Thermal (Steam) Power Plant

Methods of improving performance of a steam power plant

The efficiency of a Rankine (steam) cycle is $\eta = 1 - \dfrac{T_{\text{low}}}{T_{m,\text{in}}}$ roughly, so it improves by raising the mean temperature of heat addition $T_{m}$ or lowering the temperature of heat rejection. Common methods:

1. Increasing boiler (steam) pressure - raises the saturation temperature at which heat is added.
2. Superheating the steam (higher turbine inlet temperature) - raises mean temperature of heat addition and dryness at exhaust.
3. Reducing condenser pressure (better vacuum) - lowers heat rejection temperature.
4. Reheating - steam partly expanded in HP turbine is reheated in the boiler and expanded in LP turbine.
5. Regenerative feed water heating - steam bled from the turbine heats the feed water in feed water heaters.
6. Using economiser and air preheater - recover heat from flue gases.
7. Supercritical / binary vapour and combined cycles - use very high pressure, or a topping cycle (gas turbine) whose waste heat runs the steam cycle.
8. Reducing losses: better turbine blading, insulation, reduced throttling.

How reheating increases efficiency

               1
  +----------+----->+------+     +------+
  |  Boiler  |      |  HP  |=====|  LP  |===> Generator
  |  + S/H   |  2   | turb |     | turb |
  | Reheater |<-----+------+  +->+------+
  |          |------------3---+     | 4
  +----------+                      v
       ^ 6                    +-----------+
       |      +------+   5    | Condenser |
       +------| Pump |<-------+-----------+
              +------+

In a reheat cycle the steam leaving the boiler (state 1) expands in the HP turbine only up to an intermediate pressure (state 2). It is taken back to the reheater in the boiler and heated at constant pressure to nearly the original temperature (state 3). It then expands in the LP turbine to condenser pressure (state 4).

How reheating increases efficiency and output:

• Higher mean temperature of heat addition: heat added in reheating (2-3) is at a high temperature. If the reheat pressure is chosen properly (about 20-25% of boiler pressure), the average temperature at which heat is supplied rises, so $\eta$ rises by about 4-5%.
• More work per kg of steam: the expansion 3-4 lies to the right of the original expansion line, so the specific work output increases. The steam consumption (kg/kWh) falls and the plant output for the same boiler size increases.
• Drier exhaust steam: without reheat, expansion from high pressure ends in very wet steam (dryness below 0.85). Reheat gives exhaust dryness about 0.9 or more, which reduces blade erosion and friction loss, so the turbine internal efficiency improves.
• It makes very high boiler pressures usable, which is itself a means of raising efficiency.

Cycle efficiency with reheat:

$$\eta = \frac{(h_1 - h_2) + (h_3 - h_4) - W_p}{(h_1 - h_6) + (h_3 - h_2)}$$

Limitations: extra cost of reheater, piping and controls; useful only for large units (above about 100 MW) and high pressures.

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

In an impulse turbine the whole pressure drop of a stage occurs in fixed nozzles, and the high-velocity jet only changes direction on the moving blades. In a reaction turbine the pressure drops in both the fixed and moving blades, so the moving blades are also pushed by the reaction of the steam accelerating through them.

Degree of reaction $R = \dfrac{\Delta h_{\text{moving}}}{\Delta h_{\text{stage}}}$ is 0 for a pure impulse stage and usually 0.5 for a Parsons (50% reaction) stage. Large modern turbines use impulse stages at the HP end and reaction stages in the IP/LP parts.

Assumptions: ideal regenerative Rankine cycle with one open feed water heater; turbine and pumps isentropic; exit of heater is saturated liquid at 400 kPa; pump work included. Property values are taken from the steam tables (IAPWS-IF97 values, as in Cengel/Rogers-Mayhew tables).

              1
  +--------+------>+---------------+   +-----+
  | Boiler |       |    Turbine    |===| Gen |
  |  + S/H |       +---------------+   +-----+
  +--------+          | m kg (2)  | (1-m) kg (3)
      ^ 7             v           v
      |         +-----------+ +-----------+
  +--------+  6 |  Open FWH | | Condenser |
  | Pump 2 |<---| (mixing)  | +-----------+
  +--------+    +-----------+       | 4
                      ^ 5           |
                 +--------+         |
                 | Pump 1 |<--------+
                 +--------+

Steam table data

At 4 MPa, 400 C (superheated): $h_1 = 3214.4$ kJ/kg, $s_1 = 6.7712$ kJ/kg K.

State 2 (bled steam, 400 kPa, $s_2 = s_1$)

$$\begin{aligned} x_2 &= \frac{6.7712 - 1.7766}{5.1188} = 0.9757 \\ h_2 &= 604.72 + 0.9757 \times 2133.33 = 2686.3\ \text{kJ/kg} \end{aligned}$$

State 3 (exhaust, 10 kPa, $s_3 = s_1$)

$$\begin{aligned} x_3 &= \frac{6.7712 - 0.6492}{7.4997} = 0.8163 \\ h_3 &= 191.81 + 0.8163 \times 2392.07 = 2144.5\ \text{kJ/kg} \end{aligned}$$

Pumps

$$\begin{aligned} W_{p1} &= v_f (p_5 - p_4) = 0.001010(400 - 10) = 0.39\ \text{kJ/kg} \\ h_5 &= 191.81 + 0.39 = 192.21\ \text{kJ/kg} \\ W_{p2} &= 0.001084(4000 - 400) = 3.90\ \text{kJ/kg} \\ h_7 &= h_6 + W_{p2} = 604.72 + 3.90 = 608.62\ \text{kJ/kg} \end{aligned}$$

Bled steam fraction (energy balance on open FWH)

$m h_2 + (1-m) h_5 = h_6$:

$$m = \frac{h_6 - h_5}{h_2 - h_5} = \frac{604.72 - 192.21}{2686.3 - 192.21} = 0.1654\ \text{kg/kg}$$

Work and heat (per kg of steam at boiler exit)

$$\begin{aligned} W_T &= (h_1 - h_2) + (1-m)(h_2 - h_3) \\ &= 528.1 + 0.8346 \times 541.8 = 980.3\ \text{kJ/kg} \\ W_P &= (1-m) W_{p1} + W_{p2} = 0.33 + 3.90 = 4.23\ \text{kJ/kg} \\ W_{net} &= 980.3 - 4.23 = 976.1\ \text{kJ/kg} \\ Q_s &= h_1 - h_7 = 3214.4 - 608.62 = 2605.7\ \text{kJ/kg} \end{aligned}$$

Cycle efficiency

$$\eta = \frac{W_{net}}{Q_s} = \frac{976.1}{2605.7} = 0.3746$$

Answer: cycle efficiency $\approx 37.5\%$ (bled fraction $m = 0.165$ kg per kg of steam).

  T
  ^                    1
  |                   /|
  |      f----------g  |
  |     /              |
  |    7               |
  |    6 . . . . . . . 2  bleed (m kg)
  |   /                |
  |  5                 |
  |  4-----------------3  (1-m) kg
  +-------------------------> s
  4-5 pump 1, 5 and 2 mix in FWH -> 6,
  6-7 pump 2, 7-f-g-1 boiler,
  1-2-3 turbine, 3-4 condenser

For comparison, a simple Rankine cycle between the same limits gives about 35.3%, so one open heater raises the efficiency by about 2 percentage points.

Methods of improving performance of a steam power plant

The efficiency of a Rankine (steam) cycle is $\eta = 1 - \dfrac{T_{\text{low}}}{T_{m,\text{in}}}$ roughly, so it improves by raising the mean temperature of heat addition $T_{m}$ or lowering the temperature of heat rejection. Common methods:

1. Increasing boiler (steam) pressure - raises the saturation temperature at which heat is added.
2. Superheating the steam (higher turbine inlet temperature) - raises mean temperature of heat addition and dryness at exhaust.
3. Reducing condenser pressure (better vacuum) - lowers heat rejection temperature.
4. Reheating - steam partly expanded in HP turbine is reheated in the boiler and expanded in LP turbine.
5. Regenerative feed water heating - steam bled from the turbine heats the feed water in feed water heaters.
6. Using economiser and air preheater - recover heat from flue gases.
7. Supercritical / binary vapour and combined cycles - use very high pressure, or a topping cycle (gas turbine) whose waste heat runs the steam cycle.
8. Reducing losses: better turbine blading, insulation, reduced throttling.

How regeneration increases efficiency

              1
  +--------+------>+---------------+   +-----+
  | Boiler |       |    Turbine    |===| Gen |
  |  + S/H |       +---------------+   +-----+
  +--------+          | m kg (2)  | (1-m) kg (3)
      ^ 7             v           v
      |         +-----------+ +-----------+
  +--------+  6 |  Open FWH | | Condenser |
  | Pump 2 |<---| (mixing)  | +-----------+
  +--------+    +-----------+       | 4
                      ^ 5           |
                 +--------+         |
                 | Pump 1 |<--------+
                 +--------+

Regeneration means heating the feed water, before it enters the boiler, with steam bled (extracted) from the turbine at one or more intermediate stages.

In the simple Rankine cycle the cold feed water (about 40 C) enters the boiler and is heated by the hot flue gases over a large temperature range. This low-temperature part of heat addition lowers the mean temperature of heat addition and so lowers efficiency.

In the regenerative cycle a fraction $m$ kg of steam per kg is bled from the turbine at state 2 and used to heat the feed water in a feed water heater (FWH). The remaining $(1-m)$ kg expands to the condenser.

Why efficiency increases:

• The feed water enters the boiler hotter (state 7 instead of 5), so the heat supplied in the boiler falls from $(h_1 - h_5)$ to $(h_1 - h_7)$, and all of it is added at a higher mean temperature. In the limit (infinite heaters) the cycle approaches the Carnot efficiency.
• The latent heat of the bled steam is not rejected in the condenser; it is returned to the feed water. Heat rejected per kg of boiler steam is only $(1-m)(h_3 - h_4)$.
• Work output per kg falls slightly (bled steam does not expand fully), but heat supplied falls more, so the ratio $W/Q$ rises (typically by 10-15% with several heaters).
• Other benefits: less thermal stress in the boiler, smaller condenser and LP blade height (less steam flow at the exhaust), deaeration in an open heater.

Efficiency (one open heater):

$$\eta = \frac{(h_1 - h_2) + (1-m)(h_2 - h_3) - W_p}{h_1 - h_7}, \qquad m = \frac{h_6 - h_5}{h_2 - h_5}$$

  T
  ^                    1
  |                   /|
  |      f----------g  |
  |     /              |
  |    7               |
  |    6 . . . . . . . 2  bleed (m kg)
  |   /                |
  |  5                 |
  |  4-----------------3  (1-m) kg
  +-------------------------> s
  4-5 pump 1, 5 and 2 mix in FWH -> 6,
  6-7 pump 2, 7-f-g-1 boiler,
  1-2-3 turbine, 3-4 condenser

Main components of a steam turbine power plant

A steam (thermal) power plant works on the Rankine cycle. Its main parts are:

                superheated steam (1)
  +---------------+ -------------> +---------+   +-----+
  | Boiler        |                | Steam   |===| Gen |
  | (furnace,     |                | turbine |   +-----+
  |  economiser,  |                +---------+
  |  superheater) |                     | exhaust (2)
  +---------------+                     v
     ^   ^   |                    +-----------+
 fuel| air|  v flue gas           | Condenser |<--cooling
     |   |  chimney               +-----------+   water
     |                                  | condensate (3)
     |  feed water (4)  +-----------+   |
     +------------------| Feed pump |<--+
                        +-----------+

• Boiler (steam generator): burns coal/oil/gas and converts feed water into high-pressure steam. Includes furnace, water walls, drum, superheater, reheater, economiser (heats feed water by flue gas) and air preheater.
• Steam turbine: expands steam and converts its heat energy into shaft work; drives the alternator (generator).
• Condenser: condenses exhaust steam under vacuum using cooling water; the low back pressure increases turbine work. Cooling water is cooled in a cooling tower or taken from a river.
• Feed pump (with condensate pump): returns the condensate to boiler pressure, usually through feed water heaters (regeneration).
• Fuel and ash handling, draught system (FD/ID fans), chimney, ESP/dust collector.
• Water treatment plant for make-up water.

How reheating increases efficiency

In a reheat cycle the steam leaving the boiler (state 1) expands in the HP turbine only up to an intermediate pressure (state 2). It is taken back to the reheater in the boiler and heated at constant pressure to nearly the original temperature (state 3). It then expands in the LP turbine to condenser pressure (state 4).

How reheating increases efficiency and output:

• Higher mean temperature of heat addition: heat added in reheating (2-3) is at a high temperature. If the reheat pressure is chosen properly (about 20-25% of boiler pressure), the average temperature at which heat is supplied rises, so $\eta$ rises by about 4-5%.
• More work per kg of steam: the expansion 3-4 lies to the right of the original expansion line, so the specific work output increases. The steam consumption (kg/kWh) falls and the plant output for the same boiler size increases.
• Drier exhaust steam: without reheat, expansion from high pressure ends in very wet steam (dryness below 0.85). Reheat gives exhaust dryness about 0.9 or more, which reduces blade erosion and friction loss, so the turbine internal efficiency improves.
• It makes very high boiler pressures usable, which is itself a means of raising efficiency.

Cycle efficiency with reheat:

$$\eta = \frac{(h_1 - h_2) + (h_3 - h_4) - W_p}{(h_1 - h_6) + (h_3 - h_2)}$$

Limitations: extra cost of reheater, piping and controls; useful only for large units (above about 100 MW) and high pressures.

Layout and T-s diagram of reheat cycle

               1
  +----------+----->+------+     +------+
  |  Boiler  |      |  HP  |=====|  LP  |===> Generator
  |  + S/H   |  2   | turb |     | turb |
  | Reheater |<-----+------+  +->+------+
  |          |------------3---+     | 4
  +----------+                      v
       ^ 6                    +-----------+
       |      +------+   5    | Condenser |
       +------| Pump |<-------+-----------+
              +------+

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

Main components of a steam turbine power plant

A steam (thermal) power plant works on the Rankine cycle. Its main parts are:

                superheated steam (1)
  +---------------+ -------------> +---------+   +-----+
  | Boiler        |                | Steam   |===| Gen |
  | (furnace,     |                | turbine |   +-----+
  |  economiser,  |                +---------+
  |  superheater) |                     | exhaust (2)
  +---------------+                     v
     ^   ^   |                    +-----------+
 fuel| air|  v flue gas           | Condenser |<--cooling
     |   |  chimney               +-----------+   water
     |                                  | condensate (3)
     |  feed water (4)  +-----------+   |
     +------------------| Feed pump |<--+
                        +-----------+

• Boiler (steam generator): burns coal/oil/gas and converts feed water into high-pressure steam. Includes furnace, water walls, drum, superheater, reheater, economiser (heats feed water by flue gas) and air preheater.
• Steam turbine: expands steam and converts its heat energy into shaft work; drives the alternator (generator).
• Condenser: condenses exhaust steam under vacuum using cooling water; the low back pressure increases turbine work. Cooling water is cooled in a cooling tower or taken from a river.
• Feed pump (with condensate pump): returns the condensate to boiler pressure, usually through feed water heaters (regeneration).
• Fuel and ash handling, draught system (FD/ID fans), chimney, ESP/dust collector.
• Water treatment plant for make-up water.

Ways of increasing the performance

The efficiency of a Rankine (steam) cycle is $\eta = 1 - \dfrac{T_{\text{low}}}{T_{m,\text{in}}}$ roughly, so it improves by raising the mean temperature of heat addition $T_{m}$ or lowering the temperature of heat rejection. Common methods:

1. Increasing boiler (steam) pressure - raises the saturation temperature at which heat is added.
2. Superheating the steam (higher turbine inlet temperature) - raises mean temperature of heat addition and dryness at exhaust.
3. Reducing condenser pressure (better vacuum) - lowers heat rejection temperature.
4. Reheating - steam partly expanded in HP turbine is reheated in the boiler and expanded in LP turbine.
5. Regenerative feed water heating - steam bled from the turbine heats the feed water in feed water heaters.
6. Using economiser and air preheater - recover heat from flue gases.
7. Supercritical / binary vapour and combined cycles - use very high pressure, or a topping cycle (gas turbine) whose waste heat runs the steam cycle.
8. Reducing losses: better turbine blading, insulation, reduced throttling.

Typical effect: raising boiler pressure from 40 to 160 bar, superheat to about 540 C, one reheat and 6-7 regenerative heaters together raise a plant's efficiency from about 25% to about 38-40%.

Advantages of thermal (steam) power plant

• Fuel (coal, oil, gas) is cheaper and easier to transport than building large hydro works; initial cost is lower than hydro and nuclear plants.
• Can be located near the load centre, so transmission cost and losses are small.
• Needs less space than a hydro plant of the same capacity.
• Construction time is short compared to hydro plants.
• Output does not depend on rainfall; it can run as a base-load plant all year.
• Unit sizes up to about 1000 MW are possible; the steam can also be used for process heating (cogeneration).
• Overload capacity is good.

Superheating

Superheating is heating dry saturated steam at constant boiler pressure, in the superheater, to a temperature above its saturation temperature (process g-1).

  T
  ^                   1
  |                  /|    superheat g-1
  |      f---------g  |
  |     /  boiling    |
  |    /              |
  |   3               |
  |   4---------------2
  +-----------------------> s
  3-4 pump, 4-f-g-1 boiler (heating,
  boiling, superheating), 1-2 turbine,
  2-3 condenser (4 and 3 almost coincide)

Benefits:

• Heat is added at a higher temperature, so the mean temperature of heat addition and cycle efficiency increase.
• Work per kg of steam increases (area of the T-s diagram grows), so steam consumption falls.
• Exhaust steam (state 2) is drier, reducing erosion and friction loss in the last turbine stages.
• Superheated steam has no moisture, so losses in pipes are lower.

Limit: maximum temperature is fixed by metallurgy of tubes and blades (about 540-600 C).

Reheating

In reheating the steam expanded partially in the HP turbine is returned to the boiler and reheated at constant (intermediate) pressure to about the original temperature, then expanded in the LP turbine.

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

Benefits:

• Higher mean temperature of heat addition (reheat at 20-25% of boiler pressure), so efficiency increases by about 4-5%.
• Work output per kg increases, steam rate falls.
• Exhaust dryness increases (above about 0.88), reducing blade erosion; allows use of high boiler pressure.

Drawbacks: higher cost and more complex piping and control; economic only for large units.

Ways to increase the efficiency of the Rankine cycle

Rankine efficiency $\eta = \dfrac{W_T - W_P}{Q_s}$ increases when heat is added at a higher mean temperature or rejected at a lower temperature:

1. Higher boiler pressure - higher saturation temperature during boiling.
2. Superheating to a higher turbine inlet temperature.
3. Lower condenser pressure - lower heat rejection temperature (limited by cooling water temperature).
4. Reheating the partly expanded steam.
5. Regenerative feed heating with bled steam.
6. Recovering flue gas heat with economiser and air preheater; using supercritical pressure or combined/binary cycles.

Impulse vs reaction steam turbine

Assumptions: ideal cycle, isentropic expansion, feed pump work included ($W_p = v_f \Delta p$). Values from steam tables (IAPWS-IF97).

States: 1 = 14 bar, 300 C; 2 = 5 bar after HP turbine; 3 = 5 bar, 300 C (after reheat); 4 = 0.2 bar exhaust; 5 = saturated water at 0.2 bar.

Steam table data

(h in kJ/kg, s in kJ/kg K)

State 2: $s_2 = 6.9553 > s_g$ at 5 bar, so steam is slightly superheated (about 177.6 C). From the superheated table, $h_2 = 2807.1$ kJ/kg.

State 4:

$$\begin{aligned} x_4 &= \frac{7.4614 - 0.8320}{7.0753} = 0.9370 \\ h_4 &= 251.40 + 0.9370 \times 2357.55 = 2460.4\ \text{kJ/kg} \end{aligned}$$

Pump work: $W_p = 0.001017 (1400 - 20) = 1.40$ kJ/kg

(a) With reheating

$$\begin{aligned} W_T &= (h_1 - h_2) + (h_3 - h_4) \\ &= (3041.0 - 2807.1) + (3064.6 - 2460.4) \\ &= 233.9 + 604.2 = 838.1\ \text{kJ/kg} \\ W_{net} &= 838.1 - 1.4 = 836.7\ \text{kJ/kg} \\ Q_s &= (h_1 - h_5 - W_p) + (h_3 - h_2) \\ &= (3041.0 - 251.40 - 1.40) + (3064.6 - 2807.1) \\ &= 2788.2 + 257.5 = 3045.7\ \text{kJ/kg} \\ \eta &= \frac{836.7}{3045.7} = 0.2747 \end{aligned}$$

Answer (a): work done $\approx 836.7$ kJ/kg (838.1 kJ/kg turbine work), ideal efficiency $\approx 27.5\%$

(b) Without reheating

Steam expands directly from 14 bar, 300 C to 0.2 bar with $s = 6.9553$:

$$\begin{aligned} x &= \frac{6.9553 - 0.8320}{7.0753} = 0.8655 \\ h &= 251.40 + 0.8655 \times 2357.55 = 2291.8\ \text{kJ/kg} \\ W_T &= 3041.0 - 2291.8 = 749.2\ \text{kJ/kg} \\ W_{net} &= 749.2 - 1.4 = 747.8\ \text{kJ/kg} \\ Q_s &= 3041.0 - 251.40 - 1.40 = 2788.2\ \text{kJ/kg} \\ \eta &= \frac{747.8}{2788.2} = 0.2682 \end{aligned}$$

Answer (b): work done $\approx 747.8$ kJ/kg (749.2 kJ/kg turbine work), ideal efficiency $\approx 26.8\%$

If pump work is neglected, the efficiencies are 27.5% and 26.9%. Reheat increases work by about 12%, efficiency slightly, and makes the exhaust much drier.

Common methods for performance improvement

The efficiency of a Rankine (steam) cycle is $\eta = 1 - \dfrac{T_{\text{low}}}{T_{m,\text{in}}}$ roughly, so it improves by raising the mean temperature of heat addition $T_{m}$ or lowering the temperature of heat rejection. Common methods:

1. Increasing boiler (steam) pressure - raises the saturation temperature at which heat is added.
2. Superheating the steam (higher turbine inlet temperature) - raises mean temperature of heat addition and dryness at exhaust.
3. Reducing condenser pressure (better vacuum) - lowers heat rejection temperature.
4. Reheating - steam partly expanded in HP turbine is reheated in the boiler and expanded in LP turbine.
5. Regenerative feed water heating - steam bled from the turbine heats the feed water in feed water heaters.
6. Using economiser and air preheater - recover heat from flue gases.
7. Supercritical / binary vapour and combined cycles - use very high pressure, or a topping cycle (gas turbine) whose waste heat runs the steam cycle.
8. Reducing losses: better turbine blading, insulation, reduced throttling.

How reheating increases efficiency

In a reheat cycle the steam leaving the boiler (state 1) expands in the HP turbine only up to an intermediate pressure (state 2). It is taken back to the reheater in the boiler and heated at constant pressure to nearly the original temperature (state 3). It then expands in the LP turbine to condenser pressure (state 4).

How reheating increases efficiency and output:

• Higher mean temperature of heat addition: heat added in reheating (2-3) is at a high temperature. If the reheat pressure is chosen properly (about 20-25% of boiler pressure), the average temperature at which heat is supplied rises, so $\eta$ rises by about 4-5%.
• More work per kg of steam: the expansion 3-4 lies to the right of the original expansion line, so the specific work output increases. The steam consumption (kg/kWh) falls and the plant output for the same boiler size increases.
• Drier exhaust steam: without reheat, expansion from high pressure ends in very wet steam (dryness below 0.85). Reheat gives exhaust dryness about 0.9 or more, which reduces blade erosion and friction loss, so the turbine internal efficiency improves.
• It makes very high boiler pressures usable, which is itself a means of raising efficiency.

Cycle efficiency with reheat:

$$\eta = \frac{(h_1 - h_2) + (h_3 - h_4) - W_p}{(h_1 - h_6) + (h_3 - h_2)}$$

Limitations: extra cost of reheater, piping and controls; useful only for large units (above about 100 MW) and high pressures.

Layout and T-s diagram

               1
  +----------+----->+------+     +------+
  |  Boiler  |      |  HP  |=====|  LP  |===> Generator
  |  + S/H   |  2   | turb |     | turb |
  | Reheater |<-----+------+  +->+------+
  |          |------------3---+     | 4
  +----------+                      v
       ^ 6                    +-----------+
       |      +------+   5    | Condenser |
       +------| Pump |<-------+-----------+
              +------+

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

Regeneration is the heating of boiler feed water by steam bled from the turbine, instead of by the boiler fuel alone. It recovers latent heat of the bled steam that would otherwise be lost in the condenser.

Layout (one open feed water heater)

              1
  +--------+------>+---------------+   +-----+
  | Boiler |       |    Turbine    |===| Gen |
  |  + S/H |       +---------------+   +-----+
  +--------+          | m kg (2)  | (1-m) kg (3)
      ^ 7             v           v
      |         +-----------+ +-----------+
  +--------+  6 |  Open FWH | | Condenser |
  | Pump 2 |<---| (mixing)  | +-----------+
  +--------+    +-----------+       | 4
                      ^ 5           |
                 +--------+         |
                 | Pump 1 |<--------+
                 +--------+

Working

1. Steam at boiler pressure enters the turbine (1).
2. At an intermediate pressure, $m$ kg per kg of steam is bled (2) and sent to the feed water heater.
3. The rest, $(1-m)$ kg, expands to condenser pressure (3) and is condensed (4).
4. Pump 1 raises condensate to heater pressure (5). In the heater the bled steam mixes with it and condenses, giving saturated water at heater pressure (6).
5. Pump 2 raises it to boiler pressure (7) and it enters the boiler much hotter than in a simple cycle.

Why efficiency (and effective output) increases

• Heat supplied falls from $(h_1 - h_5)$ to $(h_1 - h_7)$; the remaining heat is added at higher temperature, so the mean temperature of heat addition rises.
• The bled steam's latent heat goes to the feed water, not to the cooling water, so heat rejected falls to $(1-m)(h_3-h_4)$.
• Although work per kg of boiler steam falls slightly, efficiency rises by about 10-15% with several heaters; fuel per kWh falls.
• Smaller exhaust flow means smaller LP blades and condenser, and turbine size can be raised for the same exhaust area, so plant output increases.
• Hot feed water reduces thermal stresses in the boiler; an open heater also deaerates the water.

$$m = \frac{h_6 - h_5}{h_2 - h_5}, \qquad \eta = \frac{(h_1-h_2) + (1-m)(h_2-h_3) - W_p}{h_1 - h_7}$$

P-v diagram

  p
  ^
  | 7 ________________ 1
  |  |                 \
  |  |                  \  expansion
  | 6|_ _ _ _ _ _ _ _ _ _2 (m kg bled)
  | 5|                    \
  |  |                     \___
  | 4|_________________________3
  +--------------------------------> v
  4-5, 6-7 pumps (water, very small v)
  7-1 boiler, 1-2-3 turbine, 3-4 condenser

T-s diagram

  T
  ^                    1
  |                   /|
  |      f----------g  |
  |     /              |
  |    7               |
  |    6 . . . . . . . 2  bleed (m kg)
  |   /                |
  |  5                 |
  |  4-----------------3  (1-m) kg
  +-------------------------> s
  4-5 pump 1, 5 and 2 mix in FWH -> 6,
  6-7 pump 2, 7-f-g-1 boiler,
  1-2-3 turbine, 3-4 condenser

Data: boiler 50 bar, 450 C; throttled to 30 bar; HP stage 30 bar to 3 bar, exit dry saturated; reheat at 3 bar to 300 C; LP stage 3 bar to 0.06 bar, exit dry saturated. Values from steam tables (IAPWS-IF97).

At 3 bar: $h_f = 561.46$, $h_{fg} = 2163.44$, $s_f = 1.6718$, $s_{fg} = 5.3198$. At 0.06 bar: $h_{fg} = 2415.17$, $s_{fg} = 7.8083$, $v_f = 0.001006$.

 1 (50 bar) --throttle--> 1' (30 bar) --HP stage-->
 2 (3 bar) --reheat--> 3 (3 bar) --LP stage-->
 4 (0.06 bar) --condenser--> 5 --pump--> boiler

HP stage efficiency

Throttling is the governing device of the HP stage, so the isentropic reference is taken from the stop-valve state 1 (50 bar, 450 C) to 3 bar:

$$\begin{aligned} x_{2s} &= \frac{6.8208 - 1.6718}{5.3198} = 0.9679 \\ h_{2s} &= 561.46 + 0.9679 \times 2163.44 = 2655.4\ \text{kJ/kg} \\ \eta_{HP} &= \frac{h_1 - h_2}{h_1 - h_{2s}} = \frac{3317.0 - 2724.9}{3317.0 - 2655.4} = \frac{592.1}{661.6} = 0.895 \end{aligned}$$

Note: if the reference is taken from the throttled state 1' ($s = 7.0468 > s_g$ at 3 bar), the isentropic end point is superheated with $h = 2747.6$ kJ/kg, which is higher than the given actual exit (2724.9). That would give an efficiency above 100%, so with these data the stage efficiency must be based on the stop-valve state (it then includes the throttling loss).

LP stage efficiency

$$\begin{aligned} x_{4s} &= \frac{7.7037 - 0.5209}{7.8083} = 0.9199 \\ h_{4s} &= 151.49 + 0.9199 \times 2415.17 = 2373.2\ \text{kJ/kg} \\ \eta_{LP} &= \frac{h_3 - h_4}{h_3 - h_{4s}} = \frac{3069.6 - 2566.7}{3069.6 - 2373.2} = \frac{502.9}{696.4} = 0.722 \end{aligned}$$

Overall cycle efficiency

$$\begin{aligned} W_{HP} &= 3317.0 - 2724.9 = 592.1\ \text{kJ/kg} \\ W_{LP} &= 3069.6 - 2566.7 = 502.9\ \text{kJ/kg} \\ W_p &= 0.001006 (5000 - 6) = 5.03\ \text{kJ/kg} \\ Q_s &= (h_1 - h_5 - W_p) + (h_3 - h_2) \\ &= (3317.0 - 151.49 - 5.03) + (3069.6 - 2724.9) \\ &= 3160.5 + 344.7 = 3505.2\ \text{kJ/kg} \\ \eta &= \frac{592.1 + 502.9 - 5.03}{3505.2} = \frac{1090.0}{3505.2} = 0.311 \end{aligned}$$

(Neglecting pump work: $\eta = 1095.0 / 3510.3 = 0.312$.)

Work ratio HP : LP

$$\frac{W_{HP}}{W_{LP}} = \frac{592.1}{502.9} = 1.177$$

Answer: $\eta_{HP} \approx 89.5\%$, $\eta_{LP} \approx 72.2\%$, overall $\eta \approx 31.1\%$, $W_{HP}/W_{LP} \approx 1.18$.

A steam power station must produce electricity reliably, cheaply and safely with least harm to the environment. The essential design requirements are:

1. Site selection: near a fuel source or good rail/road access, large supply of cooling water (river, lake), cheap and firm land with good bearing capacity, space for ash disposal and future extension, nearness to load centre, away from towns (pollution).
2. High efficiency / low fuel cost: high steam pressure and temperature, reheating, regenerative feed heating, economiser and air preheater, good condenser vacuum.
3. Low capital and operating cost: proper unit size, standardised equipment, automation, minimum staff.
4. Reliability and availability: good quality equipment, adequate spare (standby) units, easy maintenance, proper protection.
5. Flexibility: ability to follow load changes, quick start-up, good part-load efficiency.
6. Fuel and ash handling: reliable storage, handling and firing equipment; safe ash disposal.
7. Water treatment: treated make-up water to avoid scale and corrosion in boiler and turbine.
8. Environmental control: ESP/bag filters, flue gas desulphurisation, tall chimney, treatment of waste water, noise control, cooling towers to avoid thermal pollution.
9. Safety: fire protection, safety valves, proper layout and access.
10. Proper layout: short steam and water pipes, logical flow of coal - boiler - turbine - switchyard, space for maintenance cranes.

A steam power plant converts the heat of fuel (coal, oil, gas) into electricity using a boiler, steam turbine and generator on the Rankine cycle.

Advantages

• Fuel is cheaper and widely available; initial cost is lower than hydro and nuclear plants.
• Can be built near the load centre, reducing transmission cost and losses.
• Requires less space than a hydro plant of equal capacity.
• Construction time is short.
• Not dependent on rainfall; suitable for base load throughout the year.
• Large unit sizes are possible; exhaust/bled steam can be used for process heating.
• Good overload capacity.

Disadvantages

• High running cost (fuel cost is continuous, fuel price rises).
• Low overall efficiency (about 30-40%); large heat loss in condenser.
• Air pollution (CO2, SO2, NOx, fly ash) and thermal pollution of water.
• Needs large amount of cooling water and fuel transport.
• Problems of ash handling and disposal.
• Slow start-up; not suitable for peak loads.
• Maintenance and operating staff costs are higher than hydro; plant life is shorter.

A reheater is a heat exchanger in the boiler that reheats steam coming from the HP turbine at constant intermediate pressure before it enters the LP turbine.

Layout

               1
  +----------+----->+------+     +------+
  |  Boiler  |      |  HP  |=====|  LP  |===> Generator
  |  + S/H   |  2   | turb |     | turb |
  | Reheater |<-----+------+  +->+------+
  |          |------------3---+     | 4
  +----------+                      v
       ^ 6                    +-----------+
       |      +------+   5    | Condenser |
       +------| Pump |<-------+-----------+
              +------+

Working

1. Feed pump (5-6) sends water to the boiler where it is heated, boiled and superheated (6-1).
2. Steam expands in the HP turbine (1-2) to about 20-25% of boiler pressure.
3. It returns to the reheater and is heated at constant pressure to almost the initial temperature (2-3).
4. Reheated steam expands in the LP turbine to condenser pressure (3-4); the condensate is pumped back (4-5).

How reheating increases output and efficiency

• Output: each kg of steam now does work $(h_1-h_2) + (h_3-h_4)$, which is larger than $(h_1 - h_{4'})$ without reheat, because constant-pressure lines diverge on the h-s chart. Steam consumption per kWh falls, so for the same boiler the plant output rises.
• Efficiency: heat in the reheater is added at a high mean temperature, so the cycle's mean temperature of heat addition rises (gain about 4-5%).
• Dryness: exhaust steam becomes much drier (about 0.9 or more), reducing blade erosion and wetness loss, so turbine internal efficiency improves.
• Allows higher boiler pressures without excess moisture at exhaust.

$$\eta = \frac{(h_1 - h_2) + (h_3 - h_4) - W_p}{(h_1 - h_6) + (h_3 - h_2)}$$

T-s diagram

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

Assumptions: ideal reheat Rankine cycle; isentropic turbines and pump; pump work included. Values from steam tables (IAPWS-IF97).

States: 1 = 4 MPa, 400 C; 2 = 400 kPa (HP exit); 3 = 400 kPa, 400 C; 4 = 10 kPa; 5 = saturated water at 10 kPa; 6 = pump exit.

               1
  +----------+----->+------+     +------+
  |  Boiler  |      |  HP  |=====|  LP  |===> Generator
  |  + S/H   |  2   | turb |     | turb |
  | Reheater |<-----+------+  +->+------+
  |          |------------3---+     | 4
  +----------+                      v
       ^ 6                    +-----------+
       |      +------+   5    | Condenser |
       +------| Pump |<-------+-----------+
              +------+

Steam table data

State 2 ($s_2 = s_1$)

$$\begin{aligned} x_2 &= \frac{6.7712 - 1.7766}{5.1188} = 0.9757 \\ h_2 &= 604.72 + 0.9757 \times 2133.33 = 2686.3\ \text{kJ/kg} \end{aligned}$$

State 4 ($s_4 = s_3$)

$$\begin{aligned} x_4 &= \frac{7.9001 - 0.6492}{7.4997} = 0.9668 \\ h_4 &= 191.81 + 0.9668 \times 2392.07 = 2504.5\ \text{kJ/kg} \end{aligned}$$

Pump

$$\begin{aligned} W_p &= v_f (p_6 - p_5) = 0.001010 (4000 - 10) = 4.03\ \text{kJ/kg} \\ h_6 &= 191.81 + 4.03 = 195.84\ \text{kJ/kg} \end{aligned}$$

Work, heat and efficiency

$$\begin{aligned} W_T &= (h_1 - h_2) + (h_3 - h_4) \\ &= (3214.4 - 2686.3) + (3273.9 - 2504.5) \\ &= 528.1 + 769.3 = 1297.4\ \text{kJ/kg} \\ W_{net} &= 1297.4 - 4.03 = 1293.4\ \text{kJ/kg} \\ Q_s &= (h_1 - h_6) + (h_3 - h_2) \\ &= (3214.4 - 195.84) + (3273.9 - 2686.3) \\ &= 3018.5 + 587.6 = 3606.1\ \text{kJ/kg} \\ \eta &= \frac{1293.4}{3606.1} = 0.3587 \end{aligned}$$

Answer: cycle efficiency $\approx 35.9\%$ (net work 1293.4 kJ/kg, exhaust dryness 0.967).

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

Compared with a simple Rankine cycle between 4 MPa, 400 C and 10 kPa (about 35.3%, exhaust dryness 0.816), reheat increases efficiency slightly, raises the net work by about 21% and makes the exhaust steam much drier.

Common methods of improving performance

The efficiency of a Rankine (steam) cycle is $\eta = 1 - \dfrac{T_{\text{low}}}{T_{m,\text{in}}}$ roughly, so it improves by raising the mean temperature of heat addition $T_{m}$ or lowering the temperature of heat rejection. Common methods:

1. Increasing boiler (steam) pressure - raises the saturation temperature at which heat is added.
2. Superheating the steam (higher turbine inlet temperature) - raises mean temperature of heat addition and dryness at exhaust.
3. Reducing condenser pressure (better vacuum) - lowers heat rejection temperature.
4. Reheating - steam partly expanded in HP turbine is reheated in the boiler and expanded in LP turbine.
5. Regenerative feed water heating - steam bled from the turbine heats the feed water in feed water heaters.
6. Using economiser and air preheater - recover heat from flue gases.
7. Supercritical / binary vapour and combined cycles - use very high pressure, or a topping cycle (gas turbine) whose waste heat runs the steam cycle.
8. Reducing losses: better turbine blading, insulation, reduced throttling.

Regenerative scheme with an open feed water heater

An open (direct contact) feed water heater is a mixing chamber in which bled steam and feed water mix directly; the outlet is saturated water at heater pressure.

              1
  +--------+------>+---------------+   +-----+
  | Boiler |       |    Turbine    |===| Gen |
  |  + S/H |       +---------------+   +-----+
  +--------+          | m kg (2)  | (1-m) kg (3)
      ^ 7             v           v
      |         +-----------+ +-----------+
  +--------+  6 |  Open FWH | | Condenser |
  | Pump 2 |<---| (mixing)  | +-----------+
  +--------+    +-----------+       | 4
                      ^ 5           |
                 +--------+         |
                 | Pump 1 |<--------+
                 +--------+

Working

1. Superheated steam from the boiler enters the turbine at state 1.
2. A fraction $m$ kg/kg is extracted at the intermediate pressure (state 2) and sent to the open heater.
3. The remaining $(1-m)$ kg expands to condenser pressure (3) and is condensed to saturated water (4).
4. Pump 1 raises the condensate to heater pressure (5).
5. In the open heater the bled steam condenses and gives its latent heat to the feed water; the mixture leaves as saturated water at heater pressure (6). Energy balance: $m h_2 + (1-m) h_5 = h_6$.
6. Pump 2 raises it to boiler pressure (7); the boiler heats it from state 7 instead of from cold condensate.

Because feed water enters the boiler hot, the mean temperature of heat addition rises and less heat is rejected in the condenser, so the efficiency increases. A separate pump is needed after each open heater; the open heater also removes dissolved gases (deaerator).

T-s diagram

  T
  ^                    1
  |                   /|
  |      f----------g  |
  |     /              |
  |    7               |
  |    6 . . . . . . . 2  bleed (m kg)
  |   /                |
  |  5                 |
  |  4-----------------3  (1-m) kg
  +-------------------------> s
  4-5 pump 1, 5 and 2 mix in FWH -> 6,
  6-7 pump 2, 7-f-g-1 boiler,
  1-2-3 turbine, 3-4 condenser

$$\eta = \frac{(h_1 - h_2) + (1-m)(h_2 - h_3) - [(1-m)W_{p1} + W_{p2}]}{h_1 - h_7}$$

Assumptions: ideal reheat Rankine cycle, isentropic turbines and pump, pump work included. Values from steam tables (IAPWS-IF97).

States: 1 = 20 MPa, 500 C (HP inlet); 2 = HP exit at reheat pressure $p_r$; 3 = $p_r$, 500 C (LP inlet); 4 = 0.005 MPa, $x = 0.896$; 5 = saturated water at 5 kPa; 6 = pump exit.

Steam table data

(a) Pressure at which steam leaves the HP turbine

State 4:

$$\begin{aligned} s_4 &= 0.4763 + 0.896 \times 7.9177 = 7.5705\ \text{kJ/kg K} \\ h_4 &= 137.77 + 0.896 \times 2423.0 = 2308.8\ \text{kJ/kg} \end{aligned}$$

LP expansion is isentropic, so $s_3 = s_4 = 7.5705$ at 500 C. From the superheated table at 500 C: $s = 7.6045$ at 1.4 MPa and $s = 7.5407$ at 1.6 MPa. Interpolating:

$$p_r = 1.4 + 0.2 \times \frac{7.6045 - 7.5705}{7.6045 - 7.5407} = 1.507 \approx 1.5\ \text{MPa}$$

Taking $p_r = 1.5$ MPa: at 1.5 MPa, 500 C, $h_3 = 3473.6$ kJ/kg.

Answer (a): steam leaves the HP turbine at about 1.5 MPa.

State 2 (1.5 MPa, $s_2 = s_1 = 6.1445$)

At 1.5 MPa: $h_f = 844.7$, $h_{fg} = 1946.3$, $s_f = 2.3147$, $s_{fg} = 4.1284$.

$$\begin{aligned} x_2 &= \frac{6.1445 - 2.3147}{4.1284} = 0.9277 \\ h_2 &= 844.7 + 0.9277 \times 1946.3 = 2650.2\ \text{kJ/kg} \end{aligned}$$

Pump

$$\begin{aligned} W_p &= 0.001005 (20000 - 5) = 20.10\ \text{kJ/kg} \\ h_6 &= 137.77 + 20.10 = 157.87\ \text{kJ/kg} \end{aligned}$$

(b) Thermal efficiency

$$\begin{aligned} W_T &= (h_1 - h_2) + (h_3 - h_4) \\ &= (3241.2 - 2650.2) + (3473.6 - 2308.8) \\ &= 591.0 + 1164.8 = 1755.8\ \text{kJ/kg} \\ W_{net} &= 1755.8 - 20.1 = 1735.7\ \text{kJ/kg} \\ Q_s &= (h_1 - h_6) + (h_3 - h_2) \\ &= (3241.2 - 157.87) + (3473.6 - 2650.2) \\ &= 3083.3 + 823.4 = 3906.7\ \text{kJ/kg} \\ \eta &= \frac{1735.7}{3906.7} = 0.4443 \end{aligned}$$

Answer (b): thermal efficiency $\approx 44.4\%$ (net work 1735.7 kJ/kg).

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser