The short-term forecasting of real-time locational marginal price (LMP) and network congestion is considered from a system operator perspective. A new probabilistic forecasting technique is proposed based on a multiparametric programming formulation that partitions the uncertainty parameter space into critical regions from which the conditional probability distribution of the real-time LMP congestion is obtained. The proposed method incorporates load generation forecast, time varying operation constraints, and contingency models. By shifting the computation cost associated with multiparametric programs offline, the online computation cost is significantly reduced. An online simulation technique by generating critical regions dynamically is also proposed, which results in several orders of magnitude improvement in the computational cost over standard Monte Carlo methods.
In contrast to @cite_4 , our objective is to forecast directly the probability distribution of future LMP congestion, . Because a system operator has access to all private and public information about system conditions, the critical regions are computed exactly via a multiparametric program. This allows us to incorporate load and generation forecasts and obtain the (conditional) probability distribution of future LMP congestion directly.
@cite_4
2136340918 2124895057 2165594353 2010590907
We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. In power market studies, the forecast of locational marginal price (LMP) relies on the load forecasting results from the viewpoint of planning. It is well known that short-term load forecasting results always carry certain degree of errors mainly due to the random nature of the load. At the same time, LMP step changes occur at critical load levels (CLLs). Therefore, it is interesting to investigate the impact of load forecasting uncertainty on LMP. With the assumption of a certain probability distribution of the actual load, this paper proposes the concept of probabilistic LMP and formulates the probability mass function of this random variable. The expected value of probabilistic LMP is then derived, as well as the lower and upper bound of its sensitivity. In addition, two useful curves, alignment probability of deterministic LMP versus forecasted load and expected value of probabilistic LMP versus forecasted load, are presented. The first curve is designed to identify the probability that the forecasted price in a deterministic LMP matches the actual price at the forecasted load level. The second curve is demonstrated to be smooth and therefore eliminates the step changes in deterministic LMP forecasting. This helps planners avoid the possible sharp changes during decision-making process. The proposed concept and method are illustrated with a modified PJM five-bus system and the IEEE 118-bus system. This paper introduces a probabilistic method for short-term transmission congestion forecasting, which is recently developed by EPRI. The proposed method applies the sequential Monte Carlo simulation (MCS) in a probabilistic load flow as the conceptual framework, adds all the significant uncertainties and their probability distributions to be modeled, develops the models, and most importantly specifies how to accurately model the key input assumptions in order to derive valid confidence levels of the forecasted congestion variables. The developed probabilistic method is successfully applied to the four-area WECC equivalent system. Focus is on the confidence levels of making such forecasts, so that a window of forecast-ability is defined, beyond which any forecast would be considered to contain little actionable information. Within the window of forecast-ability, the probabilistic forecasts of congestion would provide confidence limits and information for ranking the potential benefits of alleviating congestion at the various transmission bottlenecks. The problem of forecasting the real-time locational marginal price (LMP) by a system operator is considered. A new probabilistic forecasting framework is developed based on a time in-homogeneous Markov chain representation of the realtime LMP calculation. By incorporating real-time measurements and forecasts, the proposed forecasting algorithm generates the posterior probability distribution of future locational marginal prices with forecast horizons of 6–8 hours. Such a short-term forecast provides actionable information for market participants and system operators. A Monte Carlo technique is used to estimate the posterior transition probabilities of the Markov chain, and the real-time LMP forecast is computed by the product of the estimated transition matrices. The proposed forecasting algorithm is tested on the PJM 5-bus system. Simulations show marked improvements over benchmark techniques.