28 research outputs found
Linear/Quadratic Programming-Based Optimal Power Flow using Linear Power Flow and Absolute Loss Approximations
This paper presents novel methods to approximate the nonlinear AC optimal
power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF
problems that can be used for power system planning and operation. We derive a
linear power flow approximation and consider a convex reformulation of the
power losses in the form of absolute value functions. We show four ways how to
incorporate this approximation into LP/QP based OPF problems. In a
comprehensive case study the usefulness of our OPF methods is analyzed and
compared with an existing OPF relaxation and approximation method. As a result,
the errors on voltage magnitudes and angles are reasonable, while obtaining
near-optimal results for typical scenarios. We find that our methods reduce
significantly the computational complexity compared to the nonlinear AC-OPF
making them a good choice for planning purposes
Principal Flow Patterns across renewable electricity networks
Using Principal Component Analysis (PCA), the nodal injection and line flow
patterns in a network model of a future highly renewable European electricity
system are investigated. It is shown that the number of principal components
needed to describe 95 of the nodal power injection variance first increases
with the spatial resolution of the system representation. The number of
relevant components then saturates at around 76 components for network sizes
larger than 512 nodes, which can be related to the correlation length of wind
patterns over Europe. Remarkably, the application of PCA to the transmission
line power flow statistics shows that irrespective of the spatial scale of the
system representation a very low number of only 8 principal flow patterns is
sufficient to capture 95 of the corresponding spatio-temporal variance.
This result can be theoretically explained by a particular alignment of some
principal injection patterns with topological patterns inherent to the network
structure of the European transmission system
Optimal Power Flow in Direct Current Networks
The optimal power flow (OPF) problem determines power generations/demands that minimize a certain objective such as generation cost or power loss. It is non-convex and NP-hard in general. In this paper, we study the OPF problem in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered for solving the OPF problem. We prove that the SOCP relaxation is exact if either 1) voltage upper bounds do not bind; or 2) voltage upper bounds are uniform and power injection lower bounds are negative. Based on 1), a modified OPF problem is proposed, whose corresponding SOCP is guaranteed to be exact. We also prove that SOCP has at most one optimal solution if it is exact. Finally, we discuss how to improve numerical stability and how to include line constraints
Evaluating Resilience of Electricity Distribution Networks via A Modification of Generalized Benders Decomposition Method
This paper presents a computational approach to evaluate the resilience of
electricity Distribution Networks (DNs) to cyber-physical failures. In our
model, we consider an attacker who targets multiple DN components to maximize
the loss of the DN operator. We consider two types of operator response: (i)
Coordinated emergency response; (ii) Uncoordinated autonomous disconnects,
which may lead to cascading failures. To evaluate resilience under response
(i), we solve a Bilevel Mixed-Integer Second-Order Cone Program which is
computationally challenging due to mixed-integer variables in the inner problem
and non-convex constraints. Our solution approach is based on the Generalized
Benders Decomposition method, which achieves a reasonable tradeoff between
computational time and solution accuracy. Our approach involves modifying the
Benders cut based on structural insights on power flow over radial DNs. We
evaluate DN resilience under response (ii) by sequentially computing autonomous
component disconnects due to operating bound violations resulting from the
initial attack and the potential cascading failures. Our approach helps
estimate the gain in resilience under response (i), relative to (ii)