Providing a mathematical model to select governmental supporting scenarios for renewable energy plants

Figures & data

Table 1. A review of the conducted studies.

Title	Description	Model type	Region of conduction
Zhang, Zhou, and Zhou (2014)	The results show that, if an advanced CO2 market can be employed, then investing in renewable energy in China will be attractive, otherwise the Chinese government should not expect to attract investors to build renewable energy units in the short run.	Quantitative	China
ShahNazari et al. (2014)	Providing feed-in tariffs and taking into account CO2 price fluctuations in government subsidy policies will attract more investment in this area.	Quantitative	China
Zhang et al. (2017)	A model is proposed for investing in biomass energy production in China. In the proposed model, the aim was to take into account the uncertainty in the market price of electricity and CO2 prices. Similarly, this study also emphasises that the implementation of the carbon emissions trading plan theoretically helps to improve the value of the investment and advances the most likely optimal investment time. On the other hand, it is pointed out that the current CO2 price is not enough to advance the most probable optimal investment time, any further.	Quantitative	China
Zhang, Zhou, Zhou, et al. (2016)	The effects of government subsidies on energy production investment in the optimal design of micro-grid systems was investigated. In this paper, the effects of various government supportive policy measures on the optimal structuring of small networks, in the island state are investigated. To this end, by providing a computational model, they conducted a sensitivity analysis and evaluation of the impact of government subsidies and electricity prices on the balanced cost of electricity in different systems.	Qualitative	Poland
Zhang, Zhou, Ding, et al. (2016)	A model is presented for optimising renewable energy subsidies and carbon taxes for small and medium-sized multi-energy systems using two-tier planning. At the top level of the model, as the government minimises its support costs, sets subsidies to meet the target of reducing emissions; at the low level, to design and operate energy production optimally, with respect to the costs, subsidies, and the amount of investment made, the multi-energy system manufacturing companies make decisions in a way that minimises their overall costs, i.e. total investment and operating costs.	Quantitative	Italy

Figure 1. The flowchart of the proposed method.

Table 2. Uncertainty factor parameters.

Parameters	Variables	Initial Value	Drift Rate	fluctuations $(\sigma )$
Electricity market prices	$p^e$	0.0516 $/kWh	0.02	0.02
Cost CO2	$p^c$	0.0144 $/kWh	0.02	0.03
Unit investment price	$p^l$	1440 $/kWh	−0.06	0.04

Table 3. Key technical and economic parameters of the project (https://www.satba.gov.ir/en/home).

Parameter	Variables	Amount
Unit maintenance and operation costs	$uom{c}_t$	$0.024\mathrm{\$}/\mathrm{kWh}$
Unit production capacity	$q^e$	$7500\mathrm{kWh}$
Amount added to tax	$r^v$	$9\text{\%}$
Amount added to tax rate	$r^i$	$25\text{\%}$
Discount rate	$r$	$0.08$
Course studied	$t_v$	16 Years
Lifecycle of a solar power project	$L$	25 Years
Annual reduction rate of unit production capacity	$dr$	$2\text{\%}$
Installed capacity	$IC$	$5\mathrm{kW}$
Proportion of marketable carbon in total carbon emissions	$K$	1
Property demand rate	$r^{zy}$	0

Figure 2. Unit production capacity without considering carbon emissions.

Figure 3. Unit generating capacity (with CO₂ emission).

Figure 4. The impact of electricity market prices in a state without considering carbon emissions.

Figure 5. The impact of electricity market prices on carbon emission considerations.

Figure 6. The impact of electricity market prices in the state without considering carbon emissions in the state of market price fluctuations.

Figure 7. The effect of electricity market prices under the consideration of carbon emissions condition in the event of market price fluctuations.

Figure 8. Impact of discount rate on subsidy amount, threshold and project value.

Figure 9. Impact of discount rate considering carbon emissions.

Figure 10. Impact of CO₂ price fluctuations on subsidy amount, threshold and project value.

Figure 11. The impact of CO₂ emission reduction price.

Figure 12. The effect of CO₂ emission threshold value on the profitability of a company with a nominal production of 1 MW in Iran.

Table 4. Main results (dollars per kilowatt).

Scenario	Subsidy (RO)	Subsidy (NPV)	Project value	Threshold value
Without carbon right sales	972.69	945.86	−945.86	29.78
With carbon right sales	121.33	789.04	−789.04	103.85

Table 5. The effect of uncertainty rate on model results.

Uncertainty rate	Without carbon right sales		With carbon right sales
	(NPV)	(RO)	(NPV)	(RO)
0	945.86	972.69	789.04	921.33
0.1	940.26	968.43	780.49	919.39
0.2	934.18	963.76	723.18	869.03
0.3	924.62	955.67	703.52	856.66
0.4	917.8	950.41	684.61	845.41
0.5	900.34	934.58	633.97	802.81
0.6	882.34	918.29	607.15	784.43
0.7	863.19	900.94	550.56	736.71
0.8	834.28	873.92	503.14	698.59
0.9	784.2	825.82	446.97	652.2

Figure 13. Changes in NPV and RO value of the project at different rates of uncertainty.

Figure 14. Standard deviation of robust box method in NPV results.

Zhang, M., D. Zhou, and P. Zhou. 2014. “A Real Option Model for Renewable Energy Policy Evaluation with Application to Solar PV Power Generation in China.” Renewable and Sustainable Energy Reviews 40: 944–955. doi:10.1016/j.rser.2014.08.021.

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ShahNazari, Mahdi, Adam McHugh, Bryan Maybee, and Jonathan Whale. 2014. “The Effect of Political Cycles on Power Investment Decisions: Expectations Over the Repeal and Reinstatement of Carbon Policy Mechanisms in Australia.” Applied Energy 130: 157–165. doi:10.1016/j.apenergy.2014.05.040.

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Zhang, M. M., D. Q. Zhou, P. Zhou, and H. T. Chen. 2017. “Optimal Design of Subsidy to Stimulate Renewable Energy Investments: The Case of China.” Renewable and Sustainable Energy Reviews 71: 873–883. doi:10.1016/j.rser.2016.12.115.

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Zhang, M. M., D. Q. Zhou, P. Zhou, and G. Q. Liu. 2016. “Optimal Feed-in Tariff for Solar Photovoltaic Power Generation in China: A Real Options Analysis.” Energy Policy 97: 181–192. doi:10.1016/j.enpol.2016.07.028.

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Zhang, Mingming, Dequn Zhou, Hao Ding, and Jingliang Jin. 2016. “Biomass Power Generation Investment in China: A Real Options Evaluation.” Sustainability 8 (6): 563. doi:10.3390/su8060563.

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