Robust optimization scheduling of microgrid considering carbon capture equipment

To cope with the carbon dioxide generated during the operation of the microgrid and consider the wind power fluctuations, a robust optimization scheduling model for the microgrid is proposed, considering carbon capture equipment. Considering the large amount of carbon emissions caused by micro-turbine power generation and electricity purchase during the operation of microgrid, two operating modes of carbon capture equipment are considered, the carbon trading costs are considered in the objective function, and the output of all wind power is included through a box uncertain set. The C&CG algorithm was used to solve the constructed model and obtain the corresponding scheduling plan. Finally, the effectiveness of the model was verified through numerical examples. The results indicate that the total operating cost of microgrids can be further reduced by setting up carbon capture equipment to operate in flexible mode.


Introduction
With the development of society, the reserves of traditional fossil fuels are gradually decreasing, and the environmental pollution caused by burning fossil fuels is also becoming increasingly serious.The microgrid that can absorb renewable energy has to some extent alleviated these problems [1][2][3].However, the volatility of renewable energy is a challenge that needs to be considered for the safe and stable operation of microgrids.At present, the mainstream methods for dealing with uncertainty include stochastic optimization and robust optimization [4].Stochastic optimization generates a certain number of uncertain scenarios, and optimizes them with the goal of minimizing expected costs, which undoubtedly increases the computational burden.As a comparison, robust optimization obtains optimization results by constructing an uncertain set and considering the worst-case scenario.Liu et al. [5] constructed an economic dispatch model for microgrids based on robust optimization, and solved it to obtain the dispatch plan for the worst scenario.At the same time, decision-makers can adjust the conservatism of the scheduling plan by controlling the fluctuation of uncertain variables.Zhu et al. [6] built a double-layer economic dispatch model for microgrids considering wind power consumption.However, none of the above literature considers the carbon emissions caused by the actual operation of microgrids.
Tan et al. [7] not only considered carbon trading costs in the objective function, but also analyzed the impact of two scheduling modes on thermal power generation.The results show that the system achieves a balance between energy conservation, emission reduction, and system stability.On the basis of introducing a carbon trading mechanism, Chen et al. [8] further considered the role of carbon capture equipment in reducing carbon emissions and constructed a low-carbon economic dispatch model for the power system, proving the effectiveness of the model in reducing carbon emissions and total costs.However, the above literature did not consider the impact of renewable energy uncertainty on the operation of the power system.
In summary, there are few studies that comprehensively consider uncertainty and carbon emissions in microgrids.Therefore, based on the above research, this article comprehensively considers the impact of renewable energy and carbon capture equipment on the operation of microgrids, constructs an economic dispatch model for microgrids considering carbon capture equipment, and studies the changes in total costs of carbon capture equipment under different working modes.

Modeling of microgrid system
The microgrid includes wind turbine(WT), electric energy storage(EES), large power grid, electrical load, gas boiler(GB), micro-turbine(MT), carbon capture equipment(CCE), heat storage device, and heat load, as shown in Figure 1.

Carbon capture equipment
There are two operating modes for carbon capture equipment, namely fixed operating mode and flexible operating mode [8].
When the CCE operates in a fixed operating mode, the carbon capture level remains unchanged.In this mode, the effect of reducing carbon emissions is significant, but the cost is higher.
where  is a constant set artificially, and e buy () t  is the electricity purchase price for time period t .
where c E is the total free carbon emission quota, and MT  , M  and GB  represent the carbon emission quotas per unit power of MT, GB, and electricity purchasing behavior, respectively.T is the total scheduling period. where is the total amount of carbon dioxide actually emitted into the environment. where represents the carbon trading cost, and  is the unit carbon emission trading price.

Uncertainty set
where U denotes the uncertainty set; * wt () Bt represent binary variables that represent the degree to which the uncertain variables of wind power output, electrical load power, and heat load power deviate from the predicted values.When 0 is taken, the value of the uncertain variable is the predicted value.When 1 is taken, The fluctuation of the value of uncertain variables to the interval boundary.corresponds to fluctuations in wind power, electrical load, and heat load, respectively.

Robust optimization scheduling model
The robust optimization scheduling model constructed in this article is formulated as: ss ( 1) Ht , e MT ()

Pt and h MT ()
Pt express the charging and discharging power of EES, charging and discharging power of heat storage device, purchasing and selling power of microgrid from the large grid, the thermal power of GB and the electrical and thermal power output of MT during the time period t , respectively.power output and ramping rate of MT.LHV denotes the low heating value of natural gas.

GB ()
Vt and

MT ()
Vt indicate the intake volume of the GB and MT during time t .Equations (13)-( 14) limit the charging and discharging power of EES, where e () Ut denotes the binary variable that is equal to 1 if EES is charging, and equal to 0 otherwise.Equation (15) ensures equal capacity of EES at the beginning and end of scheduling.Equation ( 16) ensures the remaining capacity of EES is between min s E and max s E .Equations ( 17)-(20) give the operational constraints of the heat storage device, which have a similar meaning to EES.Equations (21)-( 22) limit the purchasing and selling power of the microgrid, where M () Ut denotes the binary variable that is equal to 1 if the microgrid purchases electricity from the large grid, and equal to 0 otherwise.Equation (23) shows how to calculate the thermal power of GB.Equation (24) limits the thermal power of GB.Equations ( 25) stands for the ramping rate of GB.In Equation ( 27), Et is the carbon emissions of MT during the time period t , where e MT e and h MT e correspond to the carbon emissions per unit electrical power and thermal power of MT, respectively.The meaning of Equations ( 26), (28), and ( 29) is similar to the corresponding constraints of GB.Equations ( 30) and (31) describe the balance of electrical and thermal energy in microgrid systems.
Equation ( 9) can be decomposed into the main problem and sub-problems and solved using the C&CG algorithm [9].

Case study
The microgrid shown in Figure 1 is used as an example for simulation analysis.The wind power, electricity load, and heat load prediction curves are shown in Figure 2. The parameter values in the microgrid system mentioned in this article refer to [5], [8] and [10].uncertainty adjustment parameters for wind power, electrical load power, and thermal load power are set to 6, 12, and 12, respectively.Figures 3 and 4 show that in 1 h~7 h, although the WT output can basically meet the power load demand, the MT still outputs the maximum power.This is because if the MT output is small, the corresponding thermal power output under the condition of thermoelectric coupling will also be small, and relying only on the heat storage device and GB is not enough to satisfy the heat load demand.In 8 h~18 h, the demand for electric load is mainly met through electricity purchasing behavior.This is also because if the output of the MT is too large, the output thermal power is also large, and the demand for thermal load is small in 8 h~18 h, so the excess thermal power cannot be absorbed by the heat storage device.Finally, in 19 h~24 h, due to the large demand for heat load, the MT must be mainly used for heat supply, and the corresponding output of electric power is also too much, so the excess electric energy generated can be absorbed through electricity sales and EES.Figures 5 and 6 show the comparison of energy consumption costs and carbon trading costs of carbon capture equipment under different operating modes.During the same electricity price period (1 h-6 h, 23h-24h), the energy consumption cost and carbon trading cost of carbon capture equipment in both modes are the same.When the electricity price increases, the energy consumption cost in flexible mode decreases and the carbon trading cost increases.This is because the capture level of CCE in flexible mode decreases and carbon dioxide emissions increase when the electricity price increases.Figure 7 shows the changes in the total operating cost of microgrids under different uncertainties.Under various uncertainties, the total cost of CCE in flexible operating mode is lower than that in fixed mode.This is because when the carbon capture level decreases, the energy consumption power of CCE decreases, and the output power of MT decreases.The operation and maintenance costs related to the output power of MT have both decreased, ultimately resulting in a decrease in total costs.

Conclusion
This article constructs a robust optimization scheduling model for microgrids considering CCE.Through the case study, it can be seen that when CCE operates in a flexible operating mode, the system's carbon emissions increase, energy consumption costs decrease, and total costs decrease.Therefore, decision-makers can select the working mode of CCE according to the actual situation to focus on the economy or low-carbon.

P
efficiency of EES, heat storage device, GB and thermal efficiency of the MT, respectively.denotes the maximum charging and discharging power of EES, heat storage device and purchasing and selling power of microgrid from large grid.max GB H and max GB R represent the maximum thermal power and ramping rate of GB. e,max MT P and e max MT R ， represent the maximum electrical 2023 5th International Conference on Energy, Power and Grid (ICEPG 2023)

Figure 2 .
Figure 2. Wind power and load forecasting curve.

Figure 3 .
Figure 3. Electrical power output diagram of each unit.

Figure 4 .
Figure 4. Thermal power output diagram of each unit.

Figure 5 .
Figure 5. Energy consumption cost of carbon capture equipment under different modes.

Figure 6 .
Figure 6.Carbon trading costs under different modes.

Figure 7 .
Figure 7.Total operating costs with different uncertainties.
When carbon capture equipment operates in a flexible mode, the level of carbon capture varies based on real-time power grid electricity prices, thereby reducing carbon capture energy consumption.
e cap buy()