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MCGILL UNIVERSITY

ASSIGNMENT NO.1D

Simulation and Summary Report of Simulink

Model

Naresh Gaj - ID: 260538617

2/27/2013

Faculty: Agricultu ral and Environmental Sciences

Dept: Bioresource Engineering (Macdonald campus)

Course: BREE 501 - Simulation and Modelling (Winter 2013) Lecturer: Dr. Grant Clark



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Figure 1: Generic steps in the modelling process.

The second component of the modelling process was to develop the mathematical model of the

system. Thus, a clear relationship between the inputs and outputs was formalized in the form of

mathematical equations. This was then implemented into Simulink as the computational model in the

third component of the assignment.

The final component was to run simulations using the computational model by changing parametersand input variables and comparing the output results, the contents of which are summarized in this final

report. Refinements to the initial computational model were made to extend the simulation time from 24

hrs to 30 days and to incorporate the cost component into the system.

The following sections describe in detail, the components of the modelling process specific to the

design of a hybrid solar and wind power supply system for a domestic house in the tropical region. The

results of the simulations are included along with a brief discussion on the validity of the model.

Introduction

This assignment is based on developing a computational model in Simulink. It was split into several

parts to coincide with the different stages of the modelling process (Figure 1). The first component was

to develop a conceptual model of a system intended to answer a research question or to achieve anengineering objective. A brief description of the systems components and their interaction was outlined

in this section (see next section on Conceptual model for Simulink) with emphasis on the inputs and

outputs for the model.

Conceptualize

Formalize

Computation

Verification

Simulation



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Figure 2: Schematic representation of a hybrid power supply systemfor a domestic household in the tropical region.

Research Question

What are the cost savings of a hybrid solar and wind power supply system for a domestic household in

the tropical region?

This system will be developed specifically for the tropical region where theseasonal variation in solar energy during autumn and winter is notsignificant. The important components of the system are: the sources ofenergy supply (solar, wind and grid); the main regulator (control switch); themain load (domestic demand) and the unit cost of each energy source. Thesolar and wind energy components will include solar panels, wind turbinesand batteries. Also, the unit cost for these two power sources will includethe market prices for all components after installation as well as an estimateof the annual maintenance cost based on usage.

Description of the model

The main regulator will control the combination of the three power sourcebased on the off grid energy output and daily domestic demand generatedfrom the main load. The unit cost of each energy source will then beapplied to the respective energy type produced to give the total cost ofenergy consumption on an annual basis. This will allow for an economic justification of using the hybrid power supply system through simulations ofusing the grid supply only against the combined configuration over a designperiod of 20 years.

The analysis will be of the synthesis type with known inputs and outputs and hence it will involve designing asystem to fit these criteria through optimization. As such, the excitations are: the size and number of the solarpanels and wind turbines; and meteorological data on average wind speed and duration, solar intensity and

daylight hours on a given year. The responses are: the average daily domestic consumption rate per annum andthe unit cost for each energy source.

Grid

Solar Energy

Wind Energy

Total

Consumption

(Total Cost)

Unit Cost

(Solar Energy)

Unit Cost

(Wind Energy)

Unit Cost

(Grid Supply - Ceiling)

Main

Regulator

(Control

Switch)

Main Load

(Domestic

household)

Figure 3: Wind and Solar Hybrid System.

Source:http://www.renewableenergyfocus.

com/view/21235/wind-and-solar-hybrid-



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Mathematical Model for Simulink

Input variables and parameters

The electricity demand from the main load (domestic household) was chosen from the average residential load

profile from Southern California across 30 day. This data was stored in an excel file as hourly data and was

imported into Matlab as the Energy Demand variable. It was assumed that this data was representative for an

annual load.

The energy generated by solar radiation was computed from the following:

= × × × … 2 (ℎ)

where np is the number of solar panels, Ap is the area of a panel (m2) and Sr is the average hourly solar intensity

per day (Wh/m2). The efficiency of energy conversion was estimated as 84%. The intensity data was stored in

excel and imported into Matlab as the Solar Radiation variable. A standard size 1.2 m2 solar panel was used.

The energy generated by wind was computed from the following:

= × 18.972.168 × … 3 (ℎ)

where nw

The energy balance will be governed by ≤ + + … 4 and the logic equations are:

+ ≥ , ℎ = 0

+ ≱ , ℎ = − ( + )

The total cost of the energy output was simply the sum of each component (solar, wind and grid) multiplied by its

respective unit cost. The unit cost for the solar and wind power supply was estimated based on ownership costs

and maintenance and operating costs. This was projected over the design period of 20 yrs and then converted to

a cost per unit energy consumption ($ per watt-hour) based on the forecasted demand for that period. It was

assumed that the cost for a unit of solar power generated would decrease as the number of solar panel in the

system increased. For this analysis, the maximum number of solar panels used was 2 as this was thought to be

practical for a characteristic domestic household.

is the number of wind turbines, and v is the average hourly wind intensity per day (m/sec), 3 ≤ v ≤ 13.

This equation is based on the power rating curve for the GES 3kW pole mounted wind turbine. The efficiency of

energy conversion was estimated as 60%. The wind data was also stored in excel and imported into Matlab as

the Wind Speed variable.

As stated in the conceptual model, the main regulator (control switch) will be responsible for distributing the three

main energy supply (solar, wind and grid) in appropriate proportions in response to the demand from the mainload. The following logic equations show the relationships between the input variables defined above and how

the regulator will feed electricity to the main load.

Electricity Demand (D), Solar Energy (S), Wind Energy (W) and Grid Electricity (G)



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Figure 4: Computational (Simulink) model of a hybrid solar and wind power supply system

for a domestic household in the tropical region

The computational model in Figure 4 closely resembles that for the conceptual model of the hybrid power supply

system. The primary inputs are the solar energy, wind energy and main load (domestic household). These were

represent by subsystems as shown in Figure 4 and each subsystem was built using their respective equations as

previously defined in the mathematical model. These input signals are fed into the main regulator (control switch)

which is represented with another subsystem. This subsystem was built using the two logic equations relating the

three input variables to the grid supply. Thus, it determines the amount of grid supplied electricity for input into

the system if needed. As an example, if the input wind and solar energy combined is less than the demand from

the main load, the difference will be fed to the system by the grid supply. When the combined wind and solar

energy is greater than the demand, the excess will be stored for possible supply to the grid.

The simulation time posed the biggest challenge while developing the computational model. This was because

initially the input variables, parameters and hence mathematical equations were valid only for hourly time input

per day. This was partially rectified by changing from an energy demand equation to actual hourly data on

domestic energy consumption over a 30 days period. This had to be done for the solar and wind input data as

well.

Also, the conceptual model was designed with a cost component in mind. This was to compare the cost of the

grid supply only simulation against combination of the three power source simulation. This idea was later

incorporated into the revised model and simulations with cost outputs were generated to do a comparison as

stated in the modified research objective

The model has some flexibility as the number of solar panels and wind turbines can be varied as well as the size

of the solar panels. Longer periods of solar and wind intensity data can also be incorporated into the model to

refine and improve the accuracy of the results.

Computational Model Implemented in Simulink



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Simulations

Three simulations were ran using the computational model developed in Simulink. These were as

follows:

1) No solar and wind power inputs (baseline grid supply only condition)2) 1 no. solar panel and 1 no. wind turbine

3) 2 nos. solar panel and 1 no. wind turbine

Table no.1 shows the result from these simulations based on the set unit cost parameters. As

previously stated, the first simulation represents no hybrid power supply system and hence serves as

the base line cost for purchasing power from the grid. The second simulation is based on using a single

solar panel and wind turbine to generate power while Simulation 3 is based on 2 solar panels.

Simulation 1 Simulation 2 Simulation 3Unit cost ($/Wh) Unit cost ($/Wh) Unit cost ($/Wh)

Solar Power 0.00 0.01 0.003

Wind Power 0.00 0.02 0.02

Grid Power 0.05 0.05 0.05

Total cost (30 days) $25,750 $23,033 $17,355

Total cost (20 yrs) $6,180,000 $5,527,824 $4,165,200Table 1: Results from the simulation scenarios ran using the computational model developed in Simulink

Note the amount quoted is in Guyanese Dollars ($GYD).

The cost savings over the analysis period is $652,176 using Simulation 2 (1 solar + 1 wind) and

$2,014,800 (2 solar + 1 wind) using Simulation 3 when compared to the baseline cost of Simulation 1

(Grid only). This is a direct answer to the research objective and hence using 2 solar panels with 1 wind

turbine would generate savings of approximately 33% over 20 years.

These results do not serve as validation of the model against a prototype of the system. This is as a

results of numerous assumptions that were made while developing the model. These include: assuming

the monthly demand is constant over 20 years, assuming the 30 days period of wind and solar intensity

data is representative of the annual climate data in the tropical region and, estimating a constant

efficiency factor for both the solar and wind power hybrid systems over the design period. It isrecommended to use a larger time series of input data (preferably annual demand and weather data)

for the model to generate cost savings more accurately.

References:

GES. 2012. Pole mounted VAWT solutions technical data sheet. Green Energy Solutions.

Miao, Z. and Fan, L. 2008. The art of modelling and simulation of induction generator in wind generation

applications using high-order model. Simulation Modelling Practice and Theory, 16(9): 1239-1253.

NAHB. 2001. Review of residential electrical energy use data. NAHB Research Center, Inc. Upper Marlboro, MD20774.

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