^{1}

^{2}

Increased pollution levels have caused damage to our planet. Many scientists are now warning on the long term effects. Green houses gases causes more of the sunlight to be trapped within the Earth’s atmosphere and thus causing increased Earth temperature. Individuals, governments, and private entities are now acting on fixing this problem. One of the most promising solutions is installing an array of solar cells in residential areas. Doing so makes sense for areas with abundant sunlight as the dependency on the grid can be minimized and even completely illuminated while providing a feasible economic perspective at the same time. This paper presents the modelling of a residential setup as a complete system along with an electric vehicle. The modelled components include: Photovoltaic Cells, Home Load Usage, Electric Vehicle, High-Voltage battery as an energy storage, Boost, and Inverter. The presented analysis will help engineers and system designers do better cost analysis. The study can also be used as a basis for maximizing the solar energy usage and perform component optimization.

Reducing CO_{2} emissions is a must for the survival of the planet, to do so, a tremendous effort is underway to make this possible. Individuals, organizations, and governments are all working together to help reduce emissions and greenhouse gases. Governments have big tax incentives for individuals that install and use solar cells in their households. This caused a spike in the installation of photovoltaic systems. Photovoltaic Cells (PV) have many advantages other than reducing the pollution levels. PV can help stabilize the grid [

In a previous work we analyzed a high level description for this problem from a geographic perspective [

This section will get into the details of the components of the PV system and how these components can come together to form different configurations. The different components that compromise a complete PV setup for a residential system with an EV can be compromised of the following:

1) PV Cells,

2) High Voltage Battery,

3) Electric or Plugin Electric Vehicle,

4) Household Loads,

5) Boost,

6) Inverter.

Based on these 5 different configurations, we might use different components to setup the system that we might be designing. Configuration 1 consists of all the 6 components connected together in a fashion shown in

Configuration 2 shown in

PV Cells | H. V. Battery | Electric or Plugin E.V. | Home Load | Boost | Inverter | |
---|---|---|---|---|---|---|

Configuration 1 | ü | ü | ü | ü | ü | ü |

Configuration 2 | ü | û | ü | ü | û | ü |

Configuration 3 | ü | û | ü | ü | ü | ü |

Configuration 4 | ü | û | û | ü | û | ü |

Configuration 5 | ü | ü | û | ü | ü | ü |

charge the battery. This process yields a lot of inefficiencies and thus a significant amount of energy is lost in the energy transfer between the PV cells and the electric vehicle battery.

The next section will model all of the components that used in the 5 configurations listed earlier. After the components are modeled, this will provide a benchmark and a solid foundation to do further analysis on any configuration we decide to analyze.

This section will model each of the components that were listed in Section 2 which is

an analysis of 5 configurations before any further analysis can be done on the system. The next subsections will model each of the components separately. The first component to model is the battery. We will then model the Electric or Plugin Electric Vehicle; photovoltaic cells will come next, followed by the inverter, booster, and finally the home load.

Lithium-Ion (Li-Ion) is becoming the battery chemistry of choice for most portable and energy storage applications. This is true because of many reasons. These batteries possess high energy and power densities, slow self-discharge rate, and high nominal cell voltage when compared to other chemistries. Laptops, energy storage banks, cell phones, unamend aerial vehicles, electric vehicles, plug in hybrid electric vehicles as well as many other applications use li-ion batteries as the main or secondary source of power [_{S} represents the internal resistance of the battery as shown in

parallel) combinations can exist [

The summation of forces acting on a moving vehicle is shown in (1). The principles of vehicle dynamics have been known and studied for years and the physics has already been established. This applies to any moving mass whether it’s electric or not [

where:

1) F_{roll} represents the rolling force i.e. the force between the vehicle tires and the road.

2) F_{grade} represents the grade force. This force might be negative if the vehicle is going downhill because the gravity will be helping to propel the vehicle downwards.

3) F_{air} represents the air resistance of the vehicle.

4) F_{acc} represents the acceleration force that is acting on the vehicle.

Propelling the vehicle across some distance at a specified velocity v means that the instantaneous power can be represented as shown in (2). Equation (2) is simply equation (1) multiplied by the velocity of the vehicle. Using (1) and (2) we can calculate the total energy needed for the vehicle to move some distance. This is represented as shown in (3). Equation (3) represents the energy in joules that is needed to move the vehicle for some time t (seconds) at speed v.

The power calculation as shown in (2) is not and almost never steady due to the fact that neither the velocity nor the forces acting on the moving mass are constant. This deems (3) as unusable as it is described. To calculate the energy consumed by the moving vehicle, integration of hundreds and thousands of energy segments is needed. These segments represent the different accelerations, speeds, different grades, rolling resistance, and other factors.

As mentioned earlier the dynamics shown in (1) is straightforward and can be represented as the following:

・ F_{roll} (rolling resistance) can be expressed as shown in (4). is the vehicle’s mass in kg, g is the gravitational acceleration, and f_{r} is the tire rolling resistance coefficient. (f_{r} is dependent on the tire pressure, tire composition, and most importantly on the driven road) [

・ F_{grade} is shown in (5). i represents the road grade.

・ F_{air} is shown in (6). P_{a} is the air mass density, C_{D} is the aerodynamic drag coefficient, A_{f} is the frontal area of the vehicle in m^{2}, v is the vehicle speed in m/s, and v_{wind} is the head wind speed. V_{wind} can be positive or negative depending on the direction of the wind, it can also change abruptly between them as well.

・ F_{acc} is shown in (7). M is the vehicle’s mass in kg, δ is the rotational inertia factor, and a is the vehicle acceleration in m/s^{2}.

Putting Equations (4), (5), (6), and (7) back into Equation (1) and rearranging we get the total force that is acting on the vehicle. This new representation is shown in (8) below.

Applying the same principle as (2) on (8) i.e. multiplying (8) by the velocity yields to (9). Where (9) represents the total power acting on the moving vehicle.

Electric vehicles are capable of regenerative braking [_{in}. Regenerative energy is created whenever the driver steps on the brake pedal or when the vehicle is coasting. Lastly, the total energy acting on the vehicle is shown in (11). Equation (11) is just the summation of the total positive and negative energy acting on the vehicle.

Different papers have studied and analyzed the modelling perspective for photovoltaic cells. Some work used Matlab and Simulink to do the analysis as shown by Salmi et al. [

The output current from the PV cell can be done using the equation:

where

and

where:

1) V_{d} is the diode’s voltage,

2) I_{0} is the reverse saturation current of the diode,

3) t is the junction temperature in Kelvin,

4) q is the electro charge valued at 1.602 × 10^{−}^{23},

5) k is Boltzmann’s constant valued at 1.381 × 10^{−}^{23} J/K.

The simplest way to define an inverter is to say that it converts direct current into alternating current. This is needed in our setup because the solar cells and the battery bank produce and store electric power in a direct current form and this power needs to be converted into alternating current so it can be used by the household or pushed back to the grid. Sine wave inverters represent the current technology, this is because the power delivered to the utility have the harmonics almost eliminated. One drawback is that these kind of inverters are more complicated and expensive to implement. _{n} represents the transistor switch.

A buck-boost transformer is often used to increase or decrease the voltage level to match the voltage level between 2 components. In our setup it is being used to boost the voltage between the PV cells and the high voltage energy storage battery bank and/or between the PV cells and the electric vehicle in case DC charging is performed.

(L1), an output capacitor (C_{out}), a diode (D1) with an equivalent series resistance (R_{Cout}). The load is the resistor R_{OUT}, and the switch Q1 is assumed to be ideal. We assume that V_{IN}, V_{OUT}, and V_{COUT} to be the input voltage, output voltage, and the voltage across C_{OUT} respectively. IL1 is the current across L1, and VD1 is the forward voltage drop across D1. When Q1 is switched on, the state equations are represented as the following:

The output equation is:

when Q1 is switched off, the output equation listed above stays the same while the state equations become:

The modelling of a home load is straightforward. The process works as follows: the driver returns home from work at around 5 - 6 P.M. This time is usually the peak hours for the electric grid demand [

This paper presented a whole system modelling and representation for a full residential system with all the different components that make up a PV residential setup with a possible EV load. All the possible configurations were presented as well. The work presented in this paper can be used a basis for future development for any optimization that can be done on the system. Furthermore, we would like to expand our work by considering optimization control methods by making sure that each component is run at its highest optimization point to improve performance, reduce costs, and deliver more renewable energy to the users. More advanced control techniques might also be considered to fulfill these tasks such as the ones described in [

Alghassab, M. and Zohdy, M.A. (2016) Modelling of a Residential Solar Energy Recuperation System Setup. Open Journal of Energy Efficiency, 5, 135-147. http://dx.doi.org/10.4236/ojee.2016.54012