Machine response
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The document discusses machine responses during system disturbances, particularly focusing on the frequency and voltage deviations caused by incidents like short circuits. It outlines the stages of the machine's response, including initial, primary, secondary, and final responses, highlighting the importance of quick recovery to ensure system reliability. Additionally, the concepts of kinetic energy, governor control, and the impact of dead band on system stability are examined.
Machine response
- 1. Machine Response During System Disturbances (By Sarath Chandrasiri) 1. System Disturbances: A system disturbance can be defined as any event that causes the frequency and/or voltage of the system to deviate from the normal range of operation. These are caused by incidents such as occurrence of short circuits, generator trips, feeder trips, sudden increase of power output of a generator due to a defect in its control system. The responses of the healthy machines for such events should be so as to return the system to the normal status as quickly as possible and with as little manual intervention as possible. Therefore, the response of machines is of utmost importance from the point of view of system security and reliability. Machine response to system disturbances: The response of machines should be considered from two main aspects. 1. Load- frequency response (Governor response) 2. MVAR – Voltage response (AVR response) Only the first will be considered below. 2. Load- frequency response (Governor response) The frequency and load response of a machine that remains connected to the system during the event is shown below: fdev_dyn= Dynamic frequency deviation Δf = Quasi steady state frequency deviation Machine Load t Page 1 f1 fdev_dyn 0 t1 t2 t3 t4 Δf t f B A
- 2. Fig 1 – Frequency variation of a machine after disturbance The response can be considered to be in 4 stages. i. Initial response ii. Primary response iii. Secondary response iv. Final stage due to manual action or automatic action through a power system controller. These will now be considered in detail. 3. Initial Response (period from t=0 to t=t1 sec) The initial response of the machine lasts between 0.5 to a few seconds depending on the speed of response of the machine governors and the system involved. In the case of the Bahrain system the initial response time duration is between 0.5 and 1 sec. This period occurs immediately after the incident and the response comes due to the kinetic energy of the GT rotor (GT + generator). The governor has not started responding yet. Since any governor, however fast, has a mechanical device (fuel control valve) as the final element, the response will be delayed due to the inertia of the mechanical parts. If the incident is due to a generation loss then the rest of the machines in the system make a contribution to compensate for the short fall. As given before, the governor has no time to respond and the opening of the fuel control valve remains unchanged during this period. Then from where does the energy required for the increased output of the generators come? It comes from the kinetic energy stored in the generator rotors. A contribution also comes from the rotating loads such as induction motors which is produced as a result a decrease in the KE stored in their rotors. The frequency of the system falls linearly during the period as the stored kinetic energy is converted to electrical energy. Telec = Opposing Torque of Generator Mover Tmech = Mechanical Torque of Prime Mover Mover SHAFT of Moment of Inertia I Page 2
- 3. FIG-2 To analyze the situation consider Fig-2, which gives the torques acting on the Machine shaft. Tnett =Tmech – Telec = I dω/dt where ωis the shaft angular speed in radians/sec. Under normal system conditions, Tnett = 0 as Tmech = Telec. Therefore, ω remains constant and consequently, the kinetic energy of the rotor remains constant. Before analyzing the behavior of the generator after the disturbance, occurs it is useful to consider some basic ideas. For ease of analysis, it is useful to consider the process to be consisting of 2 different periods: 1. Pre fault period (t<0) 2. Post fault period (t>0) The disturbance is considered to occur at the instant t = 0. Certain physical quantities remain constant as the pre-fault stage ends and the post fault stage begins while other quantities undergo an abrupt change (step change) at t=0. Physical quantities that do not undergo any step change at t=0: These are associated with energy. It is a physical principle that the energy of a system cannot be changed abruptly as this would mean that dE/dt (Power) is infinite. Thus the following quantities do not undergo step changes at t=0. a) Kinetic energy of the rotor b) Speed (and hence system frequency) c) The nett magnetic flux in the direct axis of the generator d) Mechanical torque produced by the GT. Physical quantities that undergo a step change at t=0: Some of these are as follows: a) Electrical power output of the generator b) Reverse torque generated by the generator. c) Generator terminal voltage and current Page 3
- 4. During this period Tnett < 0 as Tmech < Telec. Thus ω decreases linearly as shown below. is negative but constant. Tnett = I dω/dt dω/dt = Tnett/I (a constant) The shaft decelerates from a speed corresponding to the rated frequency of f Hz to one corresponding to f1 Hz. Storage of Kinetic Energy in the Rotor Due to its moment of inertia the rotor stores kinetic energy. KE energy stored in the rotor (EKE) = ½ I ω2 X 10-6 (MJ) The power available from the shaft can be obtained by differentiating the above. Rotor Power (EKE) = I ω . dω/dt X 10-6 MW As shown in the diagram below this power can flow both ways. • When the speed is decreasing the KE is converted to Electrical Power. • When the speed is increasing the Mechanical Power is converted to KE. When the system is considered as a whole the recovery process depends on the Kinetic energy of the Generating sets and the Motors connected as loads. Page 4 FIG-3
- 5. 4. The H-Constant It is useful to define a quantity called H which is directly proportional to the Moment of Inertia I of the rotor. If the f0 is the rated frequency in Hz (50 Hz) Pn the Rated Load in MW KE0 the Kinetic Energy of the rotor in MWs Then H=( KE0 / Pn) The advantage of using the H constant is that it is essentially independent of the generator size. Typical values of H lie in the range 2 to 8 sec. Initial rate of decrease of frequency = (df/dt)0 = ΔPf0/2H Thus the rate of drop of frequency will increase with decreasing H and increasing ΔP (pu). Therefore, it is advantageous to have a high H. 5. Primary Response (period from t= t1 to t=t3 sec) At the beginning of this period the fuel control valve starts to move, increasing its opening in response to the output signal from the governor (PRIMARY CONTROLLER), which increases in response to the drop in frequency. With the increased flow of fuel, the Mechanical Torque of the GT (Tmech) starts to increase and at point B on the graph in Fig -1 it Tmech becomes equal to Telec . Therefore at this point deceleration of the shaft ceases. The controller continues to increase its output signal and the shaft accelerates back to a speed corresponding to a freq of f2 Hz. However, the controller cannot bring the frequency back to f due to the droop of the control system, which is explained in the next section. During this period the primary controllers alter the power delivered by the generators until a balance is re-established between the load power and the generated power. The period is characterized by oscillatory phenomena due to the dynamic response of the controllers and the process. Dynamic Frequency Deviation (fdev_dyn): The magnitude of this (See Fig-1) depends on the following: • The magnitude of the disturbance Page 5
- 6. • KE of rotating machines in the system • The primary controller reserve of all generators • Dynamic characteristics of the machines (including controllers) • Dynamic characteristics of the loads, particularly the self regulating effect loads. Quasi Steady State Frequency Deviation (Δf): The magnitude of this (See Fig-1) depends on the following: The magnitude of the disturbance Power – frequency characteristic of the system 6. Secondary Response (period from to t=t3 to t4 sec) During this period, the generator operates at a steady frequency of f2 Hz, which is less than the rated frequency Δf = (f-f2) H z. The magnitude of Δf depends on the Speed Droop of the governor. Speed Droop: The steady state Load vs. frequency characteristic of the governor system has a drooping characteristic, which is built in to achieve stable operation of the generators ting in parallel. FIG-4 The interpretation of the above speed droops is as follows: Page 6
- 7. If the machine is operating initially at 50% load and a frequency of 50 Hz and a disturbance occurs, which causes a steady state drop of frequency by 0.5 % (0.25 Hz), then the steady state load rise would be, • 10% if the droop was 5% and • 25% if the droop was 2%. In general the droop SG of a generator is defined as follows: Under steady state (secondary response) conditions, Δ PG = The change in load due to Primary Control action PGn = Rated Load Δf = The change in frequency that is necessary for the Primary Controller to produce the above load change f0= Rated frequency Then, SG = (-Δf / f0) / (Δ PG / PGn) in % The – sign takes care of the fact that a negative Δf produces a positive Δ PG and vice versa, provided the Primary Control Reserve has not been completely used up (see below). FIG-5 The contribution of a generator to a system disturbance depends mainly upon • The Droop • The Primary Control Reserve Referring to FIG-5, in case of a minor disturbance (frequency offset < ΔfB ) the contribution of generator a (which has the controller with a smaller droop) will be greater than that of generator b which has the controller with the smaller droop. Page 7 fA fB fN PMAX fN = Rated Freq
- 8. In case of a major disturbance (frequency offset > ΔfB ), the contributions of both generators to PRIMARY CONTROL under quasi – steady-state conditions will be equal. The operation of the system though stable in terms of frequency and voltage is not acceptable for an extended period as the above parameters would be out of their normal range. It is also undesirable from the point of view of power flow in the tie lines (if there are any) as the actual active and reactive power flows are different from the specified levels. Furthermore, since the system frequency and voltage are lower than rated there is a possibility that those of the system stability will be lost if another disturbance occurs. Due to these reasons it is necessary to restore the frequency and voltage to rated levels as soon as possible. This can be done manually or through a power system controller. In the secondary response period the governor load set points are adjusted by the operators to bring the system frequency back to normal. Final Response: 7. Dead Band: Usually there is a provision in the governor control system to introduce a dead band. The dead band makes the controller insensitive to small band of frequency changes (Ex 0.1 Hz) around the rated frequency. The dead band serves the following purposes: • Immunity to power system noise: If the GT is is only to play a stabilizing role when large frequency deviations occur, the dead band can be switched on to obtain some insensitivity to frequency. The governor would not react to frequency deviations adjustable over a range of ±0.5 Hz from the set point frequency. The dead band functions only when the machine is on load. • In interconnected systems, where a stable system frequency with very narrow tolerances (± 0.05 Hz) and closely defined cross border tie line power between subsystems are required the dead band merely suppresses the power system noise. • Lower thermal loading of the turbine blades: Turbine blades are highly susceptible to temperature gradients. Therefore, the dead band provides a way of suppressing constant changes of turbine inlet temperature to some extent. This prolongs the life of the blades. • Compressor surges: The dead band also has the effect of keeping the operating point away from the point at which the compressor surge protection starts to operate. Page 8
- 9. Prepared by K. A. Chandrasiri Senior General Engineer Office of the Director of Electricity Production Page 9
- 10. References: Electrical Energy Systems Theory by Olle L. Elgerd Transient Processes in Electrical Systems by V. Venikov Page 10