A Sensitivity Analysis Toolkit for Mitigation of Distributed Generation Voltage Rise
Fabian Tamp
October 2012
this little guy is a solar panel. He makes electricity from the sun, but he makes the voltage go up a little bit when he connects.
One generator doesn't affect things much. But when you have lots, some of them automatically disconnect to stop things from blowing up. Then everybody gets cranky because they're not getting paid for generating electricity.
This isn't your average problem - you can't just fix it by buying a better generator. You need COORDINATION
People have come up with heaps of ideas for coordinating generation, but they usually involve simulations. Building simulations is a pain.
So, I built a toolkit based on SENSITIVITY ANALYSIS, A magical technique that makes understanding and working with network voltage relationships much simpler.

Simulation

  • Difficult to calculate
  • Lots of information required
  • Calculates all values, even if we only need two or three.

Sensitivity Analysis

  • Easy formula!
  • Sensitivities show what has the biggest impact
  • Not quite as accurate
I calculated the sensitivities in a simulation with a trick called PERTURB-AND-OBSERVE, Which basically just means DROP A GENERATOR ON THE NETWORK AND SEE WHAT HAPPENS
There's no point in having this information unless we use it for decision-making, so I used the sensitivity analysis toolkit to implement a technique called VAR CONTROL On a model of a network in Western Sydney. Doing the coordination was really easy because sensitivity analysis makes it really obvious where you get the most 'bang for your buck'.
Using this strategy, I could fix around 90% of the voltage rise. Hooray!
Danger! Fixed!

Before

After
Then, I tried to find network sensitivities from actual network data. That would be awesome, because you could make INFORMED DECISIONS WITHOUT SIMULATIONS. But, nobody had the network load data I needed... so I faked... erm, synthesised the data, using the MIGHTY POWER OF STATISTICS!!!
Here's a graph of some actual data, and some data I synthesised. It's for a weekday in summer on one feeder. They match up pretty well!
Here's a visualisation of the synthesised network load data and the resultant voltages. Colour represents voltage, and blobs represents load size. Pretty!
To get the sensitivities, I thought it best to look for situations where perturb-and-observe has occurred naturally. The thing is, you need A LOT OF DATA before that happens coincidentally, and with a lot of data comes A LOT OF PROBLEMS.
For one days' data, a test algorithm took 15 minutes to run. Two days' data took an hour. A weeks' data took 12 hours. A year's data was going to take 3.8 years to process. I'll leave that task for someone else.