using matlab and excel to solve building energy simulation problems

Using MatLab and Excel to Solve Building Energy Simulation Problems

Jordan [email protected]

Objectives

• Intro to MatLab (if needed)• Briefly discuss linear equations• Solving systems of non-linear equations– Using solve function• Example 1

– Using loops to solve for multiple time steps• Example 2

– Importing data from Excel• Example 3

Linear Equations in MATLAB

• Solve system of equations:3x +2y –z = 10-x +3y +2z = 5

x -y -z = -1


• Pose as a matrix problemAx=b

Where A =

x =, b =


• 3 ways to solve in MATLAB:– Inv– A^-1– Left division


• For all three, first define matrices:A= [3 2 -1; -1 3 2; 1 -1 -1];B= [10; 5; -1];

• Can be solved by any of the following syntaxes:X=inv(A)*BX=A^-1*BX=A\B NOT X=A/B or X=B\A

• Each gives equivalent answer• Left division is more computationally efficient: less

time to compute for large matrices

Non-Linear Equations in MATLAB

• Distinguish between symbolic variables (ones you will solve for) and variables with numeric values (i.e. e, F12, etc.)

• Define symbolic variables:– Can create multiple symbolic variables at once

with syms command– Syntax:

syms x y z a b corsyms T1 T2 T3


• Say we have defined symbolic variable x and want to solve an equation for x.

• With symbolic variables defined, create equation using syntax:

E1=x-3• Notice your equation must be in the form

f(x)=0• If it is not, rearrange it so it is


• We can now use solve function to find x:• If we just write solve (E1) we will get ans = 3• If we want to redefine x as the solution, we

can input x= solve(E1)

Non-Linear Equations in MATLAB• For systems of equations, process is similar.– Define variables using syms– Write multiple homogeneous equations

e.g. E1= x + y + z +2 E2= 3*x -2*y + z E3= -x + y -4*z +6

– Then use [x,y,z]=solve(E1, E2, E3)

– Variables must be listed in alphabetical order on left side because right side outputs answers in alphabetical order of symbolic variables


• Sometimes you will be working with both symbolic and numerical variables.

• This is ok.


Example 1: Find both T2 and Q for the steady state conduction problem, given k=4W/mK, wall thickness is 0.2m, T1=30, T3=40, and the area of the wall is 4m2

T1 T2 T3

Q


Example 1 Code:

k=4; %W/mKA=4; %m^2L=0.1; %mT1=30; %degrees CT3=40; syms Q T2;E1= k*A/L*(T3-T2)-Q;E2= k*A/L*(T2-T1)-Q;[Q, T2]=solve(E1, E2)

Output:Q =800T2 =35


Example 2: Using a loop to solve for multiple time steps• Now suppose the temperature of the outside

wall changes every hour, in discrete jumps (steady state assumption can be used for each hour)

• We need an efficient means of calculating T2 and Q for each hour

• Will use a loop


• Say we are given this data for the outside temperature, T3:

• and we want to find T2 and Q at each time

Time T3

12 midnight 20

1 20

2 20

3 20

4 21

5 24

6 27

7 28

8 30

9 33

10 35

11 39

noon 41


Example 2• 1st create an array with the temperatures:

T3=[20 20 20 20 21 24 27 28 30 33 35 39 41]

• Then loop through each value of T3 to calculate a corresponding value of Q and T2, and store these values in a Q and T2 array

Non-Linear Equations in MATLABExample 2 code:k=4; %W/mKA=4; %m^2L=0.1; %mT1=30; %degrees CT3=[20 20 20 20 21 24 27 28 30 33 35 39 41]; %input temperature arraysyms Q T2; % define symbolic variables for i=1:13 % tells the program to loop through 13 iterations % (corresponding to 13 hours for which we have data) E1= k*A/L*(T3(i)-T2)-Q; %notice an individual value of the data is called for T3E2= k*A/L*(T2-T1)-Q; %by using the index "i" in T3(i) [Qarray(i), T2array(i)]=solve(E1, E2) %we save our data in a separate array, % which is appended automatically each iteration endT2array=double(T2array) %when doing symbolic math, answer is often returned in fractional form. %to convert it to decimal form, use the function "double", as in double precision

Non-Linear Equations in MATLABExample 2: Qarray= -800 -800 -800 -800 -720 -480 -240 -160 0 240 400 720 880

Output:

T2array= 25.0000 25.0000 25.0000 25.0000 25.5000 27.0000 28.5000 29.0000 30.0000 31.5000 32.5000 34.5000 35.5000


Example 3: Importing Data from Excel• Sometimes we have a lot of data and cannot input

it by hand, e.g. TMY data• There are a few ways to import data from Excel– Cut and paste– Use import wizard by selecting

File > Import Data or Use function uiimport

• When using the wizard, make sure the file is saved in your working directory


Example 3• Say we now are not given T3, but we have an outdoor

convection coefficient, h, which changes with time, and an outdoor air temperature.

T1=30 T2 T3

Q

Tout

• We want to find all T values and Q using the import wizard


Example 3: Importing Data from Excel• Here is the data we have, in a worksheet by itself:

• If we just use the wizard, a 13x3 matrix is created, with the name of the Excel file (I called mine tdata)

Time (h) Tout (C) h (W/m^2-K)0 19 11 19 1.12 19 0.93 19 14 19 0.95 19 1.16 20 1.57 22 1.78 27 1.39 29 1

10 32 1.211 38 112 42 1.5

Non-Linear Equations in MATLABExample 3: Importing Data from ExcelWe can make separate arrays if we like for each variable by using commands such as

>> Tout=tdata (:,2) %which says the array “Tout” is the 2nd column of “tdata”

Tout =19 19 19 19 19 19 20 22 27 29 32 38 42


Example 3: Importing Data from Excel• Once we identify the h values in a similar way,

we can solve our problem• Code on next slide

Non-Linear Equations in MATLABExample 3 Code

k=4; %W/mKA=4; %m^2L=0.1; %mT1=30; %degrees C syms Q T2 T3; for i=1:13 E1= k*A/L*(T3-T2)-Q; E2= k*A/L*(T2-T1)-Q; %we now have 3 eqns + 3 unknownsE3= h(i)*A*(Tout(i)-T3)-Q; %notice indices on h and Tout [Qarray(i), T2array(i), T3array(i)]=solve(E1, E2, E3) endQarray=double(Qarray)'T2array=double(T2array)'T3array=double(T3array)'

Non-Linear Equations in MATLABExample 3 Output

Qarray =

-41.9048 -45.8768 -37.8947 -41.9048 -37.8947 -45.8768 -55.8140 -50.1382 -14.6479 -3.8095 9.0566 30.4762 66.9767

T2array =

29.7381 29.7133 29.7632 29.7381 29.7632 29.7133 29.6512 29.6866 29.9085 29.9762 30.0566 30.1905 30.4186

T3array =

29.4762 29.4265 29.5263 29.4762 29.5263 29.4265 29.3023 29.3733 29.8169 29.9524 30.1132 30.3810 30.8372

Conclusion

• Should be everything you need to finish homework

• Additional help (2 equation model form the class) on the course website, handouts section

• Please contact me with questions about Matlab or about B.E.S.

[email protected]

• Questions now????

using matlab and excel to solve building energy simulation problems

Documents