In this study, a speed sensorless control method is proposed for a photovoltaic water-pump system operating under variable atmospheric conditions. The developed system not only continuously determines the maximum power point of the photovoltaic system but also generates a reference speed appropriate for each power value produced. The MATLAB/Simulink model of the driver system incorporates Adaptive Power Control, Direct Torque Control, a 3-phase induction motor, and the power plant. The determination of the maximum power point of the photovoltaic system and the input reference speed information for the Direct Torque Control under varying atmospheric conditions is accomplished through the application of the Adaptive Power Control algorithm. Notably, the control process operates as a closed-loop system without the requirement of a speed sensor. Instead, the Extended Kalman–Bucy estimator is employed for speed estimation. Empirical evaluation of the proposed method was conducted under constant temperature conditions and varying irradiance values. The results clearly illustrate the consistent operation of the motor, with a constant torque production aligned with each identified maximum power point corresponding to distinct irradiance levels. The control system demonstrates robust performance and operational efficiency across the entire range of operating points. The efficacy of the Kalman estimator in monitoring the reference speed, the utilization of a single solar radiation sensor, and the successful implementation of sensorless operation are significant advantages of the developed adaptive approach. The demonstrated performance of the proposed system showcases its potential for enhancing the efficient and reliable control of photovoltaic water-pump systems in real-world applications.