## 3 Results
### Comparison of Mass and Energy Allocation Indicators  
The mass allocation indicator is calculated by the following formula:  
\[MA=\frac{RCR}{RCR+1} \tag{20}\]  
This expression resembles Equation (17), which is used to determine the energy allocation indicator. The only difference is that the energy allocation indicator takes into account lower heating values of grain and straw. Based on Figure 6, it is apparent that the mass allocation indicator can be considered as a special case of the energy allocation indicator.  
Figure 5: The share of energy associated with straw formation.  
Figure 6: Comparison of mass and energy allocation indicators (share of energy for straw formation).  
We took the derivative of Equation (17) with respect to the lower heating value of the grain-to-straw ratio and found the rate of change:  
\[RC=100\cdot\frac{\partial(SR)}{\partial\left(\frac{LHVg}{LHVs}\right)}=100\cdot \frac{\partial\left(\frac{RCR}{LHVg}\right)}{\partial\left(\frac{LHVg}{LHVs} \right)}=-100\cdot\frac{RCR}{\left(RCR+\frac{LHVg}{LHVs}\right)^{2}} \tag{21}\]  
The results of our calculations are presented in Figure 7. The shape of the graph (Figure 7) depicts that the increase in the lower heating value of the grain-to-straw ratio results in a decrease in the rate of change of the energy allocation indicator.  
Power Generation: Energy Specific Costs and Carbon Dioxide Emissions Associated with Straw Formation  
The carbon dioxide emissions of straw-fired power generation can be expressed as:  
\[CDE=\frac{3.6}{\eta_{e}\cdot LHVs}\cdot EFs,\;\mathrm{kg\;CO_{2}/kWh}, \tag{22}\]  
where \(\eta_{e}\) is the efficiency of power generation; \(EFs\) is the carbon dioxide emission factor associated with straw formation, kg CO\({}_{2}\)/kg.  
And the saving of carbon dioxide emissions compared with a fossil fuel power plant can be expressed as:  
\[SCDE=EFcf-\frac{3.6}{\eta_{e}\cdot LHVs}\cdot EFs,\;\mathrm{kg\;CO_{2}/kWh}, \tag{23}\]  
where \(EFcf\) is the carbon dioxide emissions factor (fossil fuel), kg CO\({}_{2}\)/kWh.  
The carbon dioxide emissions factor associated with straw formation was calculated for conventional wheat production technology used in Ukraine. The following initial data were used: the yield of grain--4110 kg/ha; the yield of straw--5138 kg/ha; the total carbon dioxide emissions--1747.9 kg CO\({}_{2}\)/ha; the share of energy that is used for straw formation--0.5. Our calculations showed that the carbon dioxide emissions factor associated with straw formation is around 0.17 kg CO\({}_{2}\)/kg. It results in 0.146 kg carbon dioxide emissions per kWh for a straw-fired power plant.  
Energy specific costs (\(ESC\)) are the energy-input-to-electricity-production ratio:  
\[ESC=\frac{LHVs+\Delta H}{Ws},\;\mathrm{MJ/kWh}, \tag{24}\]  
where \(\Delta H\) is the energy used for straw formation, MJ/kg; \(Ws\) is the quantity of electricity generated by one kilogram of straw, kWh/kg.  
Figure 7: Derivative of energy allocation indicator.  
One kilogram of straw generates:  
\[Ws=\frac{\eta_{e}\cdot LHVs}{3.6},\ \text{kWh/kg}. \tag{25}\]  
Then, the required energy specific costs are:  
\[ESC=\frac{3.6\cdot(LHVs+\Delta H)}{\eta_{e}\cdot LHVs}=\frac{3.6}{\eta_{e}} \cdot\left[1+\frac{\Delta H}{LHVs}\right],\ \text{MJ/kWh}. \tag{26}\]  
Energy specific costs were calculated for the following conditions:  
* The efficiency ranges from 10% to 40%.
* The relative energy used for straw formation (100 \(\Delta H\)/\(LHVs\), %) has two meanings: 0% (energy for straw formation is not taken into account) and 40% (maximum possible value for biomass direct-fired power plants).  
Figure 8 presents the results of our computation. This figure depicts that the increase in the efficiency results in a decrease in the influence of the embodied energy of straw on the absolute energy specific costs.