European Symposium on Computer Aided Process Engineering

26th European Symposium on Computer Aided Process Engineering

Okechukwu Kelechi, Hella Tokos, in Computer Aided Chemical Engineering, 2016

2.2 Wind energy conversion sub-model

Wind turbines are included in the model with aim to satisfy entirely or partially the electricity demand in the considered demand zones. Horizontal axis wind turbines have the ability to collect maximum amount of wind energy for time of day and season and their blades can be adjusted to avoid high wind storm. The output power of a wind turbine is determined as (Npower Renewables, 2015):

(1)$Wpo{w}_{{}_{b,i,q,t}}=0.5\cdot {\rho }^{\mathrm{AIR}}\cdot \pi \cdot B{L}_q^2\cdot N{T}_{i,q}\cdot A_{b,i,t}^3\cdot PC$

where Wpowb,i,q,t/(kW) the power converted from the wind b on harvesting site i by wind turbine type q at time period t, ρAIR/(kg/m3) is the air density (1.225 kg/m3), BLq/(m) is the blade length of wind turbine type q (the term π · BLq2 represents the swept area of the wind turbine in m2), NTi,q/(-) is the number of wind turbine type q which can be installed at harvesting site i, Ab,i,t/(m/s) is the average speed of wind b at harvesting site i at time period t and CP is the power coefficient or Betz limit.

The number of wind turbines type q, NTi,q, which could be constructed on harvesting site i is limited by the available area:

(2)$N{T}_{i,q}\le \frac{A{A}_i}{AO{T}_q}\cdot WS{y}_{i,q}$

where AAi/(m2) is the area available for construction of wind turbines on harvesting site i, AOTq/(m2) is the ground area occupied by one wind turbine type q and WSyi,q is a binary variable associated with conversion of wind energy on harvesting site i by wind turbine type q. This binary variable is included into Eq. (11) which ensures that the location is utilized for harvesting no more than one renewable energy resource.

The economic objective function, CWind/(£), aims to minimize the annualized total cost which includes the total annualized capital cost for installing wind turbines and the annual governmental incentives.

(3)$C_{\mathrm{Wind}}=\sum _i\sum _{q}N{T}_{i,q}\cdot WI{C}_q-\sum _{b\in B_{\mathrm{Wind}}}\sum _i\sum _q\sum _{t}Wpo{w}_{b,i,q,t}\cdot EPW$

where EPW/(£/kWh) is the incentive for electricity production from wind energy and WICq/(£) is the investment cost for a single wind turbine type q.

The environmental objective function, EWind/(kg of CO2-equivalent GHG emission), in form of total annual CO2-equivalent GHG emission is related only to the production and operation of the wind turbines.

(4)$E_{\mathrm{Wind}}=\sum _{b\in B_{\mathrm{Wind}}}\sum _i\sum _q\sum _{t}EW{P}_q\cdot Wpo{w}_{b,i,q,t}$

where EWPq/(kg CO2/kW) is the emission producing a unit of power (1 kW) with wind turbine type q.

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