Near-zero carbon stochastic dispatch optimization model for power-to-gas-based virtual power plant considering information gap status theory

Set

t

= index for time; and

j

= index for step.

Scalar

QP2Grated

= rated gas production power of P2G;

α

= maximum degree of uncertainty;

δ

= carbon emissions per unit of electricity;

η_CGT,t

= conversion efficiency of natural gas;

η_BPG,t

= conversion efficiency of biomass fuel;

λ

= government or the regulatory authority sets the carbon emission reduction allocation rate;

a

= calculation coefficients of carbon emissions from CGT power generation;

b

= calculation coefficients of carbon emissions from biomass power generation(BPG) power generation;

c

= calculation coefficients of carbon emissions from utility power grid (UPG) power generation;

d

= length of the carbon emission growth interval;

σ

= increase of the carbon trading price of each step;

η

= price range of the carbon emission;

a_CGT

= calculation coefficients of CGT power generation fuel cost;

b_CGT

= calculation coefficients of CGT power generation fuel cost;

c_CGT

= calculation coefficients of CGT power generation fuel cost; and

σ_risk

= expected target deviation coefficient.

Parameter

CCO2

= carbon trading cost of GVPP;

PCO2

= carbon trading price on the market;

P_UPG,t

= price of electricity purchased;

C_CGT,t

= power generation cost of CGT at time t;

C_BPG,t

= power generation cost of BPG at time t;

CCGT,tsd

= start and stop cost of CGT at time t;

NCGThot

= hot start cost of CGT;

NCGTcold

= cold start cost of CGT;

NCGToff

= shutdown cost of CGT;

Q_P2G,t

= natural gas production by P2G at time t;

SGST,T0

= gas storage in GST at the initial moment;

QGST,tP2G

= the amount of natural gas entering GST at time t;

QGST,tCGT

= the amount of natural gas that GST inputs to CGT at time t;

QGST,tCH4

= the amount of natural gas that GST enters the natural gas network at time t;

SGST,tmax

= maximum gas storage capacity of GST at time t;

SGST,tmin

= minimum gas storage capacity of GST at time t;

QGST,tP2G,min

= minimum power of the gas storage of GST at time t;

QGST,tP2G,max

= maximum power of the gas storage of GST at time t;

QP2G,tmin⁡

= minimum power of natural gas output by P2G at time t;

QP2G,tmax⁡

= maximum power of natural gas output by P2G at time t;

QGST,tmin⁡

= minimum power of natural gas output by GST at time t;

QGST,tmax⁡

= maximum power of natural gas output by GST at time t;

gCGTmax⁡

= maximum power generation of CGT;

gCGTmin⁡

= minimum power generation of CGT;

ΔgCGT+

= up climbing power of CGT;

ΔgCGT−

= down climbing power of CGT;

MCGTon

= shortest starting time of CGT;

MCGToff

= shortest downtime of CGT;

gPSD,tmax⁡

= maximum charge and discharge power of the PSD at time t, respectively;

gPSD,tmin⁡

= minimum charge and discharge power of the PSD at time t, respectively;

ECO2,tP2G

= carbon emissions that can be converted by P2G;

SPSD,tmax⁡

= maximum power storage capacity of the PSD at time t;

SPSD,tmin⁡

= minimum power storage capacity of the PSD at time t;

S_PSD,t+1

= storage capacity of the PSD at time t+1;

D^j,min

= minimum power generation output provided by DRP at step j;

Dtj

= power generation output that DRP can provide at step j at time t;

ΔLDRP,tmax⁡

= maximum power generation output allowed by DRP at time t;

gGVPP,tmax⁡

= maximum and minimum output power of GVPP at time t;

gGVPP,tmin⁡

= maximum and minimum output power of GVPP at time t;

gPSD,tdis,max⁡

= maximum discharge power of the PSD at time t;

gPSD,tchr,max⁡

= maximum charge power of the PSD at time t;

P_R,t

= peak shaving cost of wind power and PV in response to power deviation at time t;

g_t

= output state of traditional power generation resources other than wind and solar at time t;

u_t

= start-stop state of traditional power generation resources other than wind and solar at time t;

TCGT,ton

= continuous running time of CGT at time t;

TCGT,toff

= down time of CGT at time t;

TCGTmin⁡

= shortest hot start time of CGT;

TCGTcold

= cold start time of CGT;

TCGToff,min⁡

= down time of CGT;

TCGT,t−1on

= continuous running time of CGT at t − 1;

TCGT,t−1off

= continuous downtime of CGT at t − 1;

ηPSD,tchr

= charge power of the PSD at time t;

ηPSD,tdis

= discharge power of the PSD at time t;

ηPSD,tchr

= charge power of the PSD at time t;

ηPSD,tdis

= discharge power of the PSD at time t; and

E˜

= free carbon emission quota obtained by GVPP.

Variables

g_CGT, _t

= power generation of CGT at time t;

g_BPG,t

= power generation of BPG at time t;

g_UPG,t

= purchased electricity of GVPP at time t;

E

= actual carbon emissions of GVPP;

gCGT,tP2G

= power generation of CGT using methane provided by P2G at time t;

gCGT,tGST

= power generation of CGT using methane provided by GST at time t;

gPSD,tchr

= charging power of energy storage at time t;

g_UPG,t

= outsourced power output of GVPP at time t;

ΔL_DRP,t

= output provided by the demand response integrator (DRP) at time t;

L_t

= load demand at time t;

ΔL_P2G,t

= power load of P2G at time t;

ΔLtj

= actual power generation output provided by DRP at step j at time t;

F_cost

= operating cost of GVPP;

g_UPG,t

= electricity purchased by GVPP at time t;

u_CGT,t

= operating state of CGT at time t;

g_PV,t

= power generation output of PV at time t;

g_WPP,t

= power generation output of WPP at time t;

gPSD,tdis

= discharging power of energy storage at time t;

gWPP,t*

= actual output power generation of wind power;

gPV,t*

= actual output power generation of PV;

F_risk

= expected target value of the decision-maker;

Fcos⁡topt

= optimal GVPP target value;

L_net,t

= net load demand at time t; and

S_swort

= the worst scenario of GVPP operation.

1.1 Power-to-gas-based virtual power plant system composition

GVPP integrates P2G devices and gas storage tank (GST) with conventional VPP distributed energy sources such as WPP, PV station, CGT, PSD and controllable loads. Among them, the controllable load participates in system dispatch through an incentive demand response method, which is mainly provided by a demand response provider (DRP) and is generally industrial loads with flexible power characteristics, electric vehicle loads and some commercial loads. PSD and GSD are based on real-time electricity price and gas price, choose discharge/gas or charge/gas, so as to earn “spread” income. Figure 1 is a schematic diagram of the structure of GVPP.

In GVPP, P2G operations are divided into two processes: electrolysis and methanation. Electrolysis is the direct injection of hydrogen into natural gas pipelines or hydrogen storage equipment after the excess electric energy is produced by electrolyzing water to produce hydrogen, and its energy conversion efficiency can reach 75% to 85%. The methanation process is based on electrolysis. Under the action of a catalyst, the hydrogen and carbon dioxide generated by the electrolysis of water react to form methane and water. The specific chemical reactions are as follows:

Through the abovementioned two-stage chemical reaction, the comprehensive efficiency of electricity-to-natural gas conversion is between 45% and 60%. After the electricity is converted into natural gas, it can be injected into a natural gas network or GSD. It can be seen that the H₂O input and output of the P2G chemical reaction are the same, and only CO₂ is consumed, which is conducive to reducing the carbon emissions of GVPP power generation. Figure 2 is a schematic diagram of P2G technology.

1.2 Power-to-gas-based virtual power plant carbon transaction costs

Carbon trading is a trading mechanism that allows participants to trade carbon emissions as commodities by establishing a fair, open and just carbon trading market, thereby achieving the goal of systematic carbon emission reduction (Geert et al., 2018). Generally speaking, the allocation of carbon emission allowances is mainly based on free allocation. All participating entities formulate and adjust production plans based on the carbon emission allowances they have obtained. If the actual carbon emissions are higher than the allocated allowances, they need to purchase excess shares in the carbon trading market. On the contrary, the remaining allowances can be sold in the carbon trading market. For GVPP, the initial free carbon emission allowance is directly related to the power generation of different components, and carbon trading can be carried out for the excess or deficiency. GVPP carbon emission sources include two channels, namely traditional power generation resources and purchased power. Among them, traditional power generation resources include gas-fired power generation and biomass fuel power generation. At the same time, for the convenience of analysis, it is assumed that the electricity purchased by GVPP is thermal power. At this time, the carbon emission allowances obtained by GVPP is calculated as follows:

where δ refer to Geert et al. (2018), set to 0.648; further, to calculate the carbon emission cost of GVPP, it is necessary to calculate the actual carbon emission of GVPP. According to the Ju et al. (2019a), the carbon emission of CGT and BPG power generation is actually a quadratic function, and the specific calculation is as follows:

where ECO2,tP2G is a carbon emission reduction.

To perform differentiated cost accounting for different carbon emission statuses, drawing on the ideas of Geert et al. (2018), constructing a stepped carbon transaction cost calculation model, based on the free carbon emissions calculated in formula (3), divide a number of different carbon emission ranges. When the carbon emissions are higher, the carbon trading settlement price is also higher. The calculation formula of GVPP ladder carbon transaction cost is as follows:

When E,E˜, CCO2 is a negative value, indicating that the actual carbon emissions of the system will be lower than the free carbon emissions. At this time, the initial carbon trading price can be purchased and stored to obtain carbon trading benefits.

2.1 Objective function

Considering that GVPP participates in power system dispatch as a whole, that is, it is a low-carbon economic dispatch optimization problem 24 h before the day. According to formula (4), if E = 0 at the end of the scheduling period, it indicates that all the CO₂ generated by GVPP is converted into CH₄, which enters the gas network or is stored in the GST. It is considered that GVPP has achieved the goal of zero carbon emissions. However, zero carbon emissions requires P2G to fully use clean energy to generate electricity and convert CO₂ in the last period of the dispatch cycle, which is difficult to achieve. Therefore, this study pursues the goal of near-zero carbon emissions, considering the maximum value of E→0, the carbon transaction cost is as small as possible. At the same time, the operating cost of GVPP also includes the cost of power generation fuel and the cost of outsourcing electricity. Therefore, this study chooses to minimize the operating cost as the optimization objective. The specific objective function is as follows:

where C_CGT,t and C_BPG,t mainly include fuel cost and start-up and stop cost. Taking CGT as an example, the specific calculation is as follows:

2.2 Constraint conditions

In the process of GVPP operation, it is necessary to consider the load supply and demand balance constraints, the operation of each component unit and the spinning reserve constraints. The specific constraints are as follows.

3.1 Information gap decision theory

There are uncertain variables such as wind power and PV power generation in GVPP, because its scheduling optimization decision is based on the forecast information of uncertain variables. When the actual value of the uncertainty variable deviates from the predicted value, it is considered that the uncertainty variable has an information gap. Yakov Ben-Haim et al. proposed and improved the IGDT in the 1980s continuously, which is used to describe the gap state between the known and unknown uncertain information (Pilar et al., 2018). When the information gap is generated, if the actual value deviates in a bad direction, it will have a negative impact on the decision-making system. Conversely, when the actual value deviates in a good direction, it will bring opportunity benefits to the decision-making system. The IGDT forms an open decision-making optimization strategy by separately constructing the risk aversion (robust) model and the risk speculation (opportunity) model corresponding to the above two directions and analyzes the degree of uncertainty and consequences, so as to formulate a more realistic decision-making plan (Pilar et al., 2018). The basic model of IGDT includes system model, uncertainty model and minimum demand model, which are described as follows:

For any initial system model, it can be written in the form of objective function, inequality constraint and equality constraint, as follows:

where R is the objective function; q is the determined parameter; v is the uncertain parameter; H(q, v) is the inequality constraint; and G(q, v) is the equality constraint.

Considering the uncertainty parameter v, and its corresponding predicted value is v˜, the interval can be used to describe the floating state of the uncertainty variable U(α,v˜) as follows:

where α is the uncertainty of the parameter v; that is, for v in the set U(α,v˜), the maximum perturbation relative to the predicted value v˜ is α v˜.

The minimum demand model is mainly used to describe the impact of the uncertainty variable predicted value deviation on the system decision. Considering that the parameter r_c is the lower limit of the target value acceptable to the decision-maker, for any parameter v, the objective function R(q, v) can satisfy the following constraints:

According to formulas (28) to (30), the original initial system decision-making model can be transformed into an uncertain decision-making model as follows:

Through the abovementioned optimal model, it can be ensured that under the premise of the target value acceptable to the decision-maker, the maximum fluctuation of the uncertainty parameter can be withstood. The decision value q is obtained by formula (31), which can ensure that when v is disturbed in the set U(α,v˜), the target value r_c acceptable to the decision-maker can be obtained.

The IGDT stochastic scheduling optimization model shown in formula (31) ensures that the obtained decision-making scheme has strong applicability, which is also called robustness, by considering the extreme situations of uncertain variables. However, the prerequisite for the optimal scheme determined by formula (36) is that the objective function changes monotonously with the wind and solar uncertainty parameters, which can be calculated by using formula (35). However, in GVPP low-carbon stochastic dispatch, when carbon transaction costs are considered, wind power and PV generation have a carbon emission reduction effect, which causes the uncertain costs of wind and solar and carbon transaction costs to offset each other. It may cause the objective function to show non-monotonic changes with the uncertainty variable; this leads to the inability to directly apply formula (35) to obtain the extreme value, the decision cost corresponding to the scene with the largest or smallest wind power is not necessarily the largest. In this case, it is necessary to establish a method for obtaining the worst scenario.

3.2 Stochastic scheduling model

This section uses IGDT to deal with the certainty of wind power and PV generation and proposes a GVPP stochastic scheduling optimization model that considers the state of information gaps. The specific process is as follows.

3.3 Worst-case scenario analysis

Wind power and PV power generation in GVPP have strong uncertainties. When the actual output power is lower than the predicted value and the net load of the system increases rapidly, the wind and solar uncertainty will have the greatest impact on the stable operation of the system, which is the worst scenario. Therefore, it is first necessary to find the moment when the system net load fluctuates the most. The specific calculation is as follows:

According to formula (38), the net load fluctuation characteristics can be obtained, and the scenario with the largest load fluctuation is further selected as the worst scenario for GVPP operation. The specific calculation is as follows:

Further, construct the GVPP scheduling optimization decision objective function corresponding to the worst scenario as follows:

According to formula (40), the GVPP system peak shaving transaction decision-making objective in the worst scenario is established, and the GVPP scheduling optimization decision-making plan obtained in this scenario is the most conservative transaction plan.

4.1 Basic data

This study chooses nine-node energy concentrator system as the simulation system, H1 to H9 are nine energy concentrators. Among them, H1 is configured with 2 × 1MW WPP, H5 is configured with 2 × 0.5 MW PV and 1 × 1MW BPG, and H6 is configured with 1 × 1MW CGT and 1 × 1 MW·h PSD. H7 is equipped with 1 × 0.2 MW P2G and 200 m³ GSD. Set the maximum charge and discharge power of ESD to be 1 × 0.2 MW, the electrical energy conversion efficiency of P2G is 60%, the calorific value of natural gas is 39 MJ/m³, and the gas storage loss rate is 5%. It is assumed that BPG power generation fuels are mainly user biogas digesters and large pig farms. The daily biogas output of a typical load is about 4746 m³, and the relationship between biogas and output power is about 0.55–0.62 m³/kW·h (Götz et al., 2016). The power generation cost parameters and emission coefficients of CGT and BPG are selected in Ju et al. (2019b), and the carbon emission rights transaction price is set to 45 yuan/ton. Figure 3 is a diagram of the node energy concentrator system structure.

Furthermore, considering that WPP, PV, CGT and BPG are all dispatched by GVPP, refer to Ting et al. (2018) to set the on-grid power price for power generation and the price of natural gas sales for a typical load day. When GVPP cannot meet its own load demand, it can purchase electricity from UPG, and the purchase price is set at 0.8 yuan/kW·h. Using the scenario production and reduction strategy proposed in Ju et al. (2019a), setting the WPP and PV power generation output parameters, simulating the WPP and PV power generation scenarios of the typical load day, select the scenario with the highest probability as the input data. At the same time, considering the flexibility of end users to participate in GVPP power generation scheduling through DRP agents, the maximum positive and negative output provided by DRPs does not exceed 10% of the original load. Figure 4 shows the forecast values of wind power, PV power generation and load demand on a typical load day.

Finally, to analyze the effectiveness of IGDT in dealing with the uncertainty of WPP and PV, the initial value of the expected target deviation coefficient of decision-makers is set to 0.5, and the sensitivity analysis of the predicted deviation coefficient is performed to verify the effectiveness of the IGDT. After inputting the basic data, the model is solved by the general algebraic modeling system (GAMS) software using CPLEX 11.0 linear solver from ILOG_solver (Ju et al., 2019b). The CPU time required for solving the problem for different case studies with a thinkpad X1 carbon series laptop computer powered by core i5 processor and 8 GB of RAM. When the optimization is mixed integer linear programming, the GAMs software could get a satisfactory solution quickly.

4.2 Validity verification

IGDT is used to describe the optimal operation of GVPP scheduling considering the uncertainty of wind and solar, and the degree of uncertainty under different expected target deviation coefficients is measured. Overall, the degree of uncertainty has a linear relationship with the predicted target deviation coefficient, as the expected target deviation coefficient increases, that is, the increase in the cost that the decision-maker can bear, the allowable degree of uncertainty in the scenery also increases. For example, when the prediction target deviation coefficient is 0.5, the degree of uncertainty σ_risk = 0.142. It shows that when the wind and solar output power fluctuates within the range of [0.858, 1.142] times the predicted value, the decision-making scheme obtained by the method in this study can ensure that the cost of the dispatching decision-making scheme is less than the expected cost of the decision-maker. Figure 5 shows the relationship between the tolerance of GVPP and the expected target deviation coefficient.

Further, consider the GVPP scheduling optimization scheme in deterministic scenarios and uncertain scenarios, respectively, when σ_risk = 0, the decision-maker believes that the predicted value of wind and solar output power is consistent with the actual value; when the decision-maker considers the uncertainty of wind and solar, this study sets the initial prediction target deviation coefficient to 0.5; the degree of uncertainty is obtained as σ_risk = 0.142. Correspondingly, the optimal scheduling schemes of GVPP in deterministic and uncertain scenarios are calculated, respectively. Figure 6 shows the optimal scheduling scheme of GVPP under different prediction target deviation coefficients.

According to Figure 6, if we do not consider the uncertainty of the scenery, to pursue the goal of minimizing the cost of power generation, GVPP will give priority to using WPP and PV for power generation. CGT is mainly used to meet the basic load, and GST, DRP and PSD mainly provide peak shaving services; when considering the uncertainty of wind and solar, to increase the flexibility of the system, CGT began to participate in wind and solar peak shaving. At this time, to reduce the overall cost of power generation, BPG power generation output increased, and P2G converts more CO₂ into CH₄, reducing the carbon emission cost of GVPP, and the range of DRP and PSD calls are significantly increased to improve GVPP’s ability to cope with the uncertainty of scenery. Table 1 shows the GVPP scheduling optimization plan under different scenarios.

According to Table 1, when considering the uncertainty of wind and solar output power, the power output of CGT and BPG increased by 4.68 MW·h and 14.64 MW·h, while the output of wind power decreased by 7.88 MW·h. At the same time, because P2G and PSD have the ability to use energy waste during valley hours and supply power during peak hours, DRP has the ability to provide negative output during peak hours. Therefore, to pursue the goal of the lowest power generation cost, PV power generation increases by 1.39 MW·h during peak hours during the day. In addition, when the expected target deviation coefficient is 0.5, the corresponding degree of uncertainty is 0.142. At this time, the carbon emissions have been reduced to 0 tons, that is, zero carbon emissions have been achieved.

In summary, this study proposes to apply the IGDT to the uncertainty of the wind and solar and establishes the GVPP low-carbon random call optimization model. The results of the above calculation examples verify that the optimization results are in line with the actual scheduling experience and reflect the effectiveness of the method in this study. In general, the GVPP low-carbon stochastic scheduling optimization model proposed in this study can reasonably set the expected target deviation coefficient for decision-makers based on their own risk attitudes and then obtain the optimal decision-making plan that meets their own requirements and provide effective decision-making tools.

4.3 Near-zero carbon dispatching plan

Applying the GVPP low-carbon stochastic scheduling optimization model based on the IGDT proposed in this study, this section takes zero carbon emissions from GVPP operations as the goal and calculates the corresponding prediction target deviation coefficient and uncertainty cost. When the predicted target deviation coefficient is equal to 0.326, GVPP achieves near-zero carbon scheduling, and the degree of uncertainty at this time is equal to 0.131. Figure 7 shows the GVPP optimal dispatch plan under the zero carbon emission scenario and the worst scenario.

According to Figure 7, when the decision-maker expects that the target deviation coefficient is set to 0.326, GVPP operation can reach the critical value of zero carbon emissions. At this time, GVPP can sell carbon emission allowances through the trading market. To achieve the goal of zero carbon emissions, BPG was not used due to high carbon emissions per unit of power generation. Peak shaving services for wind power and PV power generation are mainly satisfied by P2G, PSD and DRP. It is particularly noteworthy that the PSD and DRP operation basically strictly match the peak and valley distribution of the load curve at this time. Further, analyzing the operation of P2G-GST, it can be seen in Figure 8 that P2G mainly converts electricity to gas to generate CH₄ during the low period, most of which are stored in GST, and a small part is directly sold to the gas network. GST inputs natural gas into CGT during peak hours for gas-to-electricity, thereby providing peak shaving output for wind power and PV power generation. Until the end of the dispatch period, the remaining CH₄ is stored in the GST to achieve zero carbon emissions during the dispatch period. Furthermore, the worst scenario established by formulas (37) to (40) is analyzed. Figure 9 shows the GVPP scheduling optimization result under the worst scenario.

According to Figure 9, in the worst scenario, WPP and PV power generation output is lower than other scenarios significantly. At this time, P2G, PSD and DRP can meet the demand of wind and solar peak shaving, so the CGT power generation output is linear; the output of the upper limit meets the benchmark load demand. Similarly, in pursuit of the objective function of minimizing the cost of GVPP power generation, BPG did not generate power. Different from the zero-carbon emission scenario, in the worst scenario, the PSD and DRP output adjustments are relatively large to deal with the uncertainty of the scenery. Since the output of wind power and PV power generation is the lowest, and BPG is not called, GVPP has a strong ability to deal with the uncertainty of wind power and PV power generation, so the degree of uncertainty σ_risk = 0.203; it can be seen that the proposed method can better deal with the worst scenario. Furthermore, the sensitivity analysis of carbon trading prices is carried out. Table 2 shows the cost value and degree of uncertainty of GVPP operations under different carbon trading prices.

According to Table 1, the sensitivity analysis of carbon trading prices is carried out, and the scheduling costs and uncertainty levels of GVPP under certain, near-zero carbon and worst-case scenarios under different carbon trading prices are measured. When the carbon trading price is lower than 50 yuan/ton, the GVPP scheduling cost will decrease as the carbon trading price increases, and the degree of uncertainty will decrease in the near-zero carbon scenario gradually. Since P2G converts more CO₂ into CH₄ and provides greater peak shaving capabilities, so GVPP has an increased ability to cope with the uncertainty of the scenery. However, when the carbon trading price is higher than 55 yuan/ton, CGT and BPG generate electricity to generate CO₂, which is used to obtain carbon trading income, which reduces the ability of GVPP to deal with the uncertainty of scenery. For the worst scenario, due to the extremely magnified risk of wind and solar uncertainty, as the price of carbon trading increases, more CGT and BPG power generation will bring higher carbon trading costs. Therefore, the cost of GVPP scheduling is increasing gradually, and the degree of uncertainty is increasing gradually, indicating that the tolerance of decision-makers to the uncertainty of scenery is decreasing gradually. In summary, the actual load dispatch experience of the sensitivity analysis results in Table 2 reflects the effectiveness of the method in this study.