Optimal Energy Management of an Off-Grid PV-Diesel System Using Hybrid Energy Storage and Battery Ramp-Rate Constraints

Abstract

This study presents a convex Quadratic Programming (QP) energy management strategy for an off-grid hybrid power system comprising a Photovoltaic (PV) generator, a Diesel Generator (DG), and a Hybrid Energy Storage System (HESS) consisting of a battery and a Supercapacitor (SC). The QP framework, solved using MATLAB's quadprog solver, minimizes diesel fuel consumption cost while satisfying the power balance, State-of-Charge (SOC) limits, and a battery ramp-rate constraint formulated as a full-matrix linear inequality and parameterized by a maximum ramp rate ( ). Two operational scenarios were investigated: a baseline dispatch without a ramp-rate limitation (Scenario 1) and a constrained dispatch with  = 0.25 kW/step (Scenario 2), simulated over a 12-hour window with a 20-second resolution (  = 2,160 steps). Results show that the ramp-rate constraint reduces the maximum battery ramp rate from 0.3950 to 0.2208 kW/step (a 44.1% reduction), whereas both scenarios converge to an identical fuel cost of $1.1917, confirming that battery stress reduction and economic optimality are fully compatible. A sensitivity analysis across six  values (0.15–0.40 kW/step) further confirms that the fuel cost remains invariant at $1.1917 across all tested levels, while peak battery power increases monotonically from 2.1877 kW to 2.3355 kW as  increases. These results demonstrate that the proposed QP framework effectively decouples battery dynamic stress from economic performance, providing a computationally tractable approach for practical off-grid energy management design.