My research in Spain

Many people have been asking me about my research, so here’s the abbreviated version:
In one year, the average Canadian household has a carbon footprint of 30 tons CO2 per year. The majority of this comes from fossil fuels used to create energy services, such as heating, transportation, and work reduction.

Quick facts on residential energy consumption, personally calculated and verified by multiple sources:

• The average car is driven approximately 20 000 km/year, and each liter of gasoline produces approximately 2.3 kg of CO2. Assuming a fuel economy of 10 km/L, gasoline for a car would cost approximately 2000$, and emit 4.6 tons CO2/year.
• A Canadian household needs approximately 25 MWh of space heating per year. A house with an 80% efficient gas furnace would require 1650 kg of natural gas, cost approximately 730$ (6.5$ per GJ), and emit 5.7 tons of CO2
• It also needs approximately 6-7 MWh of water heating, equivalent 200$ and 1.6 tons of CO2.
• Together, electrical appliances (fridge, cooking, cleaning) consume approximately 4.2 MWh of electricity. In Alberta, with a grid emissions factor of 0.71 tons CO2/MWh and residential electricity costing 0.08 per kWh, it would cost 330$ and emit 3.0 tons CO2
• Lighting consumes approximately 1.2 MWh (before Canada’s incandescant lightbulb ban), cost 96 $ and produces 0.85 t CO2 annually.
• Air conditioning on average, consumes 0.5 MWh, costing 40$ and producing 0.35 ton CO2 annually. However, since the majority of Canadians do not use air conditioning, the average is much lower than the typical consumption from an air conditioning unit.

I’m trying to see what can be done to help reduce costs and emissions, by coordinating the use of these residential systems. You see, you may think that gasoline prices vary often, but energy on the electricity market varies much faster, and can change hourly anywhere from 0-1000$/MWh. In addition, while the emissions from gasoline remains constant at 2.3 kg CO2/L, emissions from the electrical grid changes by region (Almost 0 tCO2/MWh in BC and QC to 0.71 tCO2/MWh in Alberta) and by time. For example, during windy periods, the emissions value decreases since there is more renewable energy injected into the grid.

I am currently working on a system that can use forecasts (electricity prices, emissions, wind speeds) and information from sensors to help make decisions on how to control residential devices. For example, if electricity prices or emissions rates are high in one particular hour, then it may be worthwhile to delay the operations of a drying machine by a couple hours. Of course, you don’t really KNOW the price of electricity in the next hour, but it is possible to try making the best decisions based on certain guesses about the future. This process is called stochastic optimization.

Remember those problems where farmer Bill had 36 meters of fencing, and had to maximize a rectangular area for his cows to graze along a river bank? The area would be the width x times the height y, and there is a constraint that by sum of the fence lengths is 36. So our problem is to maximize x*y subject to the constraint 2x + y = 36, which yields an answer of x=9, y=18. Now imagine scaling up this problem to approximately one million variables and one million constraints to be able to represent the operations of each residential system during each timeframe for each potential forecast that may occur. Of course, I have computer software that can do the computation for me, but I still need to do the modelling and programming.

So I’m no expert on Stochastic Optimization, and I still have a lot to learn, so my academic supervisor thought that it may be a good idea to collaborate with a very competent professor in Spain so that I can improve my techniques of implementing stochastic optimization techniques.