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2.4 Equipment for Combined Heat and Power
Now that the heating, cooling and power generation loads and use are known, it is possible to estimate how they are met by the various energy devices that the system includes. But first it is necessary to explain the basics of heat and power generating equipments, and how their fuel consumption and heating capacity can be estimated.
The RETScreen CHP model is able to calculate a number of combined heat and power options, including steam turbines, steam turbines with extraction port, gas turbines, and combined cycle gas turbines. The model also covers (although not with the same degree of detail) reciprocating engines, fuel cells, etc.
Now that the heating, cooling and power generation loads and use are known, it is possible to estimate how they are met by the various energy devices that the system includes. But first it is necessary to explain the basics of heat and power generating equipments, and how their fuel consumption and heating capacity can be estimated.
The RETScreen CHP model is able to calculate a number of combined heat and power options, including steam turbines, steam turbines with extraction port, gas turbines, and combined cycle gas turbines. The model also covers (although not with the same degree of detail) reciprocating engines, fuel cells, etc.
2.4.1 Steam turbine
Background
A steam turbine uses high pressure and saturated or superheated steam produced in a boiler, and converts the thermal energy by expanding it in the turbine to generate shaft power that drives a generator to produce electricity.
Turbines can be of two types, radial or axial flow. Axial flow is the most common for power generation. The steam is directed by nozzles to rotating blades or buckets mounted radially on a rotating wheel. The length of the blades is short in proportion to the radius of the turbine. Several stages of expansion are used in high efficiency turbines. Vacuum exhaust can be achieved by mounting the different stages on a single shaft, and supporting the nozzles of all the stages from a continuous housing. Large turbines must not be operated in conditions where the exhaust steam contains more than 10 to 13% water. Water droplets can seriously erode nozzles and blades. Some turbines may have special stages designed for the removal of moisture. This type of design is used when the superheated steam temperature is limited. The moisture content of the exhaust is dependent on the inlet steam pressure combination.
Superheating the steam increases the cycle efficiency. Reheat is sometime used to further increase the efficiency. The steam is then re-superheated after partial expansion.
Back pressure operation refers to non-condensing steam turbines designed to utilize the exhaust steam for heating or a process. In a condensing turbine the steam exhausts to a condenser and the latent heat of the steam is transferred to the cooling water. The condensed steam is returned to the boiler as feed water.
Extraction, controlled automatic operation, refers to a steam turbine designed to permit a controlled extraction steam flow to be matched to the steam demand; steam can be used for heating or process purposes. Steam that is not extracted is condensed. Large steam turbines might have more than one extraction port. The RETScreen CHP model only allows the user to use one extraction port.
Thermodynamic cycle
In the RETScreen CHP model the steam turbine is assumed to be an isentropic device. In practice it is not an ideal device, and efficiencies will be introduced later to account for that fact.
The diagram for a steam turbine is shown in Figure 8. The corresponding thermodynamic cycle (known as the Rankine cycle) is shown in Figure 9. The four phases of the cycle are:
1 to 2: heat transfer to the working fluid. The heat is provided by the combustion of fuel. Water enters the boiler, receives heat provided by the combustion of fuel, and exits as superheated vapour.
Background
A steam turbine uses high pressure and saturated or superheated steam produced in a boiler, and converts the thermal energy by expanding it in the turbine to generate shaft power that drives a generator to produce electricity.
Turbines can be of two types, radial or axial flow. Axial flow is the most common for power generation. The steam is directed by nozzles to rotating blades or buckets mounted radially on a rotating wheel. The length of the blades is short in proportion to the radius of the turbine. Several stages of expansion are used in high efficiency turbines. Vacuum exhaust can be achieved by mounting the different stages on a single shaft, and supporting the nozzles of all the stages from a continuous housing. Large turbines must not be operated in conditions where the exhaust steam contains more than 10 to 13% water. Water droplets can seriously erode nozzles and blades. Some turbines may have special stages designed for the removal of moisture. This type of design is used when the superheated steam temperature is limited. The moisture content of the exhaust is dependent on the inlet steam pressure combination.
Superheating the steam increases the cycle efficiency. Reheat is sometime used to further increase the efficiency. The steam is then re-superheated after partial expansion.
Back pressure operation refers to non-condensing steam turbines designed to utilize the exhaust steam for heating or a process. In a condensing turbine the steam exhausts to a condenser and the latent heat of the steam is transferred to the cooling water. The condensed steam is returned to the boiler as feed water.
Extraction, controlled automatic operation, refers to a steam turbine designed to permit a controlled extraction steam flow to be matched to the steam demand; steam can be used for heating or process purposes. Steam that is not extracted is condensed. Large steam turbines might have more than one extraction port. The RETScreen CHP model only allows the user to use one extraction port.
Thermodynamic cycle
In the RETScreen CHP model the steam turbine is assumed to be an isentropic device. In practice it is not an ideal device, and efficiencies will be introduced later to account for that fact.
The diagram for a steam turbine is shown in Figure 8. The corresponding thermodynamic cycle (known as the Rankine cycle) is shown in Figure 9. The four phases of the cycle are:
1 to 2: heat transfer to the working fluid. The heat is provided by the combustion of fuel. Water enters the boiler, receives heat provided by the combustion of fuel, and exits as superheated vapour.
Figure 8: Steam Turbine
Figure 9: Ideal Rankine Cycle with Superheating
2 to 3: expansion. The steam is expanded in the turning turbine, converting the enthalpy in the working fluid into work.
3 to 4: transfer of heat to the environment. As the water condenses it rejects heat to the environment. This usually takes place in a condenser. Heat can also be extracted by co-generation loads.
4 to 1: isentropic pressure increase. The pump is used to increase the pressure of the working fluid. The water enters the pump as a saturated liquid and exits it as a subcooled liquid. The process requires work, and a small fraction of the work generated by the turbine (typically 5%) is used to power the pump.
3 to 4: transfer of heat to the environment. As the water condenses it rejects heat to the environment. This usually takes place in a condenser. Heat can also be extracted by co-generation loads.
4 to 1: isentropic pressure increase. The pump is used to increase the pressure of the working fluid. The water enters the pump as a saturated liquid and exits it as a subcooled liquid. The process requires work, and a small fraction of the work generated by the turbine (typically 5%) is used to power the pump.
Calculation of work, heating capacity, and fuel consumption
The turbine’s specific work (work per mass), or Rankine cycle work, is simply given by:
The turbine’s specific work (work per mass), or Rankine cycle work, is simply given by:
where Wideal is the Rankine cycle work or theoretical steam rate, h2 is the input steam enthalpy and h3 is the exhaust steam enthalpy. The enthalpies h2 and h3 correspond to phases 2 and 3 shown on Figure 9, which have the same entropy. The actual steam turbine specific work w or actual steam rate is calculated with:
where ηs is the isentropic efficiency of the turbine.
Equation (30) requires the knowledge of input steam and exhaust steam enthalpy. The enthalpy h2 and entropy s2 of the input steam can be calculated from the operating pressure P2 and the superheated temperature T2 (both specified by the user) of the input steam. The enthalpy h3 at the back port can be calculated from the back pressure P3 (also specified by the user) and the back port entropy ( s3=s2 since the process is assumed to be isentropic). The formulae used to calculate steam and water properties for the RETScreen CHP model are those published by the International Association for the Properties of Water and Steam (IAPWS, 1997) (see note 8).
In practice the system does not behave ideally, and additional inefficiencies have to be taken into account. The actual steam rate can be calculated from the total turbine generator package efficiency:
In practice the system does not behave ideally, and additional inefficiencies have to be taken into account. The actual steam rate can be calculated from the total turbine generator package efficiency:
where ηtg is the combined total efficiency of the turbine generator set. The efficiency is in reality dependent upon many factors in the steam path including exhaust size. However to simplify the amount of inputs for the RETScreen CHP model (for example the energy lost to power the pump), these efficiencies have been combined into one overall number, which is entered by the user.
The total amount of power (electricity) produced from a turbine can now be calculated by multiplying with the mass flow of steam:
The total amount of power (electricity) produced from a turbine can now be calculated by multiplying with the mass flow of steam:
where W is the power produced by the steam turbine generator, m is the mass flow of steam feeding the turbine and w the actual steam rate for the turbine generator set. The heating capacity Wth of the turbine is:
Finally the fuel consumption for the steam cycle can be defined by the difference of enthalpy of the water returning to the boiler and the enthalpy of the steam produced, divided by the boiler’s seasonal efficiency:
where Wf is the boiler fuel consumption, m is the mass flow of the input steam, h2 is the input steam enthalpy, h1 is the return water enthalpy and ηb is the seasonal boiler efficiency including blow-down losses (i.e. due to the periodic removal of water to get rid of accumulated solids or sludges).
Steam quality
If the entropy is between fluid and vapour entropy at the exit pressure, the exit quality of the steam mixture is calculated from the two phase mixture as:
Steam quality
If the entropy is between fluid and vapour entropy at the exit pressure, the exit quality of the steam mixture is calculated from the two phase mixture as:
where, x3 is the exit quality, s3 the entropy of the exhaust steam, s1 the entropy of the fluid feeding the boiler, but at the exit pressure and sv the entropy of saturated steam at the exit pressure. When the steam quality is less than one, a warning message is displayed to the user to indicate that the steam is wet.
2.4.2 Steam turbine with extraction port
The RETScreen CHP model also allows the calculation of a turbine that has one extraction port as seen in Figure 10. The corresponding thermodynamic cycle is shown in Figure 11.
The RETScreen CHP model also allows the calculation of a turbine that has one extraction port as seen in Figure 10. The corresponding thermodynamic cycle is shown in Figure 11.
Figure 10: Steam Turbine with Extraction
Figure 11: Ideal Rankine Cycle with Superheating and Steam Extraction
The power produced by an extraction turbine depends on rate of extraction. The steam turbine will always need to have a minimum flow to the back pressure port. The maximum extraction is specified by the turbine design and the pressure and size of the extraction port. The minimum and maximum power generated are:
where W is the power generated, m is the mass flow of the input steam, e is the maximum allowable extraction rate, expressed as a fraction, h2 is the input steam enthalpy, h3 is the extraction steam enthalpy, h4 is the exhaust steam enthalpy and ηtg is the combined total efficiency of the turbine generator set. The extraction enthalpy h3 and the exhaust steam enthalpy h4 can be readily calculated from user inputs using formulae similar to the ones used in section 2.4.1.
Maximum and minimum available heating capacities for this turbine are:
Maximum and minimum available heating capacities for this turbine are:
where Wth is the available heating capacity as a function of the fraction of steam extracted. The maximum heating capacity of this turbine will be during operation at full extraction.
The fuel consumption of the system is calculated with the same equation as in the steam turbine case (see equation (35)).
The fuel consumption of the system is calculated with the same equation as in the steam turbine case (see equation (35)).
2.4.3 Gas turbine
Background
A gas turbine is a machine that compresses a gas (typically air), and then adds heat energy into the compressed gas. The heat can be added either firing (combusting) a fuel in the compressed air or transferring the heat via a heat exchanger. This is followed by the expansion of the hot pressurized gas to produce work. Part of the work produced is used to compress the gas, and the remaining part can either drive a generator for electricity production or some other machinery. An aircraft jet engine is a gas turbine where the useful work is produced as trust from the exhaust.
Background
A gas turbine is a machine that compresses a gas (typically air), and then adds heat energy into the compressed gas. The heat can be added either firing (combusting) a fuel in the compressed air or transferring the heat via a heat exchanger. This is followed by the expansion of the hot pressurized gas to produce work. Part of the work produced is used to compress the gas, and the remaining part can either drive a generator for electricity production or some other machinery. An aircraft jet engine is a gas turbine where the useful work is produced as trust from the exhaust.
Figure 12: Typical Gas Turbine System with Heat Recovery
There are two types of land based gas turbines namely, heavy frame engines and aero derivative engines. Heavy frame engines are larger and typically operate at lower compression rates than the smaller and more compact aero derivative engines.
In the RETScreen CHP model the gas turbine is characterized by its power capacity [kW], its minimum capacity [%], its heat rate [kJ/kWh] or [Btu/kWh] and its heat recovery efficiency [%].
Power capacity or output of the generating equipment is measured in [kW]. The power capacity is the output to the grid. All efficiency factors such as altitude, atmospheric conditions, generator, transformer etc. are assumed to have been already deducted from the power capacity entered by the user.
Minimum capacity is sometimes also referred to as turndown ratio. The minimum capacity (load) for the equipment selected is entered in percent of total capacity. If the system selected cannot be turned down to the anticipated load, the electricity either has to be sold or the turbine stopped. A warning will be shown if the system is too large to follow the system load. If the user selects several smaller turbines, load following can typically be achieved. If the monthly load is less than the minimum capacity, the model will assume that the system is off during that period. Then the load for that period will need to be met by the intermediate or peak load systems.
The heat rate and the heat recovery efficiency are used to specify the efficiency of the power producing equipment. The heat rate is a measure of fuel consumption per unit of power output: the higher a turbine's efficiency, the lower its heat rate. Heat rate is typically described in [kJ/kWh] but other units are also used . Heat recovery efficiency in percent is used to specify the amount of available heat that can be recovered by the proposed system. All heat that is produced cannot be recovered, as sometimes the temperature of the available heat is too low.
Calculation of work, heating capacity, and fuel consumption
From the quantities defined above, and from the gas turbine power capacity W , it is fairly easy to calculate the thermal output and the fuel consumption. Indeed one has by definition:
In the RETScreen CHP model the gas turbine is characterized by its power capacity [kW], its minimum capacity [%], its heat rate [kJ/kWh] or [Btu/kWh] and its heat recovery efficiency [%].
Power capacity or output of the generating equipment is measured in [kW]. The power capacity is the output to the grid. All efficiency factors such as altitude, atmospheric conditions, generator, transformer etc. are assumed to have been already deducted from the power capacity entered by the user.
Minimum capacity is sometimes also referred to as turndown ratio. The minimum capacity (load) for the equipment selected is entered in percent of total capacity. If the system selected cannot be turned down to the anticipated load, the electricity either has to be sold or the turbine stopped. A warning will be shown if the system is too large to follow the system load. If the user selects several smaller turbines, load following can typically be achieved. If the monthly load is less than the minimum capacity, the model will assume that the system is off during that period. Then the load for that period will need to be met by the intermediate or peak load systems.
The heat rate and the heat recovery efficiency are used to specify the efficiency of the power producing equipment. The heat rate is a measure of fuel consumption per unit of power output: the higher a turbine's efficiency, the lower its heat rate. Heat rate is typically described in [kJ/kWh] but other units are also used . Heat recovery efficiency in percent is used to specify the amount of available heat that can be recovered by the proposed system. All heat that is produced cannot be recovered, as sometimes the temperature of the available heat is too low.
Calculation of work, heating capacity, and fuel consumption
From the quantities defined above, and from the gas turbine power capacity W , it is fairly easy to calculate the thermal output and the fuel consumption. Indeed one has by definition:
where HR is the heat rate and Wf is the gross total fuel input; and:
where ηth is the efficiency of the heat recovery system and Wth is the heating capacity of the system. As a consequence,
and:
HR , ηth and W are specified by the user.
2.4.4 Combined cycle gas turbine
The exhaust from a stationary gas turbine can be recovered to generate heat or steam for power generation in a steam turbine. In the combined cycle arrangement the heat is converted to steam in a heat recovery steam generator. This steam is then typically used to produce power.
In some systems duct firing is used; this means that supplementary fuel is burned to increase the output of steam produced. Note also that, as shown in Figure 13, the model allows the use of one extraction port of the steam turbine. In more complex CHP plants, steam turbines have more than one extraction port, but the RETScreen CHP model only models one.
The exhaust from a stationary gas turbine can be recovered to generate heat or steam for power generation in a steam turbine. In the combined cycle arrangement the heat is converted to steam in a heat recovery steam generator. This steam is then typically used to produce power.
In some systems duct firing is used; this means that supplementary fuel is burned to increase the output of steam produced. Note also that, as shown in Figure 13, the model allows the use of one extraction port of the steam turbine. In more complex CHP plants, steam turbines have more than one extraction port, but the RETScreen CHP model only models one.
Figure 13: Typical Combined Cycle Gas Turbine System with Duct Firing and Extraction on the Steam Turbine
When duct firing is not used, equations (43) and (44) can still be used to calculate the gross fuel input Wf and the thermal output Wth of the system, as a function of the gas turbine’s electrical output W . If duct firing is present in the system these equations have to be replaced with:
and:
where WDuctFiring is the gross duct firing fuel input.
The calculation of the steam turbine side of the system then proceeds in a very similar fashion to what was exposed previously in sections 2.4.1 and 2.4.2. The only difference is that the thermal input to the steam turbine Wth is known, rather than the steam mass flow rate m . The following relationship relates the two:
where h1 is the return water enthalpy and h2 is the input steam enthalpy (these two quantities are, as in sections 2.4.1 and 2.4.2, calculated from the operating pressure, superheated temperature, extraction rate and pressure, and back pressure).
The total combined cycle gas turbine power capacity is
The total combined cycle gas turbine power capacity is
where W is the total electrical capacity of the combined cycle gas turbine, WeGasTurbine is the electrical capacity of the gas turbine and WeSteamTurbine is the electrical capacity of the steam turbine.
In some cases the gas turbine and steam turbine are packaged and only the total heat rate for the combined cycle system is known. The heat rate is then calculated as:
In some cases the gas turbine and steam turbine are packaged and only the total heat rate for the combined cycle system is known. The heat rate is then calculated as:
where HR is the gross total heat rate, Wf is the gross total fuel input, WeGasTurbine is the electrical capacity of the gas turbine and WeSteamTurbine is the electrical capacity of the steam turbine. In the RETScreen CHP model, if the combined cycle heat rate is known and no extra duct firing nor extraction is required, the “gas turbine” section can be used to evaluate the combined cycle plant.
2.4.5 Reciprocating engine, fuel cell, or other power equipment consuming fuel
All these systems are calculated with the same inputs (power capacity, heat rate, and heat recovery efficiency) as the gas turbine. The equations used in section 2.4.3 apply as well.
All these systems are calculated with the same inputs (power capacity, heat rate, and heat recovery efficiency) as the gas turbine. The equations used in section 2.4.3 apply as well.
2.4.6 Geothermal system
The geothermal system is treated as a steam turbine, with the difference that the steam is produced through geothermal means, not by burning fuel; therefore there is no calculation of the fuel needed.
The geothermal system is treated as a steam turbine, with the difference that the steam is produced through geothermal means, not by burning fuel; therefore there is no calculation of the fuel needed.
8. In that reference, of particular interest are equations 7 for entropy and enthalpy in the liquid stage, 15, 18 and 19 in the vapour stage, and 31 for saturation temperature.
9. The Tools worksheet contains methods to convert between the different methods published by equipment manufacturers.
9. The Tools worksheet contains methods to convert between the different methods published by equipment manufacturers.
