Enterprises world-wide are increasingly prioritizing sustainability due to the growing focus on carbon neutrality as well as the requirement to adhere to emerging strict regulations from governments across the globe. With many enterprise workloads deployed on cloud and data centers, to fulfill the mandatory carbon reporting requirements of their clients, it is becoming inevitable for cloud providers and data center operators to quantify each client's share of the total carbon emission from their facility. Accurate carbon quantification requires power measurements to be available at the lowest level of the hardware infrastructure such as physical servers and network switches. However, power sensing is quite limited in many data centers, with measurements normally available only at an aggregated level such as the rack level. To drill down to the level of a workload to capture the correct power usage per workload, it is very important to dis-aggregate this power across servers. In this paper, we propose a software based non-linear model using the Newton-Raphson method to estimate the power model parameters of individual servers using server utilizations when the overall rack level power measurements are given. The methodology is applicable to data centers with multiple types of servers in a rack and is light-weight in the sense that it does not require mechanisms such as shutting down individual servers in order to estimate idle power. The method is also generalized to account for the real world scenario where the time granularity of rack power and server utilization measurements may not match. We have conducted detailed evaluations of the methods proposed and find good convergence for parameter estimation even when tested with multiple different initial conditions.