746 research outputs found
Geometry of Power Flows and Optimization in Distribution Networks
We investigate the geometry of injection regions and its relationship to
optimization of power flows in tree networks. The injection region is the set
of all vectors of bus power injections that satisfy the network and operation
constraints. The geometrical object of interest is the set of Pareto-optimal
points of the injection region. If the voltage magnitudes are fixed, the
injection region of a tree network can be written as a linear transformation of
the product of two-bus injection regions, one for each line in the network.
Using this decomposition, we show that under the practical condition that the
angle difference across each line is not too large, the set of Pareto-optimal
points of the injection region remains unchanged by taking the convex hull.
Moreover, the resulting convexified optimal power flow problem can be
efficiently solved via }{ semi-definite programming or second order cone
relaxations. These results improve upon earlier works by removing the
assumptions on active power lower bounds. It is also shown that our practical
angle assumption guarantees two other properties: (i) the uniqueness of the
solution of the power flow problem, and (ii) the non-negativity of the
locational marginal prices. Partial results are presented for the case when the
voltage magnitudes are not fixed but can lie within certain bounds.Comment: To Appear in IEEE Transaction on Power System
Dynamic Energy Management
We present a unified method, based on convex optimization, for managing the
power produced and consumed by a network of devices over time. We start with
the simple setting of optimizing power flows in a static network, and then
proceed to the case of optimizing dynamic power flows, i.e., power flows that
change with time over a horizon. We leverage this to develop a real-time
control strategy, model predictive control, which at each time step solves a
dynamic power flow optimization problem, using forecasts of future quantities
such as demands, capacities, or prices, to choose the current power flow
values. Finally, we consider a useful extension of model predictive control
that explicitly accounts for uncertainty in the forecasts. We mirror our
framework with an object-oriented software implementation, an open-source
Python library for planning and controlling power flows at any scale. We
demonstrate our method with various examples. Appendices give more detail about
the package, and describe some basic but very effective methods for
constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar
An exact solution method for binary equilibrium problems with compensation and the power market uplift problem
We propose a novel method to find Nash equilibria in games with binary
decision variables by including compensation payments and
incentive-compatibility constraints from non-cooperative game theory directly
into an optimization framework in lieu of using first order conditions of a
linearization, or relaxation of integrality conditions. The reformulation
offers a new approach to obtain and interpret dual variables to binary
constraints using the benefit or loss from deviation rather than marginal
relaxations. The method endogenizes the trade-off between overall (societal)
efficiency and compensation payments necessary to align incentives of
individual players. We provide existence results and conditions under which
this problem can be solved as a mixed-binary linear program.
We apply the solution approach to a stylized nodal power-market equilibrium
problem with binary on-off decisions. This illustrative example shows that our
approach yields an exact solution to the binary Nash game with compensation. We
compare different implementations of actual market rules within our model, in
particular constraints ensuring non-negative profits (no-loss rule) and
restrictions on the compensation payments to non-dispatched generators. We
discuss the resulting equilibria in terms of overall welfare, efficiency, and
allocational equity
- …