The objective of the upper-layer model is to minimize the expected value of the total operating cost in the province. Considering the uncertainty of the user load and renewable energy output in the province, the model adopts Latin hypercube sampling combined with synchronous back generation technology to generate multiple provincial loads and renewable energy output scenarios and then obtains the total operating cost in the province of each scenario. The goal is to optimize the expected value of the total cost in each scenario. And provide renewable energy demand information for the lower-level model. The upper-level objective function is:

(1)min∑ωπ(ω)⋅Or(ω)

(2){Or(ω)=∑t=1T[Ea(ω)+Eg(ω)+Er(ω)+ECO2(ω)]+Ej+EcEa(ω)=∑m=1MStmPtm(ω)Eg(ω)=∑n=1NSg,tnPg,tn(ω)Er(ω)=∑n=1NSr,tnPr,tn(ω)ECO2(ω)=∑n=1Nλtco2Sco2[Pg,tn(ω)+Pr,tn(ω)]Ej=∑t=1TStjPtjEc=ScPc

where ω is different scenes; π(ω) is the occurrence probability of scenes ω; Or(ω) is the operation cost of the provincial market under the scenario ω. T is the number of system operating periods; M is the number of renewable energy units in the province; N is the number of traditional energy units in the province; Ea(ω) is the total electricity purchase cost of renewable energy under the scenario ω in the province; Stm is the electric energy quotation of renewable energy unit m in the province at time t; Ptm(ω) is the clearing electricity quantity of the provincial renewable energy unit m under the scene ω in time period t; Eg(ω) is the total power purchase cost of traditional energy under the ω scenario in the province; Sg,tn is the electric energy quotation of traditional energy unit n in the province at time t; Pg,tn(ω) is the clearing quantity of traditional energy unit n in the province under the scene ω in the t period; Er(ω) is the total cost of traditional energy reserve capacity under the ω scenario in the province; Sr,tn is the quotation of reserve capacity of traditional energy unit n in the province at time t; Pr,tn(ω) is the reserve capacity of traditional energy unit n in the province in the t time frame scenario ω clearing; ECO2(ω) is the total cost of CO₂ emission under the ω scenario in the province; λtco2 is the carbon emission factor in time period t; Sco2 is the cost per ton of CO₂ emission; Ej is the total electricity purchasing cost of renewable energy between provinces; Stj is the clearing price of the inter-provincial renewable energy market; Ptj is electricity purchased from renewable energy between provinces; Ec is the total purchase cost of the consumption voucher; Sc is the price of unit absorption voucher; Pc is the electricity quantity corresponding to the consumption voucher purchased during the trading period T.

The upper-layer model constraints are

1) Power balance constraints:

(3)∑m=1MPtm(ω)+∑n=1NPg,tn(ω)+Ptj=PtD(ω),∀t∈T

where PtD is the total demand of ω under load in the t period scene in the province.

2) Reserve capacity constraints:

(4)∑n=1NPr,tn(ω)≥α⋅PtD(ω),∀t∈Twhere α is the reserve coefficient of the power grid in a province.

3) Constraint of absorption responsibility:

(5)∑t=1T[∑m=1MPtm(ω)+Ptj]+Pc≥β∑t=1TPtD(ω),∀t∈Twhere β is the weight of non-water renewable energy consumption responsibility in a province.

4) Output constraints of generator set:

(6){Pm_≤Ptm(ω)≤Pm¯,∀t∈T,∀m∈MPn_≤Ptn(ω)≤Pn¯,∀t∈T,∀n∈Nwhere Pm_, Pm¯ are the lower limit and upper limit of output of renewable energy unit m, respectively, Pn_, Pn¯ are the output lower limit and upper limit of traditional energy unit n.

5) Climbing constraints of generator set:

(7){Pt+1m(ω)−Ptm(ω)≤PUPm,∀t∈T,∀m∈MPtm(ω)−Pt+1m(ω)≤PDOWNm,∀t∈T,∀m∈MPt+1n(ω)−Ptn(ω)≤PUPn,∀t∈T,∀n∈NPtn(ω)−Pt+1n(ω)≤PDOWNn,∀t∈T,∀n∈Nwhere PUPm, PDOWNm are the climbing upper and lower limits of renewable energy unit m, PUPn, PDOWNn are respectively the climbing upper and lower limits of the traditional energy unit n.

6) Constraints on the affordable acquisition of renewable energy within the province:

(8)Ptm(ω)≥λPm¯,∀t∈T,∀m∈M

In the formula, λ is the proportional coefficient of guaranteed renewable energy acquisition in the province.

7) Non-negative constraint of decision variables:

(9){Ptm(ω)≥0Pg,tn(ω)≥0Pr,tn(ω)≥0Ptj≥0Pc≥0

In the upper model, there are user load fluctuation and renewable energy output uncertainty in the provincial market, which leads to an increase in the total cost of intra-provincial operation. The deviation between the forecast of renewable energy output and user load demand will cause the electricity purchase demand declared by traders before the operation of the inter-provincial market to deviate from the actual demand. If the demand for electricity purchase is greater than the actual demand, the cost of electricity purchase between provinces increases; If the demand for electricity purchase is less than the actual demand, it is necessary to purchase electricity from the unit with a high quotation in the province, increasing in the cost of clearing the unit in the province.

In this paper, CVaR theory is used to measure the market risk loss in the province. When the confidence level of the provincial power company is ε, the objective function of CVaR risk value in the provincial market is:

(10)minPCVaR=ξ+11−ε∑ωπ(ω)ψ(ω)

The constraint conditions are:

(11){ψ(ω)−Or(ω)+ξ≥0ψ(ω)≥0where ε is the confidence degree of CVaR value in the provincial market; ξ is the CVaR value of the provincial market operation cost; ψ(ω) is a non-negative auxiliary variable.

By minimizing the CVaR risk value in the provincial market, the provincial power company will adjust the power purchase strategy to minimize the risk of the provincial market. Considering the objective of minimizing the provincial market operation cost and value-at-risk, the multi-objective is converted into a single objective function. When the risk aversion coefficient of the provincial power company is γ, the final upper objective function is:

(12){min∑ωπ(ω)Or(ω)+γPCVaRs.t. Eqs.(3)∼(9),(11)

In the equation, γ is the risk aversion coefficient.

In the upper-level model, provincial power companies participate in inter-provincial electricity market trading after obtaining the renewable energy demand of provincial users. Power balance, the transmission capacity of the inter-provincial liaison line, and the output of renewable energy units at the transmission end is taken as constraints to form the objective function of minimizing inter-provincial power purchase cost, and the clearing price of renewable energy returns to the upper-level model. The objective function of the lower model is:

(13)min∑t=1T∑y=1Y∑k=1Ky(Stk+Sty,l)Pty,kwhere T is the number of operating periods of the system; Y is the number of provinces delivering renewable energy; Kk is the number of renewable energy units in the sending province y; Sty,k is the quotation for the renewable energy unit k in the sending province y to participate in the inter-provincial transaction; Sty,l is the transmission cost of the interprovincial liaison line of the sending province y; Pty,k clearing electric energy for the inter-provincial transaction of renewable energy unit k in sending province y.

The constraints of the lower model are

1) Interprovincial renewable energy transmission power balance:

(14)∑y=1Y∑k=1Ky(1−ζy)Pty,k=Ptj,∀t∈T,∀k∈Ky

ζy is the line loss rate of the inter-provincial contact line connected to the sending province y.

2) Transport capacity constraints of inter-provincial contact lines:

(15)Pty,l_≤∑k=1KyPty,k≤Pty,l¯,∀t∈T,∀y∈Ywhere Pty,l¯, Pty,l_ are the upper and lower limits of inter-provincial transmission capacity connected to the sending province, y, respectively.

3) Power constraints of renewable energy units in the delivery province:

(16)Ptk,q_≤Pty,k≤Ptk,q¯,∀t∈T,∀k∈Kywhere Ptk,q¯, Ptk,q_ are respectively the upper and lower limits of the amount of electricity traded by the renewable energy unit k in the sending province y.

4) Inter-provincial renewable energy clearance price

The lower model inter-provincial clearing tariff Stj is:

(17)Stj=λt,∀t∈T

In the equation λt is the dual variable of the constraint of the lower equation, see Appendix A.

A province is taken as the target province for optimal clearing, and three renewable energy delivery provinces are taken as inter-provincial transaction objects for example analysis, as shown in Fig. 3.

This section takes a typical day in the target receiving province as the research object and assumes that the provincial power company needs to complete the corresponding non-water renewable energy consumption of the load on a typical day. It is assumed that the intra-day demand forecast of provincial load obeys a normal distribution with the expectation of μ_r and a standard deviation of 0.2 μ_r, and the intra-day output forecast of provincial wind power and PV obeys a normal distribution with the expectation of μ_w and μ_s and standard deviation of 0.15 μ_w and 0.15 μ_s, respectively. The sampling method is used to generate 1000 scene data for each. See Appendix B for details.

The influence of traditional energy and renewable energy output on carbon emission factors was considered [28], CO₂ emission factor λtco2 as shown in Fig. 4.

Example verification Under default conditions, the main parameters are shown in Table 1, where the quotation of spare capacity of traditional energy units in the province is 5% of the quotation of electric energy.

In this case analysis, the differences in market operation costs in different scenarios are compared under three market mechanism environments. They are as follows:

Mechanism 1: The units and loads in the province are cleared, and the units have not participated in the inter-provincial power market trading, and there is no renewable energy absorption responsibility weight index or quota system constraint, which needs to include carbon emission charges.

Mechanism 2: Based on mechanism 1, it evaluates the consumption situation of the provincial market and puts forward constraints on the consumption responsibility weight index of renewable energy. However, provincial power companies only organize and participate in the clearing operation of the provincial power market, but do not participate in inter-provincial transactions.

Mechanism 3: Based on mechanism 2, provincial power companies can participate in inter-provincial power market trading to obtain renewable energy electricity, and complete the consumption responsibility weight index within the province.

The total cost of market operation is shown in Fig. 5. Mechanism 2 is compared with mechanism 1. The absorption responsibility assessment mechanism is introduced to restrain provincial power companies, which increases the market operation cost. After participating in the inter-provincial renewable energy market trading, the market operation cost of mechanism 3 has decreased, because the renewable energy units sent to the provinces through the inter-provincial contact line, enable the receiving provinces to consume the low price of renewable energy electricity and achieve the consumption responsibility weight assessment index.

As can be seen from Appendix B, in the 27 combination scenarios, scenario 4, which is composed of load demand scenario 1, wind power output scenario 2, and photovoltaic output scenario 1, has the highest probability. Under three different market mechanisms, the output of various units in the province in scenario 4 is shown in Fig. 6.

As can be seen from Fig. 6, the provincial wind power is preferentially cleared among the three mechanisms because its quotation is lower than that of the provincial PV, thermal power, and gas power units, and the electricity quantity is consistent with the prediction of the provincial power output in scenario 4. In Fig. 6a, when the absorption responsibility guarantee mechanism is not implemented in mechanism 1, the photovoltaic units in the province are cleared at the proportion of affordable renewable energy acquisition. In Fig. 6b, the provincial power grid company in mechanism 2 has significantly improved its photovoltaic clearance level to complete the 15% absorption responsibility weight index. It can be seen that the introduction of the absorption responsibility guarantee mechanism promotes the absorption of renewable energy. In Fig. 6c, mechanism 3 introduced inter-provincial renewable energy trading, which gave provincial power companies more ways to complete power supply and realized the absorption responsibility weight index. Compared with mechanism 2, the output of photovoltaic units in the province decreased.

Table 2 shows the results of the three market mechanisms in operation in scenario 4. It can be seen from the table that the total market operation cost and CVaR risk value of mechanism 1 are in the middle position among the three mechanisms. Because the absorption responsibility guarantee mechanism has not been introduced, the provincial market only absorbs wind power and part of guaranteed photovoltaic power output at low prices, resulting in serious light abandonment and the highest carbon emission cost. In mechanism 2, the absorption responsibility guarantee mechanism is introduced, the total cost of market operation is the highest, and the assessment index brings risks, making CVaR the highest risk value. The renewable energy electricity in the province is not enough to achieve the absorption responsibility weight index, so it is necessary to purchase the consumption voucher to complete the intra-day assessment index. Mechanism 3 has the lowest market operation cost and consumes wind power at a lower prices in the province, but there is a phenomenon of more abandoned light power. This is because inter-provincial transactions bring more low-price renewable energy, and the quotation of photovoltaic units in the province is not dominant. Mechanism 3 completes the target of intra-day consumption responsibility weight through the actual consumption of renewable energy, without the additional purchase of consumption vouchers. The carbon emission cost and CVaR risk value are the lowest in the three scenarios.

This example mainly analyzes the results of mechanism 3, when provincial power companies participate in the inter-provincial transaction after obtaining the inter-provincial renewable energy purchasing demand, and clearing the provincial renewable energy units sent to the end, as shown in Fig. 7.

From Figs. 7a–7c, it can be seen that the wind turbines with the lower quotation of A, B, and C have priority over the photovoltaic units in a clearing, while the wind turbines with the lowest quotation of PV and the largest amount of clearing power among the three provinces. The photovoltaic output of the three sending provinces is mainly concentrated in the two periods with high load demand: 6:00–10:00 and 15:00–20:00. In the two periods of 3:00–4:00 and 22:00–23:00, the power of the three sending provinces and receiving provinces is 0. It can be seen from Fig. 8 that in the absence of photovoltaic clearing, the clearing price of the inter-provincial market is mainly determined by the clearing price of wind turbines in the three sending provinces. Since the price of wind turbines in the three sending provinces, inter-provincial contact line loss rate, and transmission cost levels are relatively close, the clearing price remains unchanged at 380.11 yuan/MW·h. When the output of the three provincial PV units starts, the inter-provincial clearing price is mainly determined by the PV units during the two periods of 6:00–10:00 and 15:00–20:00. In the two periods from 6:00 to 9:00 and from 18:00 to 20:00, photovoltaic power is generated in all the three provinces. At this time, the clearing price is the highest, 466.13 yuan. From 9:00 to 10:00 and from 16:00 to 17:00, only photovoltaic units in two provinces B and C are sent for output, and the price is 443.16 yuan. From 15:00 to 16:00, only B with the lowest PV quotation can save PV power, and the clearing price is 437.97 yuan. As can be seen from Fig. 7, the wind turbines with the lower quotation of A, B, and C have priority over the photovoltaic units in a clearing, while the wind turbines with the lowest quotation of PV and the largest amount of clearing power among the three provinces. The photovoltaic output of the three sending provinces is mainly concentrated in the two periods with high load demand: 6:00–10:00 and 15:00–20:00. In the two periods of 3:00–4:00 and 22:00–23:00, the power of the three sending provinces and receiving provinces is 0.

This example analyzes the risk control ability of provincial power companies in mechanism 3, and the influence of different risk aversion coefficients γ, namely different risk preference degrees, on operation costs. As shown in Table 3, with the gradual increase of the risk aversion coefficient, power purchasing decisions become more conservative, and provincial power companies are more inclined to choose thermal power and gas power with accurate output prediction when making power purchasing decisions, thus increasing carbon emission costs.

As shown in Table 3, with the gradual increase of the risk aversion coefficient, provincial power companies become more risk averse and make more conservative power purchase decisions. The CVaR risk value of market operation gradually decreases, and the actual consumption expectation of renewable energy electricity in each scenario decreases, including the electricity purchase of renewable energy between provinces. Provincial power companies are more inclined to choose thermal power and gas power with accurate output prediction when making power purchase decisions, so the carbon emission costs will increase accordingly.

As can be seen from Fig. 9, with the increase in risk aversion coefficient, provincial power companies are more risk averse, and the total cost difference of market operation between scenarios gradually decreases. Among the 27 scenarios, the scenario of high market operation total cost shows a trend of decreasing with the increase of the risk aversion coefficient. It can be seen that the adoption of CVaR risk theory to measure market operation risk can improve the ability of provincial power companies to change their power purchase decision and control market operation costs under the scenario of uncertain risk.

This example mainly studies the influence of the absorption liability guarantee mechanism on the market operation results. With the price of consumption vouchers (i.e., green certificate and excess consumption price) and the weight of non-water consumption responsibility of provincial power companies as variables in mechanism 2 and mechanism 3. Analyze the impact on the expected total running cost of each scenario. The market operation cost of mechanism 2 is shown in Fig. 10a, and the market operation cost of mechanism 3 is shown in Fig. 10b.

According to Fig. 10a, under the condition that the absorption responsibility guarantee mechanism is implemented in the mechanism 2 market and the output of renewable energy units remains unchanged, the market operation cost gradually increases with the increase of the weight of non-water absorption responsibility. At the same time, the market operation cost is also affected by the price parameters of the consumption voucher. The higher the intra-day green certificate and the excess consumption price level, the more sensitive the market operation cost is to the change degree of the absorption responsibility weight. As shown in Fig. 10b, inter-provincial renewable energy trading is introduced in mechanism 3. Provincial power companies participate in inter-provincial trading according to the provincial renewable energy electricity quantity and consumption demand. With the increase of the weight of non-water consumption responsibility, the expected value of the total cost of market operation has increased since the weight value of 23%. At this time, the renewable energy resources within and between provinces gradually cannot meet the demand of the weight of consumption responsibility, so it is necessary to purchase the consumption voucher to achieve the assessment index of the weight of consumption responsibility.