## 3 Problem Formulation
### Datacenter Power Efficiency  
The PUE metric is a valuable parameter used to assess the power utilization of a datacenter [3]. Within a datacenter, the energy consumed by non-IT equipment sources like cooling systems, power supplies, and lighting is categorized as overhead power (calculated through Equations (6) and (7)). The PUE is calculated by dividing the total power consumption of the datacenter (Pdc) by the power consumption of the IT equipment (PIT). \[PUE=\frac{Total\ Power}{IT\ Device\ power}=\frac{P_{dc}}{P_{IT}} \tag{6}\]  
This ratio provides insights into how efficiently a datacenter utilizes power resources. A PUE value greater than one indicates the presence of overhead power, while a value of one represents an ideal scenario where all power consumption is attributed to IT equipment. In this study, we consider both the increase in IT power consumption and the impact of overhead power after the initial placement of VMs. Instead of using a fixed PUE value, we adopt a dynamic PUE model proposed by [3] to accurately calculate the overhead power and minimize energy consumption in datacenters. \[PUE(U_{t},H_{t})=1+\frac{0.2+0.01\cdot U_{t}+0.01\cdot U_{t}\cdot H_{t}}{U_{t}} \tag{7}\]  
The constants 0.2 and 0.01 are adopted directly from [3]. In their work, these values were obtained by linear regression on measured PUE data collected across four geographically dispersed U.S. datacenters, covering various utilization levels and ambient temperatures. Integration of Renewable Energy and Dynamic PUE  
To achieve sustainable cloud operations, our framework embeds real-time solar energy availability and dynamic PUE modeling into the ACO algorithm. These two inputs influence both the heuristic evaluation and objective function during VM placement decisions. * Dynamic PUE Modeling  
This work adopts a dynamic PUE model that varies with external temperature and workload intensity. Overhead power, calculated using Equation (7), is updated in each placement cycle based on the datacenter's current state. This adjustment allows the algorithm to penalize inefficient datacenters with higher overhead power due to less favorable operating conditions. Figure 2 below illustrates the flow of how solar energy and dynamic PUE modeling are integrated into the ACO optimization process:  
* Solar Energy Availability  
Each datacenter is associated with hourly solar irradiance profiles obtained from national datasets. The available solar energy is converted into usable power based on panel area and efficiency parameters and is treated as a free and zero-emission energy source. For each placement decision, the algorithm first attempts to satisfy demand using the available solar power. Any remaining unmet demand is assumed to be drawn from the grid, thereby incurring energy costs and carbon emissions. During placement, the algorithm prioritizes solutions that maximize solar energy utilization--especially when this leads to a reduced  
Figure 2: Dataflow diagram for dynamic PUE and real-time solar energy integration into the ACO heuristic calculation. total cost and carbon footprint. This green-energy-first principle drives inter-datacenter selection within the optimization process. * Incorporating Wind Energy into the Renewable-Aware Framework  
Although this work concentrates on solar irradiance as the primary renewable input, the underlying framework can be readily extended to accommodate additional energy sources such as wind. In practice, we would augment the hourly solar irradiance curves described in Section 5.1.3 with wind-speed profiles obtained from meteorological datasets. A standard turbine-power conversion model would then translate wind speed into usable power output. By defining a composite renewable-availability metric, the placement algorithm can prioritize on-site renewables and only draw from the grid to satisfy any residual demand.