For 2 or More Units: Create Two New Evaluator Nodes
Top Height [ft] | Base Radius | Gross Floor Area | Gross Surface Area | Cumulative Insolation [Wh/m2] | cost savings / yr | construction cost |
600 | 150 | 2945067 | 631087.5 | 1.02E+10 | $43,947,103 | $1,470,000,000 |
600 | 180 | 3229181 | 673101.5 | 1.02E+10 | $43,937,479 | $1,610,000,000 |
700 | 150 | 2512669 | 617080 | 4.96E+10 | $214,000,000 | $1,260,000,000 |
700 | 180 | 2760280 | 659176.2 | 4.96E+10 | $214,000,000 | $1,380,000,000 |
- Custom nodes
- PV Solar Analysis
- I started by finding the total insolation on the roof. There was a bug in the starting custom node, BuildingForm.SelectRoofSurfaces, where it would return all surface except the ground surface. I fixed this bug by only returning the last element in the surfaces list, which represented the roof.
- I used the following formulas to calculate the cost savings:
- I used the following assumptions:
- usableRoofFraction = 0.70
- pvEfficiency = 0.20
- performanceRatio = 0.80
- electricityRate = 0.12
- Construction Cost
- I made a custom node to calculate the construction cost. Since I constrained the height to be less than 750 ft, the cost per square foot is $500. I took the total floor area and multiplied it by $500/sqft.
- I integrated both custom nodes into a custom testing node, where 2 parameters could vary at a time. As in Module 5, I varied the top height and the base radius.
pvEnergy_kWh = avgInsolation_WhPerM2 * usableRoofArea_m2 * pvEfficiency * performanceRatio *365/ 1000;
costSavings = pvEnergy_kWh * electricityRate;
In this exercise, I wanted to show that even though the construction cost of the building is very high, there is potential for cost savings by adding solar PV panels to the roof.
💡Point to Ponder: Do the new evaluation metrics that you’ve designed capture the meaningful differences between the building form alternatives? What other metrics would be useful to compute to help understand and make the case for which alternatives are truly better than others?
- Yes, the metrics I calculated capture meaningful differences between building alternatives because they show how altering the geometry can lead to higher or lower construction costs yet also lead to savings when there is larger roof area. It may also be useful to calculate the expected energy load on the building to show the extent to which the building is energy independent.
For 3 or More Units: Develop a Single-Objective Optimization Scheme
- Brief descriptions outlining:
- Your Single-Objective Optimization scheme (combination/comparison/ranking approach)
- function:
- F = A*normalized[(construction cost - pv savings)] + B*normalized[(gross surface area/ gross floor area)]
- A and B are weightings
- minimize(F)
- It is ideal to maximize gross floor area:gross surface area, but since the scheme will minimize F, we invert the ratio.
- Cost will be minimized. PV savings is a function of insolation, so it accounts for the objective of maximizing insolation.
- One tradeoff would be that a compact building form usually has a lower surface area to floor area ratio, which is good for energy efficiency and cost. But a compact form may also have less roof surface area available for PV, which can reduce solar savings.
- I set A = .7 and B = .3, since a developer would likely care more about the cost than the slenderness of the building. However, both objectives are interlinked since a more efficient design can have lower capital costs.
Top 3 results:
- base height = 700 ft, base radius = 150 ft
- base height = 675 ft, base radius = 180 ft
- base height = 675 ft, base radius = 170 ft
Top Height [ft] | Base Radius | Gross Floor Area | Gross Surface Area | Cumulative Insolation [Wh/m2] | cost savings / yr | construction cost | objective score |
600 | 150 | 2945067 | 631087.5 | 1.02E+10 | $43,936,350 | $1,470,000,000 | 1 |
600 | 160 | 3036518 | 644728.1 | 1.02E+10 | $43,936,898 | $1,520,000,000 | 0.865778 |
600 | 170 | 3131227 | 658732.8 | 1.02E+10 | $43,933,911 | $1,570,000,000 | 0.823883 |
600 | 180 | 3229181 | 673101.5 | 1.02E+10 | $43,929,393 | $1,610,000,000 | 0.788199 |
625 | 150 | 2729220 | 613552 | 1.21E+10 | $52,169,116 | $1,360,000,000 | 0.757597 |
625 | 160 | 2815168 | 627108.5 | 1.21E+10 | $52,174,890 | $1,410,000,000 | 0.369203 |
625 | 170 | 2904190 | 641016 | 1.21E+10 | $52,174,964 | $1,450,000,000 | 0.329424 |
625 | 180 | 2996262 | 655274.9 | 1.21E+10 | $52,191,003 | $1,500,000,000 | 0.295549 |
650 | 150 | 2602898 | 608552.4 | 3.68E+10 | $159,000,000 | $1,300,000,000 | 0.266937 |
650 | 160 | 2685722 | 622129.5 | 3.68E+10 | $159,000,000 | $1,340,000,000 | 0.242169 |
650 | 170 | 2771523 | 636051.1 | 3.68E+10 | $159,000,000 | $1,390,000,000 | 0.20371 |
650 | 180 | 2860281 | 650316.5 | 3.68E+10 | $159,000,000 | $1,430,000,000 | 0.17093 |
675 | 150 | 2538934 | 610659.9 | 4.22E+10 | $182,000,000 | $1,270,000,000 | 0.142926 |
675 | 160 | 2619839 | 624293.3 | 4.22E+10 | $182,000,000 | $1,310,000,000 | 0.098833 |
675 | 170 | 2703679 | 638266.2 | 4.22E+10 | $182,000,000 | $1,350,000,000 | 0.060504 |
675 | 180 | 2790425 | 652577.7 | 4.22E+10 | $182,000,000 | $1,400,000,000 | 0.02788 |
700 | 150 | 2512669 | 617080 | 4.96E+10 | $214,000,000 | $1,260,000,000 | 0 |
💡 Point to Ponder: What propelled the recommended alternative to the top of the list?
The best design is the one with the lowest objective score. The design with a top height of 700 ft and a base radius of 150 ft has a score of 0. It satisfies the gross floor area constraint, has the lowest construction cost among the visible feasible options, and has the highest PV cost savings due to its higher cumulative insolation. It also has a relatively low gross surface area compared to the other options, which helps its envelope-efficiency score.
The next best two options have a top height of 675 and a base radius of 180 and 170 and scores of 0.027 and 0.06, respectively. Although a taller building may have more gross floor area, its slenderness improves its overall material efficiency, improving its objective score.
- For 4 Units: Visualize the Recommended Alternative
- base height = 700 ft, base radius = 150 ft