EE 451 Power System Stability Power system operates in synchronous mode Power system is subjected to a wide range of disturbances (small and large) - Loads and generation changes - Network changes - Faults and outages of equipment Hence, the stability of the power system will be affected. Power system stability involves the study of the dynamics of the power system under disturbances.
From the classical point of view, power system instability can be seen as loss of synchronism (i.e., some synchronous machines going out of step)when the system is subjected to a particular disturbance. CIGRE-IEEE Def. of Power System Stability: Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact. Stability involves study of dynamics of the system about an equilibrium-initial operating condition.
Power system is highly non-linear system Stability study study of non-linear dynamics of large system. Stability (can be defined only in terms of) Initial operating condition Nature and magnitude of disturbance Def. applies to an interconnected power system as a whole. Most of the time we are interested in stability of a particular generator or a group of generators In our study we will focus on: 1- Steady-State Stability 2- Transient Stability
Steady state stability of power systems results from gradual system changes. Example: Gradual load increase as in the addition of MW at load terminals or in gradual load decrease, as in steam change at the prime mover power. Power systems in general and alternators in particular have steady state stability limit beyond which if subjected to gradual load changes will loss steady state stability. The power system is capable to resist the changes that occurs after the disturbance and hence remain in stable form that is capable of maintain equilibrium. Example of sudden system changes (Transient Stability) are: Fault occurrences, autoreclosure schemes, energization process of a T.L. and de-energization of a T.L.
Recalling some definitions: - Steady state stability is the ability of the power system network to remain or to stay in equilibrium following a gradual system change. - Steady state stability limit is the maximum power transfer of that system without loss of equilibrium. Machines (Generator / Motor) T m T e T e T m Turbin P f Generator P O P S P i P l
P i : Input power to alternator (Generator) (i.e. mechanical power input) P O : Output power from alternator (Generator) (i.e. electrical power input) P f : Internal generated field power P S : Mechanical losses due to (friction etc) P l : Electrical stator losses Turbin P f Generator P O P S P i P l Power balanced equation for generator P f = P i - P S (1) P O = P f - P l (2) From (1) & (2) P O = P i - P S - P l Power balanced under equilibrium state
Synchronous Motor P e Motor \ P f \ P l \ P S P m From (1) & (2) under equilibrium (1) & (2)
I- Generator feeding an Inductive load: Z s s I - E 0 Inductive Load V - (1) Internal field power is: S f = P f + jq f = ExI * ExI * = Substituting for, the angle
i.e. for large turbo-alternators: Therefore: and the power angle diagram will be: P fmax P f 0
Generator output Power P O Take V as a reference, Substituting the complementary of the impedance angle The power output from the generator is given as: Since is generally a small angle for large turbo-alternator At, P O = P max
P max is the steady-state stability limit of the alternator P O (MW) Margin for safety operation P max P f P 0 Load angle
II- Alternator Feeding an Infinite Bus System: Infinite bus means: 1- Voltage is constant 2- Frequency is constant 3- Internal Impedance is zero P O Infinite Bus P O = P O (MW) P max P O 0 Load angle
III- Two Machine System: I E g V M E m E g = V + I Z g E m = V + I Z m Generator power Motor power
If is small then steady state stability limit: P gmax = Where = - P m max is the load angle P Pg max -Pm max
IV- Transmission System: E S T1 T X 2 l E r X S X r V S V r Assumption: Ignore system resistance and consider system reactance only. System power transfer (point to point) is: P =
Power transfer between individual components: At stability limit: P max = Where X t : is known as the system transfer reactance. P P max Power angle diagram for transmission network
Improvement of steady state stability limit 1- Improving excitation system 2- Reduce system transfer reactance 3- Parallel circuit arrangement 4- Series Compensation