4.2.1. Initial investment subsidy

To promote the development of the DPV market, the government provides a certain amount of subsidy S to improve the investment return of DPV so that the ROI of DPV investment can reach or exceed SAIY.

$$r_{g1} = P/( {E-S} ) = r$$

However, the goal of enterprises is to achieve maximum profit. In the early stage of the initial investment subsidy, once the government issues the level of subsidy S, private enterprises tend to increase their return and profits through delay, rent seeking, or shoddy engineering.

① Delay

Considering the learning curve and scale effect, the CAPEX of DPV decreases sharply over time, and the delay in construction reduces the investment cost and enhances the investment profit. We assume that the ROI of DPV investment is only half of the SAIY, namely, r_g = P/E = ½r; then, the government considers subsidizing DPV enterprises half of the initial investment: S = ½E. Now, the ROI of DPV projects with subsidy r _g1a = P/(E-½E) = 2P/E = r, which is equal to SAIY. If the enterprises extend the construction one more year, and suppose that CAPEX will fall by 25% during the period, to 0.75E. Although the income and the subsidy are still the same, but the ROI of the same project doubled.

$$r_{g1b} = P/( {0.75E-0.5E} ) = 4P/E = 2r$$

This means that enterprises can double their ROI by delaying construction. In 2010, the administration calculated the DPV CAPEX at around 30 CNY/w and subsidized GSP projects at 15 CNY/w, half of the CAPEX. Then, CAPEX declined to 18 CNY/w in 2011, and if a 2010 GSP project completed construction in 2011, the investors would only spend 3 CNY/w by themselves. By 2012, the CAPEX dropped to 11 CNY/w, so the 2010 GSP projects completed by 2012 did not need any private investment; in contrast, they provided a net profit of 4 CNY/w to the developers directly.

② Rent-seeking

According to the GSP program, the CAPEX was 30 CNY/w in 2010, 18 CNY/w in 2011, and 11 CNY/w in 2012, which were all higher than the actual market prices at that time. In addition, the DPV cost decreased significantly over time, providing space and opportunities for rent-seeking. If GSP's CAPEX has 20% premium over the actual cost, so the over-subsidy is equivalent to 20%*0.5 = 10% of the actual total investment if the government subsidizes 50% of the exaggerated CAPEX. The 10% subsidy would be converted into a value for rent-seeking. According to IRENA's data, the total investment of a 10MW GSP was 280 million CNY (IRENA. Renewable Power Generation Costs in 2020. Abu Dhabi 2020.) in 2010, and the upfront cost, which is known as road-fee (Road-fee refers to the expense of PV project development, including application fee and compliance documents’ cost.), would reach 28 million CNY and occupy 10% of the total investment.

③ Shoddy engineering

Due to the high initial investment subsidy of GSP, as well as the lack of effective and rigorous monitoring of the quality of PV construction, private enterprises might largely cut down the total investment E by using inferior products or shoddy engineering to ensure E < S. If so, the investor will obtain a one-time profit S–E through equipment sales or Engineering Procurement Construction (EPC) and no longer care about future operations and revenue (Fang et al., Reference Fang, Hao, Robert and Jun2015).

Certainly, the authorities also found these issues while implementing GSP policies, modified the policy defects, and slashed the subsidy standards. However, the initial investment subsidy level was still high, and multi-project management was difficult for authorities. Therefore, the GSP did not fully meet the government's expectations. In 2013, the MOF investigated and liquidated the fiscal funds for the GSP during 2009–2011, and found that 80% of projects had not been completed as required. By the end of 2012, only 40% GSP projects finished grid-connections on time.

4.2.2. Insufficient generation subsidies

Learning from the lessons of upfront subsidy, the authority transformed to FITs policy and provided electricity generation subsidy, and subsidized ΔP to improve the electricity price. However, due to the small scale of DPV projects and the risk of tariff collection, ROI of the DPV after the generation subsidy was still lower than that of the SAIY. Furthermore, with the unprecedented growth of UPV and wind power generation, the Renewable Energy Surcharge (RES) was running on financial fumes. The RES fund was the only source to subsidize all renewable energy, and subsidy payments appeared to lag seriously (Jianglong & Jiashun, Reference Jianglong and Jiashun2020). After the completion of PV construction, DPV projects would be applied to enter the list of governmental subsidies and wait for two or more years to obtain the first month allowance. Subsequently, enterprises lost enthusiasm and interest in DPV, and eventually, the development of DPV could not meet the government's expectations, and the market stagnated.

$${\rm Government}\colon \;( P + \Delta P) /E = r$$

$${\rm Enterprise}\colon \;r_{g2} = ( q\ast P + q^{\prime}\Delta P) /E < r$$

Note: q is the rate of successive tariff collections, q’ is the state subsidy availability rate, and q ≤ 1, q’ < 1.

4.2.3. Appropriate generation subsidies

Entering the 13th Five-Year Period, after the rapid expansion of the PV industry, especially UPV deployment, the solar PV CAPEX declined sharply. However, the authorities did not reduce the DPV's subsidies, while the UPV tariff was cut down sharply year by year, and the return of DPV projects continued to rise and gradually approached the SAIY.

$$r_{g3} = ( q\ast P + q^{\prime}\Delta P) /( E-\Delta E) = r$$

where ΔE denotes the reduce of CAPEX

Thereafter, DPV achieved rapid development using the prosumer model: self-use and the remaining electricity sold to the grid. In 2018, under the background of PV subsidy reduction, DPV began to gradually realize grid-parity on the consumer side.

4.2.4. Grid-parity

In 2021, the NDRC declared phasing out the FITs policy and weaned the industry from subsidy reliance. Since 2021, the central government would no longer provide fiscal subsidies for new UPC projects and industrial & commercial DPV projects, and PV's tariff will implement according to local DCEP (NDRC, 2021). To meet the tough dual-carbon targets, incubating and developing DPV remains undeniable during the grid-parity era. How can governments promote and support DPV diffusion through other means? Returning to Eq. (1):

(1)$$r_g = P/E$$

Without the initial investment subsidy and generation subsidy, how can we improve the ROI of DPV, optimize the investment environment, increase the investment enthusiasm of enterprises, and boost the rapid and prosperous development of DPV projects?

Enlarging qualified DPV rooftop

Regarding incremental roofs, there is vast space for DPV development. In 2019, the newly completed construction area in China was more than 4 billion square meters in China. If 5% of the area can be utilized for the installation of DPV, the annual installed capacity will approach nearly 20GW. Improving construction quality and green building standards is conducive to providing more high-quality build surfaces and decreasing the CAPEX, increasing the investment income for DPV projects.

② Green finance policy

The initial investment in DPV is huge and there is a large gap between what private capital can provide. However, private capital can expand investment and enhance yields by leveraging. Today, the share of equity can be maintained at a minimum of 20% of total investment, so the leverage effect is evident in China. Given the ROI of the DPV project r_g, the ROE r_e will be affected by the debt-equity ratio D/E of the capital structure and financing cost r_d (generally r_d < r_g). ROE can be interpreted as ROE-added benefits from financing leverage (Peter, Reference Peter2001):

(2)$$r_g = r_e\ast E/( {E + D} ) + r_d\ast D/( {E + D} ) $$

Solving the equation:

(3)$$r_e = r_g + ( {r_g-r_d} ) \ast D/E$$

Therefore, the ROE is also divided into two parts: the project yield r_g, and the effect of financing leverage. Typically, the ROI of DPV power stations is stable and predictable, and green finance can provide preferential interest for large green investments and help DPV enterprises earn higher returns on equity and lower financing costs to stimulate investment.

③ Peer-to-peer trade (P2P)

P2P trade is a more profitable and win-win solution for both DPV owners and electricity consumers, especially by mutual auctions in local microgrids (Zibo et al., Reference Zibo, Xiaodan, Yunfei and Hongjie2020). P2P transactions expand the sales range of electricity, improve the self-use proportion of prosumers, reduce the EMC contract risk, and increase the rate of tariff collection q, which raises the final electricity price P for DPV, obtains more generation income, and enhances overall investment income.

Considering the risk of tariff collection, the ROI of DPV note as:

(4)$$r_{g4} = q\ast P/E$$

The final sales price P of electricity is the weighted average of the higher discount electricity price P_c from power consumers and the lower DCEP of the rest power sold to the grid, and the weight factor is power absorption ratio of consumer c. P2P model will provide more market channels and allow DPV owners sell more electricity to surrounding enterprises with low default risk and high electricity consumption, then make electricity price P and absorption ratio c higher, so as to improve electricity income and investment return (Peiyun et al., Reference Peiyun, Yiou and Jiahai2021).

(5)$$r_{g5} = q\ast P/E = q\ast ( {c\ast P_c + ( {1-c} ) \ast DCEP} ) $$

note: DCEP < P_c, c ≤ 1, q ≤ 1

4.3.1 Model and assumption

A country has two types of energy production: low-carbon green energy, represented by DPV, and traditional energy with carbon emissions, represented by thermal coal power. Agents include the government – the decision-maker of energy policies–and energy enterprises – the economic agents. The government aims for green economic growth, which means realizing GDP growth under carbon emission control, and enterprises aim to maximize their investment returns. Using the Cobb-Douglas production function (Cobb & Douglas, Reference Cobb and Douglas1928),

Green energy production function:

(6)$${\rm F}_g={\rm A}\left( t \right)_g{\rm K}_g^\alpha $$

Traditional energy production function:

(7)$${\rm F}_o ={\rm A}\left( t \right)_o{\rm K}_o^\alpha $$

Ａ(t)_g and Ａ(t)_o are production efficiency, Ｋ_g and Ｋ_o represent the capital input respectively, and a is the output elasticity of capital a < 1. In the early stages, the production efficiency of renewable technology is lower than traditional energy, which means Ａ(t)_g/Ａ(t)_o is relatively low. Over time, green technologies have improved efficiency, significantly reducing LCOE through the learning effects, while the traditional energy will remain relatively stable. Hence, the ratio ofＡ(t)_g/Ａ(t)_o will be significantly enhanced over time.

Since 1976, PV modules have maintained a 20% learning curve rate for nearly half a century (Elshurafa et al., Reference Elshurafa, Albardi, Bigerna and Bollino2018), and the cost of PV power generation has decreased rapidly. In China, the LCOE of industrial and commercial DPV decreased from USD 0.182/kWh in 2011 to USD 0.060/kWh in 2020, a decrease of three times (IRENA, 2020), whereas the LCOE of thermal power increased from USD 0.034/kWh to USD 0.056/kWh during the same period (IEA, 2010, 2020), an increase of 1.6 times, which almost approaching the cost of DPV generation.

Green energy can not only provide energy for investors but also increase economic output and reduce carbon emissions. Moreover, an increase in economic output brings additional tax revenues and increase employment; thus, there is also a GDP effect. Here, we assume that the GDP effect of developing green energy is a linear function of its output T(F_g):

(8)$$T({\rm F}_g) \ {\rm =} \ t{\rm A}\left( t \right)_g{\rm K}_g^\alpha $$

where t denotes the GDP effect rate of green energy, which is equal to the ratio of the GDP effect to DPV output. The greater the power generation, the greater the GDP effect. Generally, t > 0.

Considering the social carbon cost, the spillover effect of DPV power generation is the carbon reduction during power generation, which is proportional to electricity generation. In short, we assume that the spillover social welfare of green energy is a linear function of its output; note S (F_g):

(9)$$S({\rm F}_g) \ {\rm =} \ s{\rm A}\left( t \right)_g{\rm K}_g^\alpha $$

where s denotes the social welfare rate of green energy and is the ratio of social benefits to DPV output. In contrast to GDP, social benefit is a relatively subjective factor that is influenced by the social value of carbon dioxide abatement, which will increase with their awareness of environmental protection and low-carbon development. During the early stages, the government and public were not conscious of climate change and carbon emissions, so s could be 0. As climate issues become increasingly serious, tackling global warming gradually becomes the main task of all human beings, and the government and public will have much more pressure on carbon emissions and care more about climate change, which will improve significantly.

At the early stage of green energy, the investment return is lower than that of SAIY and the investment return of traditional energy. Because green energy has a social effect on carbon reduction and the GDP effect, the government is motivated to support green energy under the pressure of carbon targets. The government has two schemes to support renewable energy: fiscal subsidies and green finance.

4.3.2 Fiscal subsidy

Upfront subsidies for the initial investment

The fiscal subsidy scheme can be a one-time subsidy for the initial investment or an electricity generation subsidy during operation. First, we analyze the mode of one-time subsidy for the initial investment and use formula (1) without subsidy first:

(1)$$r_g = P/E$$

To develop green energy, the government provides a proportion (f) of subsidies for one-time initial investment to improve the ROI of renewable energy to the level of traditional energy, which equals SAIY and the interest rate r, namely:

$$r = P/E( {1-f} ) $$

Solving equation:

(10)$$f = 1-P/( {E\ast r} ) $$

The total amount of one-time subsidy equals the total investment in renewable energy (K_g) multiplied by the subsidy ratio f, that is, f*K_g

From a fiscal point of view, subsidy policies have two main effects: improving GDP and reducing carbon emissions. The government's target is to maximize the earnings of social welfare and the GDP effect minus the cost of subsidies, and we discount the yearly benefit of government to the current period by interest rate r, as follows:

(11)$$Max \ U_f = \mathop \sum \limits_1^\infty ( sF_g + tF_g) /( {1 + r} ) ^n-fK_g$$

where U_f represents the government's policy earnings, t is the GDP effect rate (such as the tax rate), s is the social welfare rate, and n = 1,2,3…….

(12)$$Max \ U_f = ( s + t) {\rm \ast }F_g{\rm \ast }\mathop \sum \limits_1^\infty 1/( {1 + r} ) ^n-fK_g$$

Cause $\mathop \sum \limits_1^\infty 1/( {1 + r} ) ^n = 1/r$, therefore

(13)$$Max \ U_f = ( s + t) {\rm \ast }F_g/r-fK_g$$

Then we bring Eqs (6) and (10) into (13), then work out as follow:

$$U_f = ( s + t) /r\ast A( t ) _gK_g^a - ( {1-P/( {E\ast r} ) } ) K_g$$

First order derivative of optimization:

(14)$$\partial U_f/\partial K_g = a( s + t) /r\ast A( t ) _gK_g^{a- 1} -( {1-P/( {E\ast r} ) } ) = 0$$

Under optimal conditions, we obtain the solution:

(15)$$K_g^{1-a} = a( {s + t} ) \ast A( t ) _g/( {r-P/E} ) $$

Cause a < 1, hence 1-a > 0

By successively analyzing the variables in the above formula, we can obtain several primary inferences about the development of green energy, as follows:

1. 1. As the public awareness regarding climate change increases, the evaluation of the social welfare rate s for renewable energy will improve, thus promoting the total investment in green energy.

2. 2. The development of green energy is also affected by national and local attitudes towards GDP t. The more emphasis the administration puts on spurring economic growth, the more green energy investments will be done. The diffusion of green energy will support economic growth, provide additional tax revenues, and create employment opportunities in the future.

3. 3. With the large-scale deployment of new energy, renewable technology will continue to improve production efficiency A(t)g, and total green energy production will gradually increase.

4. 4. As global growth is sluggish and the interest rate r in capital market become lower, green energy will embrace new development opportunities, and the economic aggregate of green technology will continue to expand.

5. 5. The development of green energy is also connected with the transformation of the electricity market. With the development of electricity market liberalization and implementation of P2P trade, the proportion of self-consumption for DPV will increase, the final average DPV tariff P will also increase, and the total amount of green energy will further increase.

6. 6. With the development of green energy and technological progress, the CAPEX of green energy E decreases significantly through the learning effects (Neij, Reference Neij2008; Yue et al., Reference Yue, Jinhua and Deqiang2021), green energy enters a virtuous cycle, and the total amount of green energy further increases. Meanwhile, the government should adjust and lower its initial investment subsidy to prevent excessive subsidies.

② Generation subsidy

From the fiscal perspective, it is the same for the upfront investment and generation subsidies. Now, we return to formula (1) without subsidy:

(1)$$r_g = P/E$$

To stimulate green energy, the government provides an appropriate proportion of electricity price subsidy p to improve the investment income of DPV to SAIY r, namely,

$$r = P( 1 + p) /E$$

By solving equation:

(16)$$p = E\ast r/P -1$$

During the operation period, the government needs to subsidize projects according to the annual electricity generation. We still assume that the national average resource endowment is 1000 hours, which means that one watt panel module can generate one kilowatt-hour each year. The annual subsidy is based on the total power generation, which is the equivalent of the installed capacity, and the equal total green energy investment divided by CAPEX E. We multiplied the installed capacity by the electricity price P and price subsidy ratio p and then obtained the total amount of electricity subsidy per year: p*P*K_g/E.

From the fiscal perspective, the government's target remains to maximize social welfare and the GDP effect minus the cost of subsidies, but there are in the same year. We discount them to the current period by interest rate r, as follows:

(17)$$Max \ U_p = \mathop \sum \limits_1^\infty [ {( {sF_g + tF_g} ) -{\rm p\ast }P{\rm \ast }K_g/E} ] /( {1 + r} ) ^n$$

Simplified as:

(18)$$Max \ U_p = [ {( {sF_g + tF_g} ) -{\rm p\ast }P{\rm \ast }K_g/E} ] /{\rm r}$$

Then bring Eqs (6) and (16) to (18):

$$U_p = [ ( s + t) \ast A( t ) _gK_g^a - ( {r-P/E} ) K_g] /r$$

First order derivative of optimization:

(19)$$\partial U/\partial K_p = [ a( s + t) \ast A( t ) _gK_g^{a- 1} -( {r-P/E} ) ] /r = 0$$

Under optimal conditions, we obtain the solution:

(15)$$K_s^{1-a} = a( {s + t} ) \ast A( t ) _g/( {r-P/E} ) $$

This is the same as the result for the upfront subsidy, and we can also infer the six inferences. Meanwhile, we suggest that the intensity of FIT subsidies should be adjusted and reduced with the decrease in LCOE.

4.3.3 Green finance

Assumption: The total capital in the energy field is $\bar{K}$, which is constant in a certain period and is distributed between green energy and traditional energy:

$${\rm K}_g + {\rm K}_o = \bar{K}$$

(20)$${\rm K}_o = \bar{K}-{\rm K}_g$$

The proportion of green energy to traditional energy is k_g. The larger the proportion, the better the development of green energy.

(21)$$ k_g = {K}_g / {K}_o $$

To support green energy, the government provides green credit with a lower interest rate i_g to encourage low-carbon benefits from green technology. Although traditional energy is still subject to the market interest rate i_t, is isolated from the green finance market. Due to free competition in the financial market, the marginal return on capital of investment is equal to their respective interest rates for traditional energy and renewable energy:

(22)$$i_g = \partial F_g/\partial K_g = aA( t ) _gK_g^{a- 1} $$

(23)$$i_t = \partial F_t/\partial K_t = aA( t ) _oK_o^{a- 1} $$

The goal of the government is to maximize the sum of the net output and social benefits and the optimal objective function:

(24)$$MaxU = {\rm F}_g-i_g{\rm K}_g + S({\rm F}_g) + {\rm F}_o- i_t{\rm K}_o$$

Bring Eqs (6), (7) (21–24):

$$Max U = ( 1-a + s) A( t ) _gK_g^a + ( {1-a} ) A( t ) _oK_o^a $$

First order derivative of optimization:

(25)$$\partial U/\partial K_g = a( 1-a + s) A( t ) _gK_g^{a- 1} - a( {1-a} ) A( t ) _oK_o^{a- 1} = 0$$

Where we use formula Eq. (20) and $\bar{K}$ is constant, then we bring Eqs. (21) into (25), and obtain:

(26)$$k_g^{1-a} = ( ( {1 + s/( {1-a} ) } ) \ast A( t ) _g/A( t ) _o$$

Cause a < 1, hence 1–a > 0

By successively analyzing the variables in the equation, we can obtain two more inferences about the ratio of green energy as follows:

1. 7. With global awareness of low-carbon enhancement, the social efficiency rate s of renewable energy assessed by the government and public will increase, and the proportion of green energy in application will continue to improve.

2. 8. With the rapid development of green energy and the continuous progress of renewable technology, the production efficiency of new energy A(t)_g will be significantly upgraded compared to the production efficiency of traditional energy A(t)_o. The ratio of A(t)_g/A(t)_o will continue to increase, indicating that the proportion of green energy will become increasingly high, and the proportion of green investment in the energy field will be much larger.

As mentioned above, there is a risk of tariff collection for renewable energy, and we modify the formula to

(27)$$F_g = q{\rm A}( t )_g{\rm K}_g^\alpha$$

Notes: q is the ratio of successive tariff collection

The optimal objective function of government changed as:

Solving the equation under optimal conditions,

(28)$$k_s^{1-a} = ( ( {1 + s-a} ) q/( {1-a} ) \ast A( t ) _g/A( t ) _o$$

1. 9. With electricity market reforms and diffusion of P2P trade, we can hedge the risk of tariff collection, which will improve investment income, largely expand green energy investment, and further increase the proportion of green energy.