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NÔI DUNG CỦA PHẦN 1 BAO GỒM: • Definitions of Stability. • Types of Stability. • Angular Stability Analysis. • Operational Limits of Synchronous Operational Limits of Synchronous Machines.
eBook for You TRANSMISSION & DISTRIBUTION A Division of Global Power POWER SYSTEM STABILITY CALCULATION TRAINING D - Basic Day B i Principles Pi i l Prepared by: Peter Anderson • July 4, 2013 OUTLINE • Types T off Stability St bilit • Angular Stability Analysis • Operational Limits of Synchronous Machines eBook for You • Definitions of Stability BASIC PRINCIPLES Power System Stability: A power system at a given operating state is stable if following a given disturbance disturbance, or a set of disturbances disturbances, the system state stays within specified bounds and the system reaches a new stable equilibrium state within a specified ifi d period i d off titime Multi-faceted problem depending on: Time Span p of Interest Nature & Size of the Disturbance Physical Nature of any resulting Instability eBook for You What does it mean? BASIC PRINCIPLES Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a p g equilibrium q after being g subjected j to a state of operating physical disturbance, with most system variables bounded so that practically the entire system remains intact It is not necessary that the system regains the same steady state operating ti equilibrium ilib i as prior i to t the th disturbance di t b This Thi would ld be b the th case when e.g the disturbance has caused any power system component (line, generator, etc.) to trip Voltages and power flows will not be the same after the disturbance in such a case Most disturbances that are considered in stability analyses incur a change in system topology or structure It is important that the final steady state operating equilibrium after the fault is steady state acceptable Otherwise protections or control actions could introduce new disturbances that might influence the stability of the system Acceptable operating conditions must be clearly defined for the power system under study eBook for You Power System Stability: IEEE/CIGRE Working Group TYPES OF STABILITY Angular Stability Small Disturbances Large Disturbances Short Term Frequency Stability Short Term Long Term Voltage Stability Small Disturbances Large Disturbances Short Term Long Term eBook for You Power System Stability TYPICAL TIME SPANS Harmonics Power Flow Fault Currents eBook for You Long‐Term Stability Short‐Term Stability Stator Transients Resonance/Saturation Switching Lightning Time (s) Time (s) 1.E‐06 1.E‐03 1.E+00 1.E+03 ANGULAR STABILITY Large Disturbances (Transient Stability) Small Disturbances (Small-signal (Small signal or Dynamic Stability) eBook for You The ability of the Synchronous Machines within a Power System to remain In Synchronism following a disturbance FREQUENCY STABILITY Short-Term (Governor action) Long-Term (Turbines, Boilers, Nuclear Reactors) eBook for You The ability of the Synchronous Machines within ithi a P Power S System t tto restore t th the System S t Frequency to within an acceptable range following a disturbance At every node in the system, the “Actual Injected Reactive Power” is equal to the “Desired Injected Reactive Power” required to maintain the node voltage within acceptable t bl limits li it Local in nature since it is difficult to transport reactive power through the network (X>>R) Short-Term (1-5 s Induction motors, Electronically controlled loads, HVDC converters) Long-Term (10s-5 m Tap changers, Thermostatically controlled loads, Generation current limiters)) eBook for You VOLTAGE STABILITY 10 APPLICATION OF ANGULAR STABILITY ANALYSIS Disturbance STATE‐A' Corrective Actions STATE‐B State-A: Power Flow St t B P State-B: Power Fl Flow Transit from State-A to State-A State-A’:: Stability Analysis Transit from State-A’ to State-B: Stability Analysis eBook for You STATE‐A 11 SYNCHRONOUS MACHINES Single Phase Equivalent of a 3-phase Generator jXd U ~ eBook for You E I Im E jXd I jXd.I δ θ I Re U 12 SYNCHRONOUS MACHINES Power-Angle g Relationship p eBook for You E.U P= sin ∂ Xd 1.4 1.2 Power (pu) 0.8 0.6 04 0.4 0.2 0 30 60 90 Load Angle (deg) 120 150 180 13 STEADY STATE OPERATIONAL LIMITS STEADY-STATE Limiting Factors: Stator Current Thermal Limit Field Current Thermal Limit •Short Circuit Ratio (SCR≈1/Xd) R t A Rotor Angle l St Stability bilit Limit Li it •Dependent on Exciter Speed of Response eBook for You •Rated Current (1 (1.0 pu) 14 Xd = 2.0 pu SCR = 0.5 Power factor = 0.8 Exciter Slow‐Actingg Fast‐Acting No‐load Margin Full‐load Margin 35% 20% 20% 10% eBook for You OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS 15 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS 1.25 Q 0.75 0.5 0.25 P ‐0.25 ‐0.5 ‐0.75 ‐1 ‐1.25 1.25 0.25 0.5 0.75 1.25 eBook for You Stator Current Limit Irated = 1.0 pu Centre = 0 Centre = 0,0 Radius = 1.0 16 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS Q 0.75 05 0.5 0.25 P 0 IFrated = √{(0.5+0.6)2 1.36 = 1.36 Centre = 0,‐0.5 + 0.82} ‐0.25 ‐0.5 ‐0.75 ‐1 ‐1.25 0.25 0.5 0.75 1.25 eBook for You Field Current Limit IFrated = √{(SCR+sinθ)2 + cosθ2} Centre = ‐SCR Centre = 0,‐SCR Radius = IFrated 1.25 17 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS Lower Field Voltage = Less Stability Fast‐acting Exciter: NL Margin (NLM) = 0.2 FL Margin (FLM) = 0.1 Q 0.75 0.5 0.25 0 ‐0.25 Q = tanα * Pg ‐ (SCR‐NLM * cosθ) •tanα =tanβ‐NL M [0.258] •cosβ = 1/(1+FLM) [0.909, β = 1/(1+FLM) [0 909 β = 24.6⁰] = 24 6⁰] Q = ‐0.34 for Pg = 0 Q = 0.258*0.8‐(0.5‐0.2*0.8) = ‐0.134 for Pg=0.8 ‐0.5 ‐0.75 ‐1 ‐1.25 0.25 0.5 0.75 P 1.25 eBook for You Rotor Angle Stability Limit 18 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS Composite Operating Limits 1.25 Q 0.75 0.5 0.25 P 0 ‐0.25 ‐0.5 ‐0.75 ‐1 ‐1.25 0.25 0.5 0.75 1.25 eBook for You Limits are reduced by: Limits are reduced by: •High Xd/Low SCR •Slow Slow Exciter Exciter 19 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS Using MS‐Excel, construct the machine capability curve for the following generator: Rated MVA = 200 MVA Xd = Xd = 1.5 Rated power factor = 0.9 Using a Slow Exciter b Fast Exciter eBook for You Case Study 20 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS Case Study Rated MVA = 200 MVA/Xd = 1.5/Rated power factor = 0.9 / / REAL POWER ((MW) R 220 200 180 160 140 120 100 80 60 40 20 -100 100 -75 75 -50 50 -25 25 RATED MW 25 50 75 REACTIVE POWER (MVAR) 100 125 150 175 eBook for You 180MW Generator/Slow-Acting Exciter ... / REAL POWER ((MW) R 220 200 18 0 16 0 14 0 12 0 10 0 80 60 40 20 -10 0 10 0 -75 75 -50 50 -25 25 RATED MW 25 50 75 REACTIVE POWER (MVAR) 10 0 12 5 15 0 17 5 eBook for You 18 0MW Generator/Slow-Acting Exciter... 20% 20% 10 % eBook for You OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS 15 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS 1. 25 Q 0.75 0.5 0.25 P ‐0.25 ‐0.5 ‐0.75 ? ?1 ? ?1. 25 1. 25 0.25 0.5 0.75 1. 25... Q = 0.258*0.8‐(0.5‐0.2*0.8) = ‐0 .13 4 for Pg=0.8 ‐0.5 ‐0.75 ? ?1 ? ?1. 25 0.25 0.5 0.75 P 1. 25 eBook for You Rotor Angle Stability Limit 18 OPERATIONAL LIMITS FOR SYNCHRONOUS GENERATORS Composite Operating Limits 1. 25 Q 0.75