# Quality of Service Analysis for the Smart Grid

Contact: Andrey Bernstein

Power flow analysis is one of the most fundamental tools for the study of power systems. It is formulated as a set of precisely known nonlinear algebraic equations that must be solved simultaneously.

One of the major application of this tool is to analyse the quality of service (QoS) of the grid.
Specifically, given power generation of the generators and power consumption of the loads, some of the outputs of the power flow analysis are the voltage magnitudes at the different nodes in the grid. In order to ensure the QoS, these magnitudes should remain in a certain predefined interval.
The standard analysis is applicable whenever: (i) accurate predictions of the generation and consumption are available, and (ii) the generation and consumption profiles changing slowly compared to the desired time scale of the analysis.

However, in the Smart Grid (such as at the EPFL Smart-Grid.), with the massive introduction of distributed renewable energy sources, these assumptions are not valid anymore.
In particular, only the possible interval of power consumption/generation is known at a given instant for the next time horizon.
This interval accounts both for inaccuracies in prediction and for (unpredictable) effects of Nature. In this case, interval power flow analysis is required. Ideally, such an analysis outputs the interval of all possible voltage magnitudes at each node, and the assessment of QoS can be performed using this interval.

There are several ways to perform interval analysis, including stochastic power flow, Monte Carlo simulation, and interval arithmetics techniques. In this project, we will use interval arithmetics to tackle the problem. We will compare different methods for extending power flow analysis to interval arithmetics. Our main emphasis will be on exploring fast and efficient methods, that can be incorporated in online systems for control of the power grid. Hence, we will explore the trade-off between obtaining a tighter output interval vs faster implementation.

Required skills:

Probability, Programming, Simulation

References: