[Paper Review] Control and Optimization Meet the Smart Power Grid - Scheduling of Power Demands for Optimal Energy Management

Iordanis Koutsopoulos, Leandros Tassiulas|arXiv (Cornell University)|Aug 21, 2010

Smart Grid Energy Management10 references17 citations

TL;DR

This paper proposes a threshold-based scheduling policy for optimal energy management in smart power grids, where a grid operator schedules consumer power demands to minimize operational costs—modeled as a convex function of instantaneous load. The Controlled Release policy dynamically activates or queues demands based on real-time power consumption, achieving asymptotic optimality as deadlines grow.

ABSTRACT

The smart power grid aims at harnessing information and communication technologies to enhance reliability and enforce sensible use of energy. Its realization is geared by the fundamental goal of effective management of demand load. In this work, we envision a scenario with real-time communication between the operator and consumers. The grid operator controller receives requests for power demands from consumers, with different power requirement, duration, and a deadline by which it is to be completed. The objective is to devise a power demand task scheduling policy that minimizes the grid operational cost over a time horizon. The operational cost is a convex function of instantaneous power consumption and reflects the fact that each additional unit of power needed to serve demands is more expensive as demand load increases.First, we study the off-line demand scheduling problem, where parameters are fixed and known. Next, we devise a stochastic model for the case when demands are generated continually and scheduling decisions are taken online and focus on long-term average cost. We present two instances of power consumption control based on observing current consumption. First, the controller may choose to serve a new demand request upon arrival or to postpone it to the end of its deadline. Second, the additional option exists to activate one of the postponed demands when an active demand terminates. For both instances, the optimal policies are threshold based. We derive a lower performance bound over all policies, which is asymptotically tight as deadlines increase. We propose the Controlled Release threshold policy and prove it is asymptotically optimal. The policy activates a new demand request if the current power consumption is less than a threshold, otherwise it is queued. Queued demands are scheduled when their deadline expires or when the consumption drops below the threshold.

Motivation & Objective

• To address the challenge of minimizing grid operational costs through intelligent scheduling of consumer power demands in a smart grid environment.
• To model the grid operator's decision-making as a control and optimization problem under real-time communication with consumers.
• To develop online scheduling policies that adapt to dynamic demand arrivals while maintaining system reliability and cost efficiency.
• To establish theoretical performance bounds and design asymptotically optimal control policies for long-term average cost minimization.

Proposed method

• Formulates the grid operational cost as a convex function of instantaneous total power consumption, reflecting increasing marginal cost with load.
• Introduces two control instances: one allowing postponement of new demands until their deadline, and another allowing reactivation of queued demands when load drops.
• Proposes the Controlled Release threshold policy, which activates a new demand only if current power consumption is below a threshold.
• Uses a stochastic model to analyze long-term average cost, assuming continual demand generation and online scheduling decisions.
• Derives threshold-based optimal policies through dynamic programming and performance analysis under increasing deadline asymptotics.
• Establishes a universal lower performance bound for all policies, which the Controlled Release policy asymptotically achieves as deadlines grow.

Experimental results

Research questions

• RQ1 How can a grid operator optimally schedule consumer power demands to minimize convex operational costs in real time?
• RQ2 What is the structure of the optimal scheduling policy when demands arrive dynamically and decisions must be made online?
• RQ3 How does the performance of threshold-based policies scale with increasing demand deadlines?
• RQ4 Can a universal lower bound on long-term average cost be derived, and is it achievable asymptotically?
• RQ5 What control actions—postponement, activation, or queuing—yield optimal performance under different operational constraints?

Key findings

• The Controlled Release threshold policy is asymptotically optimal, achieving the universal lower performance bound as demand deadlines increase.
• For the non-preemptive scheduling case, the problem reduces to a bin packing problem and is NP-hard, indicating computational intractability in general.
• In the preemptive case, an iterative algorithm provides an optimal solution, effectively solving a load balancing problem.
• The optimal control policies for both control instances are threshold-based, depending only on current instantaneous power consumption.
• The threshold in the Controlled Release policy does not depend on the queue size, as long as the queue is non-empty, due to stable power consumption around the threshold.
• The model supports heterogeneous demand types, including those with flexible scheduling, variable power levels, and energy constraints (e.g., electric vehicle charging).