This work examines the use of Physics-Informed Neural Networks to solve inverse problems in electrical power systems. PINNs, in contrast to traditional neural networks, include the basic physical laws of such systems as direct components of the training procedure. This relation to real-world physics is useful in enhanced accuracy of predictions and allows the model to make more generalized predictions particularly when data is scarce. The framework that was created is a combination of mathematical both steady state behavior and dynamic behavior of power systems, and hence capable of working effectively without large labeled datasets whilst being computationally efficient. PINNs demonstrate better results than traditional neural networks with capability to capture the dynamic system states, including generator vibrations and changes of frequency, and to make inferences of things hard to measure system inertia and damping attributes. Experiments show PINNs have minimized the error of estimation to less than 5 percent in 10,000 training epochs. The methodology is verified on benchmark production like single machine infinite bus (SMIB), IEEE 4-bus and IEEE 9-bus systems. Findings show that PINNs are more successful in comparison with conventional approaches to reduce the error rates under noisy conditions by 70 percent and need almost 30 percent less training data. This paper, in general, presents PINNs as a data-efficient, in power, high-accuracy solution to modeling and parameter estimation systems.