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A Nonlinear Controller for Parallel DC-DC Converters with ZIP Load and Constrained Output Voltage

Somayyeh Bahrami

TL;DR

The paper addresses voltage regulation and current sharing in islanded DC microgrids where ZIP loads introduce strong nonlinearity and uncertainties. It advances a barrier-function-based adaptive backstepping controller that enforces voltage constraints through an invertible barrier transformation and identifies uncertain parameters online, without needing measurements of the DC input voltages. The approach yields global stability and accurate power sharing, demonstrated by simulations with four DGUs where the bus voltage remains within a tight band despite large load variations. This method improves robustness and reduces sensor requirements, making it practical for scalable, high-power DC microgrid implementations.

Abstract

In this paper, an adaptive nonlinear controller is designed for a parallel DC-DC converter system that feeds an unknown ZIP load, characterized by constant impedance (Z), constant current (I), and constant power (P), at the DC bus. The proposed controller ensures simultaneous voltage adjustment and power sharing in the large signal sense despite uncertainties in ZIP loads, DC input voltages, and other electrical parameters. To keep the output voltage within a desired range, we utilize a barrier function that is invertible, smoothly continuous, and strictly increasing. Its limits at infinity represent the upper and lower bounds for the output voltage. We apply the invertible transformation of the barrier function to the output voltage and then design the controller using the adaptive backstepping method. Using this barrier-function-based adaptive backstepping controller, uncertain parameters are identified on-line, and the voltage adjustment and power sharing objectives are established. Moreover, voltage constraint is not violated event in the presence of sudden and unknown large variations of load. The efficiency of the proposed nonlinear controller is evaluated through simulations of a parallel DC-DC converter system using the MATLAB/Simscape Electrical environment.

A Nonlinear Controller for Parallel DC-DC Converters with ZIP Load and Constrained Output Voltage

TL;DR

The paper addresses voltage regulation and current sharing in islanded DC microgrids where ZIP loads introduce strong nonlinearity and uncertainties. It advances a barrier-function-based adaptive backstepping controller that enforces voltage constraints through an invertible barrier transformation and identifies uncertain parameters online, without needing measurements of the DC input voltages. The approach yields global stability and accurate power sharing, demonstrated by simulations with four DGUs where the bus voltage remains within a tight band despite large load variations. This method improves robustness and reduces sensor requirements, making it practical for scalable, high-power DC microgrid implementations.

Abstract

In this paper, an adaptive nonlinear controller is designed for a parallel DC-DC converter system that feeds an unknown ZIP load, characterized by constant impedance (Z), constant current (I), and constant power (P), at the DC bus. The proposed controller ensures simultaneous voltage adjustment and power sharing in the large signal sense despite uncertainties in ZIP loads, DC input voltages, and other electrical parameters. To keep the output voltage within a desired range, we utilize a barrier function that is invertible, smoothly continuous, and strictly increasing. Its limits at infinity represent the upper and lower bounds for the output voltage. We apply the invertible transformation of the barrier function to the output voltage and then design the controller using the adaptive backstepping method. Using this barrier-function-based adaptive backstepping controller, uncertain parameters are identified on-line, and the voltage adjustment and power sharing objectives are established. Moreover, voltage constraint is not violated event in the presence of sudden and unknown large variations of load. The efficiency of the proposed nonlinear controller is evaluated through simulations of a parallel DC-DC converter system using the MATLAB/Simscape Electrical environment.
Paper Structure (10 sections, 1 theorem, 33 equations, 4 figures, 2 tables)

This paper contains 10 sections, 1 theorem, 33 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. problem formulation
  3. DC microgrid dynamics
  4. Control objective
  5. Control Design
  6. Barrier-function-based transformation
  7. First step of backstepping design
  8. Second step of backstepping design
  9. Simulation Results
  10. Conclusion

Key Result

Theorem 1

Consider the closed-loop system consisting of the dynamics (z22), (42ppiti) and ( 32ppiti1), the control laws (x2ref), (nu_final), and (uii) for $i=1,...,n-1$ and the adaptation laws (adtet), (adap2), (adap3), (adap4), (adap5) and (adap6) for $i=1,...,n$. With the gains $\kappa_{1}$ and $\kappa_{2}$

Figures (4)

  • Figure 1: Electrical scheme of a typical DC microgrid system
  • Figure 2: Topology of the test DC system.
  • Figure 3: (a) Load voltage and (b) Load current. Z and I loads are disconnected at $t=0.2~s$, P-load changes at $t=0.4~s$ from $120~W$ to $240~W$, and then changes at $t=0.6~s$ from $240~W$ to $120~W$.
  • Figure 4: Output currents of the converters and their estimations. Z and I loads are disconnected at $t=0.2~s$, P-load changes at $t=0.4~s$ from $120~W$ to $240~W$, and then changes at $t=0.6~s$ from $240~W$ to $120~W$.

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • Remark 2