Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

An efficient forward-backward algorithm to MSDEPP including batteries and voltage control devices

Electric distribution networks are now in the era of transition from passive to active distribution networks with the integration of energy storage devices. Optimal usage of batteries and voltage control devices along with other upgrades in network needs a distribution expansion planning (DEP) considering inter-temporal dependencies of stages. This paper presents an efficient approach for solving multi-stage distribution expansion planning problems (MSDEPP) based on a forward-backward approach considering energy storage devices such as batteries and voltage control devices such as voltage regulators and capacitors. The proposed algorithm is compared with three other techniques including full dynamic, forward fill-in, backward pull-out from the point of view of their precision and their computational efficiency. The simulation results for the IEEE 13 bus network show the proposed pseudo-dynamic forward-backward approach presents good efficiency in precision and time of optimization.

Efficient simulation of unsaturated flow in heterogeneous soils using an exponential integrator

- Provided a practical variable-stepsize implementation of the exponential Euler method (EEM). - Introduced a new second-order variant of the scheme that enables the local error to be estimated at the cost of a single additional function evaluation. - New EEM implementation outperformed sophisticated implementations of the backward differentiation formulae (BDF) of order 2 and was competitive with BDF of order 5 for moderate to high tolerances.