Multi-timescale Framework Research Articles

Economic scheduling method for voltage‐dependent loads in a power system based on a multitime scale framework

AbstractThere are many voltage‐dependent loads (VDLs) in power systems. When the unit reserve supply is low, the transmission network adjusts the voltage of grid‐connected nodes to provide additional resources. Many reactive power devices with different regulatory performance levels and timescales must be coordinated to employ flexible VDLs to the maximum extent, and consequently, a transient stability‐constrained optimal power flow (TSCOPF) problem with mixed integers and multiperiod coupling must be solved. A multitimescale scheduling ‘day‐ahead‐intraday‐real‐time’ framework is designed for the optimal economic scheduling of VDLs. In the day‐ahead stage, the optimal scheduling period of the discrete reactive power control devices is determined. In the intraday stage, a rolling optimization model based on model predictive control is established, and the specific action times of the discrete reactive power devices are determined. In the real‐time stage, the optimal regulation strategy of the continuous reactive power control device is optimized by rolling. Then, to consider the speed and accuracy of the solution at the same time, a continuous sensitivity correction method is adopted to simplify and solve the original model. Finally, with a modified IEEE‐39 system and a modified IEEE‐118 system as examples, it is verified that the multitimescale scheduling framework maximizes the exploitation of the flexible resources of VDLs to ensure voltage security and stability and improve the economy of system operation under different scenarios.

Improved State-of-Charge Estimation of Lithium-Ion Battery for Electric Vehicles Using Parameter Estimation and Multi-Innovation Adaptive Robust Unscented Kalman Filter

In this study, an improved adaptive robust unscented Kalman Filter (ARUKF) is proposed for an accurate state-of-charge (SOC) estimation of battery management system (BMS) in electric vehicles (EV). The extended Kalman Filter (EKF) algorithm is first used to achieve online identification of the model parameters. Subsequently, the identified parameters obtained from the EKF are processed to obtain the SOC of the batteries using a multi-innovation adaptive robust unscented Kalman filter (MIARUKF), developed by the ARUKF based on the principle of multi-innovation. Co-estimation of parameters and SOC is ultimately achieved. The co-estimation algorithm EKF-MIARUKF uses a multi-timescale framework with model parameters estimated on a slow timescale and the SOC estimated on a fast timescale. The EKF-MIARUKF integrates the advantages of multiple Kalman filters and eliminates the disadvantages of a single Kalman filter. The proposed algorithm outperforms other algorithms in terms of accuracy because the average root mean square error (RMSE) and the mean absolute error (MAE) of the SOC estimation were the smallest under three dynamic conditions.

A totally coupled multi time-scale framework containing full parameters online identification and SOC real-time estimation of lithium-ion battery based on a fractional order model

Fractional order model (FOM) is one of the most promising choices for lithium-ion battery simulation and internal states estimation due to its high modeling accuracy. However, online identifying the order and parameters of FOM is extremely tough, which also makes it difficult to be applied in complex and variable operating conditions. To address this issue, this paper proposes a totally coupled multi time-scale framework that contains full parameters online identification of FOM and state-of-charge (SOC) real-time estimation of lithium-ion battery. Firstly, a novel global optimization algorithm named improved particle swarm optimization is designed to update the order of FOM on macro-time scale with low computational burden. On the basis of the determined order, the rest parameters of FOM are further identified by forgetting factor recursive least square algorithm on micro-time scale. With those online identified parameters, adaptive extended Kalman filter is finally adopted to track battery SOC in every instant. The estimation accuracy, adaptability to different operating temperatures and battery aging, and robustness ability against uncertain initialization of the developed method is verified under Federal Urban Driving Schedule tests. The corresponding results demonstrate that the proposed method can realize accurate full parameters online identification of FOM and precise SOC real-time estimation against different temperatures, battery aging states and initialization. Using the developed method, the mean absolute error (MAE) and root mean square error (RMSE) of SOC estimation of the fresh battery under temperature ranging from 0 °C to 50 °C can be limited below 0.9 % and 1.1 %, respectively. Even if the SOC-OCV relationship is not timely updated, those two indexes of the aged battery achieved by the proposed method can still be controlled within 3 % under temperature ranging from 0 °C to 50 °C. Moreover, the comparison with other typical FOM-based estimation methods is also conducted, whose results indicate that the developed method has apparently superior comprehensive performance on estimation accuracy and adaptation.

A Secure and Adaptive Hierarchical Multi-Timescale Framework for Resilient Load Restoration Using a Community Microgrid

Distribution system integrated community microgrids (CMGs) can partake in restoring loads during extended duration outages. At such times, the CMGs are challenged with limited resource availability, absence of robust grid support, and heightened demand-supply uncertainty. This paper proposes a secure and adaptive three-stage hierarchical multi-timescale framework for scheduling and real-time (RT) dispatch of CMGs with hybrid PV systems to address these challenges. The framework enables the CMG to dynamically expand its boundary to support the neighboring grid sections and is adaptive to the changing forecast error impacts. The first stage solves a stochastic extended duration scheduling (EDS) problem to obtain referral plans for optimal resource rationing. The intermediate near-real-time (NRT) scheduling stage updates the EDS schedule closer to the dispatch time using new obtained forecasts, followed by the RT dispatch stage. To make the decisions more secure and robust against forecast errors, a novel concept called delayed recourse is designed. The approach is evaluated via numerical simulations on a modified IEEE 123-bus system and validated using OpenDSS and hardware-in-loop simulations. The results show superior performance in maximizing load supply and continuous secure distribution network operation under different operating scenarios.

Co-estimation of state of charge and state of health for 48 V battery system based on cubature Kalman filter and H-infinity

As a cost-effective vehicle electrification solution, 48 V system can achieve a 15 %–20 % reduction in CO2 emission without major changes to the traditional automotive architecture. The aggressive charging and discharging conditions of this system put forward higher requirements for battery management system (BMS), especially for accurate state estimation. In this paper, a multi-scale co-estimation method is proposed to obtain the state of charge (SOC) and state of health (SOH) for 48 V battery system. First, a multi-scale estimation framework is developed according to the natural characteristics of the battery parameters and states. Second, based on the equivalent circuit model of battery, the recursive least squares is used to online identify the internal resistance of battery, advanced filtering algorithms including cubature Kalman filter and H-infinity are employed to estimate battery SOC and capacity. Through the multi-timescale framework, the computing burden of co-estimation can be reduced to enable its application on an embedded BMS. Finally, a series of tests based on typical driving cycles are carried out to verify the proposed method, and the results are also compared with other existing methods. The results show that the mean absolute errors of SOC and capacity estimation are less than 0.88 %, and 0.64 %, respectively, which verifies the superiority of the proposed method.

A multi time-scale theory of economic growth and cycles

A multi time-scale framework is proposed for the simultaneous modeling of economic cycles and the long-run behavior of technical change and income distribution. The accounting structure of the model is based on Marx’s circuit of capital and uses the dynamic interaction between wages and unemployment as a “closure” for the system of equations. The model is consistent with some empirical regularities of the post-war US economy related to the cyclical behavior of the unemployment rate, the wage-share, the expected rate of profit and inventory investment, on one hand, and with the tendency of a falling wage-share and a rising capital-output ratio, on the other.

A Three-Stage Multitimescale Framework for Online Dispatch in a Microgrid With EVs and Renewable Energy

To accomplish more practical charging dispatch for electric vehicles (EVs) and effectively consider the multiuncertainties of renewable energy and load demand, this article presents a three-stage multitimescale framework for online dispatch of a grid-connected microgrid. In the first stage, a reference scheduling model is proposed to obtain the referral plans with a sampling period of 30 min. Considering these uncertainties, the second stage proposes a real-time operation method based on stochastic model predictive control, with a sampling period of 10 min, to update the referral plans by minimizing the deviation of the real results from the referral results. To sufficiently capture the operations of EV charging, a rule-based energy management model for the EV charging station is designed in the third stage. The controller of the third stage runs every minute and allocates the charging station power to the available EVs while meeting the charging demand and technical constraints. Numerical simulations are used to investigate the effectiveness and superiority of the proposed dispatch framework. The simulation results show that the proposed framework reaches 98% of ideal performance achieved by off-line optimization.

Real-Time Coordinated Scheduling for ADNs With Soft Open Points and Charging Stations

This paper proposes a real-time coordinated scheduling method for active distribution networks (ADNs) with soft open points (SOPs) and plug-in electric vehicles (PEVs) via multi-timescale framework under uncertainties. Specifically, this method is achieved with day-ahead pre-scheduling and intra-day corrective control stages by coordinating various flexible resources at different timescales. The day-ahead stage is designed to reduce operational cost, regulate voltage profile and avoid risk exposure through joint scheduling of traditional devices, SOPs and PEVs on hourly basis. In intra-day corrective control stage, an hour is further divided into two timescales. The slow-timescale scheduling (STS) aims to corrective coordination of SOPs and across-time-and-space energy transmission of PEVs, and nested within the STS, the fast-timescale scheduling optimally coordinates the active & reactive power of SOPs and PV inverters to handle fast voltage fluctuations as well as against real-time uncertainties. The formulated three models are all transformed into second-order cone programming problems via sample weighted average approximation (SWAA), linearization and conic relaxation, which can be thus efficiently solved. Case studies based on three modified distribution systems (including two IEEE test systems and one actual distribution network) are performed to verify the effectiveness of the proposed method.

An improved stochastic model predictive control operation strategy of integrated energy system based on a single-layer multi-timescale framework

Economy, robustness and computational efficiency are of paramount metrics for an operation strategy of an integrated energy system (IES). To achieve the trade-off of the three metrics, a multi-layer framework is extensively exploited in existing operation strategies. This work, however, proposes a single-layer multi-timescale framework which can coordinate different operation performances associated with various timescales simultaneously. Based on the framework, an improved stochastic model predictive control (SMPC) operation strategy is further developed by embedding the proposed framework into its prediction horizon. To solve the multi-timescale optimization of the improved SMPC, the constraints and cost function are presented in the multi-timescale form, and the supplied and demands are forecast by the least square support vector machine. A simulator of an IES is thereafter constructed to mimic real system and used to evaluate the performance of the proposed strategy by operation cost, accumulative error and computation time with respect to economy, robustness and computational efficiency, respectively. Finally, the improved SMPC strategy is compared with a traditional single-layer and a hierarchical strategy by a case study. The results show that the improved strategy has the best tradeoff performance aforementioned. The multi-timescale framework can be also integrated into other operation strategies.

A multi-timescale framework for state monitoring and lifetime prognosis of lithium-ion batteries

Battery State-of-charge (SOC) estimation and lifetime prognosis play important roles in its fuel-gauging and predictive maintenance. However, the inevitable modeling biases and measurement noises caused by the complexity of battery dynamics in nonlinearity, temperature sensitivity, and degradation, still challenge the accuracy and robustness. To bridge this research gap, this paper presents a multi-timescale framework for SOC estimation and lifetime prediction of lithium-ion batteries. In the fast timescale, a recursive-least-square-based parameter identification algorithm is first employed to eliminate the effects of identification errors on SOC estimation and reduce the dimension of the SOC observer. Then, a robust observer and dual extended-Kalman-filter (DEKF) are combined to achieve simultaneous SOC and capacity estimation against bounded modeling errors. In the slow timescale, the battery lifetime is predicted through a particle-filtering based on the capacity. The effectiveness and superiority of the proposed method are demonstrated by both simulation and experimental results conducted on LiCoO2 cells. The results indicate that the root-mean-square-error of the SOC and capacity can be achieved within 3.5% and 0.5%, respectively, in the presence of the model mismatch. In addition, the lifetime prediction framework can also ensure accurate lifetime prediction.

Analysis of a Multi-Timescale Framework for the Voltage Control of Active Distribution Grids

The development of strategies for distribution network management is an essential element for increasing network performance and reducing the upgrade of physical assets. This paper analyzes a multi-timescale framework to control the voltage of distribution grids characterized by a high penetration of renewables. The multi-timescale solution is based on three levels that coordinate Distributed Generation (DG) and Energy Storage Systems (ESSs), but differs in terms of the timescales and objectives of the control levels. Realistic load and photovoltaic generation profiles were created for cloudy and clean sky conditions to evaluate the performance features of the multi-timescale framework. The proposed solution was also compared with different frameworks featuring two of the three levels, to highlight the contribution of the combination of the three levels in achieving the best performance.

Dynamic co-movement and interdependency among real estate index in China: a multi-scale multiple correlation analysis

Purpose This study aims to investigate the dynamic co-movement and interconnection among 69 security investment indices in China using the multi-time scale framework. Design/methodology/approach The authors first use the multiple coherence analysis method to exhibit the degree of relationships among the variables under study. In addition, the wavelet multiple correlation and wavelet multiple cross-correlation analyses are used to examine the time-frequency synchronization interdependence structure among the variables. Findings From the empirical findings, one may infer less opportunity for portfolio diversification at higher time scales. Obviously, at these scales, the authors find that the 69 Chinese investment indices generate a simple security investment class, as indicated by higher interconnection between the indices. Research limitations/implications Further research can increase the sample size to re-investigate the empirical relationship for security investment indices. Practical implications In the nutshell, the results demonstrate the potential for Chinese investors to invest in security investment indices to earn from portfolio diversification at lower time frequencies. The Chinese investment market indices under study yield further opportunities of portfolio diversification toward the short-term investors than the long-term investors. Originality/value To the best of the authors’ knowledge, this is the first paper to examine the dynamic co-movement and interconnection for security investment indices in China.

A multi time-scale framework for state-of-charge and capacity estimation of lithium-ion battery under optimal operating temperature range

To reduce computation cost and improve state-of-charge (SOC) estimation accuracy over battery's whole lifetime, a multi time-scale framework is proposed to co-estimate SOC and capacity in this paper. With forgetting factor recursive least square, model parameters are online identified firstly, which are later transmitted into adaptive extended Kalman filter to predict SOC in real-time. Subsequently, the difference between two estimated SOC before and after macro time-scale is calculated and innovatively seen as measurement information of extended Kalman filter to further update capacity periodically. Considering battery optimal operating temperatures, Federal Urban Driving Schedule tests under 20°C, 30°C and 40°C are performed to verify the feasibility, co-estimation accuracy and adaptability to different macro time-scales of the presented method. The validation results show that the mean absolute error (MAE) and root mean square error (RMSE) of SOC estimation results with three different macro time-scales under optimal operating temperature range can be roughly limited within 1%, while most MAE and RMSE of capacity prediction results is below 1% and 2%, respectively. Moreover, the comparison with other three typical co-estimation methods is also conducted, whose results indicate that the proposed algorithm has more superior comprehensive performance on co-estimation accuracy and convergence speed.

Multi-timescale Forecast of Solar Irradiance Based on Multi-task Learning and Echo State Network Approaches

Solar irradiance forecast is closely related with efficiency and reliability of renewable energy systems. Multi-timescale irradiance forecast is a new and efficient way to simultaneously predict solar energy generation on different timescales for hierarchical decision making. This article newly adopts the multi-task learning mechanism to study the multi-timescale forecast for improving accuracy and computational efficiency. A novel multi-timescale (MTS) prediction framework is presented to fulfill the multi-task application, and echo state network (ESN) is studied in the proposed MTS framework. The multi-timescale ESN (MTS-ESN) is proposed to enhance the information sharing among correlated tasks. Simulation results of hourly solar data demonstrate that the proposed MTS-ESN could achieve promising performance at both hourly and daily level in parallel. The MTS-ESN outperforms the single-timescale ESN (STS-ESN), which indicates the information sharing in the multi-task learning is effective in this application.

Multi-timescale and multi-objective power dispatch strategy incorporating air pollutant temporal and spatial distribution control

Abstract Most existing environmental/economic dispatch power dispatch studies only focus on emission minimization. However, air pollutant temporal and spatial distribution (APTSD) control which considers atmospheric dispersion would be more effective, in terms of air pollution mitigation. This paper proposes a power dispatch strategy which incorporates APTSD and stimulates the potential of atmospheric environment capacity (AEC). Firstly, an APTSD model is constructed to help system operators understand how thermal power generation influences the ground level concentration (GLC), which considers the diurnal variation of the atmospheric boundary layer. Then, a multi-timescale framework is developed to accommodate the variability and uncertainty of meteorological conditions. A day-ahead sub-model and an intraday sub-model are integrated, which reduce generation cost (GC), emission of carbon dioxide (EC), and implement APTSD control of sulfur dioxide simultaneously. In particular, the AEC margin for TPPs is fully exploited to extract compromise solution, realizing a dynamic trade-off between different objectives. Case studies are first conducted on an IEEE 39 model, demonstrating that the use of AECM can reduce total GC and EC by 2.54% and 5.36% respectively, with the same power demands being satisfied and a better air quality. Advantages of the proposed APTSD strategy over the traditional emission reduction strategy are further demonstrated by practical application, which shows that not only is the average GLC reduced by 19.16%, but also the total GC and total EC are reduced by 107,460 dollars and 1450 tons, respectively.

Joint estimation of lithium-ion battery state of charge and capacity within an adaptive variable multi-timescale framework considering current measurement offset

Accurate and reliable estimation of battery state of charge (SOC) and capacity is essential for the management of the lithium-ion battery in electric vehicles. In this paper, a novel joint estimation approach of battery SOC and capacity with an adaptive variable multi-timescale framework is proposed, which also deals with the interference of current measurement offset (CMO) effectively. Aiming at the problem of unknown CMO, which will affect the accuracy of battery modeling and state estimation, an original two-stage recursive least squares algorithm is raised to identify the battery model parameters and the CMO quickly. The adaptive extended Kalman filter is applied to improve the SOC estimation accuracy by updating the noise covariance adaptively, and the recursive total least squares is used to estimate capacity with the consideration that both the battery SOC estimation and charge accumulation suffer from noises. Finally, a joint estimation of SOC and capacity structure is founded, and to address the issue of different varying characteristics of battery SOC and capacity, a novel adaptive variable multi-timescale framework is proposed. The experimental results indicate the accuracy, convergence, and adaptivity of the proposed method in different working conditions.

Twin-Timescale Artificial Intelligence Aided Mobility-Aware Edge Caching and Computing in Vehicular Networks

In this paper, we propose a joint communication, caching and computing strategy for achieving cost efficiency in vehicular networks. In particular, the resource allocation policy is specifically designed by considering the vehicle's mobility and the hard service deadline constraint. An artificial intelligence-based multi-timescale framework is proposed for tackling these challenges. To mitigate the complexity associated with the large action and search space in the sophisticated multi-timescale framework considered, we propose to maximize a carefully constructed mobility-aware reward function using the classic particle swarm optimization scheme at the associated large timescale level, while we employ deep reinforcement learning at the small timescale level of our sophisticated twin-timescale solution. Numerical results are presented to illustrate the theoretical findings and to quantify the performance gains attained.

Mobility-Aware Edge Caching and Computing in Vehicle Networks: A Deep Reinforcement Learning

This paper studies the joint communication, caching and computing design problem for achieving the operational excellence and the cost efficiency of the vehicular networks. Moreover, the resource allocation policy is designed by considering the vehicle's mobility and the hard service deadline constraint. These critical challenges have often been either neglected or addressed inadequately in the existing work on the vehicular networks because of their high complexity. We develop a deep reinforcement learning with the multi-timescale framework to tackle these grand challenges in this paper. Furthermore, we propose the mobility-aware reward estimation for the large timescale model to mitigate the complexity due to the large action space. Numerical results are presented to illustrate the theoretical findings developed in the paper and to quantify the performance gains attained.

A multi-timescale hybrid stochastic/deterministic generation scheduling framework with flexiramp and cycliramp costs

Flexible ramping products (flexiramp), provided by entitled resources to meet net demand forecast error, are the underpinning for the accommodation of the substantial uncertainties associated with variable wind power. This paper proposes an enhanced flexiramp modeling approach, cast in a hybrid stochastic/deterministic multi-timescale framework. The framework employs a chance-constrained day-ahead scheduling method, as well as deterministic scheduling on intra-hourly basis (real-time scheduling), to allow optimal procurement planning of the flexiramp products in both timescales. A stepwise and piecewise demand price curve is also proposed to calculate the flexiramp surplus procurement price. Non-generation resource (NGR), referring to energy storage, is implemented to provide extra flexibility. Additionally, cycling ramping cost (cycliramp), introduced to model operational and maintenance costs and reduce the wear and tear of generators, is also included as a penalty. Numerical tests are conducted on 6-bus and 118-bus systems. Results demonstrate the merits of the proposed scheduling model as well as the effects of flexiramp and cycliramp costs in the multi-timescale scheduling.

Chance-constrained Scheduling of Variable Generation and Energy Storage in a Multi-Timescale Framework

This paper presents a hybrid stochastic deterministic multi-timescale scheduling (SDMS) approach for generation scheduling of a power grid. SDMS considers flexible resource options including conventional generation flexibility in a chance-constrained day-ahead scheduling optimization (DASO). The prime objective of the DASO is the minimization of the daily production cost in power systems with high penetration scenarios of variable generation. Furthermore, energy storage is scheduled in an hourly-ahead deterministic real-time scheduling optimization (RTSO). DASO simulation results are used as the base starting-point values in the hour-ahead online rolling RTSO with a 15-minute time interval. RTSO considers energy storage as another source of grid flexibility, to balance out the deviation between predicted and actual net load demand values. Numerical simulations, on the IEEE RTS test system with high wind penetration levels, indicate the effectiveness of the proposed SDMS framework for managing the grid flexibility to meet the net load demand, in both day-ahead and real-time timescales. Results also highlight the adequacy of the framework to adjust the scheduling, in real-time, to cope with large prediction errors of wind forecasting.