# Development of Far-UVC-Based Surface Disinfection Prototype for Public Buses
## 2 Materials and Methods
### Energy Efficiency Evaluation Model  
In order to select the optimal far-UVC irradiation, it is necessary to create a model that, based on the parameters of the far-UVC source and the duration of exposure, would allow simulating the energy requirements for the disinfection process. An energy efficiency assessment model is developed with the following assumptions:  
1. The parameters of the electrical power supply network supplying the module remain constant over time.
2. The module has two states: connected to the electrical power supply or disconnected from it.
3. The module is passively cooled.
4. The temperature of the UVC lamp is equal to the temperature of the glass bulb of the lamp.
5. The temperature of the power supply of the module does not affect the light output of the UVC lamp.
6. The temperature of the converter of the module does not affect the light output of the UVC lamp.  
The temperature in Kelvin (K) of the UVC lamp in the module is modelled by the following Equation (1):  
\[T=T_{S}+\Delta T\Big{(}1-e^{k_{T}(t-t_{S})}\Big{)}, \tag{1}\]  
where \(t\) is a time (s) since the start of the simulation, \(t_{S}\) is the point in time (s) at which the state of the module changed, \(T_{S}\) is the temperature (K) of the UVC lamp at the moment when the state of the module changed, \(k_{T}\) is a coefficient, and \(\Delta T\) is the temperature difference (K) at the moment when the state of the module changed.  
The temperature difference \(\Delta T\) depends on the change in module state and can be expressed as follows:  
\[\Delta T=\begin{cases}T_{max}-T_{S},&\text{when state changes from OFF to }ON\\ T_{amb}-T_{S},&\text{when state changes from }ON\text{ to OFF}^{\prime}\end{cases} \tag{2}\]  
where \(T_{amb}\) is the temperature of the UVC lamp before the start of the simulation, when its temperature is equal to the ambient temperature; \(T_{max}\) is the maximum temperature that  
Figure 8: Far-UVC lamp positioning according to scenario 3.  
the UVC lamp can reach if when the module is operated for a sufficiently long time. At the start of the simulation, the values of the model parameters are set as follows: \(T_{S}=T_{amb}\), \(\Delta T\) is calculated using Equation (2) assuming that the module changes state, and \(t_{S}=t\).  
The radiance (W/m\({}^{2}\)) of a UVC lamp is modelled by the following equation:  
\[E_{e}=\begin{cases}C_{E}+e^{k_{Ea}+\frac{k_{Eb}}{T}+k_{Ec}\cdot\log{(T)}},& \text{when state is ON}\\ &0,&\text{when state is OFF}\end{cases}, \tag{3}\]  
where \(C_{E}\) is a constant and \(k_{Ea}\), \(k_{Eb}\) and \(k_{Ec}\) are coefficients.  
The instantaneous electric power (W) of the module is modelled by the following Equation:  
\[P=\begin{cases}C_{P}+k_{Pa}e^{\frac{k_{Pb}}{T+k_{Pc}}},&\text{when state is ON}\\ 0,&\text{when state is OFF}\end{cases}, \tag{4}\]  
where \(C_{P}\) is a constant and \(k_{Pa}\), \(k_{Pb}\) and \(k_{Pc}\) are coefficients.  
From the start of the simulation t\({}_{0}\) to the time point t\({}_{\text{m}}\), the power consumed (Ws) by the module is calculated thus:  
\[E=\int_{t_{0}}^{t_{m}}P(t)dt, \tag{5}\]