Optimal Scheduling Study of Multi-Source Power Generation System with an Electric Heating Unit

This paper proposes an optimal dispatching strategy for a multi-source power generation system containing electric heating devices. A multi-source co-generation system model containing electric heating devices is constructed with the minimum integrated operating cost and the minimum variance of system output power as the multi-objective functions, and the system operating constraints and heat storage constraints as the constraints. A greedy algorithm is introduced and an improved NSGA-II algorithm is proposed to solve the model. After comparison, the integrated operation cost of the multi-source co-generation system with an electric heating device is reduced by 11.35%, the scenery utilization rate is increased by 22.15%, and the total power output volatility is reduced by 29.18%. The results verify the effectiveness and accuracy of the proposed optimal scheduling strategy and the improved algorithm.


Introduction
Nowadays, it is an inevitable trend to vigorously develop new energy generation to realize the "double carbon" target as soon as possible.Joint grid-connected, the highly favored wind power and photovoltaic power generation, is the future development trend.However, the high volatility of wind power and photovoltaic power generation makes its output severely reduced, thus generating a largely abandoned wind and light phenomenon [1].Solar thermal power generation has been considered by many scholars in recent years for joint dispatch with new energy sources such as wind and photovoltaic because of the flexibility and stability of the thermal storage system that can increase power output [2].To ensure the safe, stable, and economic operation of multi-source co-generation, this paper considers the introduction of electric heating devices for co-generation systems.An electric heating unit (EH) is a device that converts electrical energy into heat energy nearly without loss [3].When wind power and photovoltaic power generation generate waste power, the electric heating unit can convert this power into heat energy and store it in the heat storage system of the solar thermal power plant [4].

Solar thermal power plant model
The photovoltaic power plant (CSP) is divided into three parts, the light field Solar Filed (SF), the thermal energy storage system (TES), and the power generation system.
The thermal power absorbed by SF can be divided into two parts: the thermal power of the heatconducting fluid (HTF) and the discarded thermal power.(3) where    is the total thermal power absorbed by SF in MW;    is the discarded thermal power of SF;    is the power flowing from SF to HTF;    is the power delivered from HTF to TES;    is the power delivered from TES to HTF;    is the power entering the solar thermal power system;   is the solar thermal power plant energy conversion coefficient.The heat of TES comes from the light field and the electric heating unit, and the outgoing force model of EH is where  ℎ,    is the input and output power of EH at moment t, respectively, in MW;   is the electric transconductance coefficient.The power of heat storage and discharge by adding an electric heating unit is , =      (6) where   ,   , is the heat storage and exergy power of TES at time t in MW;     is the heat storage and exergy loss coefficient of TES, respectively.

Co-generation system operation mechanism
The multi-source co-generation system with EH mainly consists of wind power (Pw) and photovoltaic power (Pv) generation systems, solar thermal power generation systems, and EH.In the CSP, SF absorbs solar energy through the concentrator, and then converts solar energy into heat energy through the heat absorber and heats HTF, which flows into the power generation system and generates steam to drive the synchronous generator set to generate electricity.When the SF absorbs the excess heat, the HTF heat flows into the TES to store the excess heat so that it can be released when the system cannot meet the load demand; when there is excess wind power and PV, the wind and light are discarded to generate heat through the EH and flow into the TES for storage [5]. Figure 1 shows the energy flow diagram of the co-generation system.where   ,,,ℎ is the average system output power.

Constraints
b. Storage and exotherm cannot be constrained at the same time  ,   ,  = 0 (21) c.Start and end capacity constraint of heat storage system  0 =   (22) To ensure the continuous operation of the solar thermal power plant, the initial and ending capacities of TES need to be relatively consistent during the normal dispatch cycle [8].

Model solving
Compared with the NSGA-II algorithm, INAGA-II introduces the principle of the greedy algorithm when performing polynomial variation to retain more non-dominated population individuals, which improves the optimization performance of NSGA-II.At the same time, when performing the elite retention strategy, the crossover and variation change linearly, i.e., the crossover probability decreases linearly with iteration, and the variation probability increases linearly with iteration to improve the convergence and accuracy of the algorithm are improved.The joint scheduling process based on the INASG-II algorithm is shown in Figure 2. China, as shown in Table 1, the predicted values of Pw and PV power as well as grid load are shown in Figure 3.In the calculation process, t other correlation coefficients are referred to Literature [9].Finally, the model is solved by the INSGA-II algorithm with specific parameter settings as shown in Table 2.

Comparison of the effects of the two algorithms
After programming and solving the models by the NSGA-II and INSGA-II algorithms through MATLAB software, the scenery consumption rate, grid operation cost, and output power volatility of the co-generation system are analyzed and compared.Figure 4 3. From the table, the operating cost of the model solved by the INSGA-II algorithm is lower, which can be as low as 10.757 million yuan, and the system output power variance is also the smallest at 1800.9.Therefore, the data comparison verifies that the INSGA-II algorithm has a stronger optimization-seeking capability, higher computational accuracy, and better convergence than the NSGA-II algorithm.Multi-source co-generation system with EH 10.757 1800.9 According to the optimization solution results, the comparison of the consumption of Pw and PV with and without EH is shown in Figure 5. From the figure, it can be seen that when the multi-source co-generation system does not introduce EH, there will be a large amount of wind and light abandonment phenomenon.After the introduction of EH, the Pw output is significantly improved, and the Pw and PV consumption increased by 22.15% compared with that without EH, which is a significant effect.
Figure 6 shows the comparison of the thermal storage capacity of the system with and without EH.From the comparison in the figure, it can be obtained that the introduction of EH will increase the capacity of TES, and the percentage of the increased capacity is 9.3% of the total capacity.The optimal scheduling results of the multi-source co-generation system containing EH are shown in Figure 7, from which the power output changes of Pw and PV, CSP, and EH for 24 hours a day can be seen.When the load requirements can be met, the optical TES will store the excess thermal energy, while EH will convert the abandoned power into thermal energy to supplement the TES to increase capacity.The rest of the time, when the PV plant cannot continue to produce power, TES will release thermal energy to compensate for the Pw and Pv output, to achieve the purpose of suppressing Pw and Pv fluctuations and improving the stable and safe operation of the grid.

Conclusion
(1) In this paper, the NSGA-II algorithm and the INSGA-II algorithm are used to solve the model separately.After comparing the calculated values, it is verified that the proposed INSGA-II algorithm has higher convergence and better accuracy.(2) Under the scheduling mode of the multi-source cogeneration system with EH, the utilization rate of Pw and PV is increased by 22.15%, the integrated operation cost is reduced by 11.35%, and the volatility is reduced by 29.18%.Therefore, the introduction of EH can effectively increase the system stability and economy and improve the scenery penetration rate.(3) The addition of EH not only reduces the amount of electricity discarded by wind and PV but also adds a heat path to TES and enhances the dispatchability of CSP.

Figure 1
Figure 1 Energy flow diagram of multi-source co-generation system with EH In the figure,       is the predicted power in MW for Pw and Pv, respectively;  ,  , is the gridconnected power for Pw and Pv, respectively;  , ℎ  , ℎ is the electric heating power for Pw and Pv, respectively;  , ′  , ′ is the wind and light abandonment power, respectively.

Figure 2
Figure 2 INSGA-II algorithm flow Figure 3 Predicted power of wind PV and load4.2Simulation AnalysisThe system in this paper contains one each of Pw, Pv, CSP, and EH, where the installed capacities of Pw and Pv are 120 MW and 100 MW, and the relevant data of CSP are referred to a 100 MW CSP in Qinghai, shows the Pareto solution set of the NSGA-II and INSGA-II algorithms for the scheduling model of the system with EH.

Figure 4
Figure 4 Pareto solution set Figure 5 Pv & Pw curves without and with EH

Figure 6
Figure 6 TES heat curve without and with EH Figure 7 Output curve of system with EH The power balance of CSP is

Operation Model of Wind Power Photovoltaic Photothermal Co-Generation System with EH
where   ,   are the cost factors for Pw and Pv, respectively.②Operating cost of solar thermal power plant and electric heating unit  2 = ∑(   , +  ℎ  ℎ, ) where  ℎ are the operation and maintenance cost coefficients of the solar thermal power and EH.③ Investment cost of electric heating unit  3 =     (11) where   is the cost parameter for converting the EH unit into a daily investment cost.④Grid-connected environmental benefits from wind PV and solar thermal power generation  4 = ∑(   , +    , +    , )where   ,   ,   are the environmental efficiency coefficients of grid connection for Pw, Pv, and CSP.b.Minimum variance of system output power 3 3.
[6][7]L, F, G, and R are the load, Pw, Pv, and the difference rate with CSP, respectively.f.Climbing constraint of solar thermal unit −  ≤  , −  ,−1 ≤   (19) where ,   are the maximum upward and downward climbing capacities of the CSP, respectively.3.2.2 Thermal storage operation constraintTES can cooperate with new energy sources such as wind power and PV to optimize the output of wind power and PV.The following constraints need to be met in TES operation[6][7].a. Storage and discharge thermal power constraint e. Prediction error power  , =  ,  +  ,  +  ,  +  ,  (18)

Table 3
Two algorithms to solve the optimal solution of the model Comparison of operation optimization results of joint multi-source systems with EH The INAGA-II algorithm was chosen to solve the model, and its optimal compromise solution is shown in Table4.As can be seen from the table, The system with EH has an 11.35% lower operating cost and 29.18% lower output power variance than the multi-system without EH.It is fully verified that adding EH can effectively dissipate the wind power and PV in the multi-source co-generation system, smooth out the fluctuations caused by the grid connection of Pw and PV, and achieve the double harvest of economy and stability of the co-generation system.