Microgrid Optimal Scheduling

Particle Swarm Optimization (PSO) is a stochastic optimization algorithm rooted in computational mathematics that operates on swarm intelligence principles to identify global optima of functions. The algorithm mimics the foraging behavior of bird flocks, where each individual represents a particle that continuously adjusts its velocity and position to converge toward optimal solutions. This approach has found extensive applications across diverse domains including engineering optimization, image processing, and data mining. Key implementation aspects include initializing a population of particles with random positions and velocities within search boundaries. Each particle's fitness is evaluated using an objective function (e.g., cost minimization in microgrid scheduling). The algorithm maintains personal best (pbest) and global best (gbest) positions, updating particle velocities through the formula: v_i(t+1) = w*v_i(t) + c1*r1*(pbest_i - x_i(t)) + c2*r2*(gbest - x_i(t)), where w represents inertia weight, c1/c2 are acceleration coefficients, and r1/r2 generate random values. Position updates follow x_i(t+1) = x_i(t) + v_i(t+1). Convergence is achieved through iterative updates until stopping criteria (e.g., maximum iterations or fitness threshold) are met. Practical implementations often incorporate boundary handling mechanisms and velocity clamping to ensure stability.