Bond Graph Modeling and Simulation of a Windmill ...

Bond Graph Modeling and Simulation of a Windmill System for Water Level Control 1

Abdul Rehman Chishti, 1Mohammad Jawad Masud, 1Fasih ur Rehman, 2Muhammad Fazal, 2 Usman Ahmad

1

University College of Engineering & Technology, The Islamia University of Bahawalpur, Pakistan. 2 Center For Advanced Studies In Engineering (CASE), Islamabad, Pakistan

[email protected], [email protected], [email protected], [email protected], [email protected] Abstract- Due to recent increase in energy crises of Pakistan, windmill power generation is getting much attraction as it is among the cheapest sources of power generation. This paper presents modeling of a windmill system using a graphical method of state space modeling known as Bond Graph approach. Bond Graphs are used to model each subsystem of the windmill. A thorough study of a windmill system is made in which starting from the word bond graphs, we modeled the whole system and in the end a state space model is derived. That state space model is used for the simulation purposes to achieve the desired result of greater efficiency for a certain level of water in a storage tank. Level of the water tank is controlled by the power generated from the windmill. Optimization of this model is achieved using Proportional, Integral and Derivative (PID) controller while meeting the constraints. Keywords: Windmill, Optimization, PID.

I.

Bond

Graphs,

State

Space

Model,

INTRODUCTION

As the age of modern technologies is evolving the modern world has become more and more dependent upon the electricity and hence the energy crises are rising day by day. This has made us to look for alternative energy resources. Since last few years wind power is highly considered to produce electricity. It has been reported that 10% of the world’s electricity was targeted from wind power by 2020 [1]. Up to early 2010 the world wide capacity was 159,213 MW[2] . The wind mill technology promises to be environmentally clean and gives us direct conversion to electrical energy. In the deserts where we have hot environmental conditions, water is an unavoidable necessity. Providing electrical power to such distant areas by power companies is much costly as it involves lots of power losses. Using a windmill would provide enough electrical energy to run a motor-driven water pump and hence would provide the facility of water to such dry areas. It is very important to determine the critical conditions and factors that can or cannot be controlled for a system before the system is practically implemented. It is very expensive to build up a system and analyze its dynamic behavior practically. The best way to do the task is to model the system and simulate it on a computing device. Some optimizing parameters of a dynamic system can only be

determined by simulation. The dynamic behavior of a system can be modeled by a set of mathematical equations but a complete physical presentation of a model cannot be achieved by a set of mathematical equations [3]. Modeling and simulation of a system are interactive actions. To model a dynamic system, Bond Graph Modeling is one of the most powerful tools particularly in a system where different types of physical subsystems interact together. Bond Graph Models are based on energy conversion principles and use only four variables and nine multiport basic elements to represent all type of dynamic systems. It clearly depicts the flow of energy between subsystems of a complex integrated system. This is done by a directed graph where subsystems are represented by nodes and transfer of energy is represented by arrow heads. Furthermore, the scripts of causality stipulate a tool not only for preparation of system equations, but also for perception based analysis of system behavior, via controllability, fault diagnosis and observability [4,5]. The mathematical equations of the dynamic system are determined from the directed graph which can then be converted to the state space model of the system. Some basic elements and variables that are used in bond graphs are given in Table.1.

Table.1 [6].

The windmill system discussed here controls the water level in a water tank. Bond graph modeling of the system is done which magnificently determines the behavior of the system. The control parameters are further tuned using PID controller and hence a stable response is achieved. A wind turbine works in exactly the opposite way to a fan. Instead of using electricity to make wind, like a fan, turbines use the wind to make electricity. Most wind turbines have three blades, which face into the wind. The wind turns the blades around, this spins the shaft, which connects to a generator, and this is where the electricity is made. A generator is a machine that produces electrical energy from mechanical energy, as opposed to an electric motor, which does the opposite. The basic goal of this paper is to accomplish the optimized results of the model under consideration. There is a need to develop an energy resource which will control the water level. The modeling and simulation of such system is needed. For this purpose there is a requirement of bond graph of the model which will help to develop the state space, which in turn will result in control of water level of the tank. The results of the model can be made accurate by adding the controller to the model. The work is initialized by developing the circuit diagram of the complete model. The model includes several subsystems:     

Wind Mill Generator Motor Water Pump Water Tank

Torque/ Omega

τ Generator v Motor τ Pump F WaterTank V ω ω i Fig.2 Word Bond Graph

The model comprises of several sub systems. For making the complete bond graph, these subsystems are combined to get the complete model which results in generation of state space equations. The first part includes windmill connected to the generator which charges the battery. Fig.3 shows the working of this subsystem. Rwind

Iwind

Rgenerator

Igenerator

Rgenerator

GENEART OR

BATTERY

Fig.3 Windmill Generator Circuit Diagram [7]

Voltage/ Current

Generator

Se

R

I

Rwind

Ialter

1

Se

GY

1

C

GY

Cbatt

I

R

Iwind Ralter

Fig.4 Bond Graph of Windmill Generator

BOND GRAPH MODELING

The block diagram of the windmill model for controlling the water tank level is shown in Fig.1.

WindMill Mechanial Rotation

WindMill

The bond graphs of the subsystems comprises of windmill portion connected to the generator. The bond graph of this portion is shown in Fig.4.

The bond graphs of each component are developed by 20-sim. The results of 20-sim helped to generate the state space of the model, which is discussed in next section. The poles of the system tell about the response of the model. Further then the state space parameters A, B, C, D matrices are exported to Simulink, where PID controller is implemented. The use of tuned parameters resulted in optimized system responses that are also shown in the next section. II.

converting the τ and ω to force and velocity which controls the water level in the tank. The word bond graph for the model described above is shown in the Fig.2.

Battery

The Cbatt represents the charging of the battery generated by the windmill. The battery runs the motor. The motor takes the voltage/current as input and produces τ and ω in the output resulting in gyrator action represented by Fig.5.

Rmotor

Imotor

Voltage/ Current

MOTOR

Water Tank

Force/ Velocity

Water Pump

Torque/ Omega

Motor

Fig.1 Block Diagram of the Model

The wind forces the windmill propellers to have mechanical rotation, producing τ and ω. This will run the generator, producing voltage and current which charges the battery. The battery drives the motor connected with the water pump, thus

Fig5. Electrical Motor Circuit Diagram

The corresponding bond graph of the dc motor is represented in the Fig.6.

C

I

Cbatt

Imotor

0

1

GY GY1

bond, after that effort flow equations are evaluated at each junction. There are three gyrators used in this model. The first conversion is from mechanical to electrical through generator using gyrator 1 (GY1) having gyrator ratio γ1. The second conversion is at motor where electrical input is converted back to mechanical through gyrator 2 GY2 having gyrator ratio γ 2. In the next step this mechanical movement of pump controls the water level action represented by gyrator GY3 having gyrator ratio γ3. Solving the effort/flow equations for the model gives the following system equations.

R



P20  Sew 

Rmotor

Fig6. Motor Bond Graph

The motor runs the water pump which in terns makes the water pump functional. The water pump controls the water level in the tank, represented below in Fig.7.



P15   2

P10 I motor

R  3 2  Se  P15  pump  3 I  Rtnk  pump Rtnk I pump 



Rpump

P5  Ralter PUMP

TANK 

q8 

Ipump 

Fig.7 Water Pump and Tank Circuit

P10 

The bond graph associated with this water pump and tank is shown in the Fig.8. R

R

Rpump

Rtnk

GY

1

GY

GY1

1

Se Se1

I Ipump

Fig8. Bond Graph of Water Pump and Tank

The sub systems are integrated together. The complete bond graph developed in 20-sim is shown in the Fig.9. I Ialter

  Ralter  I     alter 1  P 5    q   I alter  8    P10    0      P15       0  P20     1  I  alter

1

GY

Se

Se

1

0

GY

1

Se1

I

R

R

Rpump

Ralter

GY

C Cbatt

Iwind

1

GY2

GY

1

GY1

Rtnk

I

P5 I alter



q8   1 Cbatt I wind P10 I motor

1 Cbatt 0 1 Cbatt 0 0

I

0

0

1 I motor  Rmotor I motor 2 I motor

2 I 15

0

0

0



1  I wind   0   P5      q8  0   P10       P15  0  P    20  1  I wind 

0  0  0   Sew   3   Se  Rtnk  0 

Imotor

R R

I alter



q8 R P P  motor 10  15 Cbatt I motor I15

0 0  0  0  1

Rwind

Se

P5

Using the system equations, the state space is developed for this model. The input matrix and the system matrix is shown below

GY2

R

P20 P  1 5 I wind I alter

Rmotor

Ipump

Fig.9 Complete Bond Graph

The bond graph of the model shown previously is used to generate system equations. Numbering is applied to each

where,

 R pump  3 2        I pump Rtnk I pump  The system equations using 20-sim are:

Ialter\state = int (Ialter\p.e, Ialter\state_initial); Imotor\state = int (Imotor\p.e, Imotor\state_initial); Cbatt\state = int (Cbatt\p.f, Cbatt\state_initial); Ipump\state = int (Ipump\p.e, Ipump\state_initial); Iwind\state = int (Iwind\p.e, Iwind\state_initial); The equations for state space evaluated from the 20-sim gives the following A, B, C, D matrices . Fig.11 System Implementation in Simulink

1  1 0  1 0  0 1 2 1 0    A  1 2 0 0 0   1 0 2 0  0  1 0 0 0  1

The response of the system is tuned using PID Controller. Default values are taken as: P=1; I=1; and D=0. The tuning process is applied and PID controller gives the tuned response with altered parameters of PID. P=3.291; I=5.785;

B  0 0 0 0 1

T

D=-0.494,

C  0 0 0 0 1

D0 III.

SIMULATION RESULTS

The response of the system is plotted in the 20-sim. The system has got the stable response shown in Fig.10. It is also noted that all the system poles lie in stable region. The poles for the system are:

Filter N=4.3669 The following graph shows the tuned response of the system when unit step is applied at the input to the system. The graph of PID controller shows the stable results. The output response is tracking the reference input. Water tank level is controlled through the Rtank variable.

P1= -1.07-0.93i, P2= -1.07+0.93i P3= -0.63+2.3i, P4= -0.63-2.3i P5= -1.609

Fig.11 PID Controller tuned Response of 20-sim Model

IV.

Fig.10 Rtank Response using 20-sim

The system matrices developed in 20-sim are exported to state space block in Simulink. Reference input is applied to it and PID controller is applied. The block diagram of the system in Simulink is represented in Fig.11.

CONCLUSION

In this paper an efficient energy producing source of windmill is used to control the level of the water tank using bond graph modeling, simulation in 20-sim and Simulink. The system equations are formed in 20-sim. These equations are implemented in state space block in Simulink. Results have been ameliorated using PID controller. The parameters are tuned to get the stable response. In the system defined here we would be facing some problems when under extreme hot conditions we have low air pressure. Under low air pressure the windmill would not be producing high amount of torque and hence would not be generating enough electricity to pump out water and meet the requirements of extreme hot

conditions. If a solar power system is added to the windmill system, it would surely be producing enough electricity to compensate the short fall of electricity and meet the requirements of the time. In addition to this, we can use a number of windmill systems to produce high electricity power and supply it commercially to a small town or a village situated at a distant place from Power Provider Company. REFERENCES [1]

[2]

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[4]

[5]

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[7]

[8]

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