Principle of Operation of Turbine Generator – Electricity Generation

Most of nuclear power plants operates a single-shaft turbine-generator that consists of one multi-stage HP turbine and three parallel multi-stage LP turbines, a main generator and an exciter.  HP Turbine is usually double-flow impulse turbine (or reaction type) with about 10 stages with shrouded blades and produces about 30-40% of the gross power output of the power plant unit. LP turbines are usually double-flow reaction turbines with about 5-8 stages (with shrouded blades and with free-standing blades of last 3 stages). LP turbines produce approximately 60-70% of the gross power output of the power plant unit. Each turbine rotor is mounted on two bearings, i.e. there are double bearings between each turbine module.
Steam turbine of typical 3000MWth PWR

Schema of a steam turbine of a typical 3000MWth PWR.

From Steam Generator to Main Steam Lines – Evaporation

Steam Generator - vertical

Steam Generator – vertical

The power conversion system of typical PWR begins in the steam generators in their shell sides. Steam generators are heat exchangers used to convert feedwater into steam from heat produced in a nuclear reactor core. The feedwater (secondary circuit) is heated from ~230°C 500°F (preheated fluid by regenerators) to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Heat is transferred through the walls of these tubes to the lower pressure secondary coolant located on the secondary side of the exchanger where the coolant evaporates to pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa). The saturated steam leaves the steam generator through a steam outlet and continues to the main steam lines and further to the steam turbine.

Steam Generator to Main Steam LinesThese main steam lines are cross-tied (e.g. via steam collector pipe) near the turbine to ensure that the pressure difference between any of the steam generators does not exceed specific value thus maintaining system balance and ensuring uniform heat removal from the Reactor Coolant System (RCS). The steam flows through the main steam line isolation valves (MSIVs), which are very important from safety point of view, to the high pressure turbine. Directly at the inlet of the steam turbine, there are throttle-stop valves and control valves. Turbine control is achieved by varying these turbine valves openings. In the event of a turbine trip, the steam supply must be isolated very quickly, usually in the fraction of a second, so the stop valves must operate quickly and reliably.

Steam Generator - vertical

Steam Generator – vertical

Calculate the amount of primary coolant, which is required to evaporate 1 kg of feedwater in a typical steam generator. Assume that there are no energy losses, this is only idealized example.

Balance of the primary circuit

The hot primary coolant (water 330°C; 626°F; 16MPa) is pumped into the steam generator through primary inlet. The primary coolant leaves (water 295°C; 563°F; 16MPa) the steam generator through primary outlet.

hI, inlet = 1516 kJ/kg

=> ΔhI = -206 kJ/kg

hI, outlet = 1310 kJ/kg

Balance of the feedwater

Steam generator - counterflow heat exchanger

Temperature gradients in typical PWR steam generator.

The feedwater (water 230°C; 446°F; 6,5MPa) is pumped into the steam generator through the feedwater inlet. The feedwater (secondary circuit) is heated from ~230°C 446°F to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Feedwater is then evaporated and the pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa) leaves the steam generator through steam outlet and continues to the steam turbine.

hII, inlet = 991 kJ/kg

=> ΔhII = 1789 kJ/kg

hII, outlet = 2780 kJ/kg

Balance of the steam generator

Since the difference in specific enthalpies is less for primary coolant than for feedwater, it is obvious that the amount of primary coolant will be higher than 1kg. To produce of 1 kg of saturated steam from feedwater, about 1789/206 x 1 kg =  8.68 kg of primary coolant is required.

Rankine Cycle - Ts Diagram

Rankine Cycle – Ts Diagram

Isobaric heat addition (in a heat exchanger – boiler) – In this phase (between state 2 and state 3) there is a constant-pressure heat transfer to the liquid condensate from an external source, since the chamber is open to flow in and out.  The feedwater (secondary circuit) is heated from to the boiling point (2 → 3a) of that fluid and then evaporated in the boiler (3a → 3). The net heat added is given by Qadd = H3 - H2

From Turbine Valves to Condenser – Expansion

Rankine Cycle - Ts diagram

Rankine cycle – Ts diagram

Typically most of nuclear power plants operates multi-stage condensing steam turbines. In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C) from a steam generator and exhaust it to moisture separator-reheater (MSR – point D). The steam must be reheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. High content of water droplets can cause the rapid impingement and erosion of the blades which occurs when condensed water is blasted onto the blades. To prevent this, condensate drains are installed in the steam piping leading to the turbine. The moisture-free steam is superheated by extraction steam from the high-pressure stage of turbine and by steam directly from the main steam lines.

Source: TVO – Olkiluoto 3 NPP www.tvo.fi/uploads/julkaisut/tiedostot/ydinvoimalayks_OL3_ENG.pdf

Source: TVO – Olkiluoto 3 NPP www.tvo.fi/uploads/julkaisut/tiedostot/ydinvoimalayks_OL3_ENG.pdf

The heating steam is condensed in the tubes and is drained to the feedwater system. The reheater heats the steam (point D) and then the steam is directed to the low-pressure stage of steam turbine, where expands (point E to F). The exhausted steam then condenses in the condenser and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa), and is in a partially condensed state (point F), typically of a quality near 90%. High pressure and low pressure stages of the turbine are usually on the same shaft to drive a common generator, but they have separate cases. The main generator produces electrical power, which is supplied to the electrical grid.

Wet Steam Turbine - Expansion

A high-pressure stage of steam turbine operates at steady state with inlet conditions of  6 MPa, t = 275.6°C, x = 1 (point C). Steam leaves this stage of turbine at a pressure of 1.15 MPa, 186°C and x = 0.87 (point D). Calculate the enthalpy difference (the work done by HP Turbine) between these two states.

The enthalpy for the state C can be picked directly from steam tables, whereas the enthalpy for the state D must be calculated using vapor quality:

h1, wet = 2785 kJ/kg

h2, wet = h2,s x + (1 – x ) h2,l  = 2782 . 0.87 + (1 – 0.87) . 790 = 2420 + 103 = 2523 kJ/kg

Δh = 262 kJ/kg = WHP

Rankine Cycle - Ts Diagram

Rankine Cycle – Ts Diagram

Isentropic expansion (expansion in a steam turbine) – Steam from the boiler expands adiabatically from state 3 to state 4 in a steam turbine to produce work and then is discharged to the condenser (partially condensed). The steam does work on the surroundings (blades of the turbine) and loses an amount of enthalpy equal to the work that leaves the system. The work done by turbine is given by WT = H4 – H3. Again the entropy remains unchanged.

From Condenser to Condensate Pumps – Condensation

Condenser - LP Heaters - DeaeratorThe main condenser condenses the exhaust steam from the low-pressure stages of the main turbine and also from the steam dump system. The exhausted steam is condensed by passing over tubes containing water from the cooling system.

The pressure inside condenser is given by the ambient air temperature (i.e. temperature of water in the cooling system) and by steam ejectors or vacuum pumps, which pull the gases (non-condensibles) from the surface condenser and eject them to the atmosphere.

The lowest feasible condenser pressure is the saturation pressure corresponding to the ambient temperature (e.g. absolute pressure of 0.008 MPa, which corresponds to 41.5°C). Note that, there is always a temperature difference between (around ΔT = 14°C) the condenser temperature and the ambient temperature, which originates from finite size and efficiency of condensers. Since neither the condenser is 100% efficient heat exchanger, there is always a temperature difference between the saturation temperature (secondary side) and the temperature of the coolant in the cooling system. Moreover, there is a design inefficiciency, which decreases the overall efficiency of the turbine. Ideally the steam exhausted into the condenser would have no subcooling. But real condensers are designed to subcool the liquid by a few degrees of Celsius in order to avoid the suction cavitation in the condensate pumps. But, this subcooling increases the inefficiency of the cycle, because more energy is needed to reheat the water.

Rankine Cycle - condenser pressure

Decreasing the turbine exhaust pressure increases the net work per cycle but also decreses the vapor quality of outlet steam.

The goal of maintaining the lowest practical turbine exhaust pressure is a primary reason for including the condenser in a thermal power plant. The condenser provides a vacuum that maximizes the energy extracted from the steam, resulting in a significant increase in net work and thermal efficiency. But also this parameter (condenser pressure) has its engineering limits:

  • Decreasing the turbine exhaust pressure decreases the vapor quality (or dryness fraction). At some point the expansion must be ended to avoid damages that could be caused to blades of steam turbine by low quality steam.
  • Decreasing the turbine exhaust pressure significantly increases the specific volume of exhausted steam, which requires huge blades in last rows of low-pressure stage of the steam turbine.

In a typical wet steam turbine, the exhausted steam condenses in the condenser and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa, which corresponds to 41.5°C). This steam is in a partially condensed state (point F), typically of a quality near 90%. Note that, the pressure inside the condenser is also dependent on the ambient atmospheric conditions:

  • air temperature, pressure and humidity in case of cooling into the atmosphere
  • water temperature and the flow rate in case of cooling into a river or sea

An increase in the ambient temperature causes a proportional increase in pressure of exhausted steam (ΔT = 14°C is usually a constant) hence the thermal efficiency of the power conversion system decreases. In other words, the electrical output of a power plant may vary with ambient conditions, while the thermal power remains constant.

The condensed steam (now called condensate) is collected in the condenser’s hotwell. Condenser’s hotwell provides also a water storage capacity, which is required for operational purposes such as feedwater makeup. The condensate (saturated or slightly subcooled liquid) is delivered to the condensate pump and then pumped by condensate pumps to the deaerator through feedwater heating system. The condensate pumps increase the pressure usually to about p = 1-2 MPa. There are usually four one-third-capacity centrifugal condensate pumps with common suction and discharge headers. Three pumps are normally in operation with one in the backup.

Isobaric heat rejection (in a heat exchanger) – In this phase the cycle completes by a constant-pressure process in which heat is rejected from the partially condensed steam. There is heat transfer from the vapor to cooling water flowing in a cooling circuit. The vapor condenses and the temperature of the cooling water increases. The net heat rejected is given by Qre = H4 - H1

From Condensate Pumps to Feedwater Pumps – Heat Regeneration

Condenser - LP Heaters - DeaeratorThe condensate from condensate pumps then passes through several stages of low pressure feedwater heaters, in which the temperature of the condensate is increased by heat transfer from steam extracted from the low pressure turbines. There are usually three or four stages of low pressure feedwater heaters connected in the cascade. The condensate exits the low pressure feedwater heaters at approximately p = 1 MPa, t = 150°C and enters the deaerator. The main condensate system also contains a mechanical condensate purification system for removing impurities. The feedwater heaters are self-regulating. It means that the greater the flow of feedwater the greater the rate of heat absorption from the steam and the greater the flow of extraction steam.

There are non-return valves in the extraction steam lines between the feedwater heaters and turbine. These non-return valves prevent the reverse steam or water flow in case of turbine trip, which causes rapid decrease in the pressure inside the turbine. Any water entering the turbine in this way could cause severe damage to the turbine blading.

The process of heat regeneration significantly increases the thermal efficiency of steam turbine by reducing the amount of fuel that must be added in the boiler. This process is known as heat regeneration and a variety of heat regenerators can be used for this purpose. Sometimes engineers use the term economiser that are heat exchangers intended to reduce energy consumption, especially in case of preheating of a fluid. On the other hand, the process of draining steam from the turbine at certain point of its expansion and using this steam for heating the feedwater supplied to the boiler is known as bleeding and it must be noted, a small amount of work, WT, is lost by the turbine.

As can be seen in the article “Steam Generator”, the feedwater (secondary circuit) at the inlet of the steam generator may have about ~230°C (446°F) and then is heated to the boiling point of that fluid (280°C; 536°F; 6,5MPa) and evaporated. But the condensate at the condenser outlet may have about 40°C, so the heat regeneration in typical PWR is significant and very important:

  • Heat regeneration increases the thermal efficiency, since more of the heat flow into the cycle occurs at higher temperature.
  • Heat regeneration causes a decrease in the mass flow rate especially through low-pressure stages of the steam turbine, hence the LP Isentropic Turbine Efficiency increases. Note that at the last stage of expansion the steam has very high specific volume, which requires large blades of the last stage.
  • Heat regeneration causes an increases in working steam quality, since the drains are situated at the periphery of turbine casing, where is higher concentration of water droplets. Improved turbine drainage implies less problems with erosion of blades.

Deaerator

Deaerator

A schematic diagram of a typical tray-type deaerator. Source: wikipedia.org License: CC BY-SA 3.0

In general, a deaerator is a device that is used for the removal of oxygen and other dissolved gases from the feedwater to steam generators. The deaerator is part of the feedwater heating system. It is usually situated between the last low pressure heater and feedwater booster pumps. In particular, dissolved oxygen in the steam generator can cause serious corrosion damage by attaching to the walls of metal piping and other metallic equipment and forming oxides (rust). Furthermore, dissolved carbon dioxide combines with water to form carbonic acid that causes further corrosion.

In the deaerator, the condensate is heated to saturated conditions usually by the steam extracted from the steam turbine. The extraction steam are mixed in the deaerator by a system of spray nozzles and cascading trays between which the steam percolates. Any dissolved gases in the condensate are released in this process and removed from the deaerator by venting to the atmosphere or to the main condenser. Directly below the deaerator is the feedwater storage tank, in which a large quantity of feedwater is stored at near saturation conditions. In the turbine trip event, this feedwater can be supplied to steam generators to maintain the required water inventory during transient. The deaerator and the storage tank is usually located at a high elevation in the turbine hall to ensure an adequate net positive suction head (NPSH) at the inlet to the feedwater pumps. NPSH is used to measure how close a fluid is to saturated conditions. Lowering the pressure at the suction side can induce cavitation. This arrangement minimizes the risk of cavitation in the pump.

From Feedwater Pumps to Steam Generator

Feedwater Pumps - HP HeatersThe system of feedwater pumps usually contains of three parallel lines (3×50%) of feedwater pumps with common suction and discharge headers. Each feedwater pump consist of the booster and the main feedwater pump. The feedwater pumps (usually driven by steam turbines) increase the pressure of the condensate (~1MPa) to the pressure in the steam generator (~6.5MPa).

The booster pumps provide the required main feedwater pump suction pressure. These pumps (both feedwater pumps) are normally high pressure pumps (usually of the centrifugal pump type) that take suction from the deaerator water storage tank, which is mounted directly below the deaerator, and supply the main feedwater pumps. The water discharge from the feedwater pumps flows through the high pressure feedwater heaters, enters the containment and then flows into the steam generators.

Feedwater flow to each steam generator is controlled by feedwater regulating valves (FRVs) in each feedwater line. The regulator is controlled automatically by steam generator level, steam flow and feedwater flow.

The high pressure feedwater heaters are heated by extraction steam from the high pressure turbine, HP Turbine. Drains from the high-pressure feedwater heaters are usually routed to the deaerator.

Steam Generator - vertical

Steam Generator – vertical

The feedwater (water 230°C; 446°F; 6,5MPa) is pumped into the steam generator through the feedwater inlet. In the steam generator is the feedwater (secondary circuit) heated from ~230°C 446°F to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Feedwater is then evaporated and the pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa) leaves the steam generator through steam outlet and continues to the steam turbine, thereby completing the cycle.

Isentropic compression (compression in centrifugal pumps) – The liquid condensate is compressed adiabatically from state 1 to state 2 by centrifugal pumps (usually by condensate pumps and then by feedwater pumps). The liquid condensate is pumped from the condenser into the higher pressure boiler. In this process, the surroundings do work on the fluid, increasing its enthalpy (h = u+pv) and compressing it (increasing its pressure). On the other hand the entropy remains unchanged. The work required for the compressor is given by WPumps = H2 – H1.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.