Energy Systems

, Volume 3, Issue 2, pp 153–179 | Cite as

An energy management system for off-grid power systems

Original Paper

Abstract

Next generation power management at all scales will rely on the efficient scheduling and operation of both generating units and loads to maximize efficiency and utility. The ability to schedule and modulate the demand levels of a subset of loads within a power system can lead to more efficient use of the generating units. These methods become increasingly important for systems that operate independently of the main utility, such as microgrid and off-grid systems. This work extends the principles of unit commitment and economic dispatch problems to off-grid power systems where the loads are also schedulable. We propose a general optimization framework for solving the energy management problem in these systems. An important contribution is the description of how a wide range of sources and loads, including those with discrete states, non-convex, and nonlinear cost or utility functions, can be reformulated as a convex optimization problem using, for example, a shortest path description. Once cast in this way, solution are obtainable using a sub-gradient algorithm that also lends itself to a distributed implementation. The methods are demonstrated by a simulation of an off-grid solar powered community.

Keywords

Off-grid Energy management Lagrangian relaxation Shortest-path algorithm 

Nomenclature

G,L

number of generating units, number of loads

\(\mathcal{G},\mathcal{L}\)

set of generating units, set of loads

T

time horizon

\(\mathcal{T}\)

set of time indices

i,j,t

index for generating units, loads, and time

gi(t),yj(t)

power level of generating unit \(i \in \mathcal{G}\) and demand of load \(j \in\mathcal{L}\) at time \(t \in\mathcal{T}\)

\(x_{i}^{g}(t), u_{i}^{g}(t)\)

state and control variables for generating unit \(i \in\mathcal{G}\) at time \(t \in\mathcal{T}\)

\(x_{j}^{l}(t), u_{j}^{l}(t)\)

state and control variables for load \(j\in\mathcal{L}\) at time \(t \in\mathcal{T}\)

\(f_{i}^{g}(g_{i}(t),x_{i}^{g}(t),u_{i}^{g}(t))\)

dynamic evolution of generating unit variables for unit \(i \in\mathcal{G}\)

\(f_{j}^{l}(y_{j}(t),x_{j}^{l}(t),u_{j}^{l}(t))\)

dynamic evolution of load variables for load \(j \in\mathcal{L}\)

\(C_{i}(g_{i}(t),x_{i}^{g}(t),u_{i}^{g}(t))\)

operating cost of generator unit \(i \in\mathcal{G}\) at time \(t \in\mathcal{T}\)

\(U_{j}(y_{j}(t),x_{j}^{l}(t),u_{j}^{l}(t))\)

utility of load \(j \in\mathcal {L}\) at time \(t \in\mathcal{T}\)

\(\mathcal{S}_{i}^{g}(t),\mathcal{S}_{j}^{l}(t)\)

abstract constraint set for generator unit \(i \in\mathcal{G}\) and load \(j \in\mathcal{L}\) at time \(t \in \mathcal{T}\)

\(\mathcal{X}_{i}^{g}(t),\mathcal{U}_{i}^{g}(t)\)

abstract constraint set for generator load state and control variables at \(t \in\mathcal{T}\)

\(\mathcal{X}_{j}^{l}(t), \,\mathcal{U}_{j}^{l}(t)\)

abstract constraint set for load state and control variables at \(t \in\mathcal{T}\)

L(⋅),q(λ)

Lagrangian and dual functions

λt,v(λt),α

Lagrange multiplier and sub-gradient at time \(t \in\mathcal{T}\), step size

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute for Systems Theory and Automatic ControlUniversität StuttgartStuttgartGermany
  2. 2.Department of Aeronautics and AstronauticsUniversity of WashingtonSeattleUSA

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