## 2 Load Modeling  
In a military setting, the load on the microgrid is different than in a residential or commercial setting. A load model for a patrol base (PB) was developed with the help of an experienced member of the military [13]. First, three load tiers were identified to distinguish between loads that may be connected at a PB. Tier 1 includes loads that are critical to the mission, while Tier 2 includes loads that are important for extended operations. Tier 3 includes loads for improving quality of life and boosting morale. The loads in Tier 3 are important for maintaining the living conditions and overall attitudes for the PB members, however they could be disconnected during some time periods in order to ensure that Tier 1 and 2 loads are met. Table 1 lists some examples of equipment that might be included in each load tier. The amount of load needed in each tier varies based on time (day vs. night) as well as on activity (patrol vs. non-patrol). Table 2 shows the estimated load for a 20-40 person PB in each of these scenarios. The estimates shown in Table 2 are for the total load used in each different type of scenario. The actual load is stochastic and will vary, so it was modeled using a compound Poisson process. A Poisson process is defined as  
\[P[N(t)=k]=e^{-\lambda t}\frac{(\lambda t)^{k}}{k!} \tag{1}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Load Tier** & **Equipment** \\ \hline Tier 1 & One to ten 80 W Panasonic Toughbooks \\ (Mission & One or two AC units \\ Critical) & One–Two TVs/projectors used as large monitors for the Blue Force Tracker \\  & Three to five 100 W bulbs ( 26 W CFL) \\ \hline Tier 2 & Power tools and charging station if the platoon is equipped with vehicles \\ (Extended Operations) & ISR video feeds \\  & Portable lights powered via rechargeable battery pack \\  & One to three hotplates/coffee pots \\ \hline Tier 3 & One to three personal electronic devices (iPod, laptop, camera, etc.) \\ (Morale Boosting) & 30–80 gallon hot water heater \\  & Three to five additional AC/heater units for berthing \\  & One to three flat panel TVs or projectors \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equipment included in each load tier at a Patrol Base. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load Tier** & **Activity** & **Day** & **Night** \\ \hline Tier 1 & \begin{tabular}{c} Patrol \\ Non-Patrol \\ \end{tabular} & \begin{tabular}{c} 2–3 kW \\ 1–2.5 kW \\ \end{tabular} & \begin{tabular}{c} 2–3 kW \\ 1–2.5 kW \\ \end{tabular} \\ \hline Tier 2 & \begin{tabular}{c} Patrol \\ Non-Patrol \\ \end{tabular} & \begin{tabular}{c} 1–2 kW \\ 2–3 kW \\ \end{tabular} & \begin{tabular}{c} 1–2 kW \\ 1–2 kW \\ \end{tabular} \\ \hline Tier 3 & \begin{tabular}{c} Patrol \\ Non-Patrol \\ \end{tabular} & \
\begin{tabular}{c} 2–3 kW \\ 0.5–1.5 kW \\ \end{tabular} &
\begin{tabular}{c} 2–3 kW \\ 0.5–1 kW \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Amount of load in each tier based on time and activity. where \(\lambda\) is the rate parameter. The Poisson process \(N(t)\) is then implemented in a compound Poisson process as  
\[Y(t)=\sum_{i=1}^{N}(t)D_{i} \tag{2}\]  
where \(D_{i}\) are independent and identically distributed (iid) random variables [14]. A compound Poisson process is an appropriate method for approximating the distribution of electrical loads, since they are discrete, independent random variables [15]. Along with the load changing stochastically within each time and activity, the operation of the PB will also vary. In any combat environment, varying patrol patterns (route, length of patrol, time of departure, etc.) are used in order to limit the enemy's ability to execute a coordinated attack. Therefore, this load model also randomizes the number of patrols per day, their length, and the length of rest during both day and night. Some days may then include no patrols, to allow for debriefing or rest. Other days may include a high number of patrols, designed to limit the enemy's ability to operate.