The management of the distribution network is becoming increasingly important as the penetration of distributed energy resources is increasing. Reliable knowledge of the real-time status of the network is essential if algorithms are to be used to help distribution system operators define network configurations. State Estimation (SE) algorithms are capable of producing such an accurate snapshot of the network state but, in turn, require a wide range of information, e.g., network topology, real-time measurement and power profiles from customers/productions. Those profiles which may, in principle, be provided by smart meters are not always available due to technical limitations of existing Advanced Metering Infrastructure (AMI) in terms of communication, storage and computing power. That means that power profiles are only available for a subset of customers. The paper proposes an approach that can overcome these limitations: the remaining profiles, required by SE algorithms, are generated on the basis of customer-related information, identifying clusters of customers with similar features, such as the same contract and pattern of energy consumption. For each cluster, a power profile estimator is generated using long-term power profiles of a limited sub-set of customers, randomly selected from the cluster itself. The synthesized full power profile, representing each customer of the distribution network, is then obtained by scaling the power profile estimator of the cluster to which the customer belongs, by the monthly energy exchanged by that customer, data that are easily available. The feasibility of the proposed approach was validated considering the distribution grid of Unareti SpA, an Italian Distribution System Operator (DSO), operating in northern Italy and serving approximately one million customers. The application of the proposed approach to the actual infrastructure shows some limitations in terms of the accuracy of the estimation of the power profile of the customer. In particular, the proposed methodology is not fully able to properly represent clusters composed of customers with a large variability in terms of power exchange with the distribution network. In any case, the root mean square error of the synthesized full power profile with the respect to validation power profiles belonging to the same cluster is, in the worst case, on the order of 6.3%, while in the rest of cases is well below 5%. Thus, the proposed approach represents a good compromise between accuracy in representing the behavior of customers on the network and resources (in terms of computational power, data storage and communication resources) to achieve that results.