Stochastic Forecasts Research Articles

Краткосрочное стохастическое прогнозирование динамики потоков и запасов газа в Единой системе газоснабжения России на основе рекуррентных нейронных сетей

Краткосрочное стохастическое прогнозирование динамики потоков и запасов газа в Единой системе газоснабжения России на основе рекуррентных нейронных сетей

Quantifying the Flexibility of Electric Vehicles in Germany and California—A Case Study

The adoption of electric vehicles is incentivized by governments around the world to decarbonize the mobility sector. Simultaneously, the continuously increasing amount of renewable energy sources and electric devices such as heat pumps and electric vehicles leads to congested grids. To meet this challenge, several forms of flexibility markets are currently being researched. So far, no analysis has calculated the actual flexibility potential of electric vehicles with different operating strategies, electricity tariffs and charging power levels while taking into account realistic user behavior. Therefore, this paper presents a detailed case study of the flexibility potential of electric vehicles for fixed and dynamic prices, for three charging power levels in consideration of Californian and German user behavior. The model developed uses vehicle and mobility data that is publicly available from field trials in the USA and Germany, cost-optimizes the charging process of the vehicles, and then calculates the flexibility of each electric vehicle for every 15 min. The results show that positive flexibility is mostly available during either the evening or early morning hours. Negative flexibility follows the periodic vehicle availability at home if the user chooses to charge the vehicle as late as possible. Increased charging power levels lead to increased amounts of flexibility. Future research will focus on the integration of stochastic forecasts for vehicle availability and electricity tariffs.

Stochastic simulation of the spatio-temporal field of the average daily heat index in Southern Russia

Numerical models of the heat index time series and spatio-temporal fields can be used for a variety of purposes, from the study of the dynamics of heat waves to projections of the influence of future climate on humans. To conduct these studies one must have efficient numerical models that successfully reproduce key features of the real weather processes. In this study, 2 numerical stochastic models of the spatio-temporal non-Gaussian field of the average daily heat index (ADHI) are considered. The field is simulated on an irregular grid determined by the location of weather stations. The first model is based on the method of the inverse distribution function. The second model is constructed using the normalization method. Real data collected at weather stations located in southern Russia are used to both determine the input parameters and to verify the proposed models. It is shown that the first model reproduces the properties of the real field of the ADHI more precisely compared to the second one, but the numerical implementation of the first model is significantly more time consuming. In the future, it is intended to transform the models presented to a numerical model of the conditional spatio-temporal field of the ADHI defined on a dense spatio-temporal grid and to use the model constructed for the stochastic forecasting of the heat index.

Stochastic volatility forecasting of the Finnish housing market

ABSTRACT The purpose of the article is to assess the in-sample fit and the out-of-sample forecasting performances of four stochastic volatility (SV) models in the Finnish housing market. The competing models are the vanilla SV, the SV model where the latent volatility follows a stationary AR(2) process, the heavy-tailed SV and the SV with leverage effects. The models are estimated using Bayesian technique, and the results reveal that the SV with leverage effects is the best model for modelling the Finnish house price volatility. The heavy-tailed SV model provides accurate out-of-sample volatility forecasts in most of the studied regions. Additionally, the models’ performances are noted to vary across almost all cities and sub-areas, and by apartment types. Moreover, the AR(2) component substantially improves the in-sample fit of the standard SV, but it is unimportant for the out-of-sample forecasting performance. The study outcomes have crucial implications, such as portfolio management and investment decision-making. To establish suitable time-series volatility forecasting models of this housing market, these study outcomes will be compared to the performances of their GARCH models counterparts.

An Ensemble Stochastic Forecasting Framework for Variable Distributed Demand Loads

Accurate forecasting of demand load is momentous for the efficient economic dispatch of generating units with enormous economic and reliability implications. However, with the high integration levels of grid-tie generations, the precariousness in demand load forecasts is unreliable. This paper proposes a data-driven stochastic ensemble model framework for short-term and long-term demand load forecasts. Our proposed framework reduces uncertainties in the load forecast by fusing homogenous models that capture the dynamics in load state characteristics and exploit model diversities for accurate prediction. The ensemble model caters for factors such as meteorological and exogenous variables that affect load prediction accuracy with adaptable, scalable algorithms that consider weather conditions, load features, and state characteristics of the load. We defined a heuristic trained combiner model and an error correction model to estimate the contributions and compensate for forecast errors of each prediction model, respectively. Acquired data from the Korean Electric Power Company (KEPCO), and building data from the Korea Research Institute, together with testbed datasets, were used to evaluate the developed framework. The results obtained prove the efficacy of the proposed model for demand load forecasting.

Stochastic model predictive control of photovoltaic battery systems using a probabilistic forecast model

Photovoltaic (PV) battery systems allow citizens to take part in a more sustainable energy system. Using the electric energy produced on-site usually entails a financial benefit for the consumer. Furthermore, feed-in peaks during high photovoltaic generation sometimes cause local voltage violations. Therefore, a feed-in limit applies to PV battery systems. In our study, we present a method to generate an optimal control that takes into account the forecast uncertainties. To that end, a stochastic forecast model is developed and used in a dynamic programming framework. We carry out a simulation study assuming the regulatory constraints in Germany. In this setup, our method is shown to mitigate the effects of the forecast uncertainties better than comparable methods.

A stochastic forecast for the Croatian pension system

This paper analyses the financial sustainability of the Croatian pension system after the reform that was adopted on January 1, 2019. The Croatian pension system as we know it today was started in 1999 with a reform that created the three pillars of the pension system. Over the next twenty years, Croatian economic and social conditions shifted in an unexpected way and a new reform was needed to ensure financial stability is maintained. In this paper I will analyse population trends in Croatia and forecast movements up to 2060. Afterwards, I will analyse the net government cash flow generated from the pension system, by using the forecast population numbers. The beginning year of the forecast horizon is 2018, as some data were not yet available for this year. I use stochastic methods to perform my analysis.

Application of the method of stochastic background forecast to Kazakhstan’s river basins

The production functions of water-dependent sectors of the economy along with labor and capital investments include natural resources, in particular, the hydrological characteristics (norm, variation and skewness coefficients) determining the river flow dynamics. The purpose of the study is to test the method of stochastic forecasting of hydrological characteristics with lead time of 24 hours for the catchments of Northern Kazakhstan during the spring flood, which is characterized by a sharp rise and fall. The stochastic background forecasting method is based on solving a system of differential equations for initial statistical moments. Only average daily values of water discharge, which does change during the day but is not measured and recorded, are usually taken into account, making a statistical generalization of intraday variations in water discharges. The solution of simultaneous equations for the initial moments with daily resolution is the predicted values of the first three moments, characterizing the average daily value, the variation of water flow within a day and the deviation of the average value from the modal one (coefficient of skewness). Verification forecasts of the first and second initial moments have been made for the flood period with lead time of 24 hours. Optimization of the forecast system parameters has been carried out on 30 days preceding the forecast release date. It has been found that the first moment is predicted more reliably rather than the second one. The forecast of such statistical characteristics allows to obtain the frequency curve necessary for the production functions of the Kazakhstan economical sectors.

Convex formulation of confidence level optimization of DG affine reactive power controllers in distribution grids

Volatile productions and consumptions generate a stochastic behavior of distribution grids and make its supervision difficult to achieve. Usually, the Distributed Generators reactive powers are adjusted to perform decentralized voltage control. Industrial controllers are generally equipped with a local affine feedback law, which settings are tuned at early stage using local data. A centralized and more efficient tuning method should aim to maximize the probability that all the node voltages of distribution grids remain within prescribed bounds. When the characteristics of the stochastic power forecasts are known, the centralized algorithm allows to update the settings on a regular time basis. However, the method requires to solve stochastic optimization problem. Assuming that stochastic variables have Gaussian distributions, a procedure is given which guarantees the convergence of the stochastic optimization. Convex problems drastically reduce the difficulty and the computational time required to reach the global minimum, compared to nonconvex optimal power flow problems. The linear controllers with optimized parameters are compared to traditional control laws using simulations of a real distribution grid model. The results show that the algorithm is reliable and moreover fast enough. Hence, the proposed method can be used to update periodically the control parameters.

Quantifying cumulative effects of stochastic forecast errors of renewable energy generation on energy storage SOC and application of Hybrid-MPC approach to microgrid

Energy storage system (ESS) is crucial for microgrid to mitigate adverse impacts of renewable energy generation by participating in primary frequency regulation. In previous studies, research on evaluating the cumulative impacts of stochastic forecast errors (SFE) of renewable energy generation on the variance of SOC (state of charge) of ESS is lacking. This paper presents quantification models of the impacts of SFE on the variance of SOC of ESS. Novel SFE propagation and accumulation models are introduced. The effects of dispatch control and droop control on ESS at different time scales are comprehensively considered. The mechanism of ESS working from a stable state to an unstable state owing to SOC deviation is demonstrated. Then aiming at solving the problem that ESS is forced to quit operation owing to SOC deviation, an online hybrid model predictive control (Hybrid-MPC) based strategy is proposed. Hybrid-MPC consists of two hierarchies: one is decreasing horizon rolling optimization which is specially for handling small SFE and the other is heuristic cooperative control which is designed to tackle large SFE. Besides, feedback correction is applied to change the real-time operation status of microgrid in time. Finally, the strategy is tested in a self-developed program named microgrid real operation simulation (MG-ROS).

Influence of emerging technologies deployment in residential built stock on electric energy cost and grid load

High penetration rates of novel building energy technologies has prompted a growing concern about their microeconomic effect and grid influence. Deployment of photovoltaic (PV), solar water heating (SWH) systems and energy storage solutions, in addition to the growth of electric vehicles (EV) fleet, are reshaping the structure of built stock and lead to the changes in its electric energy demand profile. Long-term forecasting of such structural changes is necessary to guide the decision-making process that would satisfy the needs of both, energy consumers and the suppliers. Whereas electric energy price model is one of the key influencing factors of technologies acceptance for households, peak loads and grid feed-in determine the needed capacity of power grids. The objective of this study was to assess both, the aggregated cost of energy and the changes in cumulative load profiles that are excepted by 2050 for one of residential building typologies in Norway. Methodologically, it was achieved with descriptive statistics, stochastic forecasting and detailed energy performance simulation. Annual electric energy cost for consumers were evaluated under six pricing models. The results suggested that time-of-use and variable maximum power extraction models represent the lowest and the highest extremes in energy cost. At the aggregated level, peak load will decrease in range 1% to 13% compared to current level. Peak PV feed-in will reach up to 40% of peak load by 2050.

Stochastic control of a micro-grid using battery energy storage in solar-powered buildings

This paper presents an efficient data-driven building electricity management system that integrates a battery energy storage (BES) and photovoltaic panels to support decision-making capabilities. In this micro-grid (MG) system, solar panels and power grid supply the electricity to the building and the BES acts as a buffer to alleviate the uncertain effects of solar energy generation and the demands of the building. In this study, we formulate the problem as a Markov decision process and model the uncertainties in the MG system, using martingale model of forecast evolution method. To control the system, lookahead policies with deterministic/stochastic forecasts are implemented. In addition, wait-and-see, greedy and updated greedy policies are used to benchmark the performance of lookahead policies. Furthermore, by varying the charging/discharging rate, we obtain the different battery size $$ \left( {E_{s} } \right) $$ and transmission line power capacity $$ (P_{max} ) $$ accordingly, and then we investigate how the different $$ E_{s} $$ and $$ P_{max} $$ affect the performance of control policies. The numerical experiments demonstrate that the lookahead policy with stochastic forecasts performs better than the lookahead policy with deterministic forecasts when the $$ E_{s} $$ and $$ P_{max} $$ are large enough, and the lookahead policies outperform the greedy and updated policies in all case studies.

Operational ocean acoustic tomography

The estimation of sound speed fields using ocean acoustic tomography (OAT) in operational systems is limited because user intensive post processing and manual association of arrivals with ray paths are required. Furthermore, inversion techniques typically rely on CTD casts or historical data to create reference sound speed profiles and Gaussian statistical characterizations for the inversion, which may be either unavailable, out of date, or too approximate due to the intermittent ocean dynamics. A method is presented for real-time implementation of OAT, including the tracking of acoustic arrivals, model-data association of ray paths to arrivals (ray identification), and tomographic inversions. One- and two-dimensional tomographic inversions for sound speed fields are performed using stochastic ensemble forecasts of the sound speed field generated via the Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) Primitive-Equation probabilistic ocean modeling system. The method is demonstrated on simulated and real data obtained from moored tomographic sources and receivers, deployed in deep water 100 km South of Nantucket, MA. [This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). ]

Application of Hybrid Model Predictive Control (Hybrid-MPC) to Microgrid with High Penetration of Renewable Energy

Owing to the cumulative impacts of stochastic forecast errors (SFE) of renewable energy generation, energy storage system (ESS) may be forced to quit operation owing to SOC (state of charge) deviation. Aimed at solving this problem, an online hybrid model predictive control (Hybrid-MPC) based strategy is proposed. Hybrid-MPC consists of two hierarchies: one is decreasing horizon rolling optimization which is specially for handling small SFE and the other is heuristic cooperative control which is designed to tackle large SFE. Besides, feedback correction is applied to deal with SOC deviation and maintain the normal operation of ESS. The strategy is tested in a self-developed program MG-ROS. Results demonstrate the effectiveness of the proposed strategy.

A General Framework for Time Series Forecasting Model Using Autoregressive Integrated Moving Average-ARIMA and Transfer Functions

Major current econometric stochastic series forecast research are established on the failure of the scholastic process tests to differentiate between finite and stationary alternative samples of the unit root hypothesis results. The importance of forecast evaluation allows researchers to reasonably monitor and improve forecast performance. While a structured improved forecast framework have often been suggested as one possible alternative, an extended the multivariate model which incorporate distributed-lag period for independent variable gives a unique advantage over the traditional distributed-lag model and the mathematical formulation does essentially guarantee that predicated equation irrespective of the values of the predictor variables. Hence, the primary objective is mainly to determine the likelihood of autoregressive integrated moving average (ARIMA) method for practicable process choice used for predicting key economic variables for a set of market data. Once the process has been known, parameters have been obtained, and the adequacy of the model has been determined, forecasts can be checked for reliability.

A General Framework for Time Series Forecasting Model Using Autoregressive Integrated Moving Average-ARIMA and Transfer Functions

Major current econometric stochastic series forecast research are established on the failure of the scholastic process tests to differentiate between finite and stationary alternative samples of the unit root hypothesis results. The importance of forecast evaluation allows researchers to reasonably monitor and improve forecast performance. While a structured improved forecast framework have often been suggested as one possible alternative, an extended the multivariate model which incorporate distributed-lag period for independent variable gives a unique advantage over the traditional distributed-lag model and the mathematical formulation does essentially guarantee that predicated equation irrespective of the values of the predictor variables. Hence, the primary objective is mainly to determine the likelihood of autoregressive integrated moving average (ARIMA) method for practicable process choice used for predicting key economic variables for a set of market data. Once the process has been known, parameters have been obtained, and the adequacy of the model has been determined, forecasts can be checked for reliability.

Weather and Stochastic Forecasting Method for Generated Discharge Level Data at Sathanur Dam

This article forecasts the future values using stochastic forecasting models for specified fitted values by using downscaling data, which are collected from Sathanoor Dam gauging site. Due to the demand of the water in this current scenario, this study analyzed the perdays Discharge level data collected from Sathanoor Dam where the outcome is predicted in a downscaling data sets in hydrology, extended Thomas –Fiering, ARIMA, MLE models, is used to estimate perdays discharge level data of each month. The error estimates RMSE, MAE of forecasts from above models is compared to identify the most suitable approaches for forecasting trend analysis.

Novel stochastic methods to predict short-term solar radiation and photovoltaic power

Solar forecasting has evolved towards becoming a key component of economical realization of high penetration levels of photovoltaic (PV) systems. This paper presents two novel stochastic forecasting models for solar PV by utilizing historical measurement data to outline a short-term high-resolution probabilistic behavior of solar. First, an uncertain basis functions method is used to forecast both solar radiation and PV power. Three possible distributions are considered for the uncertain basis functions - Gaussian, Laplace, and Uniform distributions. Second, stochastic state-space models are applied to characterize the behaviors of solar radiation and PV power output. A filter-based expectation-maximization and Kalman filtering mechanism is employed to recursively estimate the system parameters and state variables. This enables the system to accurately forecast small as well as large fluctuations of the solar signals. The introduced forecasting models are suitable for real-time tertiary dispatch controllers and optimal power controllers. The PV forecasting models are tested using solar radiation and PV power measurement data collected from a 13.5 kW PV panel installed on the rooftop of our laboratory. The results are compared with standard time series forecasting mechanisms and show a substantial improvement in the forecasting accuracy of the total energy produced.

Using Multiple Methods to Provide Prediction Bands of K-12 Enrollment Projections

Often, demographers charged with projecting enrollments for school districts are asked to provide a range of future enrollments, as point estimates are not satisfactory to stakeholders. Three New Jersey school districts in varying populations sizes (small, medium, and large) were used to project enrollments 5 years into the future. Prediction bands were created using empirically-based methods, whereby confidence intervals were constructed, and by model-based methods, which utilizes stochastic forecasting. While stochastic forecasting is typically used in projecting the population of large geographies such as states or countries, it has rarely been used for a small level of geography such as a school district. The results showed that confidence intervals may have limited utility in projecting an enrollment range for larger districts, particularly in the short term (1–2 years). Prediction intervals using stochastic forecasting have limited utility in school district projections, regardless of school district size, as the prediction bands are too wide to allow for any meaningful use of the data.

A Bayesian Approach to Developing a Stochastic Mortality Model for China

Summary Stochastic mortality models have a wide range of applications. They are particularly important for analysing Chinese mortality, which is subject to rapid and uncertain changes. However, owing to data-related problems, stochastic modelling of Chinese mortality has not been given adequate attention. We attempt to use a Bayesian approach to model the evolution of Chinese mortality over time, taking into account all of the problems associated with the data set. We build on the Gaussian state space formulation of the Lee–Carter model, introducing new features to handle the missing data points, to acknowledge the fact that the data are obtained from different sources and to mitigate the erratic behaviour of the parameter estimates that arises from the data limitations. The approach proposed yields stochastic mortality forecasts that are in line with both the trend and the variation of the historical observations. We further use simulated pseudodata sets with resembling limitations to validate the approach. The validation result confirms our approach’s success in dealing with the limitations of the Chinese mortality data.