Time-varying Load Model Research Articles

Vibration stability and bifurcation analysis of spur gear systems based on time-varying backlash and random load

Gear backlash and random load affect the stability of gear transmission, which are the main factors causing meshing impact. This study presents the establishment of a six-degree-of-freedom model for the spur gear system, employing the lumped parameter theory and D'Alembert's principle. The model comprehensively incorporates the effects of time-varying meshing stiffness (TVMS), static transmission error (STE), time-varying gear backlash, and random load. The system's equations of motion are solved using the fourth-order Runge-Kutta method. Subsequently, the dynamic response of the constant backlash constant load model is compared with that of the time-varying backlash constant load model and the constant backlash random load model. This research quantitatively dissects the impact of the nonlinear characteristics of backlash and load on the dynamic response of the gear system. This analysis is conducted utilizing a variety of methods, including bifurcation diagrams, Floquet characteristic multipliers, Lyapunov exponents, phase diagrams, and Poincaré sections. The study demonstrates that fluctuations in backlash and load during meshing compromise the stability of the periodic solution, thereby escalating the complexity of predicting system motion. Moreover, observations include the jump phenomena, quasi-periodic and periodic motions, and the trajectory of the system transitioning into a chaotic state via bifurcation. This investigation serves as a valuable reference for future explorations into spur gear systems.

Time-varying traffic load model of expressway based on long-term monitored data from multiple regions — A case in central and eastern China

Traffic load is one of the main loads borne by highway transportation infrastructure, which seriously impacts the safe operation of the bridge and road. Due to the change in the external environment and government policy, the traffic load has obvious time-varying characteristics, which is the key to establishing the real traffic load model. The two main time-varying factors of traffic load are the growth of traffic volume and the evolution of vehicle weight. In the long-term research work, there is a lack of research based on continuous monitoring data for the above two factors. Therefore, this paper carries out a study on the time-varying traffic load model of expressways based on long-term monitored data from multiple regions. Firstly, the data sources of monitored 18 expressways in central and eastern China are introduced. Secondly, the Logistic model is selected as the basic model to study the growth laws of expressways from different provinces; meanwhile, the evolution of vehicle weight distribution is also analyzed and a simplified model is established accordingly. Finally, a case study of a newly opened eight-lane expressway is operated to characterize the influence of time-varying vehicles. The results show that the traffic volume and vehicle weight distribution change significantly with the increase of service time. The Logistic model and liner model are appropriate to characterize the evolution model of the traffic volume and vehicle weight distribution separately. The time-varying characteristics of traffic load have a significant impact on the standard fatigue traffic load model and the cumulative equivalent axle loads. The research results could provide a reference for the establishment of time-varying traffic load standard models for highways and the revision of related standards. At the same time, it could provide technical support for the full life-cycle investigation and design of the road and bridge infrastructure.

Probabilistic optimal planning of multiple photovoltaics and battery energy storage systems in distribution networks: A boosted equilibrium optimizer with time-variant load models

In recent years, there has been a rapid increase in distributed generation (DG) technologies incorporated into distribution networks (DNs) to meet the challenge of load growth. However, the stochastic nature of renewable energy, such as photovoltaic (PV), makes the amount of energy produced uncertain. This uncertainty, along with changes in generation and load demand, can increase energy losses and voltage instability. To address this issue, energy storage systems can be integrated to decrease the effects of the intermittency associated with renewable technologies. This paper proposes a new variant of an equilibrium optimizer (EO) based on reinforced learning, named RLEO, for optimal incorporation of multiple battery energy storage (BES) units integrated synchronously with solar PVs into distribution systems while minimizing energy loss. The RLEO algorithm employs reinforced learning mechanisms to prevent premature convergence of the EO and improve its exploration and exploitation capabilities. The performance of the RLEO algorithm is assessed using standard CEC 2017 benchmark functions and compared with the original EO and other popular algorithms using various statistical criteria. The RLEO algorithm is also applied to determine the optimal size and position of multiple PV units in IEEE 69-bus and 118-bus DNs with single and multi-objective optimization problems. Using the developed algorithm, the optimal arrangement of three non-dispatchable PVs results in a slight increase in the percentage reduction of energy loss across various load profiles: 53.0035 % for commercial, 19.6372 % for industrial, and 28.1783 % for residential. In contrast, by employing the optimal configuration of three PV + BES units, the reduction in energy loss percentage experiences a remarkable surge to 68.3466 % for commercial, 68.0917 % for industrial, and 68.1779 % for residential load scenarios using the proposed algorithm. This clearly indicates that the proposed RLEO algorithm significantly surpasses recent optimization methods documented in the literature when it comes to addressing the challenge of optimal allocation for multiple DGs. Furthermore, its applicability extends to more intricate optimization problems.

Investigating effect of various time varying load models in grid connected microgrid system integrated with renewables and cogeneration units

ABSTRACT The optimal allocation of sources considering voltage-dependent load models is essential as the power consumption of the loads is sensitive to voltage magnitude. In this paper, optimal allocation of microgrid system with cogeneration units, renewable energy sources (RES), shunt capacitors and heat boiler are determined for constant, residential, industrial, commercial and mixed load models. The cost, emission, energy loss, voltage deviation and voltage stability values for each load model is determined using particle swarm optimisation (PSO) integrated fuzzy max–min approach while the uncertainties in RES are taken into account. Results demonstrate that the cost, energy loss and voltage deviation values are maximum for constant power (CP) load model compared with other load models. Furthermore, the system with constant impedance (CZ) load achieves maximum loading capability than with other types of constant loads. The proposed method is validated on 33-bus grid-connected microgrid system with all the load models.

Optimal dynamic multi-microgrid structuring for improving distribution system resiliency considering time-varying voltage-dependent load models

This paper presents an innovative approach for enhancing distribution network resiliency against severe weather-related faults. Given the importance of loads in the resiliency concept, an exact and realistic load model is developed along with the consumption pattern and voltage-dependency of each load type. By defining two technical and economic objective functions, a unique method is used to combine and optimize the objective functions through Imperialist Competitive Algorithm (ICA). Two main strategies, namely the dynamic arrangement of microgrid regions via hourly network reconfiguration as well as grid voltage control through Automatic Voltage Regulation (AVR) of distributed generation facilities, are utilized for increased load restoration. The effect of each of these strategies on grid resiliency is evaluated along with the overall approach efficiency based on simulations on a sample 33-bus network comprising renewable and non-renewable resources and commercial, residential and industrial loads. Using this approach, the strategy to encounter each particular type of failure is obtained.

A Bi-level optimizer for reliability and security assessment of a radial distribution system supported by wind turbine generators and superconducting magnetic energy storages

This paper is aimed at improving the reliability and security of radial distribution system supported by wind turbine generators (WTGs) and superconducting magnetic energy storages (SMESs). For reliability indices assessment, the load-oriented indices including energy not supplied (ENS) and average energy not supplied (AENS) as well as the customers-oriented indices including system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI), customer average interruption duration index (CAIDI), and average service unavailability index (ASUI) are evaluated. Network security index (NSI) is also addressed, which refers to the risk level for current flow in the lines prior reaching to extremis. A multi-objective function is composed and formulated in order to simultaneously minimize ENS, SAIFI, SAIDI, ASUI, and NSI as indices which characterize the performance of distribution system using a hybrid approach based on equilibrium optimizer (EO) along with the loss sensitivity factors. A bi-level optimizer based on the hybrid approach addressing all constraints is applied for simultaneous minimization of reliability and security indices of distribution system. The outer level looks for an optimal sizing and sitting of WTGs and SMESs as well as optimal weighting coefficients whose evaluation is no longer assumed arbitrarily or left to the preferences of the decision maker. The inner level optimizes charging and discharging powers as well as initial state of charge of SMESs. Modeling of feeder's failure rate applying several mathematical functions is considered. The effectiveness of proposed approach is validated on the IEEE 33-bus test system considering commercial, industrial, residential, and mixed time-varying voltage-dependent load models. The performance of the distribution system is also checked as regards the energy loss in feeders, the bus voltage deviation from rated value as well as the voltage stability of the system. For validating the effectiveness of the EO algorithm, the obtained results using the EO algorithm are compared with those predicted by particle swarm optimization (PSO) and genetic algorithm (GA). Moreover, the obtained results display that the bi-level optimization can successfully achieve satisfactory improvement of the reliability and security indices of the distribution system.

Research on capacity optimization and real-time control of island microgrid considering time-shifting load

The utilization efficiency of renewable energy can be improved by the effective control of time-shifting load. In this paper, the characteristics of the time-varying energy source and load model including wind, diesel storage, and seawater desalination are studied. The optimal operation strategy of the island microgrid is established. The objective of this optimization model is to minimize the annual investment cost of joint functions. On this basis, to further improve the renewable energy consumption rate of the system, the real-time control optimization strategy under the operation of the island microgrid is studied. The calculations show that the real-time power prediction through wavelet packet neural network and the optimal allocation strategy of island microgrid capacity based on time-shifting load can improve the acceptance of renewable energy. In the long run, it can solve the problem of lack of fresh water on the island and help to improve the economy.

Analysis of Unbalanced Radial Distribution System with SVR and Impact of Phase Shifter Angle considering Time Varying Loads

ABSTRACT Distribution network experiences unbalancing due to random switching of loads, low voltage profile, high R/X ratio, and unequal loading in the different phases, which inturn causes more losses compared to transmission line. The voltage profiles, active, and reactive power in each phase are distinct due to unbalancing. In the present work, the authors analyzed unbalanced distribution network in presence of Series Voltage Regulator (SVR) considering the reduction in the losses and improvement in the voltage profile. The main highlights of the paper are: (i) placement and analysis of unbalance radial network with SVR at various phase angles; (ii) reduction in active, reactive power loss of the network and improvement in voltage profile; (iii) saving in cost of energy loss at different phase angle of SVR; and (iv) impact analysis of seasonal time varying load model. The placement of SVR at candidate node by considering real, reactive power loss reduction, and percentage rate of under voltage mitigated problem. Before and after SVR placements, the forward and backward sweep algorithm is used for the load flow calculation for analysis. The analysis is carried out on IEEE 25-bus radial distribution network with SVR phase shifter considering time varying seasonal load variations.

An investigation for battery energy storage system installation with renewable energy resources in distribution system by considering residential, commercial and industrial load models

Battery energy storage system technique work as alternative load during low demand situation by storing the excess generation and work as alternative power generation source by discharging the stored generation during peak demand. In this work, a comprehensive assessment is performed for battery energy storage system installation and their capacities selection by utilizing the Photovoltaics (PV) output in radial distribution network by considering commercial, residential and industrial time varying load models. The objective of proposed the work is to reduce annual energy losses, mitigate reverse power flow and overvoltage problem and provide peak power dispatch during peak demand in distribution network. A comparative investigation is performed by considering PV and PV-BESS case for each type of load model. Furthermore, the battery energy storage system (BESS) function developed that decide the time and capacity of charging and discharging in order to manage PV penetration and improve the voltage profile, minimize the daily energy losses and control the reverse power flow in the distribution system without deviating the operational limits. A voltage based sensitivity method is developed at initial step to find out the most prominent node in distribution network for BESS installation. The objective of the problem is resolved by genetic algorithm to find out the optimal solution and to assess the comparison of technical parameters between considered cases. The simulation results on IEEE 69 bus test system show that the proposed methodology for BESS placement decreases the annual energy losses, enhances the PV penetration and reduces the overvoltage and mitigate the reverse power flow. Results of this paper also shows that it is possible to dispatch peak power during the peak load hours for each type of load model.

Optimal Placement and Sizing of Wind Turbine Generators and Superconducting Magnetic Energy Storages in a Distribution System

High penetration of intermittent wind-turbine generation (WTG) into electric distribution system along with large variations of load demand introduce many problems to the system such as high power losses, voltage sag, and low voltage stability. To mitigate such problems, the distribution system is supported by superconducting magnetic energy storages (SMESs). This paper is aimed at determining the optimal placement and sizing of WTGs and SMESs in a distribution system using a proposed multi-objective-function based optimization method. The method is a hybrid one being based on an efficient algorithm called Equilibrium Optimizer (EO) along with loss sensitivity factor (LSF). The weighted-sum multi-objective function (IMO) is formulated for simultaneous minimization of energy-loss and voltage-deviation as well as enhancement of voltage-stability as indices characterizing the distribution system performance. The weight factors are no longer assumed or left open to the preferences of the decision maker. They are computed while optimizing the indices of the IMO in order to determine the optimal placement and sizing of WTGs and SMESs. The proposed method for optimal placement and sizing of WTGs and SMESs is tested and validated on the standard IEEE 33-bus distribution system with time-varying voltage-dependent load models including residential, industrial, commercial, and mixed loads as well as variable wind-speed. The results obtained using EO algorithm are compared with those obtained by particle swarm optimization (PSO) and genetic algorithm (GA) to validate the effectiveness of EO. The numerical results and simulations imply that the combination of WTGs and SMESs can successfully achieve minimization of energy-loss and voltage-deviation as well as enhancement of voltage-stability, and thereby significantly improve the performance of distribution system.

A Novel Framework to Determine the Impact of Time Varying Load Models on Wind DG Planning

Distributed Generation (DG) based on Renewable Energy Sources (RES) are considered as an effective and economical technology for the advancement of an Electric Power System (EPS) to fulfill the load demand. Mostly, studies pertaining to DG planning are performed while considering constant load demand and DG generation. However, these considerations may provide misleading and inconsistent values for loss reduction, voltage profile, power quality, and other operational parameters. Therefore, this paper proposes a novel framework to determine the impact of different Time Varying Voltage Dependent (TVVD) load models on wind DG planning study. Firstly, wind DG optimal allocation is performed using Salp Swarm Algorithm (SSA) for different TVVD load models. Afterwards, impact of different TVVD load models on wind DG planning is investigated. Comparative evaluation of various impact indices, real and reactive power (losses and intakes), penetration level, and apparent power support provided due to integration of wind DG are discussed for various TVVD loads. The analysis of results indicates that TVVD loads have a significant impact on performance of distribution system and DG planning studies.

Voltage Regulation and Loss Minimization in Reconfigured Distribution Systems with Capacitors and OLTC in the Presence of PV Penetration

Optimal reactive power management is one of the key operational aspects for efficient planning of distribution system. This study has become more challenging with renewable energy sources integration into the system. Objective of this paper is to address optimal reactive power planning in distribution system using hybrid optimization. This paper presents a comprehensive model for solving capacitor allocation, PV penetration and feeder reconfiguration simultaneously. The objective function considered in this paper includes cost of capacitor, PV and energy loss. The proposed work includes: (i) capacitor allocation using ant lion optimization, (ii) capacitor rating determination using general algebraic modeling system, (iii) reconfiguration of distribution system using genetic algorithm, (iv) investigated different case studies to realize the impact of various load models and load growth factors on reactive power compensation and network reconfiguration, (v) real-time procedure to determine rating of capacitor banks for practical distribution systems, (vi) reactive power dispatch for realistic time-varying load model considering coordination among capacitors, on-load tap changer and photo-voltaic (PV) penetration. The analysis is carried out considering uncertainty of load demand and PV power generation. The proposed methodology is implemented on IEEE 33-bus distribution system and real-time existing Indian distribution network to demonstrate effectiveness of the proposed methodology. It is observed that voltage-dependent load models have a significant impact on system performance and rating of capacitor banks. The proposed strategy ensures optimal solution compared to other existing techniques.

Probabilistic generation model for optimal allocation of wind DG in distribution systems with time varying load models

Renewable energy-based Distributed Generation (DG) is the most imperative part of modern power system and offers many potential benefits. To attain maximum benefits offered by DG integration, it is important to model the time varying characteristics of both load and generation. Therefore, this paper presents a new Weibull distribution-based time-coupled Probabilistic Generation model for optimal placement and sizing of wind DG with time varying voltage dependent (TVVD) loads. At first, Probabilistic model is proposed for wind speed uncertainty modeling to calculate the hourly output power from wind DG. Afterwards, the values of output power are considered for determining optimal allocation and penetration of wind DG in distribution network to minimize the Average Multi-Objective Index (AIMO) using Particle Swarm Optimization (PSO). The strength of the proposed methodology is validated on IEEE 33 and 69-bus systems. Results depict that, proposed methodology is appropriate for wind speed modeling and is suitable for implementing in power system planning. • Time-varying characteristics of load and generation are assumed for DG allocation. • Weibull distribution-based PG model is proposed to determine hourly wind DG output. • Hourly output power values are considered for the optimal allocation of DG. • The penetration level of wind DG is calculated for different TVVD load models.

A two-stage framework for ambient signal based load model parameter identification

Load modeling is a crucial part of modeling a power system. Traditional load model identification methods are mainly based on post large disturbance response, which cannot be conducted without large disturbance events. In this paper, a new approach of ambient signals based load model parameter identification is proposed to solve this problem, through which the time-varying load model parameters can be identified more frequently. First, the composite load model structure and the measurement based identification approach are introduced. Then, a two-stage identification framework to identify the load model parameters from ambient signals is proposed. In the first stage, the electromagnetic parameters are identified using an optimization method, with the predicted error as the objective function and the differential evolution as the optimization algorithm. In the second stage, the mechanical parameters are identified using linear regression. Finally, the effectiveness of the proposed identification method is validated through the simulation results in Guangdong Power Grid with practically measured ambient signals data. The proposed two-stage identification framework has shown its ability to accurately identify the load model parameters from ambient signals and the advantage over the other identification approaches.

The role of demand response in optimal sizing and siting of distribution energy resources in distribution network with time-varying load: An analytical approach

In the most studies related to allocation of distributed generation the load model assumed in constant. Such assumptions may lead to inconsistent and misleading results in the reduction of energy losses, improve system stability, etc. However, this paper is considered several different types of time-varying to allocation of units. In this study, Optimal Sizing and Siting of Distribution Generation units (Consisting of dispatchable, nondispatchable and photovoltaic) Problem are provided at the same time with considering the role of demand response and time-varying voltage-dependent load models (Consisting of commercial, industrial and residential). This method first identifies a set of buses to be placed of DG units. The optimal sizes of DG units at the identified buses are then evaluated by minimizing Multiobjective Index (Consisting of active, reactive power losses). The proposed method has been tested and validated on 33-buses test distribution system. The results show that demand response and different load models have a significant impact on the planning of Distribution Generation units in radial distribution network.

Estimation of Distribution Systems Expected Energy Not Supplied Index by Multi-level Monte Carlo Method

ABSTRACT—The article presents the estimation of power distribution systems Expected Energy Not Supplied (EENS) index by incorporating time-varying load models of different customer sectors. An application of a new and efficient advanced Monte Carlo simulation (MCS) with controllable accuracy called Multilevel Monte Carlo (MLMC) method is proposed for this estimation. The purpose of the proposed method is to increase the simulation speed of EENS estimation. The method could be easily replaced by the traditional MCS-based estimation which requires huge computational effort for achieving high level of simulation accuracy. Five distribution networks with seven different load models of Roy Billinton Test System are chosen as test distribution systems. To verify the effectiveness of the proposed method, computational time and estimated values of EENS using MLMC method are compared to the results from MCS. The computation performance of EENS estimation can be influenced by different factors and criteria which are also explored in this study. The results presented in the article show that acceptable results can be obtained using the proposed method while substantial reduction of computational effort is also achieved.

Optimal DG integration and network reconfiguration in microgrid system with realistic time varying load model using hybrid optimisation

The potential availability of renewable energy sources is unquestionable and the government is setting steep targets for renewable energy usage. Renewable-based DGs, reduce dependence on fossil fuels, mitigate global climate change, ensure energy security, and reduce emissions of CO 2 and other greenhouse gases. This study addresses microgrid system analysis with hybrid energy sources and reconfiguration simultaneously for efficient operation of the system. Microgrid zones are formulated categorically with the existing distribution system. In this study, wind, solar and small hydro-based DGs are considered. Uncertainties of renewable power generation and load are also taken care in the optimization problem. A multi-objective optimisation method proposed in this paper for optimal integration of renewable-based DGs and reconfiguration of the network to minimise power loss and maximise annual cost savings. Optimal location and sizes of DG units are determined using gravitational search algorithm and general algebraic modelling system respectively. Optimal reconfiguration of the microgrid system is obtained using genetic algorithm. Simulation results are obtained for the IEEE 33-bus system and compared with existing methods as available in the literature. Furthermore, this study has been carried out with a 24-hr time-varying distribution system. The simulation results show the efficiency and accuracy of the proposed technique.

OPF-Based CVR Operation in PV-Rich MV–LV Distribution Networks

Conservation voltage reduction (CVR) has been traditionally applied adopting moderate settings at primary substations and when distributed generation was uncommon. However, as new infrastructure is deployed across European-style medium voltage (MV) and low voltage (LV) networks, driven by increasing photovoltaic (PV) penetration levels, the opportunity arises to develop more advanced CVR schemes. This paper proposes a centralized, three-phase AC optimal power flow (OPF)-based CVR scheme that, using monitoring, on-load tap changers and capacitors across MV and LV, actively manages voltages to minimize energy consumption, even with high PV penetration, while considering MV-LV constraints. To tackle scalability issues brought by discrete variables, a two-stage approach is proposed to solve the OPF as a non-linear programming problem (relaxing integer variables). A process that continuously checks customer voltages is adopted to trigger the optimization only when needed. Moreover, CVR benefits are not only quantified at a network level but also for customers, providing useful insights to policy makers. The proposed control is assessed using a realistic, unbalanced U.K. residential MV-LV network (2,400+ customers) with high PV penetration, and 1-min resolution time-varying profiles and load models. Results demonstrate that the proposed control effectively coordinates voltage regulation in MV and LV levels throughout the day, minimizing energy imports for all customers.

Optimum Location of DG Units Considering Operation Conditions

The optimal sizing and placement of Distributed Generation units (DG) are becoming very attractive to researchers these days. In this paper a two stage approach has been used for allocation and sizing of DGs in distribution system with time varying load model. The strategic placement of DGs can help in reducing energy losses and improving voltage profile. The proposed work discusses time varying loads that can be useful for selecting the location and optimizing DG operation. The method has the potential to be used for integrating the available DGs by identifying the best locations in a power system. The proposed method has been demonstrated on 9-bus test system.

Impact of Distributed Generation Integration on Distribution System Reliability

Objectives: To study the impact of Distributed Generation (DG) integration and automation on distribution system (DS) reliability. Impact of switch operational failures is to be studied. Methods/Statistical Analysis: The system reliability is estimated using time sequential Monte Carlo Simulation (MCS) considering time varying load models. The uncertainties of wind and solar powers are modelled by using Weibull and Beta probability distribution functions respectively. The concept of expectation is used for fuse and switch operational failures to determine the average outage time. System equipment is modelled using two state continues Markov modelling. Findings: The impact of DGs and system automation on distribution system reliability is estimated. The impact analysis is done on a practical Indian distribution system. The impact on system reliability due to operational failures of the fuses and switches is analysed. The failures of substation equipment and DGs are also included for reliability evaluation. The load transfer restrictions are applied on feeders and load transfer capacity is evaluated based on the instantaneous loading of the feeder. Both system reliability and load point reliability is evaluated for impact analysis and results are compared. Application/Improvements: The results contribute the generic observations regarding the impact of DG integration and operational failures of switches. Keywords: Distribution Automation, Distributed Generation, Monte Carlo Simulation, Probability Distributions, Solar Power, Wind Power