*Article* **Direct Power Compensation in AC Distribution Networks with SCES Systems via PI-PBC Approach**

### **Walter Gil-González 1,\*, Federico Martin Serra 2, Oscar Danilo Montoya 1,3, Carlos Alberto Ramírez 4 and César Orozco-Henao 5**


Received: 18 February 2020; Accepted: 3 April 2020; Published: 23 April 2020

**Abstract:** Here, we explore the possibility of employing proportional-integral passivity-based control (PI-PBC) to support active and reactive power in alternating current (AC) distribution networks by using a supercapacitor energy storage system. A direct power control approach is proposed by taking advantage of the Park's reference frame transform direct and quadrature currents (*id* and *iq*) into active and reactive powers (*p* and *q*). Based on the open-loop Hamiltonian model of the system, we propose a closed-loop PI-PBC controller that takes advantage of Lyapunov's stability to design a global tracking controller. Numerical simulations in MATLAB/Simulink demonstrate the efficiency and robustness of the proposed controller, especially for parametric uncertainties.

**Keywords:** distribution networks; direct power control; global tracking controller; passivity-based control; supercapacitor energy storage system
