Uncertainty and Energy Modeling by wchang72

First part report Uncertainty Analysis Chanpin Building Risk analysis and optimization

Chang Wen-Yi

Warm up assignment: PV quote PV installer module 1: If the installer only have profit ratio in profit margin

Quote = N panels * [ C panels + (E factor * C install) ] *PM PV installer module 2: If the installer profit margin is a certain number

Quote = N panels * [ C panels + (E factor * C install) ] +PM Quote detail :

N panels = Area roof net / Area of the panels Area roof net = Area of roof * Utilization factor Quote for the PV installer With the first warm up assignment for UQ, the first thing to do is to start up the PV quote for the installer. In the quote have different numbers. Some of them are fixed but some of them are uncertain. To combine the quote which include the fix and uncertain it will be an PV quote. This comes out the final number get from the quote is the final number that PV installer give it to the customers. That is the main reason that the include the profit margin. Some of the profit margin might be a fixed number because some installer is going to said that their expectation profit is going earning fixed number of money. On the other hand there is going to profit margin percent. In the Quote there are also some number is going to be the main issue for the installer. Some of them are not certain number. To solve this problem, I will use @risk which I will talk about later. Number which is uncertainty

Area of roof

Roof area: For the first parameter in the quote is roof area. Since the quote must be the actual roof area, I decided to chose Georgia Tech Atlanta average roof area in the campus. The advantages for that is the roof area will also cover average Atlanta roof area. The main reason for that the campus have all kinds of building, include commercial building, normal housing and high-rise offices. Based on that reason I sum up all campus building then take the average number for the whole area. For the distribution, I chose is Lognorm. Based on my analysis the campus buildingâ&#x20AC;&#x2122;s roof area most likely going to be 3000m2 to 4000m2. Only one or two is over 4000m2.

Number which is uncertainty

Utilization factor In this legend the utilization factor is for installing solar PV on the roof. When talked about the install for solar PV, the roof condition itself is very important. In reality, not all roof is suitable for PV installing. Some of them might covered by janitor appliances and fire safety appliances. These appliances or space on the roof might not be good place for PV sitting next to them. The other things I consider about the utilization factor is the roof condition. Some of the building might not have right space for PV install. This also be into my consideration.

According to the analysis from GT campusâ&#x20AC;&#x2122;s roof top, the average utilization factor is 0.4. Some of them may get to 0.7 or 0.8. The main reason is that most of the building on the campus are commercial building. There roof top are covered by appliances. However, the normal housing (single family housing or multi family) is going to be difference. That is also the case that it goes to 0.7 etc. Number which is uncertainty

Efficiency factor Efficiency factor is the factor that effect the PV installation. The factor might caused by the shading for the roof area or roof condition it self. For example some buildings in GT might surrounded by tall trees and some of them might have unstable roof condition. These two might have caused the factor to goes down. In this part the average number I will take is going to be 1 which means the building is not covered by any trees and condition is great to install PV.

Number which is uncertainty

Cost of panels Cost of panel in this case I going to use triang distribution based on the research from DOE. Since the each quarterâ&#x20AC;&#x2122;s cost per watt become lower and lower. Each PV wattâ&#x20AC;&#x2122;s cost will continue to decrease. The other reason I used triang distribution is that even though the cost per watts is going to be lower there are still some chance is some area still using the old PV module.

Cost of install The other one that including in Cost of panel is cost of install. The installation fee is the main ingredient in total cost of panel. In that cased I set the distribution for construction worksâ&#x20AC;&#x2122; fee as the part of the consider in cost of installation. I assumed the install PV cost about one month and I divide the average construction fee in Georgia (per year) than I got the average cost of installation. Here is the basic fee distribution based on Career Explorer. It did the aggregated count for the whole distribution and I used it as my reference.

Number which is uncertainty

Profit Margin In this quote, the profit margin can be a simple factor, or it can be a simple number. The profit margin is to ket the installer company to decide how much they would like to earn during the season or in different project. The profit margin can be different from case to case or it can be different from companies t companies. The main thing to say is that based on the profit margin that company selected the final price is going to be different. This may be the main reason that affect the cost that consumer will see. In this case I took average PV solar farm company profit margin for the quote. The reason is that the normal company would like to be either good at other company or earn the same profit as other company. The company I use is First solar. I got its PM from stock market which is going to be the investment overview for the company.

Simulation Result

The result I separate in to quote for simulation, since if I continue using the same quote for the formula it will duplicate the form and continued the same number. This will make the answer remain the same. The quote separate into price and cost. The price part include the profit margin that the PV installer want to earned. The cost part is the revenue that that installer will have to pay. Then the final quote that can decide the PV installer the PV or not is to use the price minus the cost this means the money that the PV installer can earned. If the cost of the panel or install fee is bigger than the price include PM ( the part that overlapping )the PV installer will know the in these region they can not earn any money. This make them decide not to do the install construction.

Based on the result I got from the quote criteria, the distribution can show the oblivious way for the PV installer whether the installer will do the construction or not. When the PM goes to 1.1 the installer have 67% chance to make money. It also shows that how profit margin is a big issue for the installer. The more PM the more the installer will earn from the product.

Then I tried to apply the result to 1.4 PM the result shows even more different. The installer have 90 % chance to earn money. Based on these studied the PM play a big role in the PV install quote. However, in reality the case works different. Installer will have some trade off between the customer and the price.

Simulation Result: Uniform roof size and distribution for different roof size

The other thing to take about is the uniform roof size and different roof size in many projects and how it affect the profit margin and the decision for installer. Based on the result for the uniform roof size the final profit margin will have 96% chance that the installer will not loose any money however, with the same condition switch to different roof size the story is difference. It will lower the chance to 95%. The result shows that the more uniform the condition will be the more profit the installer will have chance to earn.

Simulation Result: How many panels ? Cost of panels (Market profit model) Cost of panels which means the cost of sales PV installer have to take. The cost of panels is going to be difference from state to state, since the state TAX or transportation fee etc. is going to affect the cost. According to these reason the cost of panels might be another uncertainty to consider. These will effect the installer to finalize the price of each PV panels. Take Atlanta as an example as of August 2019, the average solar panel cost in Atlanta, GA is $2.93/W. Given a solar panel system size of 5 kilowatts (kW), an average solar installation in Atlanta, GA ranges in cost from $12,452 to $16,848, with the average gross price for solar in Atlanta, GA coming in at $14,650. After accounting for the 30% Federal Investment Tax Credit (ITC) and other state and local solar incentives, the net price you'll pay for solar can fall by thousands of dollars.

Cost of panels (Compare with my PV Quote )

In my quote the mean price is 15713$ which is closed to the mean price in average Atlanta(14650$). I set another quote for counting how many PV I have to install in order to match the market model. In some cases my quote maybe so efficient that I can use less panels and reach the average market model. It also means my quote can have chance to make more money for PV installer than average PV quote in the market. The simulation result shows that the mean number of panel I will sell to reach 15713$ is 1349 but in average market model I need to have 3400 panels. The installer can have about 1500 panels profit that can they can earn by using my quote.

EPC add in with @RISK

The first scenarios that I would like test about is building air leakage level. In this parameter I use Gama distribution to set up the number. The number is based different standard average parameter. Most of the number will go to 0.25 the Gama distribution make the parameter apply to the number spread. Another reason for choosing this distribution is that the building went through the windows and doors renovation. It is clear to tell that the parameter for the air leakage level will not usually goes unusually high.

For the SFP number is different story from the air leakage level. From the beginning of the last semesterâ&#x20AC;&#x2122;s assignment, I totally not sure about the buildingâ&#x20AC;&#x2122;s HVAC system. From the basic guess I assumed the system will be VAV system and separate each floor. Since school is tied to district cooling and district heating, the assumed parameter do not have to set the uncertainty to heating and cooling COP. However, each building HVAC system is uncertain. The distribution I chose is uniform. The main reason is that the system SFP might have spread from machine to machine I did not have any clue for the system this made a briefly guess for the whole building.

Parameter inside the building I set lighting and appliance. The main reason for that the original building do have a clear occupancy but for the lighting and appliance is a little bit confused. The building is like a tutor building for student and normally the building usually have constant employee work in the building. The lighting and appliance is control by the people or student who came to the building and plug their computer and turn on the light when they needed. In this situation the lighting and appliance is not pretty sure for me. In this distribution I set both to normal. The main reason for that is the appliance and lighting have a very clear brand and the utility use for each category. The distribution is just to make sure the parameter is correct in this building. Also to prevent some of the room might have plug in there own lamp or other input lighting to the building.

Set Point D for @RISK TEMP Cool HI T 0 Heat HI T 0 Cool LO T 0 Heat LO T 0

Internal temperature and Environment temperature 30.00

25.00

20.00

15.00

10.00

5.00

0.00

Jan

Feb

Mar

Apr

May Ti_h

Jun

Jul Ti_c

Aug

Sep

Oct

Nov

Dec

The other parameter I set is the set point temperature in the building . The reason I set this one is that the set point temperature is totally unsure in the campus building. Each room in the building have there own thermostat and some of them use the same thermostat. These reason make the big uncertainty in the building. The other reason is that based on the last semester result the set point temperature is a big impact in the building. Based on these two reason I chose it as one of my parameter. Since the number is totally not certain the distribution is going to be normal. The range I set is from -5 degree C to +9 degree C. The range cover most of the temperature in Atlanta climate zone. The also tell the possible that some of the thermostat might have gone through that temperature.

For the building part which is mostly uncertain in the whole building. The U value and other parameter might have some quality change after a long time. Some of them might have some inside or others might het low quality. The first thing to set is the U value for roof and opaque. The main reason I donâ&#x20AC;&#x2122;t set emissivity of the material is that the color of the material is basically stay the same it do to have a dramatical material change based on my observation. The distribution I set goes to normal. The mean number for distribution is based on Ashrae 90.1 2016. The reason I said that is because the building got LEED certificated. It leads to some the building code have match the Ashrae 90.1. The distribution will have the same chance to go bigger than that regulation and code.

Last part is the window U value and solar transmittance. For window U value the Ashaae already have code for that, so it also goes to the regulation and distribution like opaque and roof. For the solar transmittance part is going to be tricky. The window transmittance might decrease might caused by outside weather and people reason. Some of the windows might have covered by dirt or others might have cleaned by schools' workers, For that reason, any number is possible for the building's window. Based on that I set the parameter to uniform to make sure each number have the same possibility.

Simulation Result 1 : Deliver Energy Distribution

Based on these parameter I tried to test the output from the simulation. First, I use the delivered energy for the building. The result I got from the EPC 278 which in the distribution I got 30% chance to reach that number. This also means that there are 70% of chance that the result will bigger than I simulated. Fir that reason I tried to get the reason for that. The tornado plot shows that the main reason that caused the delivered energy to raised up is that the solar transmittance. Then the other parameter also play important role. This means the baseline model still need to be improved by these parameter. That is the main thing we did in Tech OPT. However, these parameter will help us improve performance more efficient.

Simulation Result 2 : Best thing for improving cooling need

Based on the result from EPC, the cooling need is the most concerned things in the simulation result. To go through deeper, it is always good to use unusual month to test which parameter impacted the most. The month I chose to do the comparison is May and March. These two month are not in the summer but still need a lot of cooling need . The result shows that most impact on there result area the same as the one I just did in the delivered energy. The result shows that the delivered energy most likely cost by the cooling need and the main thing to do to improve cooling need is to improve window. After improve the window, the result also shows that the same optimization is not going to have the same expectation. For example the changing SPF in May might not be a good idea to do it in March.

Simulation Result 3 : Temperature exceed distribution (Cooling)

After knowing the cooling need result, I used another parameter to test different outcome. This time the outcome I would like to test is the temperature exceed normal. This means the average internal temperate in the summer that is not normal as the average temperature in the weather file. The result shows that the temperature might have 54% chance to go through more than average. In this case to solve that problem. The best way that shows on the result is to changing the set point temperature in the thermostat. Since it is the main reason that caused that situation. From this result it is also shows that in order to reduce more risk on the result we have to have some range for the simulation to improve that or let the range include the risk.

Uncertainty and Decision Making NPC and NPV

- NPC = NPV In this stage we talked more about the decision that have a clear target about decision making. The actual target about this is NPV. Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project. In the TECH OPT, there is one number called NPC which stand for Net present cost. When talking about these two number’s difference, the cash flow is clear to separate these two.

Before start the uncertainty in TECH OPT, I have to set the to approach the highest NPV in other words, highest NPC. The NPC in this stage can be always zero since TECH OPT is based on the retrofit’s cost which means is this stage is going to be positive.( No matter how many retrofits the solver will choose the result of costing money is going to be positive) To make final comparison comparable, I set the solver final target as lowest (-NPC). In this case the final target will get the parameter choice in TECH OPT be the lowest deliver energy and lowest technology add on cost. In that case it also accomplished lower the energy and make retrofit doable in the final decision making.

TechOpt Delivered Energy difference 90.00 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 -

Tech Opt Heating and Cooling Need Difference

Cooling Need [kWh/m2] (Opt before)

Nov Monthly Method Energy…

Sep

Heating Need [kWh/m2] (Opt Before)

Jul May

Cooling Need [kWh/m2] (Opt after)

Mar Jan Mar May Jul Sep Nov

Jan -

20.00

40.00

60.00

Based on the result I set in the highest NPV as my solver’s target. It is clear to see that the result is lower deliver energy is oblivious. Each deliver energy and thermal load is lower than before. The final cost is also the lowest in the whole optimization. After getting this result correct, I can take these to the next stage to simulate the uncertainty and tried to come up with quote to help installer for decision making.

Distribution for highest NPV Starting Construction Worker

Total Cost(Without worker fee)

C22

A 1 - Baseline (NULL)

0.00

A 2 - Partial sensor (25%)

375.00

0.9

A 3 - Partial sensor (50%)

750.00

0.6

A 4 - Partial sensor (75%)

1125.00

0.3

A 5 - Fully autom. sensor

1500.00

A 1 - Baseline (NULL)

0.00

Technology levels

Index

Cost $

Par.1 C23

B 1 - Baseline (NULL)

0.00

B 2 - Partial sensor (25%)

0.00

0.9

B 3 - Partial sensor (50%)

0.00

0.6

B 4 - Partial sensor (75%)

0.00

0.3

B 5 - Fully autom. sensor

0.00

B 5 - Fully autom. sensor

0.00

Technology levels Experienced Construction Worker C 1 - Baseline (NULL) C 2 - Partial dimmer C 3 - Partialy autom. Dimmer (50%) C 4 - Partialy autom. Dimmer (75%) C 5 - Fully autom. Dimmer C 1 - Baseline (NULL)

Index

Cost $

Par.1

Total Cost(Without worker fee)

C24

0.00

400.00

0.9

800.00

0.6

1200.00

0.3

1600.00

0.00

First distribution is the lighting control. In this part all parameters is unknown. Based on the on the result I got from last semesterâ&#x20AC;&#x2122;s simulation, the cooling need is the most concerned in Atlanta. The light might have been another big issue for the result. However in this stage, I did not know whether the high control factor for lighting goanna have a big impact for the result so I set each optionâ&#x20AC;&#x2122;s chance to equal.

HVAC’s COP

Heating and Cooling Plants efficiencies (COPs) Technology levels

Index

HVAC worker

Cost $

Par.1

Par.2

C28

C29

D 1 - Baseline HVAC D 2 - HVAC variation 2 D 3 - HVAC variation 3

1 2 3

0.00 10800.00 12436.00

1.46 2.28 4.28

1.54 3.21 4.75

D 4 - HVAC variation 4

14327.00

6.28

5.37

D 4 - HVAC variation 4

14327.00

6.28

5.37

Total Cost(Without worker fee)

In the last distribution I did in the EPC, I did not set the HVAC’s COP. The main reason is that in EPC the COP number is already confirmed. The COP from district cooling and heating is a constant number. However, in the TECH OPT is assumed this part can be optimized. I set the distribution for both heating and cooling to triang which means the higher COP the better which is predictable for lower the deliver energy. Infiltration Building air leakage level (Air flow m3/h per floor area at Q4Pa) Technology levels

Value

Cost $

Par.1

Top End Construction Worker

C45

Minimum infiltration

0.4

Maximum infiltration

-57272.73

Another parameter which is uncertain is the infiltration. In this part, I set the same distribution as the one in EPC. Even though I do know the better infiltration the better the result will get. I do not know in the highest NPV how will TECH OPT chose in the final the result. The result have money and deliver energy’s concerned. For infiltration it might be the best way because replace the infiltration might get high cost for installation.

5.00

On site PV system PV module Surface Area (m2)

Technology levels

Value

Cost $

Par.1

PV Construction Worker

C58

Minimum # PV modules

Maximum # PV modules

83.71

25227.15 169.00

On site PV collector Solar Collector Surface Area (m2)

Technology levels

Value

Cost $

Par.1

PV Construction Worker

C64

Minimum # Solar Col.

Maximum # Solar Col.

45.45

784.00

Min-value

Max-value

Variable

83.71

PV module area: PV module cost:

217.646

OVERALL Min-value REMODEL COST 0 840.00 Total labor time ESTIMATE (day) 7.00 Solar colector 2.6m2 area: 388.11$ Solar colector cost:

Max-value

Variable

45.45

2.60

OVERALL REMODEL COST 840.00 Total labor time ESTIMATE (day) 7.00 2.6m2 784.00$

118.17

In previous optimization the PV can be one of the main concerned in the category. When it comes to lower the deliver energy the PV usually will come to the grid. For the on site PV, I set the distribution in this stage to be uniform. It can be vary from different area and the maximum will be the roof area of building. I set each number have the same chance because in this part I do not consider the sell back power generate to compare with PV farm. So the TECH OPT might have same chance to install any number of based on TECH OPT. The other reason for that is to make sure the TECH OPT chose the best NPV in this stage not to consider any profit that the optimization will made.

Lighting Internal Condition Lighting ZONE1 (W/m2) Technology levels

Index

Starting Construction Worker

Cost $

Par.1

Total Cost(Without worker fee)

G13

100% CFL

0.00

LED and CFL combo (50% LED)

7245.00

LED

8050.00

Fluorescent lamp t5

6670.00

Fluorescent lamp t8

6900.00

Fluorescent lamp t12

7360.00

100% CFL

0.00

14 5.10 2.21 2.07 2.27 2.67 14

Lighting ZONE2 (W/m2) Technology levels

Index

Starting Construction Worker

Cost $

Par.1

Total Cost(Without worker fee)

G14

100% CFL

0.00

LED and CFL combo

3780.00 2.05

LED

4200.00 2.10

Fluorescent lamp t5

3480.00 1.97

Fluorescent lamp t8

3600.00 2.16

Fluorescent lamp t12

3840.00 2.54

100% CFL

0.00

Lighting in pervious TECH OPT is the only changeable optimization. The main reason is that lighting is only building internal condition that can be changed by the retrofit. The building is a tutoring building the appliance is not stable for different time period. In this case lighting is a good choice to changed in retrofit. The lighting I set the distribution to uniform. The main reason for that is because each option have some chance to make the building perform better than origin. The trade off for this one might be the cost and it density of using light during the simulation. In this case the chance of each option is equal.

Thermostat Set point Heat Temp Technology levels

Index

Minimize delta T Maximum delta T

Cost $

Par.1 K20

-9 5 1151.11

Set point Cool Temp Technology levels

Index

Minimize delta T Maximum delta T

Cost $

-9 Par.1 K22

-9 5 -639.50

Another scenario is the thermostat. In the previous distribution, thermostat mostly going to be triang distribution. However, in the TECH OPT stage I decided to make it uniform.. The main reason is that the thermostat control based on the internal cooling and heat temperature and internal temperature is based on the interaction with outside temperature in Atlanta. In the highest NPV, the case might be different or unknown. The uniform distribution make the increase in temperature chance to achieve the goal since I am not sure about how TECH OPT will chose based the my target. Window ratio North window ratio Technology levels Starting Construction Worker Minimize Maximum Ratio

Index

Cost $

Par.1

Total Cost(Without worker fee)

S54

Par.2

Par.3

Min-index

Max-index

Variable

0.1

0.8

0.1

0.1 Total Glazing Area

0.8 2060.23

0.1

Average Tare down window Window NUMBER(per Area window) 0 0

The other set to uniform distribution is the window ratio. Based on the heat transfer, the lower window building get the lower heating need it will get. In Atlanta even though the heating is not an big issue for the building, it still have some impacts on the building. The trade off that made me decided to use uniform distribution is the cost of changing window. In TECH OPT changing window also have a lot of installation fee and buying new windowâ&#x20AC;&#x2122;s cost. Both these two is not a very small cost for the highest NPV .As I mentioned since it did not have the actual confirm number distribution cannot have any preference on any chance.

Roof and Opaque improvement Roof Improvement Technology levels Experienced Construction Worker Roof Baseline 1 Roof Improvement 2.0 mm( new insulationEX Membrane) Roof Improvement 1.8 mm( new insulation EX Membrane) Roof Improvement 1.6 mm( new insulation EX Membrane) Roof Improvement 1.2 mm( new insulation EX Membrane) Roof Baseline 1 Wall improvement Technology levels Starting Construction Worker Wall Baseline 1 Wall Improvement 2 (R-38 insulation) Wall Improvement 3 (R-30 insulation) Wall Improvement 3 (R-21 insulation) Wall Improvement 4 (R-19 insulation) Wall Improvement 5 (R-13 insulation) Wall Improvement 6 (R-11 insulation) Wall Baseline 1

Index

Cost $

Par.1

Par.2

Total Cost(Without worker fee)

G64

H64

Par.3 I64

0.00

0.6

0.54

0.9

43572.00

0.45

0.6

0.9

68989.00

0.3

0.6

0.9

79882.00

0.2

0.6

0.9

94406.00

0.13

0.6

0.9

0.00

0.6

0.54

0.9

Index

Cost $

Par.1

Par.2

Total Cost(Without worker fee)

G66

H66

Par.3 I66

0.00

1.72

0.42

0.62

13761.83

1.7

0.4

0.62

15102.26

1.69

0.38

0.62

18229.95

1.67

0.35

0.62

21849.13

1.65

0.33

0.62

24172.56

1.63

0.32

0.62

27032.16

1.6

0.3

0.62

0.00

1.72

0.42

0.62

For roof and opaque U value I used normal distribution as mine distribution. The main reason is that the whether the retrofit of the U value is going to be greater or smaller than the before one, the U value all have to be in the range that do not match the Ashare 90.1. This restriction give TECH OPT to possible select the one that match this restriction. As the same reason as the opaque U value. The other is absorption coefficient. This part I set the distribution to uniform. The main reason for that is these do not have any fixed restriction in Ashrae 90.1. It will make the TECH OPT to have more space to chose the final option and any options is possible.

Window and shading South Shading-South Horizontal Angle Technology levels Index Starting Construction Worker Baseline 1 10 Degree 2 20 Degree 3 30 Degree 4 40 Degree 5 50 Degree 6 60 Degree 7 70 Degree 8 80 Degree 9 Baseline 1

Window Replacement Technology levels Starting Construction Worker Window Baseline 1 Double Glz: 6mm air Double Glz (Uncoated CLR CLR):3mm/12mm air (SHGC:0.66) Double Glz: 6mm argon Double Glz (e=0.40 surface2 or 3):12mm argon Triple Glz: 12mm argon Quadruple Glz (e=0.10):12mm argon Window Baseline 1

Index

Cost $ Total Cost(Without worker fee) 0.00 6600.00 6760.00 6920.00 7080.00 7240.00 7400.00 7560.00 7700.00 0.00

Par.1 Horizontal Angle

Par.2

Par.3

0 10 20 30 40 50 60 70 80 0

Cost $

Par.1

Par.2

Par.3

Min-index

Total Cost(Without worker fee)

G68

I68

J68

1 WINDOW BUYING COST(PER WINDOW)

0.00

5.91

0.53

21900.00

2.16

0.4

0.6

165

24300.00

2.27

0.8

0.2

205

25200.00

1.77

0.69

0.31

220

25800.00

1.99

0.51

0.49

230

31800.00

1.65

0.59

0.41

330

36000.00

0.68

0.8

0.2

400

0.00

5.91

0.53

First, for the windowâ&#x20AC;&#x2122;s shading device. The origin building do not have any shading material based on the observation. Any changing shading angle is going to consider to be adding shading on the building. It does improve the cooling load but it also will cost a lot of money based on that. That is the main reason I set these to uniform distribution. On the other hand for the window U value. The same reason as the wall and roof. The options have to follow Ashrae 90.1 regulation. For the emissivity of the window, I set it to uniform. That is because the changing windowâ&#x20AC;&#x2122;s glazing which mean change the window's emissivity. Glazing changing do not cost that much as install new window. These make the whole thing have equal chance.

Distribution for community PV PV calculation PV calculation

One PV deliver energy :

Quote1 =) PVwats(320,280,350K)* PeakSolarHour * PVefficiency Number of PV:

Quote2 =) DeliverEnergy(Before Retrofit) / Quote 1 Cost revenue:

Quote3 = Quote2 * [ C panels + (E factor * C install) ] Price:

Quote4 = Quote2 * [ C panels + (E factor * C install) ] *PM Before retrofit energy cost :

Quote5 =) DeliverEnergy(Before Retrofit) * Electricity tarift PV earned:

Quote6 =) Quote1 * Electricity tarift First year cash flow:

Second year cash flow etc.:

Quote7 = Quote6 – Quote5

Quote8 = Quote(6-7)*(1+Annual revenue growth rate) – Quote5 NPV of community PV.:

Quote9 = (-Quote3)+(Quote7…Quote8…..to 20years cashflow) Here is the quote and formula which I used for matching the community PV and the delivered energy from the original building. Each quote have some uncertainty in the parameter. The goal is to tell whether PV earned minus the original building cost the outcome can be balance or not. This can help the decision make for comparing community PV and the retrofit.

Distribution for community PV’s NPV and Retrofit’s NPV NPV for community PV

Based on the quote I set in previous session, the result of community’s NPV got 47 % of chance to be negative and got 53% of chance to get positive. Even though in the previous number most of the cash flow in each year are positive, the result still have some chance to get negative. When dig in the tornado chart, the main reason that impact the cell is the electricity tariff and the second one is going to be COP of the HVAC. The reason for the electricity tariff is obvious. Each cost revenue and price that generate from PV all must multiply the tariff. The tariff have a huge gap than any other impacts. These also give the clue that how we can take it into account how can affect the decision.

Distribution for community PV’s NPV and Retrofit’s NPV NPV for retrofit

The retrofit’s NPV is another story. The main impact is not the electricity tariff but the delta t. The result seems oblivious. In retrofit’s NPV, the main reason that caused the NPV to goes up and down is the delivered energy. The more delivered energy building will get the more money in one year. Not as community PV is driven by the money the Retrofit is driven by energy. For PV the more efficient PV module will reach the more energy it will produce. This means lower the cost. PV can also make the electricity tariff cheaper then lower the cost. However, in this stage it is still hard for people to decide which one is the best that is I am going to talk about.

Decision making PV or Retrofit PV’s NPV – Retrofit’s NPV

Final for the decision making, I decided to chose PV’s NPV minus the Retrofit’s NPV. The retrofit’s NPV is always going to be negative. To make the assumption, both retrofit and PV would like to achieved the highest NPV. In this stage the positive NPV( PV) is going to be positive and the negative will be bigger then become positive. Based on these result, if the PV minus Retrofit lower than 0 which means the retrofit’s NPV is bigger. On the other hand if PV minus Retrofit bigger than 0 which means the PV’s NPV is bigger. The result shows that the comparison have 67% of chance is greater than 0. To wrap it up, picking PV is better.

Decision making PV or Retrofit PV’s NPV – Retrofit’s NPV

Decision making PV or Retrofit PV’s NPV

Retrofit’s NPV

For another decision method is to compare the mean NPV for retrofit. The mean number for retrofit is $280358 and comparer with PV’s NPV. PV will have 65% chance to reach retrofit's NPV. When both reach the mean number the retrofit is $280358 but the PV only have $90851. In this case to look the caparison differently, with the same expectation to the mean parameter PV is not the best choice. The cash flow distribution of the PV is more scattered than the retrofits . In some situation, the retrofit is going to be a better choice than community PV. However, to look into the possibility the story is going to be difference. The retrofit’s NPV have 50% chance to reach 65% chance’s destination in PV. In that case the decision maybe going to chose use PV as my final decision.

Uncertainty Calibration First Parameter Setting Before Risk Optimization Calibration Parameters (continuous variables) Parameter Heating COP Cooling COP Building air leakage level Appliance(Zone1) Lighting(Zone1) Appliance(Zone2) Lighting(Zone2) WD/WE_Tset_heat Delta T WD/WE_Tset_cool Delta T Roof Uvalue Wall Uvalue Specific fan power

Unit. kW/kW kW/kW (m3/h)/m2 W/m2 W/m2 W/m2 W/m2 [C]ELSIUS [C]ELSIUS [W/m2/K] [W/m2/K] W/(l/s)

Cell C26 C27 C45 G13 G14 H13 H14 K20 K22 G64 G66 C46

Minimum 2 2 0.05 5 8 2 2 -5 -5 0.348 0.297 1

Maximum 3 3 5 13.11 14 13.11 12 9 9 1.056 2.7 5

Selection 2.5 2.5 0.0500 9.3390 11.2531 11.7136 6.2508 -5.0000 5.7205 0.7933 0.6113 2.3692

34.59%

Overall difference during entire year: non-weighted

28%

Overall difference during entire year: weighted

After Risk Optimization 1 Calibration Parameters (continuous variables) Parameter Heating COP Cooling COP WD/WE_Tset_heat Delta T WD/WE_Tset_cool Delta T Roof Uvalue Wall Uvalue

Unit.

Cell

Minimum

Maximum

kW/kW kW/kW [C]ELSIUS [C]ELSIUS [W/m2/K] [W/m2/K]

C26 C27 K20 K22 G64 G66

0.1 0.5 -5 -5 0.348 0.297

11 6 9 9 1.056 2.7

Overall difference during entire year: non-weighted Overall difference during entire year: weighted

Selectio n 4.4480 4.3752 -5.0000 -5.0000 0.3480 0.2970

30.13% 24%

In the last part is to make the optimization and applied to the model I already had. Before risk optimization, I already got very decent difference between real utility and my assumed model. The difference is about 35%.However, to look deeply into the result some parameter did not seems reasonable. The main reason is that some calibration number is very closed or even reach the boundary I set for the excel solver. In that cased the result is totally not correct. Based on that, I am going set some uncertainty and add calibration parameter at the same time to make sure the optimizer is changing the correct parameter in the calibration. Here is the first try off for the calibration with uncertainty and risk optimizer. The result do minimize the gap between utility and my proposed model but the to look deeply the situation is still the same with before one. In order to reach the goal of calibrationâ&#x20AC;&#x2122;s constrain, the optimizer make some calibration parameter the smaller the better. In this case the U value or set point are even reach the boundary. This seems clear incorrect.

Result Error Max and X Error max: 40 X=0.2 (Before)

Error max: 40 X=0.2 (After)

Based on the first result distribution I got from the Risk Optimizer, the distribution become narrow and tall. Before optimized the distribution seems have some more error for the 30% difference after that it become more closed to the result. The errors become lesser than the one before. However, like I just said the calibration parameter is too close to the boundary. The main reason for that is the wrong parameter may lead the optimizer to continuing lower down the result to make sure the error become less. In that case, if the parameter that I set not the right good choice for calibration, even though the final result seems reasonable the distribution is not good enough to use as more constrain simulation or optimization .

Uncertainty Calibration Final Parameter Setting Before Risk Optimization Calibration Parameters (continuous variables) Parameter Heating COP Cooling COP Building air leakage level Appliance(Zone1) Lighting(Zone1) Appliance(Zone2) Lighting(Zone2) WD/WE_Tset_heat Delta T WD/WE_Tset_cool Delta T Roof Uvalue Wall Uvalue Specific fan power

Unit. kW/kW kW/kW (m3/h)/m2 W/m2 W/m2 W/m2 W/m2 [C]ELSIUS [C]ELSIUS [W/m2/K] [W/m2/K] W/(l/s)

Cell C26 C27 C45 G13 G14 H13 H14 K20 K22 G64 G66 C46

Minimum 2 2 0.05 5 8 2 2 -5 -5 0.348 0.297 1

Maximum 3 3 5 13.11 14 13.11 12 9 9 1.056 2.7 5

Selection 2.5 2.5 0.0500 9.3390 11.2531 11.7136 6.2508 -5.0000 5.7205 0.7933 0.6113 2.3692

34.59%

Overall difference during entire year: non-weighted

28%

Overall difference during entire year: weighted

WD/WE Tset delta T: Based on the result I got from Tech Opt, the set point temperature delta t is one of the things I add in the new hourly calibration. This can make EPC more focus on heat and cooling difference. Roof and Wallâ&#x20AC;&#x2122;s U value: In the monthly EPC I did not change any of these number. However, in the hourly calibration in order to get the result closer to the utility data, I set the U value to be changeable. The number will give EPC some range to adjust the U value and make the cooling and heating load closer than monthly After Risk Optimization Calibration Parameters (continuous variables) Parameter Heating COP Cooling COP Roof Absorption Coefficient Wall Absorption Coefficient Building air leakage level Specific fan power Roof emissivity Window Solar Transmittance Wall Emissivity SRF S SRF N

Unit.

Cell

Minimum

Maximum

kW/kW kW/kW n/a n/a ACH W/(l/s)

C26 C27 H64 H65 C45 C46 I64 J68 I66 M50 M54

0.1 0.5 0 0 0.1 1 0 0 0 0 0

11 6 1 1 3 6 1 1 1 1 1

Overall difference during entire year: non-weighted Overall difference during entire year: weighted

Selectio n 3.4741 4.5911 0.6715 0.9988 0.1000 1.0000 0.0023 0.9894 0.0004 0.6471 0.1177

29.29% 24%

After first try of the calibrationâ&#x20AC;&#x2122;s parameters, I tried other different kind of parameter to make sure I use the correct parameter. In this case I used the absorption coefficient and infiltration, emissivity and last but not least, the SRF number. In the previous calibration mostly focus on the parameter main system control and the building material U value. However, the result shows that in order to make the lower the difference the optimization will continue lower the U value till it reach the boundary.

Uncertainty Risk Optimization (Uncertain Parameter)

The first parameter I changed from calibration to uncertainty is zone information. Zone information include the appliance and lighting and occupancy. These area the internal load in the each zones. The main reason I changed these into the uncertainty is because the in previous optimization the optimizer will modify it as low as possible to reach the constrain. This totally not true for the building. The internal load should not be the correct one to calibration. Many case the parameter of these load information is unclear but not totally wrong. For the distribution for these parameter I used uniform distribution for the occupancy since the each possibility is equal and triang distribution for lighting and appliance since these can be observe and stay the same during the whole year.

Uncertainty Risk Optimization (Uncertain Parameter)

I also changed Set point temperature to uncertainty parameter since Atlanta has both cooling and heating need during the whole year. The heating temperature and cooling set temperature in the previous calibration all reach to the boundary number. Cooing to +9 degree c and heating to -5 degree c. These can not be the real set point. The other one is the U value. These number also encounter the same situation as set point temperature. The main regulation that I have to follow is the Ashrae 90.1 regulation for U value. The final one is the SRF number for the roof. The main reason for that is because the building surrounding have tall deciduous trees that I can not estimate. However, for the South and North side I put it into calibration since the treeâ&#x20AC;&#x2122;s part which under two floor in my site do not have any flora cover.

Result Error Max and X Error max: 45 X=0.2 (Before)

Error max: 45 X=0.2 (After)

After using the correct parameter to calibrate, here is the distribution. Based on the graph, before calibration most of the distribution is very scattering. The error max in 80% more than 45 %. The distribution did not seems very precise and it even got some chance that the possibility will go to 50%. To look into it carefully before calibration the chance more than 50% is higher than after calibration one.

Result Error Max and X Error max: 40 X=0.1 (Before)

Error max: 40 X=0.1 (After)

Based on the same calibration parameter the risk optimizer can even become more accurate. The previous error max and x is 0.4 and 0.2. In this stage I would like to make the same error max but make the x in 10%. The result did improve the whole distribution. Right now the whole distribution become narrower and in the previous the 44% to 31% the is 60% but in this case it rise to 80ďź&#x2026; it did lower a lot of error based on the risk optimizer.