# Power Management Strategy for an Autonomous DC Microgrid
## 5 Economic Analysis
### DG Total Cost Modelling  
The total cost of DG power production includes fuel cost, start-up and shut-down costs, regularly replaceable components, and overhaul costs. In general, for small-scale power DGs, manufacturers do not provide data regarding DG costs. The total DG cost can therefore be calculated based on the approach presented in Reference [34], while fuel consumption data for a variety of DGs ranging from 6 to 2260 kW are given in Reference [35]. However, these data and approaches do not always contribute to an acceptable fitting model [23], and therefore, a specific calculation has to be introduced. Start-up cost is largely dependent on the temperature of the diesel engine and ambient atmospheric conditions [36]. For a large-scale power DG, fuel consumption during cold start-up is higher than during warm start-up of the diesel engine. Nonetheless, for a small-scale power DG, less than 10 kW for example, the influence of temperature has not yet been studied. Thus, the temperature influence of the DG used is first determined experimentally. For this purpose, three 12-min experiments were carried out on three consecutive days in January 2017, in the outdoor environment where the ambient temperature was about 1-3 \({}^{\circ}\)C. All three tests were under no-load conditions, so as to  
Figure 11: Experimental results of test 3: (a) DC microgrid power evolutions, (b) SOC evolution of electrochemical battery bank, (c) SOC evolution of the SC, and (d) DC bus voltage. show DG consumption conditions during the start-up. The fuel consumption curves are shown in Figure 12a, where the red lines are the measured weight of the fuel tank and the blue lines are the linear regression results. From the three experimental curves, it can be seen that there is no evident decline of diesel consumption during cold start-up. This means the temperature of the engine has little influence on this type of DG. With linear regression, fuel consumption rates were 0.2688 g/s, 0.2691 g/s, and 0.2695 g/s, respectively. Given the tiny difference, the no-load diesel fuel consumption rate can be taken as the mean value of 0.2691 g/s. To investigate the impact of load power on the DG fuel consumption rate, experiments were carried out under several power values (\(p_{DG}=v_{DG}\cdot i_{DG}\)). Like the no-load test, each test lasted 12 min during which fuel tank weight was recorded. The weight evolution is drawn partially in Figure 12b. where \(p_{DC}\) is the DG operating power level in W. According to the data given in Reference [37], the fuel price in France is currently 1.23 \(\upxi\)/L, and according to the data given in Reference [38], the diesel density is about 0.835 kg/L. The DG production tariff under different output power values is shown in Figure 13b. To obtain an accurate fuel cost model, the recorded data are fitted into a power function as given in Equation (11):  
\[c_{DG}(p_{DG})=a\times p_{DG}{}^{b}+c \tag{11}\]  
where \(c_{DG}\) is the DG power production tariff in \(\upxi\)/kWh, \(a=3203\), \(b=-1.149\), and \(c=0.5726\). The DG fuel consumption cost \(C_{DG_{-}Fuel}\) for a given time period, from initial instant \(t_{0}\) to final instant \(t_{F}\), is thus calculated as in Equation (12):  
\[C_{DG_{-}Fuel}=\frac{1}{3.6\times 10^{6}}\sum_{i=t_{0}}^{t_{F}}c_{DG}(p_{DG}(i) )\cdot p_{DG}(i)\cdot\Delta t \tag{12}\]  
Without consideration of overhaul costs, DG operation and maintenance (O&M) costs \(C_{DG_{-}O\&M}\) include oil change cost and the replacement cost of several elements: Pre-cleaner, air cleaner, low-profile air cleaner, fuel filter, and the spark plug. The DG O&M cost is described in Equation (13). \[C_{DG_{-}O\&M}=T_{DG_{-}run}\cdot c_{DG_{-}O\&M} \tag{13}\]  
where \(c_{DG_{-}O\&M}\) is the average O&M cost per hour and \(T_{DG_{-}run}\) (h) is the running time of the DG.