RESEARCH DESIGN AND METHODOLOGY
Introduction
This chapter details the methodology employed by the researcher to achieve the objectives, which
involves optimal sizing of the proposed hybrid system consisting of PV-Wind-Biomass with Battery
Bank and conducting a technical and economic evaluation of the optimal configuration.
Methodology Flowchart
The researcher aims to finish the study by following the steps shown in Figure 3-1, this figure
provides a step-by-step guide to how the study will be conducted.
Figure Error! No text of specified style in document.-1 Research Methodology Flowchart
Load and Resource Potential Assessment
Load Demand Assessment
In this research, the load profile for the community will be estimated by conducting surveys
on a select number of residential houses. The specific data to be collected is detailed in Table 3-1.
From the collected data on the community’s load demand, a dataset with an hourly timestep for a full year (equivalent to 8760 hours) will be obtained. This dataset, which will be
Start
Phase 1: Load and Resource
Potential Assessment
Phase 2: Mathematical and
Economic Modelling of HRES
Phase 3: Problem Formulation and
Optimization using ABC
Algorithm
Phase 4: Techno-Economic
Analysis
End
representative of a similar number of houses, climate, and location, will then be used to scale into
the calculated estimated load of the community.
The primary metrics that will be examined in this study include the average demand, peak
demand, and the load factor. These metrics will provide valuable insights into the community’s
energy usage patterns and will aid in the optimization of the Hybrid Renewable Energy System
(HRES).
Table Error! No text of specified style in document.-1 Estimation of Community Load
Appliance #1
H. no.
Quantity
(Q)
Hours
(H)
Wattage
(W)
Wh/day
1
2
Value
Unit
Load Demand for 10 Households
kWh/day
Load Demand per Households
kWh/day
Load Demand for 67 Households
kWh/day
Annual Load Demand
kWh/year
Resource Potential Assessment
Solar Energy Resource Data
The quantity of solar energy received within a day is termed "insolation" and is quantified in units
such as kilowatt-hours per square meter per day (kWh/m2/day) or peak sun hours (PSH). Given the
substantial disparities in insolation from one place to another, it is of utmost importance to account
for the precise solar radiation characteristics of the specific location to estimate solar energy that can
be harnessed. Hourly solar radiation incident at surface of solar PV panel (W/m2) and reference
temperature will be extracted from NASA POWER Data Access Viewer.
Wind Energy Resource Data
The mean wind speed at the turbine’s hub height plays a pivotal role. The power generated by wind
is directly related to the cube of the wind speed, implying that even minor variations in wind speed
can lead to substantial changes in power output. Wind speed fluctuates throughout the year, and
precise wind speed data for specific areas during different seasons is not readily available. Despite
the area being classified as a low potential wind site, it could still be considered for low power
generation, especially in less populated locations like Rosario. The cut in speed, rated wind speed,
cut out speed and the wind speed at desired height will be extracted from NASA POWER Data Access
Viewer.
Biomass Energy Resource Data
This study aims to assess the potential of biomass energy resources, with a particular emphasis on
livestock manure in Tagoloan. Data pertaining to the number of animals will be sourced from the
Municipal Agriculture Office, while information related to the weight and manure production per
animal type will be gathered from relevant literature.
The calculation of the total annual manure production in tons per year will be facilitated using the
“Annual Manure Production and Bedding Used Calculation Worksheet.” This worksheet, a product of
the Rockingham County Conservation District and funded by the New Hampshire Department of
Agriculture, Markets & Food Agricultural Nutrient Management Grant Program, will be employed in
Excel for the calculations.
The worksheet employs a three-step process for estimating the annual amount of manure produced:
1. Calculation of the total number of animal units (AU) on the farm: This is achieved by
multiplying the number of animals by their average weight, and then dividing by the weight
per AU (typically 1,000 lb).
2. Determination of the amount of manure produced per animal unit from a given table: This
table provides the amount of manure produced per AU per year for different types of
animals.
3. Calculation of the total amount of manure produced per year in tons: This is done by
multiplying the amount of manure produced per AU per year (from step 2) by the total
number of AU (from step 1).
This systematic approach allows for the estimation of manure production based on animal units and
their corresponding manure output.
Mathematical Modeling of the Proposed Hybrid System
This study focuses on the development of an HRES designed to meet the electrical demand
of the chosen pilot site. Figure 3-2 illustrates the various components that make up the proposed
microgrid. The system harnesses power from wind, solar, and biomass sources, which is then
managed using storage device. The load, wind turbines, and biomass gasifier are all connected to an
AC bus. Additionally, the solar PV panels and batteries are linked to the AC bus through converters.
To ensure a steady power flow and regulate the rate of battery charging and discharging, a charge
controller is also incorporated into the system.
The system proposed in this study is particularly well-suited for off-grid locations and
agricultural communities in developing countries where energy shortages are a significant issue.
However, it’s also designed to be grid-compatible. This system can help reduce reliance on the utility
grid as it’s entirely self-sustaining, powered by renewable energy sources. However, in the
optimization part the energy management will not include power from the grid. To ensure optimal
power distribution, battery banks are utilized, which help mitigate the intermittency of renewable
energy sources. The primary focus of this work is on the optimal sizing of each component to ensure
the system’s reliability. The following sections will discuss the mathematical models of the various
components.
Figure Error! No text of specified style in document.-2 Components of the Proposed HRES
Solar Photovoltaic Panel
The power output of a solar PV panel, denoted as 𝑃𝑠𝑜𝑙 (𝑡), is dependent on solar radiation. This
relationship can be expressed as follows:
𝑃𝑠𝑜𝑙 (𝑡) = 𝑁𝑃𝑉 × 𝑃𝑃𝑉𝑅𝑎𝑡𝑒𝑑 × 𝐺
𝐺
𝑟𝑒𝑓
× [1 + 𝐾𝑡 (𝑇𝑎 + (0.0256 × 𝐺ℎ (𝑡)) − 𝑇𝑟𝑒𝑓 )]
(3.1)
where 𝑃𝑃𝑉𝑅𝑎𝑡𝑒𝑑 is the output power of the PV system, and it’s fixed at 1000 W. 𝑁𝑃𝑉 is used to
represent the number of PV panels. 𝑃𝑃𝑉𝑅𝑎𝑡𝑒𝑑 is the power of a PV panel under standard test
conditions. 𝐺 denotes the solar irradiance, measured in Watts per square meter (W/m²), and 𝑇𝑎 is
the ambient temperature, measured in degrees Celsius (°C). The standard values for solar irradiance
(𝐺𝑟𝑒𝑓 ), reference temperature (𝑇𝑟𝑒𝑓 ), and temperature coefficient of power (𝐾𝑡 ) are 1000 W/m², 25
°C, and -3.7 * 10⁻³ 1/°C, respectively [30].
Wind Turbine
The power produced by a wind turbine, denoted as 𝑃𝑤𝑡 (𝑡), can be determined as follows:
0, 𝑉(𝑡) ≤ 𝑉𝑐𝑖𝑛 𝑜𝑟 𝑉(𝑡) ≥ 𝑉𝑐𝑜𝑢𝑡
𝑤
𝑃𝑟 , 𝑉𝑟𝑎𝑡 ≤ 𝑉(𝑡) ≤ 𝑉𝑐𝑜𝑢𝑡
𝑃𝑤𝑡 (𝑡) = {
𝑤 𝑉(𝑡)−𝑉𝑐𝑖𝑛
𝑃𝑟 𝑉 −𝑉 , 𝑉𝑐𝑖𝑛 ≤ 𝑉(𝑡) ≤ 𝑉𝑟𝑎𝑡
𝑟𝑎𝑡
𝑐𝑖𝑛
(3.2)
where 𝑃𝑤
𝑟 represents the rating of a single wind turbine. 𝑉𝑐𝑖𝑛 is the cut-in speed, 𝑉𝑟𝑎𝑡 is the rated
wind speed, and 𝑉𝑐𝑜𝑢𝑡 is the furlong speed. 𝑉(𝑡) represents the wind speed at the desired height.
The wind speed at the hub height is dependent on the site and geographical location, and it differs
from the reference height. This wind speed at the hub height is further expressed as follows:
𝛾
𝐻
𝑉(𝑡) = 𝑉𝑟 (𝑡) ( 𝐻𝑊𝑇 )
𝑟
(3.3)
where 𝑉(𝑡) represents the wind speed at a certain height 𝐻𝑊𝑇 , while 𝑉𝑟 (𝑡) is the wind speed at the
reference height 𝐻𝑟 . The variable 𝛾 stands for the friction coefficient. Typically, for a site with low
surface roughness and good exposure, the friction coefficient 𝛾 has a value of 1/7 [31, 32].
Biomass Gasifier
Biomass gasification technology involves the transformation of solid bio-residue into a gaseous fuel,
which is then used for electricity generation. This process occurs under partial combustion, resulting
in the production of producer gas. This combustible gas typically comprises H2 (20%), CO (20%), CH4
(1–2%), and inert gases. In the context of a biomass gasifier, this producer gas serves as the input
fuel.
For a biomass-based energy system, several parameters play a crucial role. These include the
calorific value of the biomass, the availability of biomass (measured in ton/yr), and the usage hours
of the biomass gasifier. The maximum rating of a biomass gasifier installed in a specific area can be
determined as follows:
𝑚
𝑃𝑏𝑚𝑔
=
𝑇𝑜𝑡𝑎𝑙 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝐵𝑖𝑜𝑚𝑎𝑠𝑠 (
𝑡𝑜𝑛
) ∗ 1000 ∗ 𝐶𝑉𝑏𝑚 ∗ 𝐶𝑈𝐹
𝑦𝑟
365 ∗ 860 ∗ 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐻𝑜𝑢𝑟𝑠/𝑑𝑎𝑦
(3.4)
where 𝐶𝑈𝐹 stands for the capacity utilization factor, while 𝐶𝑉𝑏𝑚 represents the calorific value
of the biomass [33, 34].
The power rating of the biomass plant (Pbmp) is calculated in the Operational Strategy under
the Energy Management System section. It will be based on the state of charge (SoC) of the system’s
energy storage and the balance between the load demand (Pload) and the power generated by the
solar (Psol) and wind (Pwt) components.
Here’s a step-by-step explanation of the calculation of Pbmp in the EMS:
1. If the power generated by the solar and wind components is greater than the load
demand:
o
If the SoC is less than its maximum value (SoCmax), the system charges the battery
(Pb). The amount of power used for charging depends on whether the wind power is
less than the load demand or not.
o
If the SoC is at its maximum, the system cannot store more energy, so the excess
power is dumped (Pdump).
o
In both cases, the biomass plant is not needed (Pbmp = 0).
2. If the power generated by the solar and wind components is less than the load
demand:
o
If the SoC is greater than its minimum value (SoCmin), the system discharges the
battery (Pb) to meet the load demand.
o
If the SoC is at its minimum, the system cannot draw more power from the battery.
The biomass plant (Pbmp) is then used to meet the remaining load demand. If the
power required is greater than the rated power of the biomass plant (Pbmp_r), the
biomass plant operates at its rated power and the excess power is dumped (Pdump).
This approach ensures that the renewable resources (solar and wind) and the battery are
utilized as much as possible before resorting to the biomass plant, thereby optimizing the system’s
operation. The power rating of the biomass plant (Pbmp) is thus determined based on the real-time
operation of the system, taking into account the state of charge of the battery and the balance
between the load demand and the renewable power generation. This allows for a more accurate and
dynamic representation of the system’s operation compared to a static rating.
Battery Energy Storage System
In a hybrid renewable energy system, batteries serve the dual purpose of storing surplus energy and
providing power when the output from renewable systems is inadequate or unavailable. The energy
stored in these batteries can be quantified through an accurate estimation of the State of Charge
(SOC). In the studied microgrid, a lithium-ion battery system is used. The SOC of a battery, which is a
function of time, can be calculated as follows:
•
Battery state of charge (SOC)’s characteristic when battery charging:
𝜂
×𝑃 (𝑡)
𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡 − 1) + 𝑐ℎ 𝐶 𝑏
𝑏
•
(3.5)
Battery state of charge (SOC)’s characteristic when battery discharging:
𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡 − 1) − 𝜂
𝑃𝑏 (𝑡)
𝑑𝑖𝑠𝑐ℎ ×𝐶𝑏
(3.6)
Where 𝜂𝑐ℎ and 𝜂𝑑𝑖𝑠𝑐ℎ are the charging and discharging efficiencies (%), 𝑃𝑏 (𝑡) is the battery charging
and discharging power at timeslot t, 𝐶𝑏 is the nominal capacity of the battery, 𝑆𝑂𝐶(𝑡) and 𝑆𝑂𝐶(𝑡 −
1) are the state of charge of the battery at timeslot t and t - 1 (%).
The BESS nominal capacity in kWh can be calculated as follows:
𝐶𝑏_𝑟𝑎𝑡𝑖𝑛𝑔 =
𝑁𝑏𝑎𝑡𝑡 𝑉𝑏𝑎𝑡𝑡 𝐶𝑏 (𝐴ℎ)
1000
(3.7)
where 𝑁𝑏𝑎𝑡𝑡 is the number of batteries, 𝑉𝑏𝑎𝑡𝑡 is the nominal voltage of battery, and 𝐶𝑏 (𝐴ℎ) is the
nominal capacity of battery expressed in ampere-hours.
Power Converter
Power converters, both DC/AC and AC/DC, are necessary in systems that include both AC and DC
components. For instance, Solar PV panels and batteries generate DC output, while the load
considered in this system is AC. The size of the converter is determined based on the peak load
demand 𝑃𝐿𝑚 (𝑡). The rating of the inverter 𝑃𝑖𝑛𝑣 can be calculated as follows:
𝑃𝑖𝑛𝑣 (𝑡) = 𝑃𝐿𝑚 (𝑡)/𝜂𝑖𝑛𝑣 (3.8)
where 𝜂𝑖𝑛𝑣 represents the efficiency of the inverter.
Problem Formulation
The primary aim of this research is to develop a hybrid energy system that is both costeffective and reliable. The key variables in this decision-making process are the ratings and sizes of
the solar PV panels, wind turbine, battery bank, and biomass gasifier. This section provides an
overview of the system’s operational strategy, the objective function, and a brief introduction to the
algorithm used.
Operational Strategy
For any hybrid energy system, it’s crucial to manage power effectively to ensure the system’s
reliability. In this particular system, the biomass gasifier is given the lowest priority. This means it
only operates when the solar panels, wind turbines, and batteries are unable to fulfill the load
demand. Here are the simplified steps of the operational strategy:
•
If the total power produced by solar PV panels and wind turbines is sufficient and wind power is
less than the load, then demand can be served only by renewable sources. After satisfying the
load, surplus power can be provided to the battery bank if 𝑆𝑂𝐶(𝑡) < 𝑆𝑂𝐶𝑚𝑎𝑥 , as follows:
𝑃𝑏 (𝑡) = 𝑃𝑃𝑉 (𝑡) − [𝑃𝐿 (𝑡) − 𝑃𝑊 (𝑡)]/𝜂𝑖𝑛𝑣
(3.9)
If 𝑆𝑂𝐶(𝑡) ≥ 𝑆𝑂𝐶𝑚𝑎𝑥 , then the surplus power will be sent to the dump load:
𝑃𝑑𝑢𝑚𝑝 (𝑡) = 𝑃𝑃𝑉 (𝑡) − [𝑃𝐿 (𝑡) − 𝑃𝑊 (𝑡)]/𝜂𝑖𝑛𝑣
(3.10)
where 𝑃𝐿 (𝑡) denotes load demand at any time and 𝜂𝑖𝑛𝑣 denotes the efficiency of the inverter. If
𝑃𝑠𝑜𝑙 (𝑡) is the power produced by an individual solar PV panel and 𝑁𝑠𝑜𝑙 is the total number of solar
PV panels, then the total power produced by solar PV panels (𝑃𝑃𝑉 (𝑡)) is given as:
𝑃𝑃𝑉 (𝑡) = 𝑃𝑠𝑜𝑙 (𝑡)𝑁𝑠𝑜𝑙
(3.11)
Further, if 𝑃𝑊 (𝑡) is the power produced by an individual wind turbine and 𝑁𝑤𝑡 is the total number of
wind turbines, then the total power generated by wind turbines (𝑃𝑤𝑡 (𝑡)) can be given as:
𝑃𝑊 (𝑡) = 𝑃𝑤𝑡 (𝑡)𝑁𝑤𝑡
•
(3.12)
If power generated solely from wind turbines is enough to supply load demand, the
remaining power (solar & wind) can be fed to the battery bank. If 𝑆𝑂𝐶(𝑡) < 𝑆𝑂𝐶𝑚𝑎𝑥 , the
battery power in this case can be calculated as:
𝑃𝑏 (𝑡) = [𝑃𝑊 (𝑡) − 𝑃𝐿 (𝑡)]𝜂𝑟𝑒𝑐 + 𝑃𝑃𝑉 (𝑡) (3.13)
where 𝜂𝑟𝑒𝑐 is the rectifier efficiency.
If 𝑆𝑂𝐶(𝑡) ≥ 𝑆𝑂𝐶𝑚𝑎𝑥 , then the surplus power will be sent to the dump load:
𝑃𝑑𝑢𝑚𝑝 (𝑡) = [𝑃𝑊 (𝑡) − 𝑃𝐿 (𝑡)]𝜂𝑟𝑒𝑐 + 𝑃𝑃𝑉 (𝑡)
•
(3.14)
If solar PV panels and wind turbines are not generating adequate power, then balance power
can be supplied by the battery and is calculated as:
𝑃𝑏 (𝑡) = [𝑃𝐿 (𝑡) − 𝑃𝑊 (𝑡)]𝜂𝑖𝑛𝑣 − 𝑃𝑃𝑉 (𝑡) (3.15)
•
If solar and wind power are inadequate and batteries 𝑆𝑂𝐶(𝑡) ≤ 𝑆𝑂𝐶𝑚𝑖𝑛 are also not able to
produce the desired power to meet the load demand, then biomass gasifier supplies power
to the load, as follows:
o
If the required power exceeding the rated power from the biomass gasifier plant:
{
𝑃𝑏𝑚𝑝 (𝑡) = 𝑃𝑏𝑚𝑝,𝑟𝑎𝑡𝑒𝑑
𝑃𝑑𝑢𝑚𝑝 (𝑡) = [𝑃𝐿 (𝑡) − 𝑃𝑊 (𝑡)] − 𝑃𝑃𝑉 (𝑡)/𝜂𝑖𝑛𝑣 − 𝑃𝑏𝑚𝑝 (𝑡)
o
(3.16)
Else:
𝑃𝑏𝑚𝑝 (𝑡) = 𝑃𝐿 (𝑡) − 𝑃𝑊 (𝑡) − 𝑃𝑃𝑉 (𝑡)/𝜂𝑖𝑛𝑣
(3.17)
A simplified flow chart illustrating the operational strategy of the proposed HRES is presented in
Figure 3-3.
Figure Error! No text of specified style in document.-3 The Operational Strategy of the Proposed
HRES in a Simplified Flow Chart
Objective Function and Constraints
This research aims to decrease the total ASC of the suggested hybrid system, while optimizing energy
flow. The optimal setup is influenced by four primary decision factors: the quantity of wind turbines,
solar PV panels, batteries, and the capacity of the biomass gasifier. The economic evaluation utilizes
the Annualized System Cost (ASC) approach. The setup with the smallest ASC is considered optimal,
as long as it satisfies all other parameters and constraints. The objective function is the total system
cost, encompassing total capital cost, replacement cost, and the operational & maintenance cost of
the components. The capital costs also include the costs of installation and civil works. The main goal
is to minimize this total system cost, given certain constraints.
Minimize:
𝐴𝑆𝐶 = 𝐹(𝑁𝑠𝑜𝑙 𝐶𝑠𝑜𝑙 + 𝑁𝑤𝑡 𝐶𝑤𝑖𝑛𝑑 + 𝑁𝑏𝑎𝑡𝑡 𝐶𝑏𝑎𝑡𝑡 + 𝑃𝑖𝑛𝑣 𝐶𝑖𝑛𝑣 + 𝑃𝑏𝑚𝑔 𝐶𝑏𝑚𝑔 ) (3.18)
where 𝐶𝑠𝑜𝑙 , 𝐶𝑤𝑖𝑛𝑑 , 𝐶𝑏𝑎𝑡𝑡 , and 𝐶𝑖𝑛𝑣 represent the costs of the solar PV panel (per kW), wind turbine
(per kW), battery (per unit), and inverter (per kW), respectively. 𝐶𝑏𝑚𝑔 stands for the cost of the
biomass gasifier (per kW), while 𝑃𝑏𝑚𝑔 refers to the rating of the biomass gasifier. 𝑃𝑖𝑛𝑣 is used to
denote the rating of the inverter.
The Annualized System Cost (ASC) of each installed component is made up of several
components, including the capital and installation cost 𝐶𝑎𝑐𝑎𝑝 , replacement cost 𝐶𝑎𝑟𝑒𝑝 , annual
maintenance cost 𝐶𝑚 , and operation cost 𝐶𝑓 . Moreover, the total ASC for each component can be
calculated as follows:
𝑎𝑐𝑎𝑝
𝐶𝑠𝑜𝑙 = 𝐶𝑠𝑜𝑙
𝑎𝑟𝑒𝑝
+ 𝐶𝑠𝑜𝑙
𝑚
+ 𝐶𝑠𝑜𝑙
𝑎𝑐𝑎𝑝
𝑎𝑟𝑒𝑝
𝑎𝑐𝑎𝑝
𝑎𝑟𝑒𝑝
𝑎𝑐𝑎𝑝
𝑎𝑟𝑒𝑝
𝑎𝑐𝑎𝑝
𝑎𝑟𝑒𝑝
(3.19)
𝑚
𝐶𝑤𝑖𝑛𝑑 = 𝐶𝑤𝑖𝑛𝑑 + 𝐶𝑤𝑖𝑛𝑑 + 𝐶𝑤𝑖𝑛𝑑
(3.20)
𝑚
𝐶𝑏𝑎𝑡𝑡 = 𝐶𝑏𝑎𝑡𝑡 + 𝐶𝑏𝑎𝑡𝑡 + 𝐶𝑏𝑎𝑡𝑡
(3.21)
𝑓
𝑚
𝐶𝑏𝑚𝑔 = 𝐶𝑏𝑚𝑔 + 𝐶𝑏𝑚𝑔 + 𝐶𝑏𝑚𝑔
+ 𝐶𝑏𝑚𝑔
(3.22)
𝑚
𝐶𝑏𝑎𝑡𝑡 = 𝐶𝑖𝑛𝑣 + 𝐶𝑖𝑛𝑣 + 𝐶𝑖𝑛𝑣
(3.23)
The annualized cost of any component can be determined using a factor known as the capacity
recovery factor (CRF). The CRF is utilized to calculate the present value of money and can be
expressed as follows:
𝑖(1+𝑖)𝑁
𝐶𝑅𝐹(𝑖, 𝑁) = (1+𝑖)𝑁−1
(3.24)
where 𝑁 represents the lifespan in years, and 𝑖 denotes the annual interest rate. The objective
function is minimized by imposing a series of constraints, which are summarized as follows:
𝑚
1 ≤ 𝑁𝑠𝑜𝑙 ≤ 𝑁𝑠𝑜𝑙
(3.25)
𝑚
1 ≤ 𝑁𝑤𝑡 ≤ 𝑁𝑤𝑡
(3.26)
𝑚
1 ≤ 𝑃𝑏𝑚𝑔 ≤ 𝑃𝑏𝑚𝑔
(3.27)
𝑚
1 ≤ 𝑁𝑏𝑎𝑡𝑡 ≤ 𝑁𝑏𝑎𝑡𝑡
(3.28)
𝑆𝑂𝐶𝑚𝑖𝑛 ≤ 𝑆𝑂𝐶 ≤ 𝑆𝑂𝐶𝑚𝑎𝑥
(3.29)
𝑚
𝑚
where 𝑁𝑠𝑜𝑙
refers to the maximum quantity of solar PV panels, 𝑁𝑏𝑎𝑡𝑡
indicates the maximum number
𝑚
𝑚
of batteries, 𝑁𝑤𝑡 represents the maximum number of wind turbines, and 𝑃𝑏𝑚𝑔
is the maximum
rating of the biomass gasifier.
The LCOE is defined as the average cost per kilowatt-hour of the useful energy produced by the
system, and it can be calculated as follows:
𝐿𝐶𝑂𝐸 =
𝐴𝑆𝐶 (
₱
)
𝑦𝑟
𝑇𝑜𝑡𝑎𝑙 𝑢𝑠𝑒𝑓𝑢𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑒𝑟𝑣𝑒𝑑 (
𝑘𝑊ℎ
)
𝑦𝑟
(3.30)
Artificial Bee Colony Algorithm
The Artificial Bee Colony (ABC) algorithm, inspired by the intelligent foraging behavior of honey bees,
provides a robust and efficient method for solving the optimization problem of finding the optimal
configuration of a hybrid system. In the ABC algorithm, the colony consists of three types of bees:
employed, onlooker, and scout bees.
The employed bees are initially randomly distributed across the search space, which represents
potential configurations of the hybrid system. These configurations are analogous to food sources in
a real bee colony. Each employed bee evaluates the quality of its assigned food source, which
corresponds to the total system cost of the respective configuration. The employed bees then return
to the hive and share this information with the onlooker bees. The onlooker bees, which are initially
waiting in the hive, use this information to choose a food source to exploit. The probability of an
onlooker bee choosing a particular food source is proportional to its quality, which ensures that
better configurations have a higher chance of being explored further. If an employed bee finds that
its food source is exhausted or if it cannot improve the solution after a certain number of iterations,
it transforms into a scout bee. The scout bees perform a random search for new food sources,
ensuring diversity in the search process and preventing the algorithm from getting stuck in local
optima. Through this iterative process, the ABC algorithm can effectively search the solution space
and find the optimal configuration of the hybrid system that minimizes the total system cost.
Algorithm 1 presents the proposed methodology for applying the ABC algorithm to the problem.
Implementation of the ABC Algorithm
The ABC algorithm, as adapted from the study [35], is implemented using MATLAB R2020. MATLAB, a
high-level language and interactive environment developed by MathWorks, is chosen for its powerful
computational capabilities and extensive built-in functions that are beneficial for algorithmic
implementation.
The implementation process involves translating the algorithm’s pseudocode into MATLAB code,
ensuring that all the steps of the algorithm are accurately represented. The code is then tested and
debugged to ensure its correctness and efficiency.
Algorithm 1
Input: Solar radiation data, wind speed data, biomass resource, 𝑃𝐿 and components prices.
Output: (𝑁𝑠𝑜𝑙 , 𝑁𝑤𝑡 , 𝑁𝑏𝑎𝑡𝑡 , 𝑃𝑏𝑚𝑔 )
1: Store 𝑆𝑂𝐶𝑚𝑎𝑥 , 𝑆𝑂𝐶𝑚𝑖𝑛 , 𝑁𝑃, 𝐷, 𝐹𝑜𝑜𝑑𝑁𝑢𝑚𝑏𝑒𝑟, 𝑀𝑎𝑥𝑐𝑦𝑐𝑙𝑒, 𝐿𝑖𝑚𝑖𝑡
𝑚
𝑚
𝑚
2: Store (𝑁𝑠𝑜𝑙
= 300), (𝑁𝑤𝑚 = 20), (𝑁𝑏𝑎𝑡𝑡
= 500) and (𝑃𝑏𝑚𝑔
= 5)
3: Compute 𝑃𝑠𝑜𝑙 (𝑡) and 𝑃𝑤𝑡 (𝑡) by using eqs. 3.1 and 3.2
4: Generate a randomly initialized population as
𝑋𝑢𝑣 = 𝑋𝑣𝑚𝑖𝑛 + 𝑟𝑎𝑛𝑑[0,1](𝑋𝑣𝑚𝑎𝑥 − 𝑋𝑣𝑚𝑖𝑛 )
(3.31)
5: Set trial counters to zero
6: Calculate following for initial randomly generated solution (𝑁𝑠𝑜𝑙 , 𝑁𝑤𝑡 , 𝑁𝑏𝑎𝑡𝑡 , 𝑃𝑏𝑚𝑔 )
•
Compute 𝑃𝑃𝑉 (𝑡) and 𝑃𝑤 (𝑡) using eqs. 3.11 and 3.12
•
Perform the steps explained in operational strategy
•
Calculate the component costs for initial solution by using eqs. 3.19-3.23
7: Evaluate objective function F (eq. 3.18) for initial food source
8: Calculate the fitness value for employed bees in the bee colony
1
, 0 ≤ 𝑓𝑖
1+𝑓𝑖
𝑓𝑖𝑡𝑛𝑒𝑠𝑠𝑖 = {
1
, 𝑓𝑖 ≤ 0
1+𝑎𝑏𝑠(𝑓 )
(3.32)
𝑖
where 𝑓𝑖 is the evaluated cost value of the solution 𝑋𝑢𝑣
9: Cycle =1
10: Generate modified food location for the employed bees.
𝑛𝑒𝑤
𝑋𝑢𝑣
= 𝑋𝑢𝑣 + 𝑟𝑎𝑛𝑑[−1,1](𝑋𝑢𝑣 − 𝑋𝑤𝑣 )
(3.33)
where 𝑤 = 1, 2, 3 … 𝑆𝑁 and 𝑣 = 1, 2, 3 … 𝐷 are randomly chosen index. The 𝑤 should not be equal
to 𝑣.
11: Compute objective function F (eq. 3.18) by following step 6.
12: Apply greedy selection process.
13: Compute probability value (𝑝𝑖 )
𝑓𝑖𝑡
0 𝑓𝑖𝑡𝑖
𝑝𝑖 = ∑𝑆𝑁 𝑖
(3.34)
where 𝑓𝑖𝑡𝑖 is the fitness value corresponding to 𝑖 𝑡ℎ solution
𝑛𝑒𝑤
14: Generate new solutions (𝑋𝑢𝑣
) by using eq. 3.33 for the onlookers’ bees on the basis of
solutions selected according to the value of 𝑝𝑖
15: Compute objective function F (eq. 3.18) for new solutions by following step 6.
16: Apply greedy selection process
17: Check if there are any abandoned solution for the scout, eq. (3.31) for scouts to generate a
new food source
18: Remember and store the best solution gained so far
19: Cycle = Cycle + 1
20: Until, Cycle = Maxcycle
Here’s a simplified explanation of the ABC algorithm above:
1. Initialization: The ABC algorithm begins by creating a “population” of solutions. Each
solution corresponds to a possible configuration of the HRES, represented by a vector of
decision variables (sizes of the PV, wind, biomass, and BESS components). These solutions
are generated randomly within specified bounds for each decision variable. The cost of each
solution is then evaluated using an objective function, which could be related to the cost and
performance of the HRES.
2. Employed Bees Phase: Each employed bee, which represents a current solution in the
population, generates a new solution by slightly modifying its current solution. This is done
by exploring the “neighborhood” of the current solution, which refers to the set of solutions
that are similar but not identical to the current solution. The modification involves changing
the decision variables (sizes of the PV, wind, biomass, and BESS components). If the new
solution has a lower cost (better “fitness”), it replaces the current solution.
3. Onlooker Bees Phase: Onlooker bees select solutions from the current population based on
their fitness. The fitness of a solution is determined by its cost, with lower costs indicating
better fitness. After selecting a solution, the onlooker bee generates a new solution by
exploring the neighborhood of the selected solution, similar to the employed bee’s phase.
4. Scout Bees Phase: If a solution cannot be improved after a certain number of iterations
(known as the “limit”), it is abandoned and replaced with a new randomly generated
solution by a scout bee.
5. Termination: The algorithm repeats the employed bees, onlooker bees, and scout bees
phases for a certain number of iterations or until a termination criterion is met.
Comparison of ABC Algorithm and HOMER Software Results
In this study, a comparison is made between the results from the ABC algorithm,
implemented in MATLAB, and those from HOMER, a recognized software for micro-grid optimization.
This comparison serves to validate the ABC algorithm’s results and assess its optimization capabilities
against a robust, established software.
Key metrics considered in this comparison include the Optimization results, the State of
Charge (SOC) of the battery, and energy production. These metrics offer an evaluation of the ABC
algorithm’s performance relative to HOMER.