Abstract: A method of Bayesian Variational Inference using Asymmetric Hamiltonian Monte Carlo includes gathering a number of data samples for a Hamiltonian Monte Carlo computation and instantiating an auxiliary distribution on the data samples, the auxiliary distribution being asymmetric. A Hamiltonian Monte Carlo computation is performed with the auxiliary distribution and the plurality of data samples. Upon determining that a metric of the computation outcome does not meet a target metric criterion that is based on a target distribution, the auxiliary distribution is adapted to an output of the computation and the Hamiltonian Monte Carlo computation is re-executed with the adapted auxiliary distribution. A report is generated in response to determining that the target metric is well estimated.

Abstract: A method for operating a power generating facility connected to a power distribution grid having an uncertain power generation condition includes predicting a probabilistic power flow forecast in a transmission line of the power distribution grid for a period of time, wherein the transmission line is electrically coupled to the power generating facility, predicting, using the probabilistic power flow forecast, a probability of congestion over the transmission line of the power distribution grid during the period of time, generating a mitigation plan, including a load adjustment on the transmission line, using the probability of congestion predicted over the transmission line and a thermal limit constraint of the transmission line, wherein the mitigation plan balances load adjustment and an overlimit line capacity on the transmission line, and controlling the power generating facility, using the mitigation plan, to achieve load modification and mitigate the probability of congestion predicted in the transmissi

Abstract: A method for determining power output levels of a plurality of nodes in an electric power system includes receiving, at a first node of the plurality of nodes, voltage information and multipliers of all neighboring nodes of the first node within the electric power system, determining, by the first node, a local power generation and a local voltage using the voltage information and the multipliers of the neighboring nodes and distributing the local power generation and the local voltage to the neighboring nodes, determining, by the first node, an estimated voltage of each of the neighboring nodes and distributing the estimated voltage to each of the neighboring nodes, and updating, by the first node, a local multiplier using the voltage information received from the neighboring nodes and the estimated voltage of each of the neighboring nodes determined by the node.

Abstract: A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Abstract: Systems and methods for modeling and forecasting cyclical demand systems in the presence of dynamic control or dynamic incentives. A method for modeling a cyclical demand system comprises obtaining historical data on one or more demand measurements over a plurality of demand cycles, obtaining historical data on incentive signals over the plurality of demand cycles, constructing a model using the obtained historical data on the one or more demand measurements and the incentive signals, wherein constructing the model comprises specifying a state-space model, specifying variance parameters in the model, and estimating unknown variance parameters.

Abstract: A method for operating a power generating facility connected to a power distribution grid having an uncertain power generation condition includes predicting a probabilistic power flow forecast in a transmission line of the power distribution grid for a period of time, wherein the transmission line is electrically coupled to the power generating facility, predicting, using the probabilistic power flow forecast, a probability of congestion over the transmission line of the power distribution grid during the period of time, generating a mitigation plan, including a load adjustment on the transmission line, using the probability of congestion predicted over the transmission line and a thermal limit constraint of the transmission line, wherein the mitigation plan balances the load adjustment and an overlimit line capacity on the transmission line, and controlling the power generating facility, using the mitigation plan, to achieve the load modification and mitigate the probability of congestion predicted in the tr

Abstract: A method for operating a power generating facility connected to a power distribution grid having an uncertain power generation condition includes predicting a probabilistic power flow forecast in a transmission line of the power distribution grid for a period of time, wherein the transmission line is electrically coupled to the power generating facility, predicting, using the probabilistic power flow forecast, a probability of congestion over the transmission line of the power distribution grid during the period of time, generating a mitigation plan, including a load adjustment on the transmission line, using the probability of congestion predicted over the transmission line and a thermal limit constraint of the transmission line, wherein the mitigation plan balances the load adjustment and an overlimit line capacity on the transmission line, and controlling the power generating facility, using the mitigation plan, to achieve the load modification and mitigate the probability of congestion predicted in the tr

Abstract: A streams platform is used. Multiple streams of electricity usage data are received, each from an electrical meter providing periodic updates to electrical usage for devices connected to the electrical meter. Weather information is received corresponding to locations where the electrical meters are. Real-time predictive modeling of electricity demand is performed based on the received multiple streams of electricity usage data and the received weather information, at least by performing: updating a state space model for electrical load curves using the usage data from the streams and the weather, wherein the updating uses current load observations for the multiple streams for a current time period; and creating forecast(s) for the electricity demand. The forecast(s) of the electricity demand are output. Appliance-level predictions may be made and used, and substitution effects and load management functions may be performed.

Abstract: A method for solving a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Certain generation decisions are made only in the first stage and fixed for the subsequent (second) stage, where the actual renewable generation is realized. The uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using high marginal-cost power sources that can be tapped in short time frames. The solution implements two outer approximation algorithms to solve this nonconvex optimization problem to optimality including the application of a decomposition approach derived from the Alternating Direction Method of Multipliers (ADMM) algorithm.

Abstract: A streams platform is used. Multiple streams of electricity usage data are received, each from an electrical meter providing periodic updates to electrical usage for devices connected to the electrical meter. Weather information is received corresponding to locations where the electrical meters are. Real-time predictive modeling of electricity demand is performed based on the received multiple streams of electricity usage data and the received weather information, at least by performing: updating a state space model for electrical load curves using the usage data from the streams and the weather, wherein the updating uses current load observations for the multiple streams for a current time period; and creating forecast(s) for the electricity demand. The forecast(s) of the electricity demand are output. Appliance-level predictions may be made and used, and substitution effects and load management functions may be performed.

Abstract: A method for operating a power generating facility connected to a power distribution grid having an uncertain power generation condition includes predicting a probabilistic power flow forecast in a transmission line of the power distribution grid for a period of time, wherein the transmission line is electrically coupled to the power generating facility, predicting, using the probabilistic power flow forecast, a probability of congestion over the transmission line of the power distribution grid during the period of time, generating a mitigation plan, including a load adjustment on the transmission line, using the probability of congestion predicted over the transmission line and a thermal limit constraint of the transmission line, wherein the mitigation plan balances the load adjustment and an overlimit line capacity on the transmission line, and controlling the power generating facility, using the mitigation plan, to achieve the load modification and mitigate the probability of congestion predicted in the tr

Abstract: A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Abstract: A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Abstract: A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Abstract: Analyzing one or more physical infrastructure elements of a data center by generating a plurality of outputs from a stochastic process for a set of inputs to the stochastic process. The inputs comprise one or more inputs of certainty and one or more inputs of uncertainty. A statistical output analysis of the outputs is utilized to generate one or more threshold reaching projections for each of the physical infrastructure elements of the data center.

Abstract: The present disclosure relates generally to the field of distributed charging of electrical assets. In various examples, distributed charging of electrical assets may be implemented in the form of systems, methods and/or algorithms.

Abstract: A method for determining power output levels of a plurality of nodes in an electric power system includes receiving, at a first node of the plurality of nodes, voltage information and multipliers of all neighboring nodes of the first node within the electric power system, determining, by the first node, a local power generation and a local voltage using the voltage information and the multipliers of the neighboring nodes and distributing the local power generation and the local voltage to the neighboring nodes, determining, by the first node, an estimated voltage of each of the neighboring nodes and distributing the estimated voltage to each of the neighboring nodes, and updating, by the first node, a local multiplier using the voltage information received from the neighboring nodes and the estimated voltage of each of the neighboring nodes determined by the node.

Abstract: A method for solving a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Certain generation decisions are made only in the first stage and fixed for the subsequent (second) stage, where the actual renewable generation is realized. The uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using high marginal-cost power sources that can be tapped in short time frames. The solution implements two outer approximation algorithms to solve this nonconvex optimization problem to optimality including the application of a decomposition approach derived from the Alternating Direction Method of Multipliers (ADMM) algorithm.

Abstract: A system and computer program product for solving a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Certain generation decisions are made only in the first stage and fixed for the subsequent (second) stage, where the actual renewable generation is realized. The uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using high marginal-cost power sources that can be tapped in short time frames. The solution implements two outer approximation algorithms to solve this nonconvex optimization problem to optimality. Under certain conditions the sequence of optimal solutions obtained under both alternatives has a limit point that is a globally-optimal solution to the original two-stage nonconvex program. A further decomposition approach derived from the Alternating Direction Method of Multipliers algorithm is implemented.

Abstract: A method for solving a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Certain generation decisions are made only in the first stage and fixed for the subsequent (second) stage, where the actual renewable generation is realized. The uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using high marginal-cost power sources that can be tapped in short time frames. The solution implements two outer approximation algorithms to solve this nonconvex optimization problem to optimality. Under certain conditions the sequence of optimal solutions obtained under both alternatives has a limit point that is a globally-optimal solution to the original two-stage nonconvex program. A further decomposition approach derived from the Alternating Direction Method of Multipliers algorithm is implemented.