# The Combined Heat and Power Plant Cost Allocation Methods: An Overview and a New Method Based on the Linear Steam Turbine Characteristic Curve. Section 3. A new method

*PDF version of the paper (0.4 MB).*

Section 1. A cost allocation problem statement

Section 2. A methods review

Section 3. A new method of the CHP plant fuel rate calculation and cost allocation based on a steam turbine linear characteristic curve

Section 4. The methods comparison

References

3.1. A steam turbine linear characteristic curve

3.2. Method description

3.3. Example

## 3.1. A steam turbine linear characteristic curve

A linear characteristic curve has been developed for both gas and steam turbines during the **CHP plant optimization project**. The details of the project are discussed in my previous paper [16]. Currently, it's in Russian, but I've scheduled its translation to English in 2021. In the present paper, a **steam turbine is considered only**.

A *linear characteristic curve for steam turbine* g looks as follows [16]:

where g∈[1:G] is a steam turbine number; α^{g}_{i} are linear coefficients; ε^{g} is the error of linearization. The algorithm to get a linear characteristic curve and α^{g}_{i} values for both steam and gas turbines is developed in work [16]. An average mean absolute percentage error of linearization of various types of turbines comprises 0.6%. See error details in the paper [16].

The total consumption of high-pressure steam by the turbine g is split into three parts:

Here, Q^{g}_{0}(E), Q^{g}_{0}(Q_{M}), Q^{g}_{0}(Q_{L}) are consumption of high-pressure steam for production electricity, industrial steam, and heat, respectively, MWh.

Define the consumption of high-pressure steam for the production of electricity based on a linear characteristic curve (19):

Value α^{g}_{0} is called *idle consumption*, i. e. consumption of high-pressure steam when the turbine doesn't generate any output. This value is allocated for electricity generation [17].

Consumption of high-pressure steam for industrial steam and heat production is determined by the following statements:

## 3.2. Method description

This method is a **thermodynamic method for the fuel rate calculation**. The method is based on the high-pressure steam equation (20).

The additional input data are the coefficients of the linear characteristic curve for the steam turbine of a CHP plant [16].

According to this method, the problem is solved in the following three steps.

**1) Find high-pressure steam consumption for CHP plant products**

For a set of CHP plant steam turbines, the consumption of high-pressure steam for electricity generation is:

where Q_{0}(E) is the total high-pressure steam consumption for CHP plant electricity production E. Note, that a similar technique has been developed for gas turbines^{7}.

^{7}If you're interested in equations for the gas turbine, please, contact me.

In the same style, I define equations for total high-pressure steam consumption for industrial steam and heat production:

**2) Allocate total fuel consumption by CHP plant products**

The fuel consumption for electricity production equals:

Analogously, the fuel consumption for industrial steam and heat production is calculated according to:

**3) Calculate fuel rates and product costs**

The specific fuel rates are calculated based on formulas (1) – (3); product costs on formulas (13) – (15).

## 3.3. Example

For the CHP plant under consideration in xlsx-appendix, the co-generation is carried out by a steam turbine ST-135. A diagram of the CHP plant operation mode is given in [4].

Input data:

- Electricity production E = 80 MWh, electricity auxiliary service E
^{AUX}= 3 MWh - Industrial steam production Q
_{M}= 144.2 MWh, industrial steam auxiliary service Q^{AUX}_{M}= 0 MWh - Heat production Q
_{L}= 93 MWh, heat auxiliary service Q^{AUX}_{L}= 0 MWh - Total fuel consumption B = 48.4 tef
- Linear coefficients for ST-135 α
_{E}= 1.8492, α_{M}= 0.7146, α_{L}= 0.2820, α_{0}= 95.6873^{8}.

^{8}The calculation of coefficients is carried out in the paper xlsx-appendix, sheet “ST-135 linear charact. Curve.”

**1) Find high-pressure steam consumption for CHP plant products**

High-pressure steam consumption for electricity production equals:

High-pressure steam consumption for industrial steam and heat production:

Total high-pressure steam consumption is the sum of the three parts above:

**2) Allocate total fuel consumption by CHP plant products**

The fuel consumption for electricity production is:

Analogously, the fuel consumption for industrial steam and heat production is:

**3) Calculate fuel rates and product costs**

Fuel rates for CHP plant products net supply are:

And product costs are:

The additional calculation is shown in the xlsx-appendix.

Section 1. A cost allocation problem statement

Section 2. A methods review

Section 3. A new method of the CHP plant fuel rate calculation and cost allocation based on a steam turbine linear characteristic curve

Section 4. The methods comparison

References