Frequency Stability of Isolated Hydropower Plant with Surge Tank Under Different Turbine Control Modes

Abstract

Currently, the Thoma criterion is often violated to diminish the cross-section of the surge tank; therefore, the surge fluctuation is aggravated and the frequency stability becomes more deteriorative. The focus of this article is on stabilizing the low-frequency oscillation of an isolated hydropower plant caused by surge fluctuation. From a new perspective of hydropower plant operation mode, frequency stability under power control is investigated and compared with frequency control by adopting the Hurwitz criterion and numerical simulation. In a theoretical derivation, the governor equations of frequency control and power control are introduced to the mathematical model. For numerical simulation, a governor model with a control mode switch-over function is built. The frequency oscillations under frequency control, power control, and control mode switch-over are simulated and investigated, respectively, with different governor parameters and operation cases. The result shows that the power control has a better performance on frequency stability at the expense of rapidity compared with the frequency control. Other recommendations regarding worst operation cases and choice of control modes are also developed.

Keywords:

• frequency control
• frequency stability
• Hurwitz criterion
• hydropower plant
• low-frequency oscillation
• numerical simulation
• isolated operation
• power control
• surge tank
• turbine governor parameter

APPENDIX A. LIST OF SYMBOLS

• is the discharge of draw-water tunnel,

• is the discharge of turbine,

• is the rotation speed of turbine,

• is the guide vane opening,

• is the dynamic moment of turbine,

• is the braking moment of generator,

• is the power of hydroelectric generating unit,

• is the given power of hydroelectric generating unit, and

• is relative change value of water level in surge tank.

The symbols above are all relative values (per unit values), and symbols with subscript 0 stand for initial value.

• △Z is the absolute change value of water level in the surge tank;

• H₀ is the net head of turbine;

• h_yo is the head loss of the draw-water tunnel;

• T_wy is the water inertia time constant of the draw-water tunnel;

• is the surge tank time constant;

• F is the cross-section area of the surge tank;

• T_a is the generating unit inertia time constant;

• e_h, e_x, and e_y are the moment transmission coefficients of the turbine;

• e_qh, e_qx, and e_qy are the discharge transmission coefficients of the turbine;

• eg is the characteristic coefficient of the power grid load; and

• K_p, K_i, K_d, T_y, b_p, and e_p are the governor parameters, which are shown in Figure 3.

APPENDIX B. DETAILS OF THE ENGINEERING CASE

• Rated power of the generating unit: 610 MW;

• Rated water head of the generating unit: 288.0 m;

• Rated discharge of the generating unit: 228.6 m³/s;

• Rated rotation speed of the generating unit: 166.7 r/min;

• Length of the draw-water tunnel: 16,662.16 m;

• T_wy of the draw-water tunnel: 23.88 sec;

• T_w of the penstock: 1.35 sec;

• Head loss: 15.67 m;

• Equivalent section area of the draw-water tunnel: 113.10 m²;

• Inertia time constant of the generating unit (T_a): 9.46 sec;

• Length of the penstock: 513.34 m;

• Other governor parameters: K_d = 0, T_y = 0.02, b_p = 0.04, e_p = 0.04, and E_f = E_y = E_p = 0;

• Characteristic coefficient of power grid load: e_g = 0.0;

• Transmission coefficient of the ideal turbine: e_h = 1.5, e_x = –1,e_y = 1, e_qh = 0.5, e_qx = 0, and e_qy = 1;

• Cross-sectional area of the surge tank (F): 415.64 m²;

• Thoma critical section area for stability (F_th): 416.08 m².

APPENDIX C. SYMBOLS IN SECTION 3.1

(1) Symbols in Eqs. (9(9) –10(10) )—frequency control:

(2) Symbols in Eq. (15)(15) —power control:

Additional information

Notes on contributors

Weijia Yang

Weijia Yang received his B.S. and M.S. from the School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China, in 2011 and 2013, respectively. He is currently pursuing his Ph.D. at the Division of Electricity, Department of Engineering Sciences, Uppsala University, Uppsala, Sweden. He is a young professional member of the International Association for Hydro-Environment Engineering and Research (IAHR). His research interests include transient process and stability of HPPs and interactions between HPP and power systems.

Jiandong Yang

Jiandong Yang received his B.S., M.S., and Ph.D. from the former Wuhan University of Hydraulic and Electrical Engineering (currently part of Wuhan University), Wuhan, China, in 1982, 1984, and 1988, respectively. He became a lecturer in 1988, an associate professor in 1990, and a full professor in 1991 in hydropower engineering at Wuhan University of Hydraulic and Electrical Engineering. During 1992–1993, he was a senior visiting scholar in Michigan State University, MI, USA. Presently, he is a professor in the School of Water Resources and Hydropower Engineering at Wuhan University. His research interests are transient process of HPPs and pumped storage plants, transient gas–liquid two-phase flow, and three-dimensional flow field numerical simulation in HPP.

Wencheng Guo

Wencheng Guo received his B.S. and M.S. in 2011 and 2013, respectively, from the School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China, where he is currently working toward his Ph.D. His research interests include hydraulic turbine regulation, transient processes, and physical model experiments for hydraulic, mechanical, and power coupling systems.

Per Norrlund

Per Norrlund received his M.S. in 2000 in engineering physics and his Ph.D. in 2005 in numerical analysis from the Department of Information Technology, Uppsala University, Uppsala, Sweden. Currently, he is a senior research engineer in Vattenfall AB and a researcher at Division of Electricity, Department of Engineering Sciences, Uppsala University. His work and research interests include hydraulic surge, torsional turbine shaft oscillations, frequency control, and discharge measurements in HPPs.