Abstract: Different aspects of the invention comprise an innovative apparatus, method, and system, for determining the steady-state temperatures of nodes in a thermal environment comprising non-linearities. The determination is performed directly, non-iteratively, and guarantees the optimum solution: the end result is an unequivocal answer: it yields the operational solution if it exists, and conversely, it signals unfeasibility when it does not exist.

Abstract: A mathematical model of load flow equations for an electrical grid having a chain of busses is embedded in a holomorphic embedding using a first embedding parameter s. The holomorphic embedding is transcribed into software for use in a computer processor. Voltages for each bus are calculated as an algebraic curve parameterized by the first embedding parameter. A second embedding parameter z is defined wherein the first embedding parameter s is a function of the second embedding parameter z. The holomorphic embedding is re-parameterized using the second embedding parameter z, such that the re-parameterized embedding provides an elimination polynomial equation relating parameters s and z. The roots of the elimination polynomial equation are determined by solving the for zero, which roots are used to compute bus voltages for each bus of the chain of busses. The bus voltages are displayed as the solution to the load flow equations.

Abstract: A system and method is presented for efficiently enforcing control limits in the calculation of powerflow studies of electrical power systems, using the Holomorphic Embedding Load-flow Method. The method applies to any automatic control in which the controlling resource is limited by a maximum or minimum value, such as Mvar limits in generators, the tap ratio in load-changing transformers, or real power output in AGC-participating generators. One key element of this invention consists in devising an equality constraint, holomorphically embedded, able to encode the switching behavior between the different control modes when limit thresholds are reached. The other key element is a novel analytic continuation scheme, here referred to as “Padé-Weierstrass”, which achieves the continuation to s=1 by means of several intermediate steps of power series re-expansions on the path from s=0 to s=1 in embedding parameter space.

Abstract: A system and method is presented for observing and efficiently enforcing control limits in powerflow studies of electrical power systems, using a novel optimality criterion. The method applies to any automatic control in which the controlling resource is limited by a maximum or minimum value, such as MVArs in generators, the tap ratio in load-changing transformers, or real power output in AGC-participating generators. In the absence of information about relative priorities among automatic controls, or about their dynamic behavior (as it is the common case in steady-state powerflow studies), the new optimality criterion provides the most reasonable method for deciding among multiple possible alternatives of saturated controls. The criterion is based on underlying physical principles that yield exact results in the idealized lossless transmission network, and hold also true to a great degree in real high-voltage transmission networks.

Abstract: A system and method is presented for enabling the simulation of smooth, unlimited controls in the Holomorphic Embedding Load-flow Method (HELM) for calculating power flows. These are controls that can be expressed as differentiable algebraic expressions of the voltages or power flows. The invention draws on the ability of HELM to turn the powerflow problem into a sequence of linear problems, as well as on the powerful physical intuition that is gained by the underlying methodology. The outcome is that any kind of smooth and unlimited control can be accommodated under the HELM method, preserving all its fundamental properties of reliability and determinism on the obtained solutions. One particularly interesting feature is the automatic treatment of conflicting and/or overlapping controls in an optimal way, via SVD techniques.

Abstract: A system and method for analyzing steady-state powerflow in DC electrical networks in the presence of constant power loads and other nonlinear devices whose I-V characteristics can be modeled using algebraic functions. The networks include high power utility-size grids and microgrids, as well as vehicular, aircraft, and spacecraft power management and distribution systems. The method draws on the mathematical framework of the Holomorphic Embedded Loadflow Method (HELM), which has previously been applied in utility AC networks. The adaptation to DC systems depends on the choice of a proper embedding and a corresponding reflection condition on the embedded voltages. Additionally, the method is extended to nonlinear devices other than constant-power loads, such as photovoltaic panel sources, which are of interest for the power systems aboard spacecraft and other electric vehicles.

Abstract: A system and method for constructively providing a set of complex-valued indices that measures the proximity of an electrical power distribution system to voltage collapse, and providing insights on general static stability issues in power networks. These indices, termed “sigmas”, are designed through a mathematical osculation of the actual load flow solution with an equivalent two-bus system at every node. The procedure for obtaining these sigmas is based on the Holomorphic Embedded Load flow Method (HELM), and the indices are, in fact, proper analytical functions of the embedding parameter, which endows them with powerful diagnostic capabilities. These indices are then used graphically on a two-dimensional chart, in order to appreciate visually the overall distance of the system to voltage collapse, while at the same time spotting the weak nodes out of the whole grid, providing new situational awareness and diagnosis tools.

Abstract: A system and method for analyzing steady-state powerflow in DC electrical networks in the presence of constant power loads and other nonlinear devices whose I-V characteristics can be modeled using algebraic functions. The networks include high power utility-size grids and microgrids, as well as vehicular, aircraft, and spacecraft power management and distribution systems. The method draws on the mathematical framework of the Holomorphic Embedded Loadflow Method (HELM), which has previously been applied in utility AC networks. The adaptation to DC systems depends on the choice of a proper embedding and a corresponding reflection condition on the embedded voltages. Additionally, the method is extended to nonlinear devices other than constant-power loads, such as photovoltaic panel sources, which are of interest for the power systems aboard spacecraft and other electric vehicles.

Abstract: A system and method for constructively providing a monetization procedure for a long tail demand curve of market goods, services or contents in the music industry through a channel such as the Internet or mobile devices, for which there exists a source providing economic scoring (sales, downloads, streaming time, etc.). Using only the scorings for a few reference items and a quantitative concept of similarity between the songs, a procedure is provided that constructively distributes the preference score from the reference items to the non-ranked ones, yielding the full scoring curve adjusted to a long tail law (power law). In order to build preference scores for non-ranked items, the method recursively defines relative preferences between songs based on their similarity, thus constructing a utility-like function. The preferences are then used within an iterative Elo-like tournament strategy between the items.

Abstract: A system and method for constructively providing a monetization procedure for a long tail demand curve of market goods, services or contents through a channel such as the Internet or mobile devices, for which there exists a source providing economic scoring (sales, downloads, streaming hours, etc.). Using only the scorings for a few reference items and a quantitative concept of similarity between the items, embodiments provide a procedure that constructively distributes the score from the reference items to the non-ranked ones, yielding the full scoring curve adjusted to a long tail law (power law). In order to build scores for non-ranked items, the method recursively defines relative preferences between items based on their similarity, thus constructing a utility-like function. The preferences are then used within an iterative tournament strategy between the items.

Abstract: A system and method for monitoring and managing three-phase power flows in electrical transmission and distribution networks through the use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the power flows in the three phases of a power generating system having an electrical grid. Such method is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse. It may be employed in either real-time or off-line analytic applications for balanced or unbalanced electric power systems, in particular for monitoring and analyzing unbalanced conditions in three-phase electrical networks and for the accurate calculation of short-circuit conditions.

Abstract: A system and method for constructively providing a set of complex-valued indices that measures the proximity of an electrical power distribution system to voltage collapse, and providing insights on general static stability issues in power networks. These indices, termed “sigmas”, are designed through a mathematical osculation of the actual load flow solution with an equivalent two-bus system at every node. The procedure for obtaining these sigmas is based on the Holomorphic Embedded Load flow Method (HELM), and the indices are, in fact, proper analytical functions of the embedding parameter, which endows them with powerful diagnostic capabilities. These indices are then used graphically on a two-dimensional chart, in order to appreciate visually the overall distance of the system to voltage collapse, while at the same time spotting the weak nodes out of the whole grid, providing new situational awareness and diagnosis tools.

Abstract: A system and method for constructively providing a monetization procedure for a long tail demand curve of market goods, services or contents through a channel such as the Internet or mobile devices, for which there exists a source providing economic scoring (sales, downloads, streaming hours, etc.). Using only the scorings for a few reference items and a quantitative concept of similarity between the items, embodiments provide a procedure that constructively distributes the score from the reference items to the non-ranked ones, yielding the full scoring curve adjusted to a long tail law (power law). In order to build scores for non-ranked items, the method recursively defines relative preferences between items based on their similarity, thus constructing a utility-like function. The preferences are then used within an iterative tournament strategy between the items.

Abstract: A system and method for monitoring and managing three-phase power flows in electrical transmission and distribution networks through the use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the power flows in the three phases of a power generating system having an electrical grid. Such method is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse. It may be employed in either real-time or off-line analytic applications for balanced or unbalanced electric power systems, in particular for monitoring and analyzing unbalanced conditions in three-phase electrical networks and for the accurate calculation of short-circuit conditions.

Abstract: A system and method for monitoring and managing electrical power transmission and distribution networks through use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the real-time load flow in a power generating system having an electrical grid. Such method may be employed for real-time or off-line applications for electric power systems reliability assessment, and is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse.

Abstract: A system and method for monitoring and managing electrical power transmission and distribution networks through use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the real-time load flow in a power generating system having an electrical grid. Such method may be employed for real-time or off-line applications for electric power systems reliability assessment, and is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse.

Abstract: A system and method for monitoring and managing electrical power transmission and distribution networks through use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the real-time load flow in a power generating system having an electrical grid. Such method may be employed for real-time or off-line applications for electric power systems reliability assessment, and is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse.

Abstract: A system and method for monitoring and managing electrical power transmission and distribution networks through use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the real-time load flow in a power generating system having an electrical grid. Such method may be employed for real-time or off-line applications for electric power systems reliability assessment, and is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse.