Hello everyone.
I am trying to solve this problem where i need to calculate the optimum capacity of PGU in combined cooling heating system (CCHP) using Genetic algorithm.
I have these equations:
The natural gas consumption by the PGU with respect to time can be expressed using the following equation:
Fpgu_t = Epgu_t/ηpgu_t .........(1)
where Fpgu is the natural gas consumed by the PGU.
The efficiency of PGU which is ηpgu, can be calculated as follows:
ηpgu_t = a+bf_t+cf_t^2..............(2)
where a, b, and c are the constant coefficients, and f_t is the partial load rate with respect to time which is the ratio of electricity generated by the PGU to the maximum output (PGU capacity) and can be defined as:
f_t = Epgu_t/(Ecap)...........(3)
A common linear relationship exists between the gas consumption and electricity generated by the PGU , which is widely used to optimize the CCHP systems and is expressed as follows:
Fpgu_t = α×Epgu_t+β........(4)
here i have the values of a,b and c for equation 2 and α and β for equation 4. Also i have common linear relation between the fuel consumption (Fpgu_t )and electricity generated by PGU (Epgu_t) which i have attached.
Other than that i also have a load profile which will be used to calculate the optimum capacity of PGU.
Please anyone can help me with that? I have consulted many different journal papers but i am still very much confused in this part.
Please help. Thanks everyone.
To be honest, I think you have to define your problem more clearly to receive meaningful inputs. If you are trying to optimize (maximize) PGU in a CCHP system, then that is an objective function to be implemented in GA. Do you have any constraints? What are the main design (decision) variables you want to investigate for optimum PGU? What are the lower and upper bounds of the decision variables? GA is an optimization algorithm, as I believe you know. If you personally answer the above-highlighted questions based on your knowledge of the problem you want to solve, I believe the optimization problem would have been better defined.
Joseph Oyetola Oyekale thank you so much for your response actually the issue i am facing is that i have more unknowns then the no of equations. i am not sure do i need to suppose some values as the data is missing. I have also consulted other papers but not able to get the solution. like in this post i have mentioned some equations but their values are missing.
I have worked on the genetic algorithm before and yes there are some constraints. I am able to understand those but what should i do if i don't have the compete data? or may be i am missing something. i don't have any issue with the constraints and genetic algorithm.
Thanks. Please guide me further.
I see. The number of unknown variables must match the number of equations. You might have to formulate some auxilliary equations so as to have number of unknown variables equal to the number of equations. Otherwise, you might have to adopt a trial by error approach: (i) assume empirical values for some of the unknown variables or based on available literature data, (ii) implement the assumed values and solve the equations numerically (iteratively), adopting a reasonable convergence criterion.
Joseph Oyetola Oyekale Thank you once again. i was also thinking about the same thing that you have mentioned but i was not sure that how accurate it would be or can i get the optimum capacity of PGU if i suppose the values?
Sorry for the disturbance but i got the main idea from your reply but is it feasible?
Actually i need to optimize the cost function of PGU that can also fulfill the load demand to some extent, should not be expensive and also environment friendly as we will take the load difference from the electric grid too but for this i need optimum capacity of PGU based on constraints etc.
So if i suppose multiple values for the capacity of PGU then i calculate the objective function for each of those values and after that i can select the capacity based on the results?
Can you please suggest if this is ok?
Thanks
It's okay, Taimoor Mohsin . It's my pleasure to offer these suggestions. That is what I think you should do. Take a reasonable range of values for your design variable (PGU capacity?), calculate your objective functions and select the optimum design variables based on the results.
If you have to also minimize cost and an environmental performance metric, you can use a multi-objective version of GA (gamultiobj) function in Matlab. Other robust multi-objective algorithms are also available in the open literature. Non-dominated sorting genetic algorithm (NSGA-II) is widely used in many good papers.
Thank you so much, Joseph Oyetola Oyekale for your precious time and kind suggestions.
I will try this method. If i have anymore confusion in future then can you please guide me further if you don't mind?
It's my pleasure, Taimoor Mohsin . I'm sure open for further scientific discussions in the future. I wish you all the best in your research!
Thank you so much, Joseph Oyetola Oyekale , You are very kind, may you got all the success in your future.
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