waveforms recorded during the melting stage of an EAF work cycle. The estimation process is conducted with a Monte Carlo method and genetic algorithm, which is applied iteratively to each of the defined frames of the input signal. The estimated coefficients have been analyzed with respect to their time variability as well as the probability distributions of their values and increments. The results have been extensively visualized. Next, the identification of the stochastic processes representing the model coefficients has been carried out. Based on the previous results and autocorrelation functions, the density functions and parameters of discrete-time stochastic processes were identified. The paper presents solutions validated with statistical tests. [ABSTRACT FROM AUTHOR]

In many power systems, the increased penetration of inverter-based renewable generation will cause a decrease in kinetic energy storage, leading to higher frequency excursions after a power disturbance. This is the case of the future Nordic Power System (NPS). The look-ahead study reported in this paper shows that the chosen units participating in Frequency Containment Reserves (FCR) cannot keep the frequency above the prescribed threshold following the outage of the largest plant. This analysis relies on a detailed model of the Northern European grid. The latter is compared to the classical single-mass equivalent, and the impact of voltage-dependent loads is assessed in some detail. Next, the paper focuses on emergency power control of the HVDC links that connect the NPS to the rest of the European grid, which can supplement or even replace part of the FCR. The proper tuning of that control is discussed. Finally, the analysis is extended to the HVDC links connecting the future North Sea Wind Power Hub under two configurations, namely low and zero inertia. The impact of outages in the latter sub-system is also assessed. The material to simulate the system with industrial software is made publicly available. [ABSTRACT FROM AUTHOR]

Analogous to the way a good driver is aware of neighboring cars, electrical loads can coordinate with other loads within a building or section of a distribution grid. This paper develops methods that enable groups of cyclic loads (devices that turn on and off periodically to maintain setpoints) to reduce their peak aggregate power demand. The methods accommodate a wide variety of cyclic loads, including those with nonlinear or unknown dynamics, and can be implemented in a fully distributed fashion. This paper targets settings with a few hundred cyclic loads or fewer, where the methods developed here could reduce demand peaks significantly while maintaining or improving quality of service. This could save ratepayers money on monthly demand charges, decrease fuel use in microgrids, or extend the life of power delivery equipment. [ABSTRACT FROM AUTHOR]

Time-of-use (TOU) is an effective price-based demand response strategy. A reasonable design of TOU strategy can effectively reduce the peak-valley difference, and then produce a lot of benefits (such as delaying power grid investment, reducing interruption cost, and improving reliability). However, changing peak-valley period has a great influence on the peak-valley difference and power supply reliability of power system. Therefore, this paper aims to investigate the optimal modification of peak-valley period considering reliability loss under multiple TOU schemes. Firstly, this paper presents a clustering model and algorithm of optimal load curve based on a minimum error iteration method. Secondly, an optimal modification of peak-valley period based on a dynamic load point method is proposed, and the traditional peak-valley difference is replaced by the global peak-valley difference to calculate the objective function. Thirdly, this paper establishes a load–reliability relation fitting model based on the back propagation neural network. Finally, the effectiveness and correctness of the proposed method are investigated by the Roy Billinton test system and reliability test system. [ABSTRACT FROM AUTHOR]

In the coded caching problem, as originally formulated by Maddah-Ali and Niesen, a server communicates via a noiseless shared broadcast link to multiple users that have local storage capability. In order for a user to decode its demanded file from the coded multicast transmission, the demands of all the users must be globally known, which may violate the privacy of the users. To overcome this privacy problem, Wan and Caire recently proposed several schemes that attain coded multicasting gain while simultaneously guarantee information theoretic privacy of the users’ demands. In Device-to-Device (D2D) networks, the demand privacy problem is further exacerbated by the fact that each user is also a transmitter, which appears to be needing the knowledge of the files demanded by the remaining users in order to form its coded multicast transmission. This paper shows how to solve this seemingly infeasible problem. The main contribution of this paper is the development of new achievable and converse bounds for D2D coded caching that are to within a constant factor of one another when privacy of the users’ demands must be guaranteed even in the presence of colluding users (i.e., when some users share cached contents and demanded file indices). First, a D2D private caching scheme is proposed, whose key feature is the addition of virtual users in the system in order to “hide” the demands of the real users. By comparing the achievable D2D private load with an existing converse bound for the shared-link model without demand privacy constraint, the proposed scheme is shown to be order optimal, except for the very low memory size regime with more files than users. Second, in order to shed light into the open parameter regime, a new achievable scheme and a new converse bound under the constraint of uncoded cache placement (i.e., when each user stores directly a subset of the bits of the library) are developed for the case of two users, and shown to be to within a constant factor of one another for all system parameters. Finally, the two-user converse bound is extended to any number of users by a cut-set type argument. With this new converse bound, the virtual users scheme is shown to be order optimal in all parameter regimes under the constraint of uncoded cache placement and user collusion. [ABSTRACT FROM AUTHOR]

Enhancing power electronics (PE) converter reliability is crucial for ensuring a reliable operation of current and future operating Wind Turbines (WTs). Achieving high reliability of variable speed WT PE systems requires careful consideration of their operation, and particularly their thermal cycling. This paper presents a methodology for evaluating and reconsidering operational strategies of WTs with relation to the thermal loading and lifetime consumption of the converter. The methodology is applied to compare control strategies for the WT generator and evaluate their impact on the converter reliability by observation of the thermal cycles and by calculating the resultant lifetime consumption of those stress cycles. The thermal stress on both the Machine Side Converter (MSC) and the Grid Side Converter (GSC) is examined and compared. It is shown that the least reliable of the three evaluated control strategies is the one that tracks the power curve below rated speed most closely. This paper suggests that dynamic transients associated with the WT control largely influence the IGBT module wear-out and their modelling needs to be prioritized for lifetime studies. These dynamic transients are captured by the improved model whose value is confirmed for the comparisons in the case study of the paper. [ABSTRACT FROM AUTHOR]

Distribution power systems (DPSs) are generally unbalanced, and their loads may have notable static voltage characteristics (ZIP loads). Hence, although many papers have focused on linear single-phase power flow models, it is still necessary to study linear three-phase distribution power flow models. This paper proposes a data-driven-aided linear three-phase power flow model for DPSs. We first formulate how to amalgamate data-driven techniques into a linear power flow equation to establish our linear model. This amalgamation makes our linear model independent of the assumptions commonly used in the literature (e.g., nodal voltages are nearly 1.0 p.u.); therefore, our model is characterized by relatively high accuracy, even when the assumptions become invalid. We then demonstrate how to apply our model to DPSs with ZIP loads. We also show that with the Huber penalty function employed, the adverse impact of bad data on our model's accuracy is significantly reduced, rendering our model robust to poor data quality. Case studies demonstrate that our model is generally more accurate, with 2- to 100-fold smaller errors, than most existing linear models, and remains fairly accurate even under poor data conditions. Our model also contributes to a rapid solution to DPS analyses and optimization problems. [ABSTRACT FROM AUTHOR]

Reliability-centered maintenance (RCM) as a subset of the reliability assessment problems, is a powerful tool for enhancing reliability, and subsequently achieving the customers’ higher satisfaction. However, deterministic RCM models could scarcely guarantee global optimality and feasibility of their solutions with real-world uncertain failure rates. In this paper, a robust model is proposed to consider the impact of failure rate uncertainty in the RCM scheduling problem, followed by a two-stage robust model development. The two-stage robust model is solved using Benders decomposition (BD) and outer approximation (OA) algorithms. The proposed model and solution method are applied to both educational RBTS2 system and real-size Finnish Distribution System, followed by demonstration of a higher financial and reliability performance, compared to that of the deterministic model. Sensitivities of the costs, available budget, uncertainty interval and computational time are analyzed and discussed, to conclude the paper. [ABSTRACT FROM AUTHOR]

In this paper, a new modulation strategy based on the carrier-based switching strategy for the non-square direct matrix converters (MC) is proposed to control the active power of distributed generation (DG) units. In this strategy, the active power of DGs is controlled by the central input current control of the non-square direct MC independent from the voltage and frequency. Conventionally, each DG has a converter, and for supplying a load with N number of DGs, N number of converters are needed and each converter has its own modulation switching and control strategy to control the power output of each DG. Needless to say, in a microgrid with N number of DGs, the control strategy of each converter has more complex structure than that of a microgrid with one converter, and surely the former strategy entails more volume and price. Using the proposed converter in this paper, it is possible to supply a load with N number of DGs through one converter. Also, the power outputs of all DGs are controlled by a central control strategy. The proposed central control strategy is described and simulated for a typical microgrid. Experimental and simulation results validate the effectiveness of the proposed converter and the proposed strategy. The results demonstrate the applicability and efficiency of the system and verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

There is an opportunity in modern power systems to explore the demand flexibility by incentivizing consumers with dynamic prices. In this paper, we quantify demand flexibility using an efficient tool called time-varying elasticity, whose value may change depending on the prices and decision dynamics. This tool is particularly useful for evaluating the demand response potential and system reliability. Recent empirical evidences have highlighted some abnormal features when studying demand flexibility, such as delayed responses and vanishing elasticities after price spikes. Existing methods fail to capture these complicated features because they heavily rely on some predefined (often over-simplified) regression expressions. Instead, this paper proposes a model-free methodology to automatically and accurately derive the optimal estimation pattern. We further develop a two-stage estimation process with Siamese long short-term memory (LSTM) networks. Here, a LSTM network encodes the price response, while the other network estimates the time-varying elasticities. In the case study, the proposed framework and models are validated to achieve higher overall estimation accuracy and better description for various abnormal features when compared with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Mechanical elastic wheel (MEW) has the advantage of explosion-proof, which helps to guarantee the safety and maneuverability of the automobile. Aiming to improve the stability of vehicles matching with MEW, this paper proposes an integrated control strategy that combines the active front steering and the active suspension systems. The integrated controller consists of feed-forward and feedback controllers. Firstly, the differential flatness system of the vehicle is constructed concerning the coupling among yaw, lateral, and roll motion. And the flatness based feed-forward control inputs of the desired front wheel angle and active roll moment are derived. At the same time, the backstepping-adaptive feedback controllers for yaw rate and roll angle are designed. Then, the feed-forward and feedback controllers are coordinated and their weight coefficients are adjusted according to the sideslip angle. Furthermore, this paper also adopts a nonlinear disturbance observer to estimate the vertical load of MEW. The influence of the vertical load is fully considered when estimating the equivalent cornering stiffness of each MEW, so as to realize the online adjustment of the controller parameters. Finally, the maneuver tests of step input steering and double lane change are simulated, respectively. The results show that the proposed control strategy yields a better control effect than the fuzzy-PID controller, and the performance of the vehicle matching with MEW has been significantly improved. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) have attracted enormous attention in recent years due to their potentials in mitigating energy crisis and air pollutions. However, the long battery charging time and lack of sufficient charging infrastructure highly restrict the popularization of EVs. In this context, it is promising to establish battery charging and swapping systems (BCSSs) based on the concept of battery swapping services. To optimally achieve the combined operation of BCSSs, this paper proposes a hybrid swapped battery charging and logistics dispatch model in continuous time domain. Identifying the special structure of the mathematical models of the two problems, this paper innovatively formulated the swapped battery charging strategy as the rectangle packing problem and the battery logistics model as the vehicle routing problem. The two models are closely linked by the delivery time of transporting the well-charged batteries from battery charging stations to battery swapping stations. A hybrid optimal operation model of BCSSs is further formulated as a mixed-integer linear programming model by incorporating the interaction between the battery charging and battery logistics. Finally, case studies are conducted on several BCSSs and numerical results validate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Considering the proliferation of power electronics applications and distributed energy resources, modern power grids are facing a significant increase in harmonic currents circulation and supply voltage deterioration, occasionally associated with small frequency variations. In such a context, the understanding of power phenomena in circuits with linear and non-linear loads under non-sinusoidal voltage conditions is nontrivial and still does not allow for an easy interpretation of harmonic sources, harmonic power flow or the identification of the parameters of a proper equivalent circuit. The main challenge is to develop modern theoretical approaches for load characterization, modeling, and parameter estimation so that new techniques can be formulated to provide adequate guiding for the analysis, compensation, revenue metering, accountability and other applications of power systems. Thus, based on the Conservative Power Theory (CPT) and further decomposition of its apparent power and power factor definitions, this paper proposes a novel methodology for estimating equivalent parameters and for proposing proper equivalent circuits capable of representing/modeling the main characteristics of single-phase generic loads (black boxes) and the related power phenomena in terms of passive dipoles (linear loads) or of harmonic voltage/current sources and their intrinsic transimpedances/transadmittances (non-linear loads). Simulation and experimental results were depicted to support and validate the proposed approach, showing that it might be a powerful modeling technique to represent generic loads in a modern power grid scenario, while being used for complex applications such as reactive power compensation or accountability in circuits with nonlinear loads and distorted voltages. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the users’ local caches. For the shared-link network with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded caching strategy. In practice, users may communicate with the server through intermediate relays. This paper studies the tradeoff between the memory size ${\mathsf M}$ and the network load ${\mathsf R}$ for the networks where a server with ${\mathsf N}$ files is connected to ${\mathsf H}$ relays (without caches), which in turn are connected to ${\mathsf K}$ users equipped with caches of ${\mathsf M}$ files. When each user is connected to a different subset of ${\mathsf r}$ relays, i.e., ${\mathsf K}= \binom {\mathsf H}{\mathsf r}$ , the system is referred to as a combination network with end-user-caches. In this work, converse bounds are derived for the practically motivated case of uncoded cache contents, that is, bits of the various files are directly pushed into the user caches without any coding. In this case, once the cache contents and the users’ demands are known, the problem reduces to a general index coding problem. This paper shows that relying on a well-known “acyclic index coding converse bound” results in converse bounds that are not tight for combination networks with end-user-caches. A novel converse bound that leverages the network topology is proposed, which is the tightest converse bound known to date. As a result of independent interest, an inequality that generalizes the well-known sub-modularity of entropy is derived. Several novel caching schemes are proposed, based on the Maddah-Ali and Niesen cache placement. These schemes leverage the structure of the combination network or/and perform interference elimination at the end-users. The proposed schemes are proved: (i) to be (order) optimal for some $({\mathsf N}, {\mathsf M}, {\mathsf H}, {\mathsf r})$ parameters regimes under the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations. [ABSTRACT FROM AUTHOR]

A suitable probabilistic scenario set of load demand and natural characteristics of renewable energy is becoming a crucial issue in power system planning studies. Properly addressing the impact of potentially thousands of residential PV plants on the resilience and reliability needs of substations necessitates the representation of inherent relations between photovoltaics and the load throughout the long-term planning period. The optimal planning of substation expansions is achievable through proper modeling of input parameters which describes the characteristics of the service areas. In this paper, the co-existence of PV plants and the load in a service area under three different states such as daytime with clear-sky and no-fault, daytime with abnormal events, and nighttime are incorporated into the stochastic dynamic optimization problem by using scenario-based approach. The scenario tree of the problem is branched from three different bases simultaneously instead of only one as in conventional approach. This paper also combines the risk-constrained stochastic dynamic SEP problem and Mixed Integer Linear Programming (MILP) framework under one roof. The comparison between integrating inherent characteristics of PV plants with and without considering abnormal events into the optimization is performed to show the impact of suitable probabilistic model on dynamic nature of investment decisions. [ABSTRACT FROM AUTHOR]

The critical nature of vehicular communications requires their extensive testing and evaluation. Analytical models can represent an attractive and cost-effective approach for such evaluation if they can adequately model all underlying effects that impact the performance of vehicular communications. Several analytical models have been proposed to date to model vehicular communications based on the IEEE 802.11p (or DSRC) standard. However, existing models normally model in detail the MAC (Medium Access Control), and generally simplify the propagation and interference effects. This reduces their value as an alternative to evaluate the performance of vehicular communications. This paper addresses this gap, and presents new analytical models that accurately model the performance of vehicle-to-vehicle communications based on the IEEE 802.11p standard. The models jointly account for a detailed modeling of the propagation and interference effects, as well as the impact of the hidden terminal problem. The model quantifies the PDR (Packet Delivery Ratio) as a function of the distance between transmitter and receiver. The paper also presents new analytical models to quantify the probability of the four different types of packet errors in IEEE 802.11p. In addition, the paper presents the first analytical model capable to accurately estimate the Channel Busy Ratio (CBR) metric even under high channel load levels. All the analytical models are validated by means of simulation for a wide range of parameters, including traffic densities, packet transmission frequencies, transmission power levels, data rates and packet sizes. An implementation of the models is provided openly to facilitate their use by the community. [ABSTRACT FROM AUTHOR]

The degradation of the electrical contact in a gas insulated switchgear (GIS) is closely related to overheating at the contact. However, the disconnector contact is one of the hot contacts in GIS. Therefore, in this paper, the finite element method was used to solve the three-dimensional multiphysics coupling temperature rise field and flow field in the Single Phase in One Tank (SPIOT) type GIS disconnector under different operating conditions. From the perspective of temperature rise field and flow field, this paper analyzed the temperature rise characteristics under different working conditions and explored the feasibility of the direct application of air, CO2 and C4F7N/CO2 mixed gas to an electrical device. The disconnector temperature rise experiment platform was then built to verify the simulation. The results showed that the temperature rise field and the flow field distribution were similar in four gas environments. SF6 gas had the smallest temperature rise, followed by C4F7N/CO2 mixed gas, and the temperature rise of CO2 and air was relatively large. Therefore, from the perspective of the temperature rise field and flow field, it was feasible to directly apply C4F7N/CO2 mixed gas to an electrical device in order to meet insulation requirements. [ABSTRACT FROM AUTHOR]

In distributed key-value stores, multiple replica servers are always available for each key-value access operation when the eventual consistency model is employed. Accordingly, the completion times of the key-value access operations generated by an end-user request at different servers may be of great difference, especially when the replica servers are heterogeneous and have time-varying performance. Accordingly, the replica selection algorithm is crucial to cut the response time of end-user requests. The main challenge of making replica selection for each light-weighted key-value access operation is to timely know the status of replica serves. Recently, the adaptive replica selection algorithm C3 suggests guiding the replica selection with the piggybacked information of replica server in the returned “value”. Although C3 has good performance, the poor timeliness of feedback information makes a large performance gap between C3 and the ideal replica selection algorithm. To narrow this gap, the Accelerated Information Dissemination (AID) mechanism is proposed in this paper. Specifically, AID removes the bottleneck of information dissemination at the “slow” servers by letting both “client” and “replica server” store the records about the status of replica servers and both “key” and “value” piggyback multiple records. AID is implemented in Cassandra and evaluated by experiments and large scale simulations. The results show AID can significantly improve the timeliness of feedback information, especially when the number of nodes is large. Accordingly, AID helps C3 to greatly reduce the latency. [ABSTRACT FROM AUTHOR]

By empowering consumers and enabling them as active players in the power and energy sector, demand flexibility requires more precise and sophisticated load modeling. In this paper, a laboratory testbed was designed and implemented for surveying the behavior of laboratory loads in different network conditions by using real-time simulation. Power hardware-in-the-loop was used to validate the load models by testing various technical network conditions. Then, in the emulation phase, the real-time simulator controlled a power amplifier and different laboratory equipment to provide a realistic testbed for validating the load models under different voltage and frequency conditions. In the case study, the power amplifier was utilized to supply a resistive load to emulate several consumer load modeling. Through the obtained results, the errors for each load level and the set of all load levels were calculated and compared. Furthermore, a fixed consumption level was considered. The frequency was changed to survey the behavior of the load during the grid's instabilities. In the end, a set of mathematical equations were proposed to calculate power consumption with respect to the actual voltage and frequency variations. [ABSTRACT FROM AUTHOR]

This paper presents an injected current sensitivity (ICS) based multi-phase load flow (LF) methodology with minimal Jacobian computation for the three-phase unbalanced distribution system with multiple Distributed Energy Resources (DERs). In the proposed approach, first, a generalized bus admittance and Jacobian matrix have been formulated that include various distribution system components such as lines, shunt capacitors, voltage control devices such as regulators, different transformer connections, and load models. Second, DERs are modeled as a PV bus and incorporated into the proposed LF algorithm by formulating a reactive power injection-based sensitivity matrix that iteratively computes its net power injections. Unlike the traditional Jacobian matrix-based LF methods where an update of Jacobian (size and element) is required for each PV bus, this method does not require any update, hence, making it faster and more flexible to include a large number of DERs. From the various tests performed on the standard IEEE three-phase distribution network and their derivatives, it has been observed that the proposed approach is accurate, efficient, computationally less complex, and scalable. [ABSTRACT FROM AUTHOR]

The increasing penetration of distributed renewable energy sources drastically alters the dynamic characteristics of distribution networks (DNs). Therefore, several equivalent models have been recently proposed, to analyze more accurately the complex behavior of modern DNs. However, relatively simple models are still commonly used in practice for dynamic power system studies. In addition, dynamic equivalent models for DNs are sensitive to different operating conditions and there is lack of systematic understanding of their performance. Scope of this paper is to propose a methodology for identifying the applicability range in terms of accuracy and generalization capability of several conventional and newly developed equivalent models for the dynamic analysis of modern DNs. A set of metrics is used for the modelling accuracy assessment and a sensitivity analysis framework is introduced to fully quantify the generalization capabilities of DN equivalent models. Based on the above, guidelines and recommendations for the development of robust equivalent models for DN analysis are proposed. [ABSTRACT FROM AUTHOR]

In the conventional sliding mode control, the four-leg distribution static compensator (DSTATCOM) currents are controlled based on a current error in each phase. However, the four currents in a four-wire system can not be independently controlled variables and hence one of the four controllers is redundant in conventional schemes. Further, the current dynamics of a DSTATCOM converter are coupled through converter pole voltages in the natural reference frame. This leads to cross-coupling in the sliding variable equations with respect to four manipulated input variables. Considering the above points, in this paper, the current due to Thevenin’s equivalent load neutral-point voltage is considered as a fourth independent controlled variable and the corresponding system dynamic equations are presented. To get a decoupled feature, a new sliding surface function is structured. The performance of a DSTATCOM with the proposed control scheme under various operating conditions is validated through a detailed simulation study and experimental results, obtained from a laboratory prototype of four-leg DSTATCOM. [ABSTRACT FROM AUTHOR]

To test electric devices such as household appliances, electric vehicle and other loads, there is need for emulators instead of real devices, which decreases the cost of testing. This paper presents a dynamically programmable load emulator that imitates the current–time characteristic of different types of the loads. The exact mathematical model of various types of electric loads is firstly extracted. These mathematical models are implemented by LabVIEW software. A non-ideal buck converter is used for the hardware part of the emulator, which is controlled by LabVIEW. The proposed emulator can mimic the types of loads given by LabVIEW software with great accuracy and is an example of an actual load simulator with good approximation. Manufacturers or laboratories of electric equipment can use the proposed emulator to perform their tests instead of using the actual device. This reduces the cost of tests and speeds them up so that all types of electric loads can be modeled with an emulator. In addition, because a simple power electronic converter structure is used, the proposed emulator has low complexity and low manufacturing cost. Simulation and laboratory results prove the efficiency of this emulator in making models of different types of loads. [ABSTRACT FROM AUTHOR]

Machine Learning (ML) workloads are increasingly deployed at the edge. Enabling efficient inference execution while considering model and system heterogeneity remains challenging, especially for ML tasks built with a network of deep neural networks (DNNs). The challenge is to maximize the utilization of all available resources on the multiprocessor system on a chip (MPSoC) at the same time. This becomes even more complicated because the optimal mapping for the network of DNNs can vary with input batch sizes and scene complexity. In this paper, a holistic hierarchical scheduling framework is presented to optimize the execution time for a network of DNN models on an edge MPSoC at runtime, considering varying input characteristics. The framework consists of a local and a global scheduler. The local scheduler maps individual DNNs in the inference pipeline to the best-performing hardware unit while the global scheduler customizes an Integer Linear Programming (ILP) solution to instantiate DNN remapping. To minimize scheduler runtime overhead, an imitation learning (IL) based scheduler is used that approximates the ILP solutions. The proposed scheduling framework (CAMDNN) was implemented on a Qualcomm Robotic RB5 platform. CAMDNN resulted in lower execution time of up to 32% than heterogeneous earliest finish time, and by factors of 6.67X, 5.6X and 2.17X than the CPU-only, GPU-only and Central Queue schedulers. [ABSTRACT FROM AUTHOR]

With low voltage (LV) distribution networks increasingly being re-purposed beyond their original design specifications to accommodate low carbon technologies, the ability to accurately calculate their actual spare capacity is critical. Traditionally, within the Great Britain (GB) power system, there has been limited monitoring of LV distribution networks, making this difficult. This paper proposes a method for estimating spare capacity of unmonitored LV networks using demand data from customer Smart Meters. In particular, the proposed method infers existing LV network capacity, as well as losses, across scenarios where only a limited number of customers have Smart Meters installed. Typical daily load profiles across customers with Smart Meters are learned using a Dirichlet sampled Gaussian mixture model (GMM). Learned profiles are then applied to all unmetered customers to estimate network parameters. Method accuracy is assessed by comparing estimations with simulated, fully observed, LV network models. The method is also compared to benchmark models for establishing unobserved demand profiles. Overall, results in the paper show that the proposed method outperforms benchmark models in terms of accurately assessing substation headroom, particularly in scenarios where only 10–50% of customers have Smart Meters installed. [ABSTRACT FROM AUTHOR]

This paper provides an overview of hyperloop technologies, including a brief discussion of key components of a hyperloop system that determine the electric power requirements as a function of time. At-scale hyperloop systems do not yet exist, so a model was used to generate a set of load profiles for conceptual hyperloop realizations at four locations in the United States: two systems in California and one each in Colorado and Ohio. In all four cases, the modeled hyperloop load profiles included pulses in both active and reactive power. Grid modeling was performed to estimate the grid impacts and for discussing grid integration challenges. The paper discusses how energy storage systems might be used to eliminate the pulsating load characteristics or significantly reduce it to accommodate current grid planning guidelines. [ABSTRACT FROM AUTHOR]

Thermostatically controlled loads (TCLs) are regarded as one of the promising resources for suppressing power fluctuations due to renewable energy (RENs). However, due to the great burdens of fully considering each users’ characteristics, it is difficult to achieve unity of the individual optimal decisions and global optimum in demand-side management (DSM). This paper proposes a game-theoretic DSM that can optimize the global power consumption schedule by individual TCL user's optimization. By integrating the prediction of REN outputs into the pricing mechanism, the proposed DSM can guide the users to make their best power consumption schedules along with intermittent REN generations, thus to smooth the tie-line power of microgrids. In this paper, a novel pricing mechanism is firstly developed based on the concave N-person game theory, which is more adaptive and flexible compared with existing game-theoretic DSM. Then, an individual's power consumption optimization and its simplified model are developed considering the constraints of the TCL model and personal preferences. The simplified model can be easily solved and achieve a fast solution in the power consumption game. An implementation framework of the proposed DSM is further developed for practical application. Finally, numerical studies verify the effectiveness of the proposed models and methods. [ABSTRACT FROM AUTHOR]

Utility-scale and small scale wind and solar power installations along with electric vehicle charging stations, and other active sources of energy are increasing at the medium and lower voltage levels in the distribution grid. This situation requires a better understanding of the impact of high penetration of weather-dependent renewable energy sources on the operating conditions of the distribution network at both medium and low voltage levels. Despite the need, a multi-voltage level distribution network model, based on real network data and weather-dependent renewable generation data, has not been presented for distribution grid studies. This paper presents a comprehensive multi-voltage level active distribution network model based on real network data along with load and generation time-series for about a year. The network topology is modelled based on geographical data for various rural, semi-urban, and urban locations. The distribution network is embodied with a large share of renewable generation sources, with generation time-series simulated from meteorological data. The network is also flexible to incorporate other assets such as electric vehicle charging stations, storage, etc. The presented active distribution network model can be used to study, optimize, and control the effects of weather-dependent generation and other network assets in the distribution grid. [ABSTRACT FROM AUTHOR]

In traditional power systems, the load consumption inside the distribution networks has a relatively passive behavior. Consequently, transmission system operators have commonly aggregated the load centers using static loads such as exponential load models. This is a practical approach for bulk power system stability studies. In modern systems, the impact of distributed generation units on the system dynamics can no longer be neglected. Static load models fall short to represent the highly dynamic behavior of active distribution networks. This paper proposes a methodology for equivalencing such networks while conserving the dynamics of interest for long-term stability studies. The methodology is based on Hammerstein-Wiener models that use only boundary variables measured at the distribution network point of common coupling. Therefore, unlike gray-box models, no previous knowledge about the system is required. Furthermore, the proposed methodology has a transparent relationship to linear systems and a convenient block representation that can be implemented in commercial power system analysis software using only standard elements. This allows for easy implementation, overcoming a barrier for a rather conservative sector such as power systems planning and operation. The conclusions are derived from time-domain simulations on the IEEE test system for voltage stability assessment. [ABSTRACT FROM AUTHOR]

Ensuring long-term voltage stability is critical for reliable operations of power grids. High share of distributed energy resources (DERs) can create complicated system operation modes that may invalidate the traditional long-term voltage stability analysis based on typical operation modes. To address this challenge, this paper investigates how to compute the shortest path to the voltage stability boundary in the DER aggregated load space with large dispersion. Instead of working in the Euclidean space, we establish the analysis and computations on the algebraic power flow manifold to better capture the curvature change of the shortest path along the direction of losing stability. A modified optimal control framework is presented for obtaining the ground-truth of the smooth shortest path on the manifold. To efficiently and accurately solve for the shortest path, we further leverage the geometric features of the power flow manifold and propose a tri-sectional approximation model that is scalable for large-scale systems. Several numerical examples, up to the 1354-bus system, with different DER penetration levels and high dimensional renewable power injection variations are evaluated. The simulation results demonstrate that the tri-sectional approximation achieves high accuracy and efficiency to approximate the shortest path to the voltage stability boundary. [ABSTRACT FROM AUTHOR]

Evaluation of conservation voltage reduction (CVR) factor is critical to peak load reduction, 556 energy conservation, and many CVR-related power system control/optimization strategies. This paper proposes a novel robust CVR factor evaluation method using soft constrained gradient analysis based on time-varying load modeling and real utility field measurements. Firstly, the time-varying ZIP parameter identification is formulated as an over-determinant problem composed of first-order gradient with respect to each coefficient and soft constraints representing temporal correlation of loads in each time step, in order to improve the robustness and smoothness of CVR factor evaluation. Then, problems in time series are coordinated with a sliding window approach. A necessary condition for selecting the smallest window size is proposed and strictly proved to guarantee the existence and uniqueness of the solution of time-varying load modeling problem. Finally, time-varying CVR factors are accurately and robustly calculated with field measurements and the identified load model. Case studies are performed using sufficient field measurements obtained from two real utilities. Unlike existing methods that require a large number of measurements to obtain precise estimation of CVR factor, the proposed method is sufficiently accurate even when the measurements are limited or of low time resolution. Further, the accuracy and robustness of the proposed approach are validated under different types of uncertainties and compared with other existing data processing and CVR factor evaluation methods. [ABSTRACT FROM AUTHOR]

Network reconfiguration (NR) has attracted much attention due to its ability to convert conventional distribution networks (DNs) into self-healing grids. This paper proposes a new strategy for real-time voltage regulation (VR) in a reconfigurable DN, whereby optimal feedforward control of distributed generators (DGs) is achieved in coordination with the operation of line switches (SWs). This enables preemptive compensation of upcoming deviations in DN voltages resulting from NR-aided load restoration. A robust optimization problem is formulated using a dynamic analytical model of NR to design the feedforward voltage controllers (FVCs) that minimize voltage deviations with respect to the H∞ norm. Errors in the estimates of DG modeling parameters and load demands are reflected in the design of optimal FVCs via polytopic uncertainty modeling. Small-signal analysis and case studies are conducted, verifying the effectiveness and robustness of the optimal FVCs in improving real-time VR when NR is activated for load restoration. The performance of the proposed FVCs is confirmed under various conditions of a self-healing DN,characterized by network islanding and size, parameter errors, SW operations, and communication time delays. [ABSTRACT FROM AUTHOR]

Despite cascading failures being the central cause of blackouts in power transmission systems, existing operational and planning decisions are made largely by ignoring their underlying cascade potential. This paper posits a reliability-aware AC Optimal Power Flow formulation that seeks to design a dispatch point which has a low operator-specified likelihood of triggering a cascade starting from any single component outage. By exploiting a recently developed analytical model of the probability of component failure, our Failure Probability-constrained ACOPF (FP-ACOPF) utilizes the system’s expected first failure time as a smoothly tunable and interpretable signature of cascade risk. We use techniques from bilevel optimization and numerical linear algebra to efficiently formulate and solve the FP-ACOPF using off-the-shelf solvers. Extensive simulations on the IEEE 118-bus case show that, when compared to the unconstrained and N-1 security-constrained ACOPF, our probability-constrained dispatch points can significantly lower the probabilities of long severe cascades and of large demand losses, while incurring only minor increases in total generation costs. [ABSTRACT FROM AUTHOR]

The wide variety of inverter control settings for solar photovoltaics (PV) causes the accurate knowledge of these settings to be difficult to obtain in practice. This paper addresses the problem of determining inverter reactive power control settings from net load advanced metering infrastructure (AMI) data. The estimation is first cast as fitting parameterized control curves. We argue for an intuitive and practical approach to preprocess the AMI data, which exposes the setting to be extracted. We then develop a more general approach with a data-driven reactive power disaggregation algorithm, reframing the problem as a maximum likelihood estimation for the native load reactive power. These methods form the first approach for reconstructing reactive power control settings of solar PV inverters from net load data. The constrained curve fitting algorithm is tested on 701 loads with behind-the-meter (BTM) PV systems with identical control settings. The settings are accurately reconstructed with mean absolute percentage errors between 0.425% and 2.870%. The disaggregation-based approach is then tested on 451 loads with variable BTM PV control settings. Different configurations of this algorithm reconstruct the PV inverter reactive power timeseries with root mean squared errors between 0.173 and 0.198 kVAR. [ABSTRACT FROM AUTHOR]

This paper proposes a reconstruction algorithm for the geometric shapes of static overhead transmission lines that is based on the spatial coordinate data (obtained by field mapping) and the corresponding inclination data (obtained by attitude sensors). The algorithm takes the piecewise cubic Hermite interpolation function as the basic framework and corrects the aforementioned two types of data based on the “minimum energy principle” of the transmission line system. The introduction of a new energy function in modified energy method (MEM) overcame the shortcomings of conventional energy method (CEM) in fairing strategy, and the new Fairing Criterion made result curves more consistent with the mechanical properties of transmission lines. In the numerical simulation tests, the two energy methods were compared in terms of load type, horizontal span, elevation difference, and anti-disturbance ability, which showed that MEM has a higher reconstruction accuracy (average Euclidean distance is less than 1 cm) and better robustness than CEM. Meanwhile, the key parameters involved in the algorithm were discussed to guide the application in practical engineering. In addition, measurement tests under non-uniform icing were carried out in the field test station, and the results showed that the maximum relative error is less than 0.1%. [ABSTRACT FROM AUTHOR]

Existing non-intrusive load identification methods face with the difficulty of being applied to industrial users whose operation and ON/OFF status are hard to be acquired. Focusing on the above challenge, this paper proposes a non-intrusive identification method of harmonic source loads for industrial users. Utilizing Clarke transform, an equation with respect to voltage and current is formulated to calculate the integrated equivalent impedance, which is then decomposed with the improved complex local mean decomposition (CLMD) and complex fast independent component analysis (C-FastICA) achieving non-intrusive separation of the equivalent impedance signals of individual branches. The separated impedance signals will be used as the basis for load type identification. The proposed method is validated by numerical simulations as well as actual three-phase voltage and current monitoring data. The case study shows that it can effectively identify the types of harmonic source loads while being resistant to noise and impacts of sampling accuracy and diverse load capacities, which obviously demonstrates its practical applicability. [ABSTRACT FROM AUTHOR]

Electricity distribution companies are in-charge-of supplying stable electric energy to urban customers over a wide geographical area. In these distribution networks, large number of Distribution-Transformers (DTs) are installed on towers or in electric-rooms with the ratings below 1000 kVA, which are the most important assets of distribution companies. Periodic maintenance and test services are not economically feasible for all in-operation transformers. Hence, estimating the remaining useful life and scheduling the maintenance times of DTs are of great technical and economic importance. An analytical approach is presented in this paper for predicting lifetime of DTs based on degree of polymerization. An appropriate Machine-Learning (ML) algorithm trained by measured data is selected for forecasting driven load according to the ambient temperature and humidity and day-hour schedules. The relation of Hot-Spot-Temperature in IEC60076∼7 is modified based on the measured data for accounting unbalanced-loading. Neutral-current is predicted using a trained ML-model. Another approach is proposed for determining times of oil filtering services aiming to minimize the maintenance cost and maximizing the remaining life. The proposed lifetime estimation method is validated by comparing its results with the damaged DT data of a sample network chosen as the case studies for this research, i.e., Bushehr province, Iran. [ABSTRACT FROM AUTHOR]

In DC distribution networks, the uncertainties of renewable energies and loads cause frequent voltage fluctuations. In this paper, a voltage regulation strategy based on the combined coordination of centralized optimal control (COC) and adaptive droop control (ADC) is proposed for droop-controlled DC distribution networks. In the COC strategy, the operation reference power of voltage source converters (VSCs) is optimized using the bus injection power measurements to improve the voltage profile and balance the power loading rates of different VSCs. The VSC capacity margin constraint is established to ensure that the capacity margin of each VSC is sufficient to cope with the unexpected fluctuation of loads and renewable energies. Then, an ADC strategy is adopted to handle voltage fluctuation between adjacent two COCs. In the ADC strategy, the operation reference power of the VSCs is further adjusted to recover the voltages. The voltage regulation is achieved based on the relationship among the VSC voltages and the minimum/maximum voltages of the whole network, which does not depend on the information of each nodal voltage and thus real-time network communication is avoided. The simulation results show that the proposed voltage regulation strategies can effectively improve the voltage profile under various uncertain environments. [ABSTRACT FROM AUTHOR]

With the new feature of multi-energy coupling and the advancement of the energy market, Energy Internet (EI) has higher requirements for the efficiency and applicability of integrated energy response. This paper proposes an indirect multi-energy transaction (IMET) to promote multi-energy collaborative optimization in local energy market (LEM) and improve energy utilization through personalized responses from We-Energies (WEs). Firstly, an indirect customer-to-customer multi-energy transaction is modeled for local multi-energy coupling market which can satisfy privacy, preference and autonomy of users. The efficiency of energy matching can be promoted through the participation of conversion devices. In addition, multi-time scale hybrid trading mechanism is constructed with the consideration of the transmission speed of different energy sources. Meanwhile, energy transaction process is built as a Markov decision process (MDP) with deep reinforcement learning algorithm so that the system modeling error can be successfully avoided. Furthermore, a distributed training structure is utilized to obtain more experience for a wider range of scenarios. The results of numerical simulations demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Renewable generation has grown rapidly these years due to its advantages in low environmental impacts. Stand-alone microgrid with renewable generation and energy storage is a promising option in remote areas beyond the reach of an existing power grid. This paper proposes a multiobjective optimization model to co-optimize the sizes of renewable generation and energy storage in stand-alone microgrids, which minimizes the load shedding risk and the total investment cost. The load shedding degree is obtained by an optimal operation problem and measured by shortfall risk, considering the uncertainties of demand and renewable resources. To deal with the inaccurate empirical distribution, distributionally robust shortfall risk is further established under a Wasserstein-metric-based ambiguity set, and an equivalent distributionally robust formulation is obtained. Then a conservative approximation is developed, and the resulting problem appears to be a bi-objective linear program. The Pareto frontier is proven to be piecewise linear, and the analytical expression of the Pareto frontier is derived. Case studies demonstrate the effectiveness and performance of the proposed method. [ABSTRACT FROM AUTHOR]

With the power system operating close to its stability margin, the increased penetration of renewable resources and loads with diverse characteristics, appropriate stability studies, and control decisions have become crucial. Due to the importance of accurate representation of aggregate loads in such studies, research interests for load modeling have increased. This paper puts forward a novel measurement-based load modeling approach that adapts itself based on the complex dynamics exhibited by the installed aggregate loads. The proposed approach primarily utilizes the collected measurements to gain insight regarding the dynamic trend in the measurements and subsequently determines the optimal order of an equivalent system or load model capable of effectively representing the aggregate load dynamics. An advanced signal pre-processing technique is employed, which effectively suppresses the noise and also preserves the transients present in the measurements. Afterward, an adaptive dynamic load model (ADLM) accurately represents the installed aggregate load. Lastly, the Refined Instrumental Variable (RIV) approach estimates the equivalent dynamic load model parameters. The results on a 2 bus and the IEEE 118 bus networks in DIgSILENT Powerfactory and a 7 bus network in Real-Time Digital Simulator (RTDS) reveal the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

The quantification of heating, ventilation, and air condition (HVAC) system flexibility is critical to the operations of both the grid and buildings in demand response (DR) programs. However, the flexibility quantification is challenging due to the non-linearity and non-convexity of thermal dynamics associated with HVAC components. This paper proposes a novel HVAC flexibility quantification method based on a semidefinite programming (SDP) formulation. The SDP is reformulated from the non-convex problem of HVAC power optimization, and can be solved efficiently in real-time. The physics-based HVAC model is incorporated to ensure the reliability and accuracy of solutions. The quantification results are organized into an HVAC flexibility table that can provide response strategies on adjusting HVAC setpoints in response to the grid signals received. The developed response strategies minimize occupant discomfort while satisfying grid requirements. A case study of a test building model is carried out to illustrate the flexibility quantification framework and compares the performance of two DR strategies. [ABSTRACT FROM AUTHOR]

Accurate estimates of network parameters are essential for modeling, monitoring, and control in power distribution systems. In this paper, we develop a physics-informed graphical learning algorithm to estimate network parameters of three-phase power distribution systems. Our proposed algorithm uses only readily available smart meter data to estimate the three-phase series resistance and reactance of the primary distribution line segments. We first develop a parametric physics-based model to replace the black-box deep neural networks in the conventional graphical neural network (GNN). Then we derive the gradient of the loss function with respect to the network parameters and use stochastic gradient descent (SGD) to estimate the physical parameters. Prior knowledge of network parameters is also considered to further improve the accuracy of estimation. Comprehensive numerical study results show that our proposed algorithm yields high accuracy and outperforms existing methods. [ABSTRACT FROM AUTHOR]

The nonlinear and nonconvex nature of ac power flow challenges the analysis and optimization of unbalanced distribution networks. To tackle this issue, this paper proposes an online feedback-based linearized power flow model for unbalanced distribution networks with both wye-connected and delta-connected loads. The online feedback-based linearized model is grounded on the first-order Taylor expansion of the branch flow model (BFM), and updates the model parameters via online feedback by leveraging the instantaneous measurements of voltages and load consumption. Exploiting the connection structure of unbalanced radial distribution networks, we also provide a unified matrix-vector compact form of the model. The numerical tests on the IEEE 123-bus test system validate its accuracy and superiority compared with other offline BFM methods. Additionally, we apply the proposed model to the optimal power flow for voltage regulation, which further demonstrates its effectiveness. [ABSTRACT FROM AUTHOR]

Recent advances in digitization, artificial intelligence, and wireless networking are revolutionizing the traditional transportation networks and the automotive industry, leading for instance to the widespread adoption of ride-sharing services and the emergence of self-driving vehicles. As a result, a considerable rise in the volume of infotainment data consumed by the vehicles’ passengers is expected. To support such traffic loads, we explore leveraging vehicles as part of the cellular infrastructure. This paper investigates and quantifies the performance gains that using Vehicle-to-Vehicle (V2V) communication to form relay clusters would enable, including (1) improving opportunistic channel access to the cellular infrastructure by relaying the cluster’s traffic through the vehicle seeing the best channel quality; and (2) balancing traffic loads across cells through cluster multihoming. We introduce a stochastic geometric model allowing us to provide a deeper understanding of the possible gains associated with cluster-based opportunistic relaying and its sensitivity to the system parameters, e.g., base station density, vehicle density on the roads, etc. We develop a natural network utility maximization problem to serve as a baseline to evaluate the performance of a simpler distributed cluster management algorithm which we show to be near-optimal. Overall the results suggest that $10-20\times$ gains in the vehicles’ shared rate can be achieved along with significant fairness improvements, while other mobile devices also benefit from the proposed network architecture. [ABSTRACT FROM AUTHOR]

The energy transition is aimed to take advantage of the operational flexibility of hydropower to extend the integration of intermittent renewable sources. Consequently, the hydrogenerators will have to operate in regimes far away from their designed best-point operation. In order to accurately assess the impact, this paper presents a useful approach to determine the overall operating efficiency of synchronous generators under intermittent operation. An accumulated average efficiency (AAE) model is proposed and compared against an alternative approach; the weighted average efficiency (WAE) model. It is found that the WAE approach produces unrealistic low efficiencies when the generator operates in synchronous condenser mode (SCM) for long periods. In general, the AAE supersedes the WAE for all the different load distributions that were investigated. This was further illustrated by a worked example and by constructing more complex load distributions. A load distribution dominated by SCM yields a difference as high as $33.18 \,\%$ , while an even distribution deviates $1.43 \,\%$ in their respective efficiencies. Finally, a yearly on-site measurement of our studied $103 \,\mathrm{MVA}$ generator’s concentrated load distribution revealed a discrepancy of $0.67 \,\%$ , which is a significant deviation considering what the operating regime would mean in terms of economic implications. [ABSTRACT FROM AUTHOR]

Frequency-domain modeling is an effective technique in the dynamic analysis of power electronic converters-based power systems. In this paper, a unified single-input single-output (SISO) loop gain modeling for the three-phase grid-tied voltage source converters (VSCs) under both symmetric and asymmetric AC grids is presented, which facilitates the physical measurement and stability analysis. Based on the linear-time-periodic (LTP) modeling technique, the harmonic admittance model of the three-phase grid-tied VSC is developed in the stationary (αβ)-frame, which accurately captures the coupling dynamics. This model can be transformed into other existing models through coordinate transformations. According to the idea of mathematical induction, a two-by-two recursive admittance matrix (RAM) model is derived, which is easy to include frequency coupling components of arbitrary order. It is illustrated that the VSC admittance is coupled with the grid admittance due to the frequency coupling effect (FCE). Furthermore, the RAM is converted to its equivalent SISO models following the concept of loop gain. The system stability is thus assessed by the SISO stability criteria (e.g., Nyquist stability criterion). In addition, the loop gain allows the traditional SISO perturbation and measurement scheme to be used for detecting the stability margin information. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above. [ABSTRACT FROM AUTHOR]

Active electricity distribution systems (AEDS) play an important role on the social welfare that is highly relies on the reliability of these systems. In this regard, maintenance management tries to decrease component failures via repairing component that are more possible to be failed in operation time. In this manuscript, a stochastic MINLP maintenance scheduling model is proposed in which the reliability of AEDS's equipment is considered through employing a three-state Markov model. This model helps us to embed the uncertainty of AEDS's equipment service restoration time by considering online monitoring system for it and FLISR functions in AEDS. In this paper, minimizing the total cost of AEDS is determined as objective function considering total customer interruption cost, total cost of energy not supplied, total cost of prevented maintenance actions, total corrective maintenance actions cost implemented in the AEDS and total cost of implementing online monitoring for AEDS's component in maintenance scheduling. The proposed framework is applied in two different cases, Case I is maintenance scheduling without online monitoring system and Case II is maintenance scheduling with online monitoring system. The aforementioned cases are implemented in an IEEE Test System as well as a real scale distribution network. Moreover, several sensitivity analyses are implemented for indicating the efficiency of the proposed model. [ABSTRACT FROM AUTHOR]