A maximum power point algorithm using the Lagrange method

The maximum power transfer problem is posed as a constrained optimization problem and the well-known Lagrange method is employed to address it in case of some simple circuits including a photovoltaic cell. In graphical terms, the maximum power point (MPP) is the point of tangency between the isopower contours and the source curve. For the example of a photovoltaic cell a Seidel type iteration is also suggested. A brief mathematical treatment of its convergence and uniqueness of the solution is given along with numerical simulations performed using MATLAB. This new algorithm lends itself to the implementation of the Lagrange MPP tracker (LMPPT). To show its working, the Solarex module MSX-60 is chosen and a simple buck-boost converter circuit is simulated with PSIM software. The terminal current, voltage and power are displayed showing the accuracy and the reliability of the proposed method under varying load and irradiance conditions.

► The Lagrange method is employed to find the maximum power point.
► A Seidel type iteration method is used to develop the algorithm.
► Uniqueness of the solution and convergence of the algorithm are mathematically shown.
► A Lagrange maximum power point tracker (LMPPT) is simulated using PSIM and MATLAB.