## Sizing Transformers

We used measurements of home loads to optimally size transformers.

Our first paper describes how to model home energy consumption using Markovian models for transformer sizing. We collected load measurements taken at six second granularities from 20 homes over four months to build these models, which can now be used by simulations and analyses for related problems [1].

Our second paper applies the Markovian model described above to determine the optimal transformer sizing for a neighbourhood. We demonstrated that the electric load distributed from a transformer can be modelled the same way as the traffic from data sources distributed from a router. Because of this equivalence, we were able to use teletraffic theory, usually used to size telecommunication access networks, to size power distribution networks. We showed that this method of sizing transformers gives results that match the sizes of transformers currently deployed in neighbourhoods. This method can be used to size transformers when building new neighbourhoods in the future [2].

[1] O. Ardakanian, S. Keshav, and C. Rosenberg. Markovian Models for Home Electricity Consumption, Proc. ACM SIGCOMM Green Networking Workshop, August 2011.

[2] O. Ardakanian, S. Keshav, and C. Rosenberg. On the Use of Teletraffic Theory in Power Distribution Systems, Proc. e-Energy, May 2012

## Control of Electric Vehicle Charging

**Problem
**Electric vehicles (EVs) pose a challenge to the electrical grid in two ways.

- First, large-scale introductions of EVs pose a
**significant load to the grid.**An EV can be charged with a load of up to 19.2kW (with Level 2 chargers), whereas a typical North American home has an average load of 1kW – this means a single EV could impose a load as large as that imposed by nearly twenty average homes. - Secondly,
**the load posed by an EV is variable by time and location**: its load on a grid will unpredictably disappear when it is being driven. It might then charge at a different location, re-appearing at a different part of the electricity distribution network.

**Solution
**Since a typical EV charger is located within 3km of the nearest substation, the transmission delay between any charger and its connected substation is less than 1ms. As such, we can design a distributed control algorithm that adjusts the charging rate of an EV every few milliseconds, in response to the load being placed on the overall distribution system. For example, if an EV is charging at a rate that affects the reliability of the grid, its charging rate can be decreased.

Three papers were written on this subject. The first paper introduces the problem and describes how the congestion control problem for a grid distribution system is similar to the congestion control problem in the Internet.

- O. Ardakanian, C. Rosenberg, and S. Keshav. Real Time Distributed Congestion Control for Electrical Vehicle Charging (invited paper), ACM SIGMETRICS Performance Evaluation Review 40.3 (2012): 38-42.

By using a mathematical framework originally developed for rate control in the Internet (TCP), each EV charger in the grid can independently update its charging rate, while ensuring that the overall load on the grid stays at an ideal level, the allocated rates for each charger are proportionally fair, and that these allocations are optimal. The second paper in this series focuses on a static network scenario, in which the non-EV load is constant, and a fixed number of EVs are connected to chargers.

- O. Ardakanian, C. Rosenberg, and S. Keshav. Distributed Control of Electric Vehicle Charging, Proc. ACM e-Energy, May 2013.
**Winner of Best Paper Award.**

The third paper goes into detail about the dynamic network scenario, which involves variable home loads and number of plugged-in EVs. Since the dynamic network scenario can be decomposed into a series of static intervals, the static control algorithm described above can be extended to be used in a dynamic network.

- O. Ardakanian, S. Keshav, C. Rosenberg. Real-Time Distributed Control for Smart Electric Vehicle Chargers: From a Static to a Dynamic Study, IEEE Transactions on Smart Grid, vol.5, no.5, pp. 2295-2305, Sept. 2014.

**Evaluation
**We show that in a test setting, only 70 EVs could be fully charged without control, whereas up to around 700 EVs can be fully charged using our control algorithm. This work was further extended to integrate EV charging control with control of distributed storage, while accounting for distributed solar generation. Details can be found here: O. Ardakanian, S. Keshav, C. Rosenberg, “Integration of Renewable Generation and Elastic Loads into Distribution Grids,”

*Springer*, 2016.