Stochastic Economic Model Research Articles

Stochastic economic model predictive control for renewable energy and ancillary services trading with storage

The provision of renewable-based ancillary services (AS) is paramount for the stable operation of power systems featuring high renewable penetration. The combined operation of storage with renewables enables aggregators to increase the reliability of their energy and frequency control AS offers. Existing dispatch strategies for the supply of both energy and AS are usually rule-based or involve tracking a technical reference signal, hence economically suboptimal for aggregators. This study proposes a comprehensive decision framework in which first a stochastic optimization derives bids on energy and AS markets, then stochastic economic model predictive control (SEMPC) optimizes the storage dispatch in order to maximize the profit and minimize the storage degradation, as a function of the predicted renewable production and the expected AS activation. The framework is applied to a real-world case study where storage combined with wind power participates in the energy market, the frequency containment market and the frequency restoration reserve market. The SEMPC-based approach increases market revenue by 15% compared to a standard reference-tracking MPC, and reduces storage degradation by 23%. The stochastic formulation lowers the sensitivity of the economic objectives to renewable energy forecast errors, compared to deterministic approaches.

Parallel Dual-DQAM for Multi-Scenario Stochastic Economic Dispatch Model by Temporal and Scenario Decompositions

Large-scale multi-scenario stochastic economic dispatch (SED) is hard to directly solve due to the huge number of variables and constraints. To reduce the computational burden, a nested dual-DQAM (Diagonal Quadratic Approximation Method) is proposed in this paper to decouple the SED problem in both scenarios and time periods, where each subproblem only contains one time period and one scenario. Moreover, these subproblems can be handled in parallel, such that the computational performance can be significantly improved. Besides, we have investigated the optimal policy to select the best parallel structure of the proposed dual-DQAM, and the theorical convergence performance is proved. Numerical results on several test systems show the effectiveness of the proposed dual-DQAM. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Nowadays, the safe operation and economic dispatch in power system are greatly challenged by the high penetration of renewable energy. Although the uncertainty of renewable energy can be well modeled by stochastic programming, the solution complexity will seriously increase due to the large number of typical scenarios. For this problem, the parallel solution using decomposition methods is the state-of-the-art strategy. In this paper, we propose an efficient solution to the multi-scenario SED problem by temporal and scenario decompositions. It realizes an important innovation in both reducing the computational burden and improving the solving efficiency, which greatly promotes the application of SED in large-scale systems. To better use this method, the following two properties should be highlighted: i) the proposed method has a convergence guarantee and works especially well on SED due to the sparsity property of linking constraint matrices. ii) the computational efficiency of the proposed method becomes more significant as the number of time periods and scenarios grows and can be further improved under a fast ramp rate.

Bovine cysticercosis epidemiology and the economic impact of the triceps brachii incision in a South African export abattoir.

Taenia saginata is a zoonotic tapeworm of humans with bovines as its intermediate host (bovine cysticercosis). Traditional meat inspection is the main measure to identify the larval stage in carcasses and prevent human infection, but has a notoriously low sensitivity, especially in low prevalence settings. The legislation in multiple African countries mandates an incision in both triceps brachii muscles to detect the parasite as part of the normal post-mortem inspection, but this has an economic cost and is not universally mandated in other countries. The primary aim of this study was to investigate the epidemiology of bovine cysticercosis at an export abattoir in South Africa and determine the validity and cost of the triceps incision. Risk factors were investigated, and the effect of additional heart incisions on the current inspection. Four incisions were made into the heart in addition to the normal post-mortem inspection in 3353 carcasses. The proportion of positive animals with and without the cardiac and triceps incisions were compared using McNemar's chi-square tests, while risk factors were assessed using binary logistic regression. The economic impact of the triceps incision was estimated using a stochastic economic cost model. Thirty-three positive carcasses were identified for an apparent prevalence of 0.98 % (95 %CI, 0.69-1.36 %), while the true prevalence was estimated at 6.6 % (95 %CI, 4.3-8.8 %). All cysts were confirmed as T. saginata on histopathology with 70 % (95 %CI, 53-83 %) located in the heart. The additional cardiac incisions resulted in the detection of significantly more cases compared to the normal inspection method prevalence of 0.72 % (95 %CI, 0.47-1.05 %; P<0.001). The apparent prevalence of T. saginata when omitting the triceps incision was not significantly lower compared to the prevalence when included in the inspection(P=0.480). External feedlots (OR= 4.17, 95 %CI: 2.04-8.54, P<0.001) and older animals (OR=3.90, 95 %CI: 1.17-13.03, P=0.027) were associated with a positive detection. The current median annual financial cost to the food business operator from the triceps incision was estimated at $30387 (95 %CI: $0-$130696), with the proportion of deboned meat exported identified as the most important factor affecting cost (Spearman's rho=0.853). The identification of risk factors could aid in the development of a more effective risk-based inspection system. The current inspection should be modified to increase exposure of the heart and remove the triceps incisions. The latter should especially be considered given the minimal contribution to cysticercosis detection, the unsupported requirement for its inclusion specifically in Africa, and its economic impact, especially as beef exports increase.

Modeling the Reserve Capacity of Wind Power and the Inherent Decision-Dependent Uncertainty in the Power System Economic Dispatch

The ever-increasing penetration of renewable generation is demanding additional flexibility for the operation of power systems. In this sense, it has been proved that wind power generators (WPGs) can provide part of the required operating reserve through pitch angle control (PAC) under a deloaded strategy. Unlike conventional operating reserve sources, however, the operating reserve provided by WPGs can't always be considered reliable, which renders the power system dispatch more challenging. In this research, the reserve capacity of the WPGs is modeled considering the decision-dependent uncertainty (DDU). The random wind speed introduces uncertainty to the available reserve capacity of the WPGs while the decisions on the deloading degrees of the WPGs directly affect their coefficients between wind speed and usable wind power, making the uncertainty decision-dependent. Moreover, the operational technical limits of the WPGs and the multiple possible wind speed scenarios are also considered in the wind power reserve capacity modeling. Then, a two-stage reliability constrained stochastic economic dispatch model with WPGs' reserve provision (SED-WRP) is developed to jointly dispatch the generation and reserve. A group-based multi-cut Benders decomposition method is applied to improve the convergence performance of the solution algorithm. Case studies are solved to quantify the impact of considering the reserve provision of WPGs and the inherent DDU in power system dispatch decisions.

Production efficiency of loblolly pine stands under roundwood and carbon price risks

This study examines the efficiency of loblolly pine ( Pinus taeda L.) production under roundwood and carbon price risks. The data are generated from the biophysical–economic optimization model, consisting of the loblolly pine growth and yield model in Georgia, United States, combined with a stochastic economic model. The model incorporates the timber and carbon price risk parameters and generates the optimal biomass volumes and the associated harvest profits for 56 scenarios given different silvicultural treatments and price risks. Timber production efficiencies under each scenario are evaluated using the data envelopment analysis. This study also assesses potential economic losses due to inefficient forest production. The result shows that forest landowners with lower risk tolerance have a higher profit foregone. Inefficient forest management could cause up to $319/ha and $405/ha of potential economic losses under herbicide and fertilizer treatment scenarios, respectively. As timber-related price risks can influence forest landowners’ decisions, the findings of this study incorporating different risks would help forestry professionals and policymakers to establish a more realistic and greater degree of accuracy in the forest productivity evaluation.

Long-term economic impacts of coastal floods in Europe: a probabilistic analysis

&lt;abstract&gt; &lt;p&gt;In this article we quantify the long-term economic impacts of coastal flooding in Europe. In particular, how the direct coastal damages generate long-term economic losses that propagate and compound throughout the century. A set of probabilistic projections of inundation-related direct damages (to residential buildings, firms' physical assets and agriculture production) is used as an exogenous shock to a dynamic stochastic economic model. The article considers explicitly the uncertainty related to the economic agents' behaviour and other relevant macroeconomic assumptions, i.e., how would consumers finance the repairing of their homes, how long does it take for a firm to reconstruct, whether firms decide to build-back-better after the inundation and possibly compensate the losses with a productivity gain. Our findings indicate that the long-term impacts of coastal floods could be larger than the direct damages. Under a high emission scenario (RCP8.5) the EU27 plus UK could lose every year between 0.25% and 0.91% of output by 2100, twice as much as the direct damages. The welfare losses present a strong regional variation, with the South (Bulgaria, Greece, Italy, Malta, Portugal and Spain), and United Kingdom (UK) plus Ireland regions showing the highest damages and a significant part of the population that could suffer significant welfare losses by the end of the century.&lt;/p&gt; &lt;/abstract&gt;

Multi-criteria analysis of options for the fuel and energy sector's development: Taking into account the energy security performance

Subject. This article discusses the methods of multi-criteria analysis of the effectiveness of energy development options. Objectives. The article aims to determine the range of criterion indicators taken into account in the comprehensive assessment of options for the development of the fuel and energy complex. Methods. For the study, we used a systems analysis applying optimization and stochastic economic and mathematical models. Results. The article offers different methodological approaches to assessing the probable status of energy security when comparing options for the energy development at different time frames of forecast research. The article also presents certain author-developed metrics that characterize the energy security performance. Conclusions. A numerical assessment of the energy security performance should become an important component of multi-criteria analysis and selection of options for the energy systems' development. The assessment methods and metrics used depend on the perspective and the task in hand.

Data-driven energy management of isolated power systems under rapidly varying operating conditions

We propose an energy management algorithm for isolated industrial power systems that integrate uncertain renewable generation and energy storage. The proposed strategy is designed to ensure sustainable and cost-effective operations by managing the energy flows in the grid, and is structured so to cope with: (1) high levels of renewable power penetration, and (2) load profiles characterized by non-smooth patterns and irregular events (i.e., events such as those occurring from connections/disconnections of large scale equipment, or from large wind speed ramps). The proposed algorithm leverages a stochastic economic model predictive control (MPC) scheme capable of dealing simultaneously with the dispatch and scheduling of the local generation units. More precisely, the scheme embeds a mixed-integer linear programming (MILP) optimal control policy formulation together with a stochastic programming approach. Moreover, the optimization problem accounts for multiple techno-economical objectives, such as minimization of operational costs, battery degradation, and non-utilized energy. We test the algorithm on a case study of an isolated offshore Oil & Gas platform producing energy onsite with conventional gas turbines and a local wind farm, while integrating a battery energy storage system. The results show that the proposed approach can issue ensemble predictions that successfully capture the potential irregular variations just by using recent past information of the associated random variable, even when no particular sudden events are anticipated in the near-future (i.e., step changes/trend reversals). In this way, the approach provides useful future information for the optimal management of the grid. This effect is numerically quantified via simulations that compare the performance of the proposed stochastic optimization approach against its deterministic MPC version in several realistic operating conditions. The empirical results suggest that the stochastic version leads to better scheduling of the conventional generators, with up to 12.86% reductions of the operating cost, 2.56% reduction in fuel consumption and emissions, and 35.29% reduction in status transitions (on/off) of the gas turbines, while keeping dumped energy and battery degradation as low as possible.

Computational analysis of the behavior of stochastic volatility models with financial applications

Volatility estimation is an important issue in certain aspects of the financial community, such as risk management and asset pricing. It is known that stock returns often exhibit volatility clustering and the tails of the distributions of these series are fatter than the normal distribution. As a response to the need of these issues, the high unconditional volatility of assets encourages the users to predict their price in an ever changing market environment. Our main focus in this paper is to study the behavior of returns and volatility dynamics of some general stochastic economic models. First, we apply the local polynomial kernel smoothing method based on nonparametric regression to estimate the mean and the variance of the returns. We then implement and develop an empirical likelihood procedure in terms of conditional variance on daily log returns for inference on the nonparametric stochastic volatility as well as to construct a confidence interval for the volatility function. It appears that the proposed algorithm is applicable to some popular financial models and represents a good fit for the behavior observed in the stock and cryptocurrency markets. Some numerical results in connection to real data on the S&P 500 index and highly volatile Bitcoin dataset are also illustrated.

A Stochastic Model of Economic Growth in Time-Space

We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such a problem has been the object of various papers in deterministic cases when the possible presence of stochastic disturbances is ignored (see, e.g., [P. Brito, The Dynamics of Growth and Distribution in a Spatially Heterogeneous World, working paper 2004/14, ISEG-Lisbon School of Economics and Management, University of Lisbon, 2004], [R. Boucekkine, C. Camacho, and G. Fabbri, J. Econom. Theory, 148 (2013), pp. 2719--2736], [G. Fabbri, J. Econom. Theory, 162 (2016), pp. 114--136], and [R. Boucekkine, G. Fabbri, S. Federico, and F. Gozzi, J. Econom. Geography, 19 (2019), pp. 1287--1318]). Here we propose and solve a stochastic generalization of such models where the stochastic term, in line with the standard stochastic economic growth models (see, e.g., the books [A. G. Malliaris and W. A. Brock, Stochastic Methods in Economics and Finance, Advanced Textbooks in Economics 17, North Holland, 1982, Chapter 3] and [H. Morimoto, Stochastic Control and Mathematical Modeling: Applications in Economics, Cambridge Books, 2010, Chapter 9]), is a multiplicative one, driven by a cylindrical Wiener process. The problem is studied using the dynamic programming approach. We find an explicit solution of the associated HJB equation, use a verification type result to prove that such a solution is the value function, and find the optimal feedback strategies. Finally, we use this result to study the asymptotic behavior of the optimal trajectories.

Three dimensional fractal attractors in a green transition economic growth model

We analyze a two-sector stochastic economic growth model of green transition with pollution externalities and foreign capital. The final good is produced by combining dirty and clean inputs, with different implications on pollution accumulation. Pollution negatively affects production capabilities and can be reduced by switching to the clean input. The clean input is produced by using the dirty input and the foreign capital received (in the form of dirty input). Random shocks make the effective economy’s ability to transition to green activities highly uncertain, eventually undermining its economic development. Such a setting gives rise to a dynamic system represented by a three dimensional affine iterated function system. We show that the economy’s steady state is represented by an invariant measure supported on a compact set, characterizing its fractal nature and showing that its attractor may be a distorted Sierpiński tetrahedron.

Neoclassical stochastic economic growth model: An application to the Bolivian economy

The following project is to consider a neoclassical model. To see the grow in one-sector a continuous-time of Ramsey-type with an utility and production function. Where each component are exposed in exogenous shocks. The corresponding dynamics are represented by stochastic differential equations. Equations are solved explicitly maximizing the average, the utility level that it has by consumption. In particular, Bolivia‟s economy, the period of analysis and the equations that describe the behaviour or long-term trajectory of real PIB, Gross Fixed Capital Formation. The total population is considered as a labor force and the optimal consumption. As a result, we presented the equations that were found through simulations to use mathematical software Mat Lab, making some replicas observed in panel data in Bolivian´s economy. Which represents fluctuations and long-term growth of the economy? To investigate the fluctuations and the economic growing in Bolivia, with the model neoclassic in a large period.

High-Dimensional Dynamic Stochastic Model Representation

We propose a generic and scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within an MPI–TBB parallel time-iteration framework, we approximate economic policy functions using an adaptive, high-dimensional model representation scheme, combined with adaptive sparse grids. With increasing dimensions, the number of points in this efficiently-chosen combination of low-dimensional grids grows much more slowly than standard tensor product grids, sparse grids, or even adaptive sparse grids. Moreover, the adaptivity within the individual component functions adds an additional layer of sparsity, since grid points are added only where they are most needed — that is to say, in regions of the computational domain with steep gradients or at non-differentiabilities. Second, we introduce a performant vectorization scheme of the interpolation compute kernel. Third, we validate our claims with numerical experiments conducted on “Piz Daint (Cray XC50) at the Swiss National Super-computing Center. We observe significant speedups over the state-of-the-art techniques, and almost ideal strong scaling up to at least 1, 000 compute nodes. Fourth, to demonstrate the broad applicability of our method, we compute global solutions to two different versions of a dynamic stochastic economic model: a high-dimensional international real business cycle model with capital adjustment costs, and with or without irreversible investment. We solve these models up to 300 continuous state variables globally.

Stochastic economic model predictive control for real-time scheduling of balance responsible parties

This paper presents stochastic economic model predictive control (SEMPC) method for real-time economic dispatch of Balance Responsible Parties (BRPs) as load balance controller in power system structure. In this regard, SEMPC method operates on the energy time scale and optimizes the expected economic performance of the BRP. Calculated set-points are average power injection of controllable generators, as well as known disturbance of prediction wind generation. The novel SEMPC scheme is able to cope with the wind uncertainty occurring in the real-time operation of BRPs. Furthermore, the proposed algorithm can take into account the technical constraints of generators and transmission line constraints of the power network. Simulations on IEEE 9-bus and 57-bus test systems with proposed method shows improvements inability to track reference production, economic performance and imbalance energy with respect to nominal predictive controllers.

A stochastic economic growth model with health capital and state-dependent probabilities

Abstract We analyze a simple stochastic model of economic growth in which physical and health capital accumulation jointly contribute to determine long run economic growth. Health capital is subject to random shocks via the effects of behavioral changes: unpredictable changes in individuals’ attitude toward healthy behaviors may reduce the effectiveness of health services provision; this in turn, by reducing the production of new health capital, lowers economic production activities negatively affecting economic growth. Unlike the extant literature, we assume that the probability with which such random shocks occur is not constant but state-dependent. Specifically, the probability that behavioral changes will negatively impact on health capital and economic growth depends on the level of economic development, proxied by the relative abundance of health capital with respect to physical capital. We show that our model’s dynamics can be converted into an iterated function system with state-dependent probabilities which converges to an invariant self-similar measure supported on a (possibly fractal) compact attractor. We develop a numerical method to approximate the invariant distribution to illustrate its features in specific model’s parametrizations, exemplifying thus the effects of state-dependent probabilities on the model’s steady state.

Yet more on a stochastic economic model: Supplement to Part 4: A model for share earnings, dividends and prices

AbstractIn this paper, we revisit the Earnings, Cover (the ratio of earnings over dividends) and Price/Earnings (P/E) Ratio models which we introduced in Part 4 of this series. Although we suggested that the significant decline in the Earnings Index over 2015-2016 might be followed by dividends and share prices, this has not happened. Instead, Earnings have risen substantially over the years 2016 to 2018. Therefore, we revise our models based on the updated data and compare the new set of models with the one in Part 4 as well as with themselves. We then compare different methods for forecasting Dividends and Share Prices.

331 Economic comparison of march and may calving systems in the nebraska sandhillls

Abstract A 3-yr study evaluated the economic differences between a March and May calving production system of crossbred beef cows and their offspring from the Gudmundsen Sandhills Laboratory, Whitman, NE. Both herds were treated as a common when not in treatment period. Adjusted calf weaning BW was higher (P) for March Calves (226.4 ± 1.1 kg vs 193.4 ± 2 kg). Pregnancy rates (89% vs 91%) were similar through both systems. The stochastic economic model used for the analysis was based on 9 yr of USDA AMS data. The model accounts for most assumptions within each system, including all labor, cull and replacement cow costs and feed costs. This analysis was on the total calf costs, total pair feed costs and average market net return at weaning. March systems wintered on hay had a positive net return 2 out of the 9 yr (Average of -$88.76/calf) and on cornstalks 8 out of 9 years in Dawson County, NE (Average of $62.75/calf). March systems on winter range feed 0.41 kg DM/(cow • d) of supplement had a positive net return 4 out of the 9 yrs (Average of $25.23/calf). The May system, no matter the treatments of range or meadow and with or without supplement, had a positive net return 2 out of the 9 years (Average of $-65.77 and $-83.90/calf). Within this analysis, even with the input costs being higher for March, the net return was still greater in a March vs May system. Further analysis will be done on different trts within each system.

Machine learning for high-dimensional dynamic stochastic economies

We present a novel computational framework that can compute global solutions to high-dimensional dynamic stochastic economic models on irregular state space geometries. This framework can also resolve value and policy functions’ local features and perform uncertainty quantification, in a single model evaluation. We achieve this by combining Gaussian process machine learning with active subspaces; we then embed this into a parallelized discrete-time dynamic programming algorithm. To demonstrate the broad applicability of our method, we compute solutions to stochastic optimal growth models of up to 500 continuous dimensions. We also show that our framework can address parameter uncertainty and can provide predictive confidence intervals for policies that correspond to the epistemic uncertainty induced by limited data. Finally, we propose an algorithm that, based on combining this framework with Bayesian Gaussian mixture models, is capable of learning irregularly shaped ergodic sets as well as performing dynamic programming on them.

Equilibria in Altruistic Economic Growth Models

In this paper, we consider a stochastic economic growth model in the form of an intergenerational dynamic game. Both paternalistic and non-paternalistic components are present in the model. Under very general assumptions allowing for unbounded utility functions and weakly continuous transitions, we establish the existence of Markov perfect equilibria that consist of a consumption strategy and an indirect utility function. In the pure paternalistic case, we obtain new results on equilibria. An important point of our contribution is that we make no separability assumptions on the utility functions of generations.

Uncertainty cost functions for solar photovoltaic generation, wind energy generation, and plug-in electric vehicles: mathematical expected value and verification by Monte Carlo simulation

Electrical power systems which incorporate solar or wind energy sources, or electric vehicles, must deal with the uncertainty about the availability of injected or demanded power. This creates uncertainty costs to be considered in stochastic economic dispatch models. The estimation of these costs is important for proper management of energy resources and accurate allocation of the amount of energy available for the system. In this paper, analytical formulas of uncertainty penalty costs are calculated, for solar and wind energy and for electric vehicles, through a mathematical expected value formulation. In order to get the proposed uncertainty cost functions, probability distribution functions (PDF) of the energy primary sources are considered, that is to say: log-normal distribution for solar irradiance PDF, Rayleigh distribution for wind speed PDF and normal distribution for loading and unloading behaviour PDF of electric vehicles. The analytical formulation is verified through Monte Carlo simulations.