Comparative analysis of PID and fractional order PID controllers in automatic generation control process with coordinated control of TCSC

Abstract

The present work focuses on the power oscillation damping of an interconnected multi-area multi-source power system depicting the load fluctuations issue in reference frame of automatic generation control (AGC). In real-time, the load profile characteristic is un-deterministic and uncertain in nature. Therefore, a diverse perspective of area load profiles such as step load disturbance, pulse load perturbation, sinusoidal load pattern, random load pattern and uniformly distributed random load are taken into study. The investigated power system model is a two-area system, classified by reheat thermal, hydro and gas generating units, lumped together in a control area with the impacts of governor deadband and generation rate constraint. AGC performance work is propagated by proportional-integral-derivative (PID) controller with filter and, then, fractional order PID (FPID) controller. Also, a fast-acting thyristor controlled series compensator (TCSC) device modified by the Taylor theorem is incorporated as a damping controller to pursuit its significances in AGC tool. In an additional work, a lead-lag compensator block is also incorporated to the basic TCSC controller to show its impact on AGC. Sensitivity analysis of both the basic and the advanced TCSC damping controller is investigated under loading and model parameter variations. The design problem i.e., the constrained optimization problem is tuned by employing the quasi-oppositional harmony search (QOHS) algorithm. From the mathematical point of view, calculations eigenvalues, performance indices and transient parameters, and sensitivity analysis are presented in support of the designed TCSC-QOHS controller. Graphically, the simulation results are presented. The obtained simulation results showed that the realization of TCSC in series with the tie-line with the FPID controller can be an effective approach for the AGC tool.

Appendices

A.1 Nominal data for the studied two-area multi-source power system model [36]

System configuration:	$f = 60$ Hz,$P_{{r1}} = P_{{r2}} = 2000$ MW, ${\text{Total}}\,\,{\text{area}}\,\,{\text{load}} = 1740$ MW, Base rating = 2000 MW, Initial loading = 87%
For reheat turbine unit	$T_{{sg}} = 0.06$ s,$T_{t} = 0.3$ s,$K_{r} = 0.3,$ $T_{r} = 10.2$ s, $N_{1} = 0.8$, $N_{2} = \frac{{ - 0.2}}{\pi }$,$R_{{th}} = 2.4$ Hz/p.u.MW, $B_{1} = B_{2} = 0.4312$ p.u.MW/Hz, $PF_{{th}} = 0.543478$, $H = 5$ MWs/MVA, $D = 0.0145$ p.u.MW/Hz,$K_{{ps1}} = K_{{ps2}} = 68.9655$ Hz/p.u.MW, $T_{{ps1}} = T_{{ps2}} = 11.49$ s
For hydro turbine unit	$T_{{gh}} = 0.2$ s,$T_{{rs}} = 4.9$ s,$T_{{rh}} = 28.749$ s,$T_{w} = 1.1$ s,$R_{{hyd}} = 2.4$ Hz/p.u.MW,$PF_{{hyd}} = 0.326084$
For gas turbine unit	$B_{g} = 0.049$ s,$C_{g} = 1$,$X_{g} = 0.6$ s,$Y_{g} = 1.1$ s,$T_{{cr}} = 0.01$ s,$T_{f} = 0.239$ s,$T_{{cd}} = 0.2$ s,$R_{g} = 2.4$ Hz/p.u.MW, $PF_{g} = 0.130438$

A.2 Determination of power system parameters at different loading conditions

Rated capacity $P_{r} = 2000$ MW, nominal load $\Delta P_{L} = 1740$ MW, nominal frequency $f = 60$ Hz, inertia constant $H = 5$ MWs/MVA, regulation parameter $R = 2.4$ Hz/p.u.MW. Assuming a linear load frequency dependence relationship:

Frequency dependency parameter $D = \frac{{\partial P_{L} }}{{\partial f}} = \frac{{1740}}{{60}} = 29$ MW/Hz.

D in per unit (= D in p.u.MW/Hz/$P_{r} )$ = 29/2000 = 0.0145 p.u.MW/Hz.

Power system parameters: $T_{{ps}} = \frac{{2H}}{{\partial f \times D}} = \frac{{2 \times 5}}{{60 \times 0.0145}} = 11.49$ s.

$K_{{ps}} = \frac{1}{D} = \frac{1}{{0.0145}} = 68.96$ Hz/p.u.MW.

A.3 Data for TCSC controller [14]

With TCSC-IPSO [14]:	$K_{{TCSC}} = 0.1812$, $T_{{TCSC}} = 0.0060$ s
With TCSC-QOHS [Proposed]:	$K_{{TCSC}} = 2.9984$, $T_{{TCSC}} = 0.0590$ s
With advanced TCSC-QOHS [Proposed]:	$K_{{TCSC}} = 0.0598$, $T_{{TCSC}} = 1.3958$ s, $T_{1} = 1.1658$ s, $T_{3} = 0.9993$ s

A.4 Flowchart of QOHS algorithm [44]

See Fig. 15.

Fig. 15

Flowchart of the QOHS algorithm