# 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

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
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

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 . 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 : (19)

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

The total consumption of high-pressure steam by the turbine g is split into three parts: (20)

Here, Qg0(E), Qg0(QM), Qg0(QL) 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 αg0 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 .

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 .

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 Q0(E) is the total high-pressure steam consumption for CHP plant electricity production E. Note, that a similar technique has been developed for gas turbines7.

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 .

Input data:

• Electricity production E = 80 MWh, electricity auxiliary service EAUX = 3 MWh
• Industrial steam production QM = 144.2 MWh, industrial steam auxiliary service QAUXM = 0 MWh
• Heat production QL = 93 MWh, heat auxiliary service QAUXL = 0 MWh
• Total fuel consumption B = 48.4 tef
• Linear coefficients for ST-135 αE = 1.8492, αM = 0.7146, αL = 0.2820, α0 = 95.68738.
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 24