Risk-Averse Resource Management in Electricity Networks

Maria Moschovitis, Term Project, Spring 2008

Supervisors: Michael Guarisco, Marco Laumanns

In industrialized countries, a reliable supply of electrical energy is taken for granted. Grid operators are responsible for an adequate quality of supply while trying to minimize investment and operating costs to allow for low network access fees. One main aspect of the quality of supply concerns the availability of electricity to customers, which is usually measured by the non-availability of supply, i.e., by duration, extent and frequency of supply interruptions. In the medium- and low-voltage power grid, generally being operated as radial distribution system, most failures cause an interruption of supply. Without remote control, the restoration of these supply interruptions requires an employment of resources on site. In the high- and extra-high-voltage power grid, due to the redundancies, its meshed operation and the possibility of remote control, most incidents do not result in an interruption of supply. Nevertheless, the affected equipment generally needs to be inspected or repaired, also requiring resources on site. Resource management is therefore a major challenge for grid operators, in particular to find an organization (spatial and temporal availability) of resources which not only guarantees the required quality of supply, but also minimizes costs.

Unlike in the medium- and low-voltage power grid, where failures can be characterized by the interrupted power, the effects on the quality of supply are not immediately measurable for failures in the high- and extra-high-voltage power grid. However, a delayed repair and consequent additional failures might lead to a large interruption of supply. In a joint project with RWE Rhein-Ruhr Netzservice GmbH (Siegen, Germany), the repair process after incidents in the power grid has been modeled. Incidents without an interruption of supply are characterized by their power-at-risk in order to compare and prioritize all incidents. The power-at-risk is a measure for the potentially interrupted power when delaying the repair. Results of this stochastic simulation model are estimated distributions of the unsupplied energy, repair times, etc.

The aim of this term project was to develop strategic indicators which allow to compare different distributions caused by a different organization of resources. The focus was on indicators that take into account the "risk" and thus incorporate information on the "tail" of the corresponding distributions in order to support a risk-averse decision maker who is particularly interested in avoiding or controlling rare but adverse events.

First, it was suggested to compare quantiles of the distributions of delay/repair times instead of average values. The probability level of the quantile thereby controls the amount of the "tail" of the distribution which is to be considered. The delay ratio compares the total repair time of all incidents for a given organization of resources to the minimum total repair time. This value contrasts the amount of (undesired) traveling and delay with the minimally required working time. Finally, the power-at-risk duration curve shows the cumulated power-at-risk in dependence of the corresponding duration. This curve not only shows the distribution of the (cumulated) power-at-risk over the considered time horizon but also allows to identify (short) periods with high power-at-risk and (long) periods with small power-at-risk.

In a case study with real-world data of RWE Rhein-Ruhr Netzservice GmbH, the proposed indicators were tested and different organizations of resources were evaluated and compared.