Welcome to the homepage of the interdisciplinary project in power substation voltage control. The project is a collaboration between researchers in the departments of Computer and Information Sciences and Elecrtical and Electronic Enginnering at the University of Strathclyde.

If you have any questions about the project, or the resources on this page email Amanda Coles.

The Basic Problem

This project is concerned with the maintenance of an appropraite voltage at a power substation against a background of changing consumer demand throughout the day. The voltage at the substation increases as consumer demand decreases, but must be kept within an acceptable range: +/- 5% of an overall desired voltage for the circuit (calling the desired voltage 1 unit volt, the voltage must be in the range 0.95-1.05 per-unit volts). The voltage can be controlled through two mechanisms, the first is through the use of auto-transformers, which can be stepped up or down to regulate the voltage; and the second is through the switching on or off of mechanically switched capacitors (MSCs).

The Objective Function

The key to the problem is the objective function (plan metric), whilst the voltage could be kept at the precise target through constant transformer movement, this causes great wear and tear on the componenets. So the objective is to minimise wear and tear whilst maximising fault tolerance of the plan. A cost is associated with each time step at which the voltage is below 0.97 per-unit volts or above 1.03 per-unit volts. The objective function for a plan is defined as follows:

a * TransformerTurns + b * MSCSwitches + c * VoltageHighOnAdvance + d * VoltageLowOnAdvance

The parameters are not fixed but reasonable suggested values are:
α = 0.1, β = 0.1,γ = 0.5,δ = 0.2
The goal of the problem is to find voltage targets: values in the range 0.95-1.05 per unit volts for each time interval; which, when set as the values the transformers/MSCs must track, find best minimise the objective function.

Further Problem Features

Whilst it may appear, at first glance, that the basic problem is a scheduling/optimisation problem a number of additional features of the management of substations mean that the problem has a significant planning component. The power network is subject to planned maintenance, when such maintenance occurs the voltage at the substation will decrease by 0.2 per unit volts. Planning around the occurence of this maintenance, or indeed deciding when this maintenance should occur is an important part of the problem.

Faults can occur on incoming or outgoing lines at any time during the day, meaning that the voltage must remain within a safe bound should this happen. A fault on an ingoing line will decrease the voltage at the substation by 0.2 per unit volts, whereas one on an outgoing line will increase the voltage by 0.2 per unit volts. It is important, therefore, to ensure the voltage remains within the acceptable boundaries were such a fault to occur: but of course we must trade off the likelihood of a fault and the wear and tear requirements on components in keeping the voltage in the 0.97-1.03 range at all times (slightly exceeding the upper boundary is acceptable for short periods of time).

Another useful aspect to using planning to solve the problem is that it is possible to predict when faults might be likely to occur and bulild more robust plans at these times. Taking in to account weather warnings can allow for the fault tolerance of plans to be tailored to times at which faults are more likely to occur.

PDDL Domain Descriptions

This section contains various encodings of the VOLTS problem in PDDL, each encodes a different set of features and requires different levels of planner functionality.

The full numeric domain description (example problem file) including faults, maintenance and storm warnings. This is a PDDL 2.1 problem using numeric fluents, but not the temporal features of the language. Metric-FF is known to be able to solve problems using this domain (although not to succesfully optimisse the objective function).


This workshop paper describes solving the basic model of the problem with no "The Application of Planning to Power Substation Voltage Control." K. Bell, A. I. Coles, M. Fox, D. Long, and A. J. Smith. ICAPS Workshop on Scheduling and Planning Applications (SPARK). 2008. Download PDF (BibTeX)

Other Resources

A presentation describing the work on the VOLTS project can be found here.

A poster displaying the VOLTS work is available here.