Roots of a linear equation-CodePudding

I have a bunch of solar panels, each one is connected to an inverter. For each solar panel I have two sensors, a wind and a west sensor. From every inverter, I collect the power output. The readings are collected for every 5 minutes, and I have a dataset over 7 days.

I know that the power can be estimated using the equation:

Equation

Here is what I did so far: I only used the west sensor as I thought the wind sensor has little effect on the power output of a solar panel(common sense?). Then, I grouped the data by hour and then day, for example, for on the 22.12.2022 I got 24 readings, and so on.

I rearranged the equation, to get something like Ax Bxy C = 0, see here:

A_e * irr_s   A_e * eta_T * (irr_s * T_m   irr_s * 25) - rho_A = 0

if I say, A = irr_s and B = irr_s * T_m irr_s * 25 and C = -rho_A,

Now I calculated the two unknowns, A_e and eta_T. I used matrixes to solve different pairs of equations using:

Let us assume the two pairs look like this:

A_1x   B_1xy   C_1 = 0 and  

A_2x   B_2xy   C_2 = 0


M1 =   
A_1, B_1  
A_2, B_2

and

M2 =   
C_1  
C_2  

ROOTS =   
R_1  
R_2

Then, ROOTS = np.linalg.inv(M1).dot(M2)

I plotted them on a graph, see below: Click here

Do you think my approach is good? How else could one approach this problem? Thank you for your inputs in advance!

CodePudding user response：

It is not linear equation.

ro = ae * irr * (1   eta * (t-25))

It is not clear what values change between measures. Let ro, irr and t:

ro1 = ae * irr1 * (1   eta * (t1-25))
ro2 = ae * irr2 * (1   eta * (t2-25))

divide these equations

ro1/ro2 = irr1/irr2 *(1   eta * (t1-25)) / (1   eta * (t2-25))
ro1 * irr2*(1   eta * (t2-25)) = ro2 * irr1*(1   eta * (t1-25))

this is linear equation for eta, we can easily solve it for eta, then substitute eta into the first equation to get ae

CodePudding user response：

From the little that I understand of your experiments, you are probably able to measure the temperature and the power. I would be surprised that you have access to irradiation.

If this is the case, you can't find any of the coefficients. Even worse if you don't record the temperatures.