Short-term Uncertainty Research Articles

Multiscale Multiresolution Generation Maintenance Scheduling: A Stochastic Affinely Adjustable Robust Approach

Generation maintenance scheduling (GMS), as a medium-term operational planning problem in power system, encounters both midterm and short-term uncertainty sources. This article presents a multiscale multiresolution uncertainty model to characterize midterm and short-term uncertainties distinctively in GMS problem. In the proposed multi-scale multi-resolution GMS (MMGMS) model, the midterm uncertainty of weekly peak loads in the scheduling horizon is characterized via plausible scenarios while short-term uncertainty of hourly loads is addressed through polyhedral uncertainty sets. To make the MMGMS approach tractable, affine policies are incorporated into the proposed model. The resulting MMGMS model, considering midterm as well as short-term uncertainties, is formulated as a stochastic affinely adjustable robust optimization (SAARO) problem. To solve this problem, a new solution methodology including stochastic optimization and probabilistic dual cut is presented. Numerical results on two test systems corroborate the effectiveness of the proposed model and solution approach.

Distributionally Robust Transmission Expansion Planning: A Multi-Scale Uncertainty Approach

We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long- and short-term uncertainties on the system demand and non-dispatchable renewable generation. On the long-term level, as is customary in industry applications, we address the deep uncertainties arising from social and economic transformations, political and environmental issues, and technology disruptions by using long-term scenarios devised by experts. In this setting, many exogenous long-term scenarios containing partial information about the random parameters, namely, the average and the support set, can be considered. For each long-term scenario, a conditional ambiguity set models the incomplete knowledge about the probability distribution of the uncertain parameters in the short-term operation. Consequently, the mathematical problem is formulated as a DRO model with multiple conditional ambiguity sets. The resulting infinite-dimensional problem is recast as an exact, although very large, finite mixed-integer linear programming problem. To circumvent scalability issues, we propose a new enhanced-column-and-constraint-generation (ECCG) decomposition approach with an additional Dantzig--Wolfe procedure. In comparison to existing methods, ECCG leads to a better representation of the recourse function and, consequently, tighter bounds. Numerical experiments based on the benchmark IEEE 118-bus system are reported to corroborate the effectiveness of the method.

Representative Days for Expansion Decisions in Power Systems

Short-term uncertainty needs to be properly modeled when analyzing a planning problem in a power system. Since the use of all available historical data may lead to problems of computational intractability, clustering algorithms may be applied in order to reduce the computational effort without compromising accurate representation of historical data. In this paper, we propose a modified version of the traditional K-means method, seeking to represent the maximum and minimum values of input data, namely, electricity demand and renewable production in several locations of a power system. Extreme values of these parameters must be represented as they are high-impact decisions that are taken with respect to expansion and operation. The method proposed is based on the K-means algorithm, which represents the correlation between demand and wind-power production. The chronology of historical data, which influences the performance of some technologies, is characterized through representative days, each made up of 24 operating conditions. A realistic case study, applying representative days, analyzes the generation and transmission expansion planning of the IEEE 24-bus Reliability Test System. Results show that the proposed method is preferable to the traditional K-means technique.

Distributionally Robust Chance-Constrained Generation Expansion Planning

This article addresses a centralized generation expansion planning problem, accounting for both long- and short-term uncertainties. The long-term uncertainty (demand growth) is modeled via a set of scenarios, while the short-term uncertainty (wind power generation) is described by a family of probability distributions with the same first- and second-order moments obtained from historical data. The resulting model is a distributionally robust chance-constrained optimization problem, which selects the conventional generating units to be built among predefined discrete options. This model includes a detailed representation of unit commitment constraints. To achieve computational tractability, we use a tight relaxation approach to convexify unit commitment constraints and solve the model with linear decision rules, resulting in a mixed-integer second-order cone program. It is observed that the proposed model exhibits better out-of-sample performance in terms of total expected system cost and its standard deviation compared to a chance-constrained model that assumes a Gaussian distribution of short-term uncertainty. A similar observation is made when comparing the proposed model against a chance-constrained program that uses empirical renewable power generation data with unknown type of distribution, recasting as either a robust optimization or a stochastic program.

Data-driven Operation Risk Assessment of Wind-integrated Power Systems via Mixture Models and Importance Sampling

The increasing penetration of highly intermittent wind generation could seriously jeopardize the operation reliability of power systems and increase the risk of electricity outages. To this end, this paper proposes a novel data-driven method for operation risk assessment of wind-integrated power systems. Firstly, a new approach is presented to model the uncertainty of wind power in lead time. The proposed approach employs k-means clustering and mixture models (MMs) to construct time-dependent probability distributions of wind power. The proposed approach can also capture the complicated statistical features of wind power such as multimodality. Then, a non-sequential Monte Carlo simulation (NSMCS) technique is adopted to evaluate the operation risk indices. To improve the computation performance of NSMCS, a cross-entropy based importance sampling (CE-IS) technique is applied. The CE-IS technique is modified to include the proposed model of wind power. The method is validated on a modified IEEE 24-bus reliability test system (RTS) and a modified IEEE 3-area RTS while employing the historical data of wind generation. The simulation results verify the importance of accurate modeling of short-term uncertainty of wind power for operation risk assessment. Further case studies have been performed to analyze the impact of transmission systems on operation risk indices. The computational performance of the framework is also examined.

Multi-period planning of multi-energy microgrid with multi-type uncertainties using chance constrained information gap decision method

In this paper, we study the multi-period planning problem of multi-energy microgrids considering the long-term uncertainty (i.e., the declining trend of battery storage investment cost) and the short-term uncertainty (i.e., renewable energy generation and electrical/heat load). We first present the joint deterministic multi-period planning approach for multi-energy microgrid coupling electricity and heat carriers. Then, an information gap decision (IGD)-based multi-energy microgrid multi-period planning model dealing with the long-term uncertainty is proposed, and the proposed model is further converted into a mixed integer linear planning (MILP) IGD-based planning model. Next, to coordinate the long-term uncertainty and the short-term uncertainty in multi-energy microgrid planning problems, we develop a chance constrained (CC) IGD-based multi-period planning model and then convert such model into a MILP CC-IGD equivalence. Finally, the strengthened bilinear Benders decomposition (SBBD) algorithm is adopted to efficiently solve our proposed MILP CC-IGD model for large-scale multi-energy microgrid planning problems. Our numerical results demonstrate the advantage of the joint planning of electricity and heat supply systems in multi-energy microgrids. Case studies verify the effectiveness of considering multi-type uncertainties in multi-energy microgrid planning, especially the declining trend uncertainty of battery storage investment cost. Experimental results also show that the SBBD algorithm is more efficient on computing our proposed MILP CC-IGD model compared to commercial solvers, such as CPLEX.

Correction to: Measuring short-term risk of initial public offering of equity securities: a hybrid Bayesian and Data-Envelopment-Analysis-based approach

This paper offers a methodology to estimate an unconditional probability density function (PDF) for the stock price of an initial public offering (IPO), at a short-term post-IPO horizon. The resultant PDF is unique to the IPO of interest (IPOI) and serves to model the short-term post-market uncertainty associated with its price. Such a methodology is unprecedented in the IPO risk literature since the ex ante quantification of the short-term uncertainty associated with the stock price of a newly public firm was viewed as burdened by the lack of sufficient accounting and market history at the IPO stage. This gap is addressed here through recognizing that common in most IPO cases are the scarcity of hard data and abundance of soft data (strong prior belief), and that one can combine Bayesian inference and Data Envelopment Analysis (DEA) to develop a unique risk quantification setting that befits and serves these two characteristics of IPOs. In this setting, DEA serves to quantify the prior belief, to be subsequently updated in the Bayesian phase. This paper remains the first of its kind which unravels the IPO risk analysis from such perspective. It develops an iterative process that uses DEA to design a multi-dimensional similarity metric to find the ‘comparables’ to IPOI, and thereof the closest comparable to it, whereupon Bayesian inference is employed to utilize the information available from these comparables to sequentially update and revise the IPOI’s prior PDF. The validity of the proposed risk methodology was examined by backtesting analyses.

Influence of the controllability of electric vehicles on generation and storage capacity expansion decisions

This paper proposes a capacity investment model to analyze the influence of the controllability of the charge of plug-in electric vehicles (PEVs) in generation and storage expansion decisions. The proposed model provides the financial incentives that should be offered to PEV users in order to implement the optimal expansion decisions. Considering that the decision-making process faced by the power system planner must simultaneously consider long- and short-term uncertainties, a three-stage stochastic programming problem is formulated. In this model, capacity investments and financial incentives for PEV users are decided in the first stage, whereas operating decisions regarding the day-ahead and real-time markets are made in the second and third stages, respectively. Numerical results are provided from a realistic case study based on the isolated power system comprising Lanzarote and Fuerteventura islands in Spain.

Considering short-term and long-term uncertainties in location and capacity planning of public healthcare facilities

This paper addresses a real-world problem faced by the public healthcare sector. The problem consists of both the patients’ and service provider's requirements (i.e., accessibility vs. costs) for locating healthcare facilities, allocating service units to those facilities, and determining the facilities’ capacities. The main contribution of this study is capturing both short-term and long-term uncertainties at the modelling stage. The queuing theory is incorporated to consider stochastic demand and service time as a short-term uncertainty, as well as a service level measurement. The developed nonlinear model is then converted into a linear model after introducing a new set of decision variables and proving the properties of the service level constraints. We also demonstrate a way in which a linearized model can become more efficient by eliminating excessive binary variables when service level constraints are approximated using their properties. Additionally, long-term demographic variations are captured through robust optimization in order to create a robust model. To solve the problem under investigation, an evolutionary solution method is designed, and its performance is investigated under different settings. We apply this solution method to determine the location and capacity of healthcare facilities in one of the provinces of Iran. The results illustrate that the suggested network can significantly improve the performance measures compared to the existing network. Furthermore, the importance of robust solution in maintaining the desired service level is demonstrated through examining three levels of demographic variations.

The multi-vehicle stochastic-dynamic inventory routing problem for bike sharing systems

We address the operational management of station-based bike sharing systems (BSSs). In BSSs, users can spontaneously rent and return bikes at any stations in the system. Demand is driven by commuter, shopping, and leisure activities. This demand constitutes a regular pattern of bike usage over the course of the day but also shows a significant short-term uncertainty. Due to the heterogeneity and the uncertainty in demand, stations may run out of bikes or congest during the day. At empty stations, no rental demand can be served. At full stations, no return demand can be served. To avoid unsatisfied demand, providers dynamically relocate bikes between stations in reaction of current shortages or congestion, but also in anticipation of potential future demand. For this real-time decision problem, we present a method that anticipates potential future demands based on historical observations and that coordinates the fleet of vehicles accordingly. We apply our method for two case studies based on real-world data of the BSSs in Minneapolis and San Francisco. We show that our policy outperforms benchmark policies from the literature. Moreover, we analyze how the interplay between anticipation and coordination is essential for the successful operational management of BSSs. Finally, we reveal that the value of coordination and anticipation based on the demand-structure of the BSS under consideration.

Effects of Short-Term Uncertainties on the Revenue Estimation of PPP Sewage Treatment Projects

Many sewage treatment facilities in China have been developed and operated using the Public-Private Partnerships (PPP) model. However, a big challenge faced by these PPP projects is that the subsidy requested from the government during the operation is normally higher than what was estimated originally, thus often exceeding the budget that the government can afford. This leads to a high risk of project failure or insufficient operation. This problem is largely caused by the uncertainties exhibited in the existing models, such as the Black-Scholes (BS) model. While being used in the budget estimation, these models cannot sufficiently account for the short-term uncertainty that may be incurred during the operation of projects. In this study, a method to account for this short-term uncertainty has been proposed to improve the BS model. This allows for investigations to address issues related to how the real option value of a government subsidy is affected. A Monte Carlo simulation was performed to take into account the noise in the estimation. A sensitivity analysis further revealed that this discrepancy is largely affected by the values of the relevant parameters in the short-term uncertainty model. We found that the short-term uncertainty has a significant effect on private revenue and government subsidy and that the changes of the latter are more sensitive to the change of short-term uncertainty. The value of the relevant variables of short-term uncertainty determined the fluctuation of the revenue. The mean value and revenue had a positive correlation. The reverting speed and revenue showed a negative correlation. The short-term volatility had a positive correlation toward the fluctuation range of the revenue. The simulation results indicate that this enhanced method can produce more accurate information for a better assessment of the PPP project under a wide range of uncertainty scenarios, allowing for the best decision making by the government.

Gumbel copula based multi interval ramp product for power system flexibility enhancement

High renewable penetration in modern power systems increases uncertainty and variability of net load, causing frequent real time system imbalances. This necessitates increased generation flexibility to mitigate such imbalances. Regulation services and transfer tie lines enhance system flexibility, but limited availability of conventional generating units with lower operational time frame and the associated high investment reduces their applicability. This requires development of flexible ramp products (FRP) to maintain real time power balance. FRP design should consider both variability and uncertainty of net load, with accurate uncertainty modeling. Existing ramp product design uses approximate net load uncertainty, which reduces their effectiveness. Further, existing FRP design primarily focus on wind dominated systems. Rapidly increasing solar generation from utility level plants show higher variability than wind in very short time frames. Rapid coherent changes from such plants cause massive generation variation. Considering very short term uncertainty and variability of utility level solar plants, this paper proposes a novel multi-interval FRP design based on net load forecasts. Proposed FRP design considers both start and end time uncertainty of each time interval, compared to existing end time uncertainty based designs. To enhance the net load uncertainty estimation accuracy, proposed model uses Gumbel copula function based joint probability distribution (JPD) of load, solar and wind forecasting errors, because it covers all extreme forecasting errors due to max-stable property. Results show that proposed design effectively manages the variability and uncertainty of net load, offering significant cost savings.

Tidal Current and Level Uncertainty Prediction via Adaptive Linear Programming

Short-term uncertainty prediction modeling of tidal power generation supports power systems in reserve and regulation markets. In tidal power generation via various tidal energy harvesting technologies, tidal current and level are the most influential factors. This paper addresses a nonparametric prediction interval (NPI)-based uncertainty model thereof. The proposed model adapts a bi-level optimization formulation, based on extreme learning machine (ELM) prediction engine and quantile regression (QR). The quantile probabilities are asymmetrically and adaptively chosen in the upper level optimization to make prediction intervals sharper for a specific reliability level (RL). Besides, the training process of ELM is improved by adaptively selecting ELM's hidden neurons via upper level optimization. The lower level optimization finds ELM's output weighting coefficients through linear programming of QR. The heuristic optimization, consisting of gray wolf optimizer and simplex method, is designed to facilitate the NPI with high exploration and exploitation capabilities in upper level optimization. The performance of the proposed NPI is examined using empirical data recorded in three different sites, located in North America. The results of case studies show that the proposed NPI can provide sharper PIs in comparison to the well-tailored rival models whilst a prespecified RL criterion is met.

Inertia, uncertainty, and exploratory partner selection

PurposeThe purpose of this paper is to examine the following research question in partner selection decisions in business-to-business strategic partnerships/collaborations literature: How do inertia and uncertainty affect partner selection? Explicitly, the paper analyzes how inertia of previous alliance selection routines and uncertainty of entire market movement shape firms’ preferences regarding exploratory partner selection (i.e. selecting new partners who never collaborate with the focal firm).Design/methodology/approachGrounded on inter-firm partnerships, partner selection and network theory literature, the study empirically tests a fine-grained sample of 511 open-end funds initiated by 61 fund management firms in China. To do so, it runs Tobit regression for main analysis and applies a variety of sensitivity analyses to check the robustness.FindingsResults show that inertia in previous partner selection has a negative effect on exploration. Importantly, these inertial forces impact domestic firms but not international firms. Market uncertainty also affects exploratory partner selection: short-term market uncertainty encourages exploration, whereas long-term uncertainty inhibits it. These effects also depend on firms’ type: long-term market uncertainty has a negative effect on exploration for international firms but not for domestic firms. Both types of firms exhibit a stronger tendency toward exploration when they encounter short-term uncertainty. However, this inclination is stronger in international firms.Originality/valueEarlier research has examined how inertia affects exploitation but largely overlooked its effect on exploration. A critical examination of firm and environment level factors provides a deeper understanding of why and when firms have inconsistent preferences for specific partner selection strategies. Thus, this study offers a unique perspective for understanding firms’ exploratory partner selection by focusing on two important characteristics of focal firms: one internal (inertia) and one external (market uncertainty) in nature.

The impact of short-term variability and uncertainty on long-term power planning

Traditionally, long-term investment planning models have been the apparent tool to analyse future developments in the energy sector. With the increasing penetration of renewable energy sources, however, the modelling of short-term operational issues becomes increasingly important in two respects: first, in relation to variability and second, with respect to uncertainty. A model that includes both may easily become intractable, while the negligence of variability and uncertainty may result in sub-optimal and/or unrealistic decision-making. This paper investigates methods for aggregating data and reducing model size to obtain tractable yet close-to-optimal investment planning decisions. The aim is to investigate whether short-term variability or uncertainty is more important and under which circumstances. In particular, we consider a generation expansion problem and compare various representations of short-term variability and uncertainty of demand and renewable supply. The main results are derived from a case study on the Danish power system. Our analysis shows that the inclusion of representative days is crucial for the feasibility and quality of long-term power planning decisions. In fact, we observe that short-term uncertainty can be ignored if a sufficient number of representative days is included.

Coordinated Investment in Transmission and Storage Systems Representing Long- and Short-Term Uncertainty

In this paper, the coordinated investment in transmission and storage systems under uncertainty is addressed from the perspective of a central planner. The problem is formulated with the objective of achieving an effective expansion of both transmission and storage that minimizes the investment cost, while achieving an effective operation of a power system with high penetration of renewable power. The problem is stated within an adaptive robust optimization framework that incorporates stochastic modeling. Future available generation capacity and peak load in the target year (long-term uncertainty) are modeled using a robust set, while daily operating conditions (short-term uncertainty) are represented with a scenario set. The expansion tradeoff between transmission and storage systems is analyzed using the IEEE RTS 24-bus and IEEE 118-bus networks.

A Comprehensive Assessment of the Short-Term Uncertainty of Grid-Connected PV Systems

One of the key aspects enabling the bulk integration of photovoltaic (PV) resources into the power grid is the short-term prediction of the maximum available power (from 100 ms to 5 min), and the quantification of the associated uncertainties. This is beneficial for the definition of robust control strategies able to account for the stochastic nature of this energy resource. We propose and validate a comprehensive method to assess the overall PV power uncertainties, even at operating conditions different from the maximum power point, i.e., to consider when power curtailment strategies are adopted on a controllable PV plant. The proposed gray-box modeling includes physical and data-driven submodels that rely on measurements of the PV currents, voltages, and the module temperature, information normally available to the PV plant operator. Furthermore, we identify which submodel is the most critical in terms of uncertainty, for different forecast horizons. Experimental results analyze the ability of the method to guarantee the target coverage probability while accounting for the uncertain nature of the PV resource. We show how modeling and forecasting information can be used to express the PV plant behaviour to a grid controller responsible for the safe operation of a microgrid.

Radial velocity measurements of an orbiting star around Sgr A*

Abstract During the next closest approach of the orbiting star S2/S0-2 to the Galactic supermassive black hole (SMBH), it is estimated that radial velocity (RV) measurements with an uncertainty of a few 10 km s−1 will allow us to detect post-Newtonian effects throughout 2018. To evaluate the best achievable uncertainty in RV and its stability, we carried out near-infrared, high-resolution (R ∼ 20000) spectroscopic monitoring observations of S2 using the Subaru telescope and its near-infrared spectrograph IRCS from 2014 to 2016. Br-γ absorption lines have been detected in the 2015 and 2016 spectra, but have not been clearly detected in the 2014 spectrum. The detected Br-γ absorption lines are used to determine the RVs of S2. The statistical uncertainties are derived using the jackknife analysis, and spectra combined from divided subdata sets. The wavelength calibrations in our three-year monitoring are stable: short-term (hours to days) uncertainties in RVs are ≲ 0.5 km s−1, and the long-term (three years) uncertainty is 1.2 km s−1. We thoroughly analyzed possible sources of systematic uncertainties, such as the incomplete subtraction of OH skylines. The relevant uncertainties are estimated to be less than several km s−1. The final results using the Br-γ line are 877 ± 25 km s−1 in 2015, and 1109 ± 14 km s−1 in 2016. When we use two He i lines at 2.113 μm in addition to Br-γ, the mean RV and its standard error are 1114 km s−1 and 5 km s−1, respectively, in 2016. However, we have found a larger scatter around the expected RV curve with the best-fitting orbiting parameters of S2, implying additional uncertainties not yet considered. The difference between the RVs estimated by Newtonian mechanics and general relativity will reach about 200 km s−1 near the next pericenter passage in 2018. Therefore, in addition to astrometric and spectroscopic data obtained with other telescopes, RV measurements with Subaru in 2018 will form important data sets with which to detect general relativistic effects from the SMBH.

A stochastic integrated planning of electricity and natural gas networks for Queensland, Australia considering high renewable penetration

This study develops a long-term integrated planning approach to electricity and gas aiming at economically optimizing the 2030's investments of both networks while considering new policies towards future clean energy. A static stochastic cost minimization model is formulated, which takes into account the short-term uncertainties of renewable power, i.e. wind and utility-scale solar photovoltaic (PV) as well as the long-term uncertainties of load growth and gas price. The equivalent networks of both electricity and gas are driven to accurately capture their existing supplies and transmission networks. In addition, the integrated planning model allows determining the location of new power plants and gas supply facilities with their optimized capacities, as well as new transmission lines and pipelines. An extension of the proposed scheme is considered to accommodate higher penetrations of renewable energy and assess their impacts on both systems. The proposed model is applied to the state of Queensland in Australia, which is a prime example of a region actively integrating electricity and gas.

Candidate line selection for transmission expansion planning considering long- and short-term uncertainty

The objective of transmission expansion planning (TEP) is to expand and/or reinforce the transmission network to satisfy the increasing future demand for electricity and to integrate new power plants while maintaining an efficient operation of the system. The candidate lines initially considered for investment largely depend on the expertise of the system planner, which may result in inaccuracies if large networks are considered, as a result of the necessarily limited expertise of the planner. In this paper, we propose an algorithm to generate an effective candidate-line set for TEP considering both long- and short-term uncertainty. The long-term uncertainty includes the peak demand and available generating capacity of the system during the target year (e.g., 10 years from now) and it is described via an uncertainty set. Then, within the target year, the short-term uncertainty pertaining to different operating conditions is represented via a scenario set.