Baxramov Umarkhodja, 1 Kaxarov Bakhodir

Solid State Technology
Volume: 65 Issue: 1 
Publication Year: 2022
65
Archives Available @ www.solidstatetechnology.us 
Where

- simulated parameter value;

and

- mathematical expectation and standard deviation of the parameter known from the 
experiment;
n

- normal random variable с
0


and

= 1.
It should be noted that when modelingprocesses of consumption of the target product, it is quite 
easy to take into account the daily uneven consumption - for this it is necessary to count in (3) value 
Q
also a random variable with variance equal to the variance of daily loads.
The processing of the data of the experimental study of water consumption modes showed that 
for simulation modeling, it is sufficient to use processes of consumption of the target product in (2)
two harmonic components with a period 24 and 12 hours. In this case, all the statistical 
characteristics of the original and simulated processes of consumption of the target product 
practically coincide. On the picture 1the data showing a good coincidence of the autocorrelation 
function of the initial and simulated processes are presented (confirmation of the coincidence of 
mathematical expectations and variance is not required, since these are the parameters of the initial 
processes of consumption of the target product used in the simulated) [3,4,8]. 
 
Results and Discussion 
Based on the prerequisites described above, an algorithm for the simulation of the processes of 
consumption of the target product was developed, shown in the figure 3.
The algorithm works as follows: 
1. For the node of the calculation scheme, random numbers are selected - t
n
(where n =1, 2, … 
,n
i
). The value is used to determine the average load on the first day of simulation for j – the node:
),
1
)(
(
1
1
j
j
Q
j
v
t
Q
M
Q



(5) 
where
)
(
j
Q
M
and
j
Q
v
- mathematical expectation and coefficient of variation of average 
hourly loads for the entire simulation period for j – th node. 
2. By values
5
2

 
the magnitudes of the amplitude and phase shift for the first day are 
determined by the formulas:
);
1
(
1
1
1
2
Qa
A
A
v
t
Q
Q



(6) 
);
1
(
2
2
2
3
QA
A
A
v
t
Q
Q



(7) 
);
1
(
1
4
1
1



v
t



(8) 
);
1
(
2
5
2
2



v
t



(9) 
where
1
A
Q
and
2
A
Q
- mathematical expectation of the amplitude of the first and second 
harmonics in (2) ; 
1

and
2

- mathematical expectations of phase shifts for the first and second harmonics in (2); 
1
2
1
,
,

v
v
v
A
A
Q
Q
and
2

v
- coefficients of variation for amplitudes and phase shift nodes.
3. Based (3) the load value in the node is calculated for all 24 hours of the first day of simulation. 
Moreover, in (3)
,
0
0
n
t
Q



n = 6,7,…, 24 (10) 
where
0

- standard deviation of random noise. 

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