MIT OpenCourseWareSession 3: Energy Efficiency Co-Flows
MIT OpenCourseWare
SEIRb cleanup and energy flows 0:00
Hazhir Rahmandad first revisits SEIRb and clears up two loose ends. He explains how to handle people who have both vaccine immunity and natural immunity without forcing two state changes at once. The cleaner rule is to let one immunity wane at a time, with separate rates, unless you model their interaction directly. He also notes that the share of people willing to vaccinate is not fixed. If unwilling people die more often, that fraction rises over time, so deaths among the unvaccinated must be counted. He then turns to equilibrium conditions, including the case with behavioral response, and points to a paper with the worked solution. After that, he shifts to energy-efficiency coflows. The goal is to track building vintages, retrofits, and new technology so you can estimate total energy use under different interventions.
Retrofitting assumptions 21:32
[21:32] Hazhir says the retrofit flow is fine if you treat demolition and retrofit as alternative end states at the end of a building's life. He notes that the model gives retrofitted buildings a new life, but it also means other stages need separate tracking if their lives differ. The main point is to keep the assumption clear.
Cohorts and limits 25:02
[25:02] He then says the model should track how much improvement each vintage can still make. That makes the best technology a coflow, not a fixed fraction. He accepts the idea of wear and tear on mature buildings, but prefers a continuous flow over a step change. He also questions using if-then-else for retrofit gains and says the real issue is the lowest feasible efficiency.
Retrofit limits 43:02
Retrofit efficiency can fall as you near a limit, so early upgrades are cheap and effective while later ones matter less. A question about an if-then-else shows that it is not required for parameters that vary by subscript level. You can simply list the values for each cohort. The same idea applies to several models, which the speaker wants to compare before doing deeper analysis.
Building coflows 45:05
A building model tracks new, mature, and old stocks, plus energy reduction. The key issue is how retrofit potential follows technology. One formulation delays current building efficiency and uses that delayed value as the achievable level for mature buildings, then again for old buildings. The speaker prefers tying this potential to the building state itself, so the coflow carries the underlying limit forward and avoids mixing it with current energy use.
Efficiency limits 1:05:31
The model discussion starts with total building energy use, built as the sum of buildings times energy use per building. The main correction is about what technology changes. One version only lowers retrofit cost. The other, preferred here, lets new efficiency levels appear over time. It also warns that not every 1950s building can realistically reach Class A without rebuilding.
Vintage subscripts 1:08:31
The later models use subscripts for vintages so the same equations can handle many cohorts without being copied by hand. New buildings enter the first cohort, demolition hits the last, and middle cohorts age forward. This makes retrofits easier to apply across all vintages, but the retrofit ceiling is still hard coded as a weighted average, so new technology cannot fully change it dynamically.
Retrofit fraction logic 1:28:31
The retrofit flow is written as current total energy consumption minus indicated energy use, divided by the time to finish retrofit. The indicated value comes from total buildings times the average energy intensity of retrofitted buildings, mixed with the not-retrofitted cohort by the fraction under retrofit. That fraction is treated as a continuous share between 0 and 1, so investment can move buildings into retrofit gradually.
Limits and subscript design 1:46:06
The model runs, but the average intensity after retrofit should not stay tied to the current average. If it multiplies the current average again, the value can keep falling past the intended limit and even go negative. The cleaner fix is to set the post-retrofit intensity from the underlying technology, not from the current average. The speaker then turns to subscript-based cohort models, starting with a simple aging chain where one group feeds the next.
Subrange Mapping 1:54:01
The model walks through how Vensim matches elements across two subranges. It takes the previous cohort and lines up infant with child, then child with teen, and so on. The key point is that you need separate subranges and a mapping rule so Vensim knows which elements belong together. Without that, it treats the match as apples and oranges and throws an error.
Predator Prey Exercise 2:08:15
The next assignment is a predator prey model with carrying capacity for the prey. It should include vegetation, so the herbivore cannot grow without food. The suggested problem frames are policy based, such as managing pests or deer crossings, reference mode based, such as explaining oscillating populations, or mechanism based, where you study what the predator prey and food web mechanisms alone produce.
Model scope and tests 2:17:32
Use one stock for predators and one for prey, or at most two if you want age groups or vegetation detail. Keep the model simple first. Test it by recreating expected behavior such as oscillations. Vary reproduction rates, initial states, hunting, land change, and disease. Track species populations and carrying capacity, then build the model in stages: deer, then wolf, then carrying capacity.
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