Fractional Order Fuzzy Control of Hybrid Power System with Renewable Generation Using Chaotic PSO

Indranil Pan; Saptarshi Das

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Fractional Order Fuzzy Control of Hybrid Power System with Renewable Generation Using Chaotic PSO

Indranil Pan, Saptarshi Das

arXiv:1611.09809v1Nov 29, 2016eess.SYcs.AImath.OCnlin.CD

TL;DR

Hybrid renewable systems must coordinate fluctuating generation, demand, and storage to limit grid-frequency deviations. The paper introduces a centralized fractional-order fuzzy PID controller tuned by chaotic PSO, and reports better performance and robustness than PID and fuzzy PID under the tested operating conditions.

Problem
Stochastic renewable generation and changing demand create grid-frequency deviations and power-quality challenges that require coordinated control of hybrid generation and storage.
Method
A centralized fractional-order fuzzy PID controller is tuned with chaotic PSO using stochastic realizations and a time-domain objective that also limits actuator-control variations.
Results
The fractional-order fuzzy controller performs better than PID and integer-order fuzzy PID and shows stronger robustness to parameter variation and rate-constraint nonlinearity.
Takeaways & Limitations
Centralized fractional-order fuzzy control is reported as a suitable approach for coordinating hybrid-system storage and generation under stochastic operating conditions.
Takeaways & Limitations
The simulations use typical fixed values M = 0.4 and D = 0.03 for the equivalent inertia and damping constants.

Abstract

from arXiv · show

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants.

1. Introduction

The paper addresses frequency and power-quality challenges caused by stochastic renewable generation and changing demand in hybrid systems. It proposes a centralized fractional-order fuzzy controller whose parameters are tuned using chaotic PSO.

Motivation: Wind and solar generation vary with weather, creating periods when electrical demand exceeds renewable supply.Battery, flywheel, and ultra-capacitor storage can mitigate these generation–load imbalances.
Motivation: Storage devices absorb surplus renewable power and release it when demand exceeds generation, requiring coordinated control.Such coordination also supports power quality and grid-frequency stability.
Related control approaches: Fractional-calculus-based control offers additional flexibility and superior design performance compared with conventional integer-order approaches.The paper situates fractional-order intelligent control within broader applications including process control and computational intelligence.
Proposed approach: The proposed controller regulates grid-frequency deviation by commanding storage devices to absorb or release power and the diesel engine to provide short-term bursts.It is evaluated against standard PID and fuzzy PID controllers, using one centralized structure for the overall hybrid system.
Parameter optimization: Chaotic PSO tunes controller parameters by optimizing a noisy time-domain performance metric produced by stochastic wind, solar, and load fluctuations.The approach targets control design in noisy and dynamic environments where gradient-based methods may be less suitable.
Evaluation: The paper compares three controller structures and examines their performance and robustness under system-parameter variation and rate-constraint nonlinearity.The study separately describes the hybrid system, fractional-order fuzzy control, chaotic-map PSO variants, and controller comparisons.

2. Description of the hybrid power system with renewable generation

The modeled hybrid power system combines renewable and conventional generation with multiple storage devices, while stochastic models represent fluctuating power and demand. A centralized controller acts through the storage feedback loop to reduce grid-frequency deviation.

Generation subsystems: The hybrid system includes wind-turbine, solar, fuel-cell, diesel-engine, and aqua-electrolyzer subsystems, with nominal component parameters listed in Table 1.The aqua-electrolyzer uses renewable power to produce hydrogen for fuel-cell generation.
Generation subsystems: Small-signal models represent the wind turbine, solar plant, fuel cell, and diesel engine with transfer functions and associated gains and time constants.The component models are identified as equations (1)–(4).
Aqua-electrolyzer: The aqua-electrolyzer transfer function models hydrogen production from a fraction of combined wind and solar power for subsequent use by two fuel cells.Its renewable-power allocation is parameterized by K_n, with K_n = 0.6 stated for the model.
Energy storage and control: The flywheel, battery, and ultra-capacitor are connected in the feedback loop and absorb or release energy according to surplus or deficit power.They are actuated by the fractional-order fuzzy controller, whose incremental control action reduces grid-frequency oscillation.
Frequency model: The grid-frequency model relates frequency deviation to net power deviation through system inertia and damping, using M = 0.4 and D = 0.03 in simulation.The model is given as equation (10).
Stochastic power model: Renewable generation and demand are modeled with deterministic mean values, stochastic fluctuations, low-pass dynamics, normalization constants, and time-dependent mean shifts.The general template defines P as power output, φ as the stochastic component, β as the mean-value contribution, and Γ as the switching signal.
Stochastic power model: Figure 2 illustrates stochastic generated and demand powers with base-value jumps at 40 sec and 80 sec, independently of the feedback controller.These jumps represent sudden large changes in power at different times.

3. Fractional order fuzzy controller

The controller extends fuzzy PID control with fractional-order differ-integration, while rational approximations make the fractional elements practical to implement. Its fuzzy logic uses error-related inputs, linguistic rules, scaling factors, and defuzzification to produce the control output.

3.1. Basics of fractional calculus: Fractional calculus permits the differ-integration order to take any real value rather than only integer values.
3.2. Hybridization of fuzzy PID and fractional order control: The fuzzy FOPID controller uses error and fractional-rate information to generate an FLC output through a defined rule base and membership functions.The linguistic variables range from Negative Large to Positive Large, and center-of-gravity defuzzification determines the crisp output.
3.2. Hybridization of fuzzy PID and fractional order control: Each fractional-order differ-integral is continuously rationalized during optimization using Oustaloup’s fifth-order approximation.The approximation is implemented as a band-limited recursive filter for practical controller realization.
3.2. Hybridization of fuzzy PID and fractional order control: The fractional controller includes differ-integration order α and an analog-filter order represented by (2N+1), with a fifth-order Oustaloup approximation over 10^-2 to 10^2 rad/sec.

4. Control objectives and optimization based tuning of the fuzzy FOPID controller parameters

Controller tuning minimizes a weighted time-domain objective that combines frequency-deviation error with control-signal deviation. Particle swarm optimization searches the controller-parameter space, while Henon and logistic chaotic maps modify random-number generation to improve search behavior.

4.1. Optimization strategy for dynamically changing objective functions: The optimization objective integrates squared grid-frequency deviation and squared deviation of the controller output from its steady-state value over 120 seconds.Equal weights are assigned to the two terms, and the steady-state control signal changes after generation or load switching.
4.1. Optimization strategy for dynamically changing objective functions: Stochastic generation and load make controller tuning a dynamic optimization problem whose objective function changes across realizations.
4.2. Chaotic map adapted particle swarm optimization: PSO updates each particle’s position and velocity using inertia, cognitive learning, and social learning terms while tracking individual and swarm-best positions.Particles search an n-dimensional space for the minimum of the objective function.
4.2. Chaotic map adapted particle swarm optimization: The implementation uses 30 particles and 300 generations, with inertia weight α decreasing linearly from 0.9 to 0.1.The cognitive and social learning rates are user-specified, with values stated as 0.5 and 1, respectively.

5. Results and discussions

Under stochastic renewable-generation and load conditions, the chaotic-PSO-tuned fuzzy FOPID controller provides the strongest nominal performance and robustness among the compared structures. Henon-map PSO is especially effective for fuzzy-controller tuning, while the fuzzy FOPID also reduces control-signal oscillations and remains superior under UC perturbations.

Nominal performance: Henon-map PSO achieves the best minimum objective for fuzzy PID and fuzzy FOPID tuning, while converging faster than the Logistic-map version.For PID tuning, the three PSO variants reach the same minimum, but Logistic-map PSO requires fewer iterations.
Nominal performance: The fuzzy FOPID controller produces a narrower control-signal oscillation band than PID and fuzzy PID, although frequency-deviation curves are difficult to distinguish visually.Lower control-signal oscillation is relevant because the signal actuates mechanical components including FESS, BESS, and DEG.
Nominal performance: The UC contributes the maximum power among the energy-storing or supplying components, followed by FESS, BESS, DEG, and FC.Positive FC and DEG powers indicate generation, whereas negative FESS, BESS, and UC powers indicate energy storage.
Robustness: Under 30% and 50% increases and decreases in UC gain and time constant, fuzzy FOPID consistently keeps ISE and ISDCO lower than PID and fuzzy PID.The UC is the highest-share feedback component, making its parameter variation a severe robustness test.
Robustness: Fuzzy FOPID outperforms PID and fuzzy PID in every perturbed UC case, although its nominal-case performance gain is relatively smaller.Its improvement over fuzzy PID is small but remains positive for all UC parameter perturbations.

I I I ISE ISDCO J k DEG FESS BESS

Disconnecting FESS, BESS, or DEG worsens frequency-oscillation suppression and controller-effort measures, with FESS disconnection having the greatest impact. Across these cases, PID performs worst, fuzzy PID performs better, and fuzzy FOPID performs best.

Robustness against component disconnection: Fuzzy FOPID has the best load-rejection ISE and controller-effort ISDCO, while PID has the worst performance across component-disconnection cases.Fuzzy PID lies between the traditional PID and fuzzy FOPID structures.
Robustness against component disconnection: Disconnecting FESS causes the largest performance deterioration, followed by BESS and DEG.The comparison uses separate disconnection cases for DEG, FESS, and BESS against the nominal system.

6. Effect of nonlinear operation of the energy storing/producing elements in the feedback path

The study tests controllers tuned on linear models under rate-constraint nonlinearities in feedback storage and generation elements. Fuzzy FOPID shows the strongest robustness among the compared controller structures.

Rate constraints restrict how quickly FESS, BESS, UC, and DEG components can store or release power, representing realistic operating limits.The nonlinearity is implemented through upper and lower bounds on component power rates.
0.02 FESS Ṗ <, 0.005 BESS Ṗ <, 1.2 UC Ṗ <, and 0.001 DEG Ṗ < define the tested rate constraints.Controllers were tuned for linear operation before applying these constraints.
Fuzzy FOPID produces the smallest increase in the cost function among the three controller structures under nonlinear rate constraints.The comparison is reported in Figure 11.
Figure 12 compares linear and nonlinear rate-constrained operation and again reports a better objective-function value for fuzzy FOPID.The figure evaluates deviations between the two operating conditions for the storage elements.

7. Discussion

The discussion emphasizes robustness of fractional-order fuzzy controllers despite linear-model tuning, while noting that more advanced alternatives and greater hardware complexity remain relevant considerations.

The controllers were initially tuned using linear models, then tested with rate-constraint nonlinearities representing more realistic component operation.The optimization approach is described as generic and applicable to other process nonlinearities.
Fractional-order fuzzy controllers retain robustness to parametric uncertainties, component disconnection, and rate-constraint nonlinearities.This robustness is attributed to the presence of fuzzy logic in the FO controller.
Model predictive control and sliding mode control could potentially outperform PID for this hybrid power system, but were not used in the comparison.PID serves as a benchmark for traditionally accepted industrial practice.
Fuzzy controller designs offer relative performance improvements over PID at the cost of more complicated designs and more expensive implementation hardware.The discussion leaves the improvement-versus-hardware trade-off to the system designer.

8. Conclusions

The paper proposes centralized fuzzy FOPID control for hybrid-system frequency oscillations, with parameters tuned by chaotic-map-adapted PSO. It reports better performance and robustness than PID and fuzzy PID structures.

The proposed centralized fuzzy FOPID controller suppresses grid-frequency oscillations in the hybrid power system.Centralization is associated with reduced maintenance, wiring, cost, and number of parameters to tune.
Chaotic-map-adapted PSO algorithms tune the fuzzy FOPID parameters and achieve faster convergence and better solution quality than traditional PSO.
Fuzzy FOPID outperforms PID and fuzzy PID controller structures in the reported comparisons.The comparison covers linear and nonlinear operating regimes.
The controller shows robustness to UC parameter variation, nonlinear feedback rate constraints, and disconnection of some components.The paper suggests nominal tuning may avoid additional retuning in these perturbed cases.