95,922 research outputs found
An efficient null space inexact Newton method for hydraulic simulation of water distribution networks
Null space Newton algorithms are efficient in solving the nonlinear equations
arising in hydraulic analysis of water distribution networks. In this article,
we propose and evaluate an inexact Newton method that relies on partial updates
of the network pipes' frictional headloss computations to solve the linear
systems more efficiently and with numerical reliability. The update set
parameters are studied to propose appropriate values. Different null space
basis generation schemes are analysed to choose methods for sparse and
well-conditioned null space bases resulting in a smaller update set. The Newton
steps are computed in the null space by solving sparse, symmetric positive
definite systems with sparse Cholesky factorizations. By using the constant
structure of the null space system matrices, a single symbolic factorization in
the Cholesky decomposition is used multiple times, reducing the computational
cost of linear solves. The algorithms and analyses are validated using medium
to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015
(https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015.
Includes extended exposition, additional case studies and new simulations and
analysi
Linear Optimal Power Flow Using Cycle Flows
Linear optimal power flow (LOPF) algorithms use a linearization of the
alternating current (AC) load flow equations to optimize generator dispatch in
a network subject to the loading constraints of the network branches. Common
algorithms use the voltage angles at the buses as optimization variables, but
alternatives can be computationally advantageous. In this article we provide a
review of existing methods and describe a new formulation that expresses the
loading constraints directly in terms of the flows themselves, using a
decomposition of the network graph into a spanning tree and closed cycles. We
provide a comprehensive study of the computational performance of the various
formulations, in settings that include computationally challenging applications
such as multi-period LOPF with storage dispatch and generation capacity
expansion. We show that the new formulation of the LOPF solves up to 7 times
faster than the angle formulation using a commercial linear programming solver,
while another existing cycle-based formulation solves up to 20 times faster,
with an average speed-up of factor 3 for the standard networks considered here.
If generation capacities are also optimized, the average speed-up rises to a
factor of 12, reaching up to factor 213 in a particular instance. The speed-up
is largest for networks with many buses and decentral generators throughout the
network, which is highly relevant given the rise of distributed renewable
generation and the computational challenge of operation and planning in such
networks.Comment: 11 pages, 5 figures; version 2 includes results for generation
capacity optimization; version 3 is the final accepted journal versio
A co-operating solver approach to building simulation
This paper describes the co-operating solver approach to building simulation as encapsulated within the ESP-r system. Possible adaptations are then considered to accommodate new functional requirements
- …