Scenario reduction for stochastic unit commitment with wind penetration

Uncertainties in the day-ahead forecasts for load and wind energy availability are considered in a reliability unit commitment problem. A two-stage stochastic program is formulated to minimize total expected cost, where commitments of thermal units are viewed as first-stage decisions and dispatch is relegated to the second stage. Scenario paths of hourly loads are generated according to a weather forecast-based load model. Wind energy scenarios are obtained by identifying analogue historical days. Net load scenarios are then created by crossing scenarios from each set and subtracting wind energy from load. A new heuristic scenario reduction method termed forward selection in recourse clusters (FSRC) is customized to alleviate the computational burden. Results of applying FSRC are compared with those of a classical scenario reduction method, fast forward selection (FFS) by evaluating the expected dispatch costs when the commitment decisions derived from each subset of scenarios are applied to the whole scenario set. In an instance down-sampled from data of an Independent System Operator in the U.S., the expected dispatch costs for both scenario reduction methods are similar, but FSRC improves reliability

Application of scenario reduction to LDC and risk based generation expansion planning

Abstract: Two-stage stochastic mixed-integer programming models are formulated for minimizing expected cost or Conditional Value-at-Risk (CVaR) of a long-term power generation expansion planning problem incorporating load duration curves. The multivariate stochastic processes, such as electricity demands and fuel prices, are modeled as geometric Brownian motion (GBM) processes. Scenario paths for their future evolution are generated by statistical extrapolation of long-term historical trends. The size of the scenario set is controlled by using increasing length time periods in a tree structure. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the forward selection heuristic for scenario reduction, a combined heuristic scenario reduction method named Forward Selection in Wait-and-see Clusters (FSWC) is applied to the large scenario set. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone

Scenario generation and reduction for long-term and short-term power system generation planning under uncertainties

This dissertation focuses on computational issues of applying two-stage stochastic programming for long-term and short-term generation planning problems from the perspective of scenario generation and reduction. It follows a three-paper format, in which each paper discusses approaches to generating probabilistic scenarios and then reducing the substantial computational burden caused by a huge number of scenarios for different applications in power systems. The first paper investigates a long-term generation expansion planning model with uncertain annual load and natural gas price. A two-stage stochastic program is formulated to minimize the total expected expansion cost, generation cost and penalties on unserved energy while satisfying aggregated operational constraints. A statistical property matching technique is applied to simulate plausible future realizations of annual load and natural gas price over the whole planning horizon. To mitigate the computational complexity of a widely used classic scenario reduction method in this context, we firstly cluster scenarios according to the wait-and-see solution for each scenario and then apply the fast forward selection (FFS) method. The second paper prepares a basis for load scenario generation for the day-ahead reliability unit commitment problem. For the purpose of creating practical load scenarios, epi-splines, based on approximation theory, are employed to approximate the relationship between load and weather forecasts. The epi-spline based short-term load model starts by classifying similar days according to daily forecast temperature as well as monthly and daily load patterns. Parameters of the epi-spline based short-term load model are then estimated by minimizing the fitted errors. The method is tested using day-ahead weather forecast and hourly load data obtained from an Independent System Operator in the U.S. By considering the non-weather dependent load pattern in the short-term load model, the model not only provides accurate load predictions and smaller prediction variances in the validated days, but also preserves similar intraday serial correlations among hourly forecast loads to those from actual load. The last paper in this dissertation proposes a solution-sensitivity based heuristic scenario reduction method, called forward selection in recourse clusters (FSRC), for a two-stage stochastic day-ahead reliability unit commitment model. FSRC alleviates the computational burden of solving the stochastic program by selecting scenarios based on their cost and reliability impacts. In addition, the variant of pre-categorizing scenarios improves the computational efficiency of FSRC by simplifying the clustering procedure. In a case study down-sampled from an Independent System Operator in the U.S., FSRC is shown to provide reliable commitment strategies and preserve solution quality even when the reduction is substantial

A new approximation method for generating day-ahead load scenarios

Unit commitment decisions made in the day-ahead market and resource adequacy assessment processes are based on forecasts of load, which depends strongly on weather. Two major sources of uncertainty in the load forecast are the errors in the day-ahead weather forecast and the variability in temporal patterns of electricity demand that is not explained by weather. We develop a stochastic model for hourly load on a given day, within a segment of similar days, based on a weather forecast available on the previous day. Identification of similar days in the past is based on weather forecasts and temporal load patterns. Trends and error distributions for the load forecasts are approximated by optimizing within a new class of functions specified by a finite number of parameters. Preliminary numerical results are presented based on data corresponding to a U.S. independent system operator

Dietary Calcium but Not Elemental Calcium from Supplements Is Associated with Body Composition and Obesity in Chinese Women

We assessed whether dietary calcium intake or calcium supplements associated with body composition and obesity in a Chinese population.A cross-sectional survey was performed in a population of 8940, aged 20 to 74 y. 8127 participants responded (90.9%). Height, weight, fat mass (FM), waist circumference (WC) and hip circumference were measured. Obesity definition: body mass index (BMI) ≥28 kg/m(2) (overall obesity); WC ≥85 cm for men or ≥80 cm for women (abdominal obesity І) and waist hip ratio (WHR) ≥0.90 for men or ≥0.85 for women (abdominal obesity П). The data on dietary calcium and calcium supplements were collected using food-frequency questionnaire and self-report questionnaire. Multivariate linear and multivariable logistic regressions were used to examine the associations between dietary calcium intake or calcium supplements and body composition and obesity.The average dietary calcium intake of all subjects was 430 mg/d. After adjusting for potential confounding factors, among women only, negative associations were observed between habitual dietary calcium intake and four measures of body composition (β, -0.086, P<0.001 for BMI; β, -0.072, P<0.001 for WC; β, -0.044, P<0.05 for WHR; and β, -0.058, P<0.01 for FM, respectively) and both measures of abdominal obesity (Odds Ratio [OR] = 0.86, 95% Confidence Interval [CI], 0.80-0.93; P<0.001, for abdominal obesity I; OR = 0.92, 95% CI, 0.86-0.99; P = 0.026, for abdominal obesity II). These associations were not observed among men (P>0.05). Similarly, among both men and women, we did not observe significant associations between calcium supplements and any measures of body composition or abdominal obesity (P>0.05).Dietary calcium from food rather than elemental calcium from calcium supplements has beneficial effects on the maintenance of body composition and preventing abdominal obesity in Chinese women

Drivers of vegetation and soil determine natural regeneration of a single plantation at different slope positions

Promoting natural regeneration in artificial forest ecosystems is crucial for sustainable management. Understanding the fundamental mechanisms and drivers of tree regeneration is the prerequisite for promoting it effectively. This study worked with Larix principis-rupprechtii, a species considered difficult to regenerate. Twenty-four sample plots measuring 30 m × 30 m were established, with eight plots at each of the lower, middle, and upper slope positions, respectively. Field investigation and multivariate analysis were performed to uncover the regeneration traits in the plantations with abundant seedlings on the continuous slope. The results revealed that ground diameter and height of the regeneration (RGD and RH) were larger at the lower slope, with significant positive correlations to available nitrogen (contribution rate, CR: 0.858) and slope (CR: 0.652). In contrast, regeneration density (RD), representing the quantity of regeneration, was greater at the middle slope. Its significant impact factors were slope position (CR: −0.648) and herb diversity, represented by Pielou index (CR: 0.961). Stand density had a significant negative effect on regeneration, particularly at the upper slope, with CRs of −0.842 and −0.764 to RGD/RH and RD, respectively. Common contribution was found among the factors, with the largest contribution groups being the topographical and soil factors (CR: 0.358). These findings provide valuable insights into the single species regeneration progress on northern mountainous slopes and offer essential information for developing facilitation methods for the natural regeneration in artificial forests