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Operation of a Cofired Generator

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A cofired generator operates on a mixture of fossil fuel and biogas. In each time step, HOMER calculates the required output of the generator and the corresponding mass flow rates of fossil fuel and biogas. This calculation is based on several key assumptions:

1.The biogas substitution ratio (zgas) is a constant, independent of engine output power or fuel mixture.

2.The system always attempts to maximize the use of biogas and minimize the use of fossil fuel.

3.The fossil fraction cannot go below a certain minimum.

4.Even if the derating factor associated with operating in dual-fuel mode is less than 100%, the generator can produce up to 100% of its rated power, provided the fossil fraction is high enough.

The fuel curve of a cofired generator defines the fuel consumption of the generator in pure fossil mode. So, the fossil fuel consumption in pure fossil mode is given by the following equation. (See the table of nomenclature below for a definition of all the symbols.)

 


equations_mdot_0def

(1)

 

And from assumption 1:


equations_mdot_0


equations_mdot_gas1

(2)

Where zgas is the biogas substitution ratio. Now from the definition of the fossil fraction:


equations_x_fossil_def

(3)

Using equations 2 and 3:


equations_mdot_gas2


equations_mdot_gas3

(4)

But for a given value of Pbio, the value of xfossil is unknown so the above equation is not enough on its own to solve for the biogas flow rate. From assumption 2, we want to maximize symbols_mdot_gas, which means we want to minimize xfossil. But from assumption 3:


equations_x_fossil_star


where symbols_x_fossil_star is the minimum fossil fraction required for ignition. So the target value for symbols_mdot_gas corresponds to . Using equation 4:


equations_mdot_gas_t

(5)

But there are two independent upper limits on the actual value of symbols_mdot_gas. At the minimum fossil fraction, the output of the generator is limited to symbols_Y_gen_star, defined as follows:

equations_Y_gen_star

where τ, the derating factor, is less than or equal to 1. This limitation can be implemented by imposing an upper limit on symbols_mdot_gas corresponding to and conditions_x_fossil equals x_fossil_star. Using equations 1 and 4, this maximum value can be defined as:


equations_mdot_gas_star

(6)

This upper limit can be thought of as a physical limitation—the maximum rate at which biogas can be ingested in the engine. The available biomass resource, agas, constitutes the other upper limit on symbols_mdot_gas. So the actual value of symbols_mdot_gas is the minimum of , symbols_mdot_gas_star, and agas:


equations_mdot_gas4

(7)

Knowing the value of symbols_mdot_gas, we can determine xfossil. Solving equation 4 for xfossil:


equations_x_fossil

(8)

And from equation 3:


equations_mdot_fossil

(9)

So at any time step, given particular values of Pbio and agas, the biogas flow rate and the fossil fuel flow rate can be calculated from equations 7 and 9, respectively.

Table of Nomenclature

Symbol

Units

Description

ρfossil

kg/L

Density of fossil fuel

τ

%

Generator derating factor

agas

kg/hr

Available biogas flow rate

symbols_mdot_0

kg/hr

Fossil fuel flow rate (in pure fossil mode)

symbols_mdot_fossil

kg/hr

Fossil fuel flow rate (in dual-fuel mode)

symbols_mdot_gas

kg/hr

Biogas flow rate (in dual-fuel mode)

symbols_mdot_gas_star

kg/hr

Maximum value of biogas flow rate

symbols_mdot_gas_t

kg/hr

Target value of biogas flow rate

xfossil

%

Fossil fraction

symbols_x_fossil_star

%

Minimum fossil fraction

zgas

none

Biogas substitution ratio

F0

L/hr/kW

Generator fuel curve intercept coefficient

F1

L/hr/kW

Generator fuel curve slope

Pgen

kW

Power output of the generator

symbols_Y_gen_star

kW

Maximum output of generator at minimum fossil fraction

Ygen

kW

Rated capacity of the generator

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