Impacts of wind farms with multi-terminal HVDC system in frequency regulation using quasi-opposition pathfinder algorithm

Abstract

As new technology is evolving and wind energy penetration is increasing in the grid integrated power system, the research of system frequency stabilization is becoming increasingly vital. This is due to variable-speed wind turbine stochastic behaviour, which results in unmanageable wind power and unexpected load demand. The frequency control services provided by a wind farm connected via a high voltage direct current link are analyzed in this article. The two-area power system is used as a test system to evaluate the power system's dynamic performance. Reheat thermal, hydro, gas, nuclear plant, and wind farm connected via the HVDC system are in the test system. Significant restrictions such as time delay, governor dead-band, and generation rate constraint are included in the load frequency control study. Using a HVDC system, the impacts of wind farms is studied in LFC system. The suggested method uses LFC to account for the wind farm's inertia and droop technique. The gain parameters of the proportional-integral-derivative controller are optimised using three optimization techniques for the LFC model design i.e., a quasi-opposition pathfinder algorithm, moth-flame optimization algorithm, and water cycle algorithm. QOPFA is determined to be more successful in the LFC problem in the study. Moreover, the improved results clearly demonstrate the significance of wind farm, reflecting a better system dynamics.

Appendix

1.1 System data (Tavakoli et al. 2018b )

$$\begin{gathered} {\text{System}}\;{\text{configuration}}:\;f = 60{\text{Hz}},{\text{P}}_{r1} = {\text{P}}_{r2} = 2000{\text{MW}},\;{\text{Total}}\;{\text{area}}\;{\text{load}} = 1740{\text{MW}},\;{\text{Base}}\;{\text{rating}} = 2000{\text{MW}}, \hfill \\ {\text{Initailloading}} = 87\% \hfill \\ \end{gathered}$$

$$\begin{gathered} {\text{For}}\,{\text{reheat}}\,{\text{turbine}}\,{\text{unit}}:\,T_{{sg}} = 0.06\,\sec ,\,T_{t} = 0.3\,\sec ,\,K_{r} = 0.3,\,T_{r} = 10.2\sec ,\,N_{1} = 0.8,\,N_{2} = \frac{{ - 0.2}}{\pi },\,R_{{{\text{th}}}} = 2.4\, \hfill \\ {\text{Hz/p.u.MW}},\,B_{1} = B_{2} = 0.4312\,{\text{p.u.MW/Hz}},\,H = 5\,{\text{MWsec/MVA}},\,D = 0.0145\, \hfill \\ {\text{p.uMW/Hz}},\,K_{{ps1}} = K_{{ps2}} = 68.9655\,{\text{Hz/p.u.MW}},\,T_{{ps1}} = T_{{ps2}} = 11.49\,\sec \hfill \\ \end{gathered}$$

$${\text{For}}\;{\text{hydroturbine}}\;{\text{unit}}:\;T_{gh} = 0.2\sec ,\;T_{rs} = 4.9\sec ,\;T_{rh} = 28.749\sec ,\;T_{w} = 1.1\sec ,\;R_{hyd} = 2.4{\text{Hz/p}}.{\text{u}}.{\text{MW}}$$

$$\begin{gathered} {\text{For}}\;{\text{gasturbine}}\;{\text{unit}}:\;B_{g} = 0.049\sec ,C_{g} = 1,\;X_{g} = 0.6\sec ,\;Y_{g} = 1.1\sec ,\;T_{cr} = 0.01\sec ,\;T_{f} = 0.239\sec , \hfill \\ T_{cd} = 0.2\sec ,\;R_{g} = 2.4{\text{Hz/p}}.{\text{u}}.{\text{MW}}. \hfill \\ \end{gathered}$$

$${\text{Wind}}\;{\text{Farm}}\quad T_{wT} = 1.5\sec ,\;k = 10.38,\;K_{DC} = 1.0,\;T_{DC} = 0.2\sec ,T_{HVDC} = 0.7\sec$$

$${\text{Participation}}\;{\text{factor}}\quad PF_{th} = 0.4347,\;PF_{hyd} = 0.25,\;PF_{g} = 0.130438,\;PF_{n} = 0.076084,\;PF_{wf} = 0.108778$$

1.2 System data calculation

Rated capacity P_r = 2000 MW, nominal load ΔP_L = 1740 MW, nominal frequency f = 60HZ, inertia constant H = 5 MWs/MVA, regulation parameter R = 2.4HZ/p.u.MW. Assuming a linear load frequency dependence relationship:

$${\text{Frequency}}\;{\text{dependence}}\;{\text{parameter}}\quad D = \frac{{\partial P_{L} }}{\partial f} = \frac{1740}{{60}} = 29{\text{MW/Hz}}$$

$$D\;i{\text{n}}\;{\text{per}}\;{\text{unit(}} = {\text{D in p}}.{\text{u}}.{\text{MW/Hz/P}}_{{\text{r}}} )\; = \;29/2000 = 0.0145{\text{p}}.{\text{u}}.{\text{MW/Hz}}$$

$${\text{Power}}\;{\text{system}}\;{\text{parameter}}:\;\begin{array}{*{20}c} {T_{ps} = \frac{2H}{{\partial f \times D}} = \;\frac{2 \times 5}{{60 \times 0.0145}} = \;11.49\sec } \\ {K_{ps} = \;\frac{1}{D}\; = \;\frac{1}{0.0145} = 68.96{\text{Hz/p}}.{\text{u}}.{\text{MW}}} \\ \end{array}$$