# Equation: Problem Formulation (TAC) And System Pollution

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Problem Formulation [1]

Figure 2 shows the utility-connected HPGS, which consists of WT, PV, SB, GT, and utility grid. The main objective functions of this system are the total annual cost (TAC) and the system pollution (SP). Equation 3 shows the multi-objective function should be minimized. f=min(TAC,SP) (3)

Equation 4 shows the first objective function, which it represents the TAC;

2.1 TAC Calculations

TAC=(∑_i▒(I_i+〖OM〗_(P_i )-S_(P_i ) ) )/N_P +〖AFC〗_NG+〖APC〗_UT (4) where, i indicates the WT, PV, SB, and GT

I_i is the initial

S_(P_i ) is the salvage value of each power source (WT, PV, and GT).

N_P is the project lifetime.

〖AFC〗_NG is the annual fuel (natural gas) cost.

〖APC〗_UT is the cost of the annual purchasing electricity.

TAC of wind turbine (WT)

Equation 5 shows the initial cost of the wind turbine, Equation 6 shows the operation and maintenance cost, and Equation 7 show the salvage value of the wind

Equation 11 shows the initial cost of the SB, and its lifetime (N_SB) actually is lower than the project lifetime (N_P). Equation 12 shows the operation and maintenance cost

I_SB=α_SB P_(〖SB〗_cap ) ∑_(i=1)^(X_SB)▒((1+v)/(1+β))^((i-1) N_SB )

Figure 2 shows the utility-connected HPGS, which consists of WT, PV, SB, GT, and utility grid. The main objective functions of this system are the total annual cost (TAC) and the system pollution (SP). Equation 3 shows the multi-objective function should be minimized. f=min(TAC,SP) (3)

Equation 4 shows the first objective function, which it represents the TAC;

2.1 TAC Calculations

TAC=(∑_i▒(I_i+〖OM〗_(P_i )-S_(P_i ) ) )/N_P +〖AFC〗_NG+〖APC〗_UT (4) where, i indicates the WT, PV, SB, and GT

I_i is the initial

*…show more content…*S_(P_i ) is the salvage value of each power source (WT, PV, and GT).

N_P is the project lifetime.

〖AFC〗_NG is the annual fuel (natural gas) cost.

〖APC〗_UT is the cost of the annual purchasing electricity.

TAC of wind turbine (WT)

Equation 5 shows the initial cost of the wind turbine, Equation 6 shows the operation and maintenance cost, and Equation 7 show the salvage value of the wind

*…show more content…*Equation 11 shows the initial cost of the SB, and its lifetime (N_SB) actually is lower than the project lifetime (N_P). Equation 12 shows the operation and maintenance cost

I_SB=α_SB P_(〖SB〗_cap ) ∑_(i=1)^(X_SB)▒((1+v)/(1+β))^((i-1) N_SB )