Optimal control model for off-grid applications: Case of fuel cost minimization 

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CHAPTER 2 OVERVIEW OF HYBRID ENERGY SYSTEMS

INTRODUCTION

This section makes a review of literature pertaining to energy optimization and management of RE-based hybrid power systems for off-grid applications. The various energy system com- ponents, which include solar PV, wind, DGs and battery storage, are reviewed. The merits and demerits of the various technologies are revealed, explaining the motivation for the usage of technologies chosen for this work.  The methodologies used by various authors to model the hybrid energy system components, depending on the data available, are explored.  Part of the literature is obtained from authors’ published papers [50, 51, 53, 55].

HYBRID ENERGY SYSTEM CONFIGURATION

The RE-diesel-battery hybrid power supply system proposed in this study is made up of the following main sub-systems: RE systems (PV and wind), the battery storage system and the DG. Controllers and inverters have been left out for simplicity purposes and are assumed to be 100% efficient in this work.  Priority for power supply is given to RE sources.  The load is met by the RE generators and the battery comes in and discharges when the RE output is not enough to meet the load if it is within its operating limits.   If RE output is above the load requirements, the battery is charged by the RE generator(s).  The DG comes in when the RE generators and/or the battery cannot meet the load but does not charge the battery.      Fig.  2.1 shows the proposed hybrid energy management system.  A supervisory system controller is incorporated just to show the principle of energy management in terms of the input or database, the data base support and the output. The main role of the hybrid energy management system is to control and optimize the interaction of various system components and control power flows within the system to provide a stable and reliable source of energy.
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Solar energy

Solar PV is an established technology that is being used throughout the world to supply autonomous power for many off-grid applications.  There is therefore a need for accurate estimates of available solar irradiation, as it is site-specific and crucial in the optimal design of conversion systems for various applications. Many meteorological or radiometric stations measure global and diffuse irradiation received on horizontal surfaces, but data on inclined surfaces are not available and are estimated using different models from those measured on horizontal surfaces. Radiation on a horizontal surface is the only radiation record available at many meteorological stations, especially in developing countries. Total radiation incident on a tilted plane consists of three components: beam radiation, diffuse radiation and reflected radiation from the ground.  The direct and reflected components are easily computed with good accuracy by using simple algorithms, but the nature of the diffuse component is more complicated and the required algorithms need to be assessed and evaluated. Various models have been developed for this purpose and some of these models are available in literature [58, 59, 60, 61]. The methods used to estimate the ratio of diffuse solar radiation on a tilted surface to that on a horizontal are categorized as isotropic and anisotropic models.   The isotropic models assume that the intensity of diffuse sky radiation is uniformly distributed over the sky dome, implying that the diffuse radiation incident on a tilted collector depends on the fraction of the sky dome seen by the collector. The anisotropic models assume the anisotropy of the diffuse sky radiation in the circumsolar region and the isotropically distributed diffuse part from the rest of the sky dome[62, 63]. The circumsolar model [64] applies to clear and cloudless skies and predicts the sky diffuse radiation component. Another isotropic model of Liu and Jordan [65], [66] incorporates the intensity of sky diffuse radiation and assumes this to be uniform over the sky dome. The anisotropic model of Klucher [67] modified the Temps and Coulson [68] model by incorporating the effect of cloudy skies.  The Hay [69] model is composed of an isotropic and circumsolar component and predicts the radiation on a tilted surface from the available data on a horizontal surface. The hourly solar irradiation incident on the PV array is a function of time of day, expressed by the hour angle, the day of the year, the tilt and azimuth of the PV array, the location of the PV array site as expressed by the latitude, as well as the hourly global solar irradiation and its diffuse fraction [70, 71, 72]. The actual expression relies on the sky model, which is a mathematical representation of the distribution of diffuse radiation over the sky dome presented in [70].
In this study, the simplified isotropic diffuse formula suggested in [71] is used.  The hourly solar irradiation incident on the PV array is given by:
In (2.1), IB  and ID  are respectively the hourly global and diffuse irradiation in kWh/m2. RB  is a geometric factor representing the ratio of beam irradiance incident on a tilted plane to that incident on a horizontal plane.  Monthly average hourly meteorological data, global irradiation, diffuse irradiation and ambient temperature are used as inputs in evaluating (2.1), (2.2) and (2.3) of the performance simulation model.  The evaluation is performed at the mid-point of each hour of the day, on the « average day » of each month as defined in [70].
The instantaneous radiation incident on the PV array, Ipv , can be obtained [71, 73] as: where Ibn  represents the direct irradiance at normal incidence, θpv  the angle of incidence of direct irradiance on the PV array, C the concentration ratio (=1 for a flat-plate collector) and Id the diffuse irradiance. If it is assumed that all radiation in an hour is concentrated at the middle of the hour, the same expression also gives the hourly irradiation incident on the PV array, with θpv  measured at the middle of the hour. Hourly radiation data or data resolved into the beam and diffuse components are usually not available from many meteorological stations, especially in developing countries [73]. Records available from most meteorological stations are those for monthly average daily hemispherical or global irradiation on a horizontal plane, Hh.  In such circumstances, the procedure described below could be employed.  The monthly average daily diffuse irradiation, Hd, can be predicted from Hh  by applying any of the many correlations that relate the ratio Hd/Hh with monthly average clearness index, Kh given by various authors including [74, 75, 76, 73]. The following correlation for climates like for the Southern Hemisphere, where δ is the sun’s declination angle. For a solar array with; tilt, β, equal latitude, φ, as assumed in this thesis, RB  is evaluated with ωs  = 0 [73].  The  fact that the operating temperature plays a crucial role in the PV conversion process is well documented in literature. The efficiency, η, of a PV cell is actually a function of cell temper- ature and array irradiation [78, 73].  It has been shown that PV cell performance decreases with increase in temperature, as carrier concentrations increase, resulting in increased in- ternal carrier recombination rates.  There are many correlations in literature, as given by [78], that express the PV cell temperature as a function of weather variables such as the ambient temperature, wind speed, solar radiation, material and system-dependent properties such as glazing-cover transmittance and plate absorbance.  The temperature dependence of the electrical efficiency of a PV cell can be traced to the fundamental power, P , equation which can be used to investigate the effect of temperature on the current, I,
The power output of a PV module also depends on the type of mounting used. Solar module mountings can be fixed, adjustable or tracking.  The above methodology can be applied to both the fixed and adjustable types. The fixed type is the most common, as it is the simplest and least expensive type; the array is completely stationary at a particular tilt angle facing the equator. Various rule of thumb tilt angle adjustments have been proposed in literature in an effort to increase the array output throughout the year [62, 81]. Some authors have used mathematical optimization approaches to optimize the tilt angle [82]. The angle of inclination of an adjustable type of mounting can be changed twice or more times during the year to cater for the lower angle of the sun in winter as the earth turns around the sun, causing seasonal changes.  This type has proven to produce increased output compared to the fixed type.  The third type is the tracking one, which follows the path of the sun during the day to maximize the solar radiation that the solar array receives. This type can be a single-axis tracker that tracks the east-to-west or a two-axis tracker, tracking the daily east-to-west and north-south movements of the sun and the seasonal declination movement of the sun.  The latter type is the most efficient but this is achieved at a cost.
Another way of maximizing module power output is by employing a Maximum Power Point Tracking (MPPT) system.  This is an electronic system that operates the PV module and enables it to produce all the power it is capable of producing. The MPPT system varies the electrical operating point of the modules so that the modules are able to deliver maximum available power. This system can be used together with a mechanical tracking system. The additional power harvested from the modules is made available as increased battery charge current. When a conventional charge controller charges a discharged battery, it just connects the modules directly to the battery, forcing the modules to operate at battery voltage, which is typically not the ideal operating voltage at which the modules are able to produce their maximum available power.  All types of solar installations can benefit from using MPPT technology as they would be able to operate at operating voltages.

Wind energy

Wind energy is one of the RE sources that has huge potential and has been in use for centuries. Wind is the movement of air from high-pressure areas to low-pressure areas caused by uneven heating of the earth’s surface by the sun. Wind will always exist as long as solar energy exists. Ancient mariners made use of wind to sail to distant lands. Wind power has been used by farmers to pump water and for grinding grain. Currently wind energy is mainly converted to electrical energy to meet critical energy needs. It is one of the fastest growing sources of electricity and one of the fastest growing markets.  The wind turbines harvest kinetic energy and convert it into usable power, which can provide electricity for residential, commercial and industrial purposes. Wind turbines are a mature technology that has been used by many customers, utilities and independent power producers to produce electricity from wind energy.  Because of the space requirements of WGs, they are more suitable for remote area applications [85] and for supply reliability; they are usually incorporated in a hybrid system. Wind farms are a common feature in countries where there is vast land and good wind resources.
There are basically two designs for modern wind turbines, namely the horizontal axis and vertical axis.  Vertical axis turbines, whose axis of rotation is vertical or perpendicular to the ground, have the advantage of being omnidirectional (powered by wind coming from all directions), with gears and the generator at the tower base. They are, however, disappearing from the mainstream commercial market owing to the weight and cost of the transmission shaft, low starting torque, low efficiency and less power production owing to less wind speed closer to the ground, compared to horizontal axis designs. Attempts are currently being made to commercialize vertical axis design for building-rooftop applications [86]. The gearbox and generator in vertical axis designs can be lowered to the ground, making construction costs lower and maintenance easier. Moreover, there is no need for the turbines to point towards the wind, making them ideal for installations in areas with inconsistent wind patterns. Horizontal axis wind turbine, whose axis of rotation is horizontal, or parallel with the ground, dominate the wind industry. While horizontal axis wind turbines are common in big wind applications, vertical axis turbines are found in small and residential wind applications. The advantage of horizontal wind turbines is that they can produce more power from a given amount of wind, though they are generally heavier and do not perform well in turbulent winds. In this work, small horizontal axis turbines with three blades are considered.

CHAPTER 1 Introduction 
1.1 Background
1.2 Motivation
1.3 Optimization and modelling
1.4 Research aim and objectives
1.5 Outline and contribution of the thesis
1.6 Conclusion
CHAPTER 2 Overview of hybrid energy systems 
2.1 Introduction
2.2 Hybrid energy system configuration
2.2.1 Solar energy
2.2.2 Wind energy
2.2.3 Diesel generator
2.2.4 Battery storage
2.3 Hybrid energy system sizing
2.4 Case study
2.5 Conclusion
CHAPTER 3 Optimal control model for off-grid applications: Case of fuel cost minimization 
3.1 Introduction
3.2 The hybrid system .
3.3 Optimization model
3.4 Results and discussion
3.5 Economic analysis
3.6 Conclusion
CHAPTER 4 Energy dispatching of a photovoltaic-diesel-battery hybrid power system: Switched model predictive control approach 
4.1 Introduction
4.2 Problem statement
4.3 Switched model predictive control design
4.4 Simulation and discussion
4.5 Conclusion
CHAPTER 5 Optimal power flow management model: Case of fuel and battery wear cost minimization 
5.1 Introduction
5.2 Problem formulation
5.3 Case study
5.4 Results and discussion
5.5 Conclusion
CHAPTER 6 Energy dispatch strategy for a photovoltaic–wind–diesel– battery hybrid power system: A model predictive model approach 
6.1 Introduction
6.2 Hybrid system configuration
6.3 Model predictive control for the photovoltaic-wind-diesel-battery hybrid system
6.4 Simulation results and discussion
6.5 Conclusion
CHAPTER 7 Conclusions 
7.1 Summary
7.2 Conclusions and contributions
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