Wind-Thermal-Energy Storage System Optimization: Evidence from Simulations of the Economical Consumption of Wind Energy

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Introduction
With the exacerbation of energy scarcity and the greenhouse efect, action to reduce pollution and carbon emissions is urgently needed [1]. A global consensus has been reached to accelerate the transition to green energy and sustainable development [2]. According to the Global Wind Energy Report 2022 from the Global Wind Energy Council, a 557 GW increase in global wind power is expected over the period 2022-2026, with a compound annual growth rate of 6.6% [3]. With the rapid development of the sector, wind energy (WE) has emerged as a key energy source on a global scale [4]. Realizing the low-carbon economic potential of WE is a current research focus [5,6].
WE grid connection should be planned in view of comprehensive social costs, such as the corresponding peaking cost and carbon emission cost [7,8]. Many countries use WE wisely: generally, the United States and certain European nations do not use all of their available WE [9]. For example, the rate of WE curtailment is approximately 5% in the United Kingdom and Ireland [10]. In some parts of Germany, wind power generators and electricity distribution companies accept reasonable levels of WE curtailment under transparent conditions, such as including wind curtailment clauses in grid-connection agreements or power-purchase contracts and allowing 1%-5% of wind power to be curtailed [11,12]. Tese countries support a green and low-carbon transformation of the energy structure at the lowest possible cost and do not see the full grid-integrated accommodation of WE consumption as a development goal.
Numerous studies have shown that the outputs of WE generators are random, erratic, and have evident antipeak-shaving characteristics [13,14]. If WE is fully incorporated into the power system indiscriminately, the safety, stability, and economics of grid operation will encounter signifcant obstacles [15]. According to statistics from the China State Grid Energy Research Institute, a "low peak power ratio" is a hallmark of many Chinese provinces' WE power-generating outputs. Not using a portion of the peak power can considerably lower the system pressure without greatly impairing the annual output of new energy sources [16]. Terefore, appropriately curtailing a certain amount of wind power under certain conditions, that is, when WE is abundant and the load demand is low, can improve the fexibility of power grid dispatch, which is an important measure of the economical consumption of WE [17,18].
Bird et al. [19] made a review of international experience in the curtailment of wind and solar energy on bulk power systems in recent years, in which it is shown that curtailment can help mitigate excess generation and provide ancillary services. Xu et al. [20] adopted the safetyconstrained economic dispatch model, introduced a sectional penalty factor for wind power curtailment, prioritized wind power consumption, and curtailed wind from each wind farm in a rational manner according to a preestablished wind power curtailment principle. Wang et al. [21] conducted a large-scale analysis of the history of wind power output and presented a theoretical research method for the rational use of high-power wind output under low loads. Y. B. Wang [22] explored the problem of the rational curtailment of new energy and found a balance between the cost and beneft of new energy consumption. Using the GESP power planning software, the study took China's major regional power grids as an example and calculated a rational energy curtailment rate of 3%-10% for 2020. Golden and Paulos [23] provided a detailed explanation of the potential positive and negative impacts of curtailment, proposing a policy that can be used to blaze a trail to a lowcarbon future through greater use of renewable electricity in California.
Termal power units (TPUs) still make up a large percentage of the energy structure in northern China [24]. Although large-scale wind power integration can minimize CO 2 emissions, it can also push TPUs away from their ideal economic operating point [25]. Demand response (DR) dispatching enables a high level of fexibility according to studies in several countries. DR dispatching can be used to explore potential interactions between various user loads [26], and it also diminishes the load peak-to-valley diference [27], which efectively enhances load-side adaptability. A review of the literature reveals the importance of DR dispatching in promoting the accommodation of new energy [28]. DR dispatching can also be used as an incentive mechanism on the user side to promote the rational allocation of resources on the source and load sides [29].
Additionally, energy storage systems (ESSs) have an essential regulatory impact on the source, grid, and load sides [30] due to their efective charging and discharging characteristics, which enable rapid power regulation [31]. Terefore, the combined use of DR dispatching and ESSs as peak-shaving resources in power system scheduling is often considered, as it can efectively enhance the economic benefts of TP operation and stabilize the power system. Te use of ESSs and DR dispatching for multisource joint optimal scheduling is an efective measure to alleviate the difculty of peak regulation for new energy-connected grids. Hamidpour et al. [32] made disruptive changes to the existing power system structures and procedures of wind farms and ESSs and took into account demand-side fexibility requirements. Hosseini Imani et al. [33] analyzed the efect of running the TOU response program and used ESS units to compensate for the stochastic nature of WE generation. MohammadGholiha et al. [34] used DR dispatching and an ESS to alleviate the uncertainties in wind power and electrical load and formulated a two-stage stochastic programming model for optimal reserve determination. In reference [35], novel DR applications were modeled to quantify additional reductions in the curtailed WE, and various combinations of ESS and DR dispatching were considered to investigate their impacts on further reducing wind curtailment. Jamali et al. [36] used ESSs and DR dispatching and proposed a stochastic bidding strategy based on virtual power plants to increase the proft of virtual power plants in short-term electricity markets.
Building on the multiobjective optimization and comprehensive decision-making two-stage model proposed in [37], combined with the day-ahead energy trading two-stage model proposed in [38], this study establishes a two-stage optimal scheduling model. Te model emphasizes the effective utilization of two peak-shaving resources: DR dispatching and ESSs. Te frst-stage model takes as input the adjusted load curve after accounting for the time-of-use (TOU) electricity price, and the optimal wind power-connected grid is obtained on this foundation by combining it with an ESS. Te main function of the ESS is minimizing changes in the grid's net load. Te optimal output power of the TPU is obtained in the second stage of the decision, and the wind-thermal-energy storage systems (WTESSs) cost is minimized. By comparing the simulated operations under various conditions, the viability and efcacy of this technique are proven, and the low-carbon economic regulation of wind power is achieved.
Tis study makes two main contributions: (1) Teoretical contribution: Tis study dispenses with the traditional assumption of full grid connection of wind power, focusing on the consumption of total wind power rather than that of the grid-connected WE at any single moment. A model of the WE utilization rate at each time point is constructed, and the impact of the rational dispatch of wind power on the overall economic beneft of the power system is explored. Tis enables the active deployment of fexible resources in the power system, the design of a two-stage optimum scheduling model for WTESSs in the setting of a low-carbon economy, and the defnition of a TPU deep peak regulation (DPR) cost function. User loads can vary depending on the price signal and can be simply classifed as reduced loads and transfer loads. Taking into account load characteristics, the users' peak period power consumption following the application of the TOU electricity price can be stated by the following two sets of equations: where Q1/f and Q0/f denote the loads during the peak period before and after the TOU, respectively; ΔQ f represents the load variation after the TOU; ΔQred/f and ΔQtrans/f represent the load reduction and load transformation during the peak period after TOU, respectively; ϕred/f is the load reduction rate at the peak period; ΔQtrans/fp and ϕtrans/fp are the load transfer quantity and rate from the peak period to the fat period, respectively; ΔQtrans/fg and ϕtrans/fg denote the load transfer quantity and rate from the peak period to the valley period, respectively.
where Q0/t and Q1/t are the electricity quantities in period t after the TOU, respectively; ε tt and ε tr are the self-elasticity and cross-elasticity, respectively (a rise in electricity prices will result in a drop in electricity during this period and an increase during other periods, so usually ε tt < 0 and ε tr > 0); ΔQ t and ΔD t are the change in electricity quantity and price in period t before and after the TOU, respectively; ΔD r is the change in electricity price in period r before and after the TOU; T is the scheduling period, which is 24 h; D0/t is the electricity price in period t before the TOU; D0/r is the electricity price in period r before the TOU. Let ϕ t denote the change in the load rate in period t after the TOU; then, where ϕred/t and ϕtrans/t are the load reduction rate and transfer rate in period t, respectively.

Load Response Model.
Load reduction and load transfer rates are employed to appropriately represent the users' reaction to the TOU and the load characteristics of the peak, fat, and valley periods. Te price of power during the fat period is denoted by Qt/0, and the peak-to-fat and valleyto-fat electricity price foating ratios are written as follows: where K f represents the fuctuating ratio of the electricity price from the peak period to the fat period; K g represents the fuctuating ratio of the electricity price from the valley period to the fat period; D f , D p , and D g represent the electricity prices during the peak, fat, and valley periods, respectively. Te load reduction rate and transfer rate of the users at any time are represented as follows when the defnitions of (2) and (3) are combined.
where ϕ ff , ϕ pp , and ϕ gg are the load decrease rates during the peak, fat, and valley periods, respectively (because ; ϕ fp , ϕ fg , and ϕ pg are the load transfer rates during the peak-to-fat, peak-to-valley, and fat-to-valley periods, respectively. Finally, the load response model that takes into account the mechanism of action of the TOU is as follows:

Peak-Shaving Model for TPU considering LCT
2.2.1. DPR Process of TPU. P max is the TPU's maximum output; P min is its minimum output under regular peak Mathematical Problems in Engineering regulation (RPR); P ndo is its minimum output under DPR; P do is its minimum output under deep peak regulation with oil (DPRO), as shown in Figure 1.

LCT Model.
To control carbon emissions, a carbon trading scheme is established. Each carbon emission source has a certain amount of carbon emission allowances, according to which producers arrange their production. If producers emit less carbon than the corresponding allowances, the remaining allowances can be sold through the carbon trading market, whereas if they exceed the corresponding allowances, additional allowances must be purchased. To solve the problems of the traditional carbon trading pricing mechanism, which has only a weak efect on carbon emissions, the LCT pricing mechanism is adopted, in which the carbon emission price varies with the distribution of additional carbon emission rights that producers need to purchase.
(1) Initial Carbon Emission Quota where E free is the TPUs' total allowance for carbon emissions; ψ free is the allowable amount of carbon emissions per unit of energy used; N G is the total number of TPUs; Punit/i, t is the output value of TPUs in period t.
(2) Actual Carbon Emissions where E CO 2 are the total real carbon emissions from all TPUs; β 2i , β 1i , and β 0i are the variables used to calculate each TPU's carbon emissions.
(3) Carbon Trading Cost where C CO 2 denotes the carbon trading cost; b denotes the carbon trading base price; δ denotes the price growth rate; l denotes the carbon emission range.

DPR Cost Model for TPUs considering LCT
(1) Under usual circumstances, the TPU operates in the RPR. During that time, C coal represents the peakshaving cost. TPUs generate signifcant carbon emissions. Te peak-shaving cost of C unit1 , taking LCT into account, is calculated as follows: Here, α 2i , α 1i , and α 0i are the coal consumption cost coefcients associated with TPU i. (2) Te TPUs must lower their output and transition into the DPR stage when additional energy is incorporated into the grid on a considerable scale, especially during the low load time at night. When a TPU's output is between P min and the P ndo , the rotor metal experiences alternating stress that causes low-cycle fatigue loss, which raises the TPU loss cost C unit2 : Here, δ(unit/i) is the life loss rate of the TPU. load. As a result, the TPU incurs increased oil costs, entering DPRO. Te following equation is derived.
where S oil−price is the oil price; Q oil is the oil consumption in DPRO.
To summarize, the following is an expression for the peak-shaving cost of TPUs: Given that C unit is a discontinuous function, (11) is transformed into a continuous function in the form of linear constraints using Boolean variables: where X bty and Y ty are the Boolean variables corresponding to the life loss cost and the oil cost, respectively.

Two-Stage Optimal Scheduling Model.
Having established the above basic model, a two-stage optimal scheduling model of the WESS is constructed; its structure is shown in Figure 2. Te open-source solver CPLEX [39], developed by IBM, is used to represent complex economic problems as mathematical programming models. It is based on a fusion of the branch-cut plane method, interior point method, and other methods such as preprocessing and heuristics to enable rapid solutions to these problems. Te scheduling model in this study is a mixed integer quadratic model designed to transform the practical problem of economical wind power dispatch into a mathematical model for solving the utilization rate of each time period, for which CPLEX is highly suitable.

First-Stage Model
(1) Objective Function. In the frst stage, with consideration of the TOU and ESS, the grid-connected wind power and the ESS's charge-discharge power is optimized with the aim of reducing the variance in the net load, while satisfying the corresponding restrictions. Te following objective function intends to enhance the valley load and cut peak load, lessen the net load fuctuation, and avoid frequent output adjustments for TPUs.
where A is the variance in the grid's net load; L net,t is the net load value in period t; L net,ave is the average value of the net load during the whole dispatch period; Q1/t is the load value after the TOU; λuse/w, t is the rate at which WE is used in period t(0 ≤ λuse/w, t ≤ 1); Ptot/w, t represents the wind farm's output power value; Pcha/es, t and Pdis/es, t represent the charging and discharging power values, respectively; ηcha/es and ηdis/es indicate the charge and discharge effciencies of the ESS, respectively.
(2) Constraints (1) Wind power output constraints Te grid-connected wind power in each period is less than the actual output power of the wind farm Here, Pmax/w, t indicates the greatest output of the wind farm during period t.

(2) WE utilization constraints
To avoid a large amount of wind curtailment due to the minimization of the net load variance under the optimized solution, a minimum utilization rate of WE is stipulated Here, R w, min is the minimal total WE utilization. (3) Charge and discharge power constraints 0 ≤ P cha es,t ≤ P cha es, max , 0 ≤ P dis es,t ≤ P dis es, max .
Here, P cha es,t and P dis es, max denote the maximum charge and discharge powers of the ESS, respectively. (4) Charge and discharge logic state constraints I cha es,t + I dis es,t ≤ 1, W es,t + W es,t−1 − I cha es,t + I dis es,t � 0.
Here, Icha/es, t and Idis/es, t are binary variables used to transition between the charging state and the discharging state of the ESS, respectively (the ESS enters the charging state in period t when Icha/es, t � 1, signaling that it is going to be charged; the ESS switches from the charging state to the discharging state in period t when Idis/es, t � 1, indicating that it is going to be discharged). W es,t and W es,t−1 represent the charging and discharging states of the ESS in period t and period t−1, respectively. (When the value is 1, the ESS is charging, and when the value is 0, the ESS is discharging.) (5) State-of-charge (SOC) constraints To ensure the sustainability of the ESS participating in the scheduling operation, SOC constraints need to be added.
where S oc,t is the SOC for the ESS in period t; S oc, max is the maximum SOC; S oc, min is the minimum SOC; Ccap/es is the ESS's capacity.

Second-Stage Model
(1) Objective Function. Te second stage determines the optimal outputs of the TPUs by satisfying various operation constraints, together with the net load curve that is inherited from the frst stage. Minimizing the peak cost of the WESS is the objective of the second-stage model, and the solution indicates how economical the power system is. Te objective solution accounts for the costs of wind power operation and maintenance, wind power curtailment, peak-shaving of thermal power plants, and peakshaving of the ESS. Te following is the formula: (1) Wind power operation and maintenance costs C wyw � α wyw P w,t .
Here, S power−price represents the charge and discharge cost per unit power of the ESS.
where μ poll is the emission density of ESS-emitted pollutants; S poll−price is the unit emission cost of pollutants (the pollutants referred to in this paper are SO 2 and NO x ).

(2) Constraints
(1) Constraints on the system's power balance When excluding the system network loss, the real-time load is equal to the total output power of TPUs and WE and the charge and discharge power of the ESS (2) TPU output constraints Here, Punit/i, max is the maximum output of TPU i; Punit/i, min is the minimum output of TPU i.
Here, ΔPunit/i, up denotes the TPU's capacity to ascend to its upper limit, and ΔPunit/i, down denotes its ability to drop to its lower limit. (4) Line transmission capacity constraints Where P line,t is the line's transmission power in period t; Pmax/line, t is the line's maximum transmission capacity in period t.  Figure 3 depicts the categorized user load curve and wind power output curve. Other relevant parameters are as follows:

Results and Discussion
(1) Because there are signifcant diferences in the degree to which various users participate in the TOU, the elasticity coefcient, and the division of peak, fat, and valley periods, this study classifes users into industrial, commercial, and residential users. Table 2 itemizes the peak, fat, Table 3 and valley periods for the three diferent user groups as well as the peak-tovalley price variations in relation to the initial price of power and the corresponding price elasticity coefcients. (Te electricity price is expressed in CNY/kWh and remains constant during the fat period, rises during the peak period, and falls during the valley period.) Additionally, it is assumed that 20% of commercial and residential users and 50% of industrial users engage in the TOU.

TOU Optimization Results.
Te load curves before and after the TOU for industrial, commercial, and residential users can be seen in Figure 4. Industrial customers have more fexibility and adaptability in power consumption, so the peak-shaving and valley-flling impacts are more visible for these customers. Commercial and residential customers have more fxed power consumption times and a lower proportion of users that respond to the changes. Terefore, the infuence of TOU on peak-shaving and valley-flling is not as large as that of industrial users.

Analysis of Optimization
Results. Te total load curve prior to and following TOU, the net load curve prior to and following the frst stage of model optimization, the wind power integrated into the power grid curve, and the WE utilization rate throughout all periods can be seen in Figure 5. Te peak-to-valley diference of the entire load curve is 965.1 MW, which is 251.65 MW less than that before the TOU. Tis diference permits additional space for wind power grid connection. Te graph illustrates that wind curtailment does not occur except at 1 : 00, 2 : 00, 4 : 00, and 24 : 00, and the wind energy consumption rate is 100% at all other times. By combining the wind power output curve and the load characteristic curve, it can be observed that wind curtailment is maximized at times of low load and large wind Mathematical Problems in Engineering power output, and the lowest WE utilization rate is 27.44%. Te outcome is closely related to the frst-stage model's target function and the antipeaking properties of wind power itself. Furthermore, the largest peak-to-valley difference of the net load curve before optimization is only 720.67 MW, but after optimization, it is 1370.46 MW (without including the TOU, ESS, and WE use). Tis demonstrates that the proposed scheduling method significantly reduces load variance and peak control costs. Te charging power, discharging power, and SOC of the ESS for each period are illustrated in Figure 6, showing that the SOC of the ESS always remains within the limiting range. Te ESS has a peak-shaving power of 467.95 MW. As wind power outputs are low at the six load peak hours of 10 : 00,     Figure 7. Te outputs of the three smaller TPUs, units 4, 5, and 6, remain relatively stable during the scheduling period. Units 4 and 6 work in RPR and simply produce the associated coal consumption costs. Consequently, unit 5 runs most often in DPR. Due to their enormous capacities, units 1, 2, and 3 handle the majority of the peak-shaving work. As the net load curve's fuctuation range has been greatly reduced and the units' peak-shaving efciency has been strengthened, it is notable that none of the thermal units need to enter DPRO. Te load characteristic curves and wind power output forecast curves applied in this research serve as the basis for all four scenarios, and the frst and second stages of model optimization have the same purposes as before. Figure 8 displays the net load curve optimization outcomes for each scenario. Figure 9 displays the precise output of each TPU per time period in scenarios 2, 3, and 4. All three peak-   shaving measures (WE utilization rate, TOU, and ESSs) have demonstrable smoothing impacts on the volatility of the net load curve, which can facilitate the consistent adjustment of TPUs' output. Te peak-to-valley diference of the net load can be reduced from 1 073.55 MW to 720.67 MW in the TOU environment combined with the ESS if the WE utilization rate is factored into the equation (scenario 1). Tis markedly lowers the burden of peak regulation and assures the electricity grid's reliable and safe functioning. With a unit of cost of 10,000 CNY, the calculated system costs under various scenarios are displayed in Table 4. Scenario 1 has the lowest peak-shaving cost (4.0253 million CNY). Scenarios 2, 3, and 4 have peak-shaving costs that are 0.629 million, 1.2679 million, and 0.6594 million CNY higher than that of scenario 1, respectively. Tese fndings demonstrate that coordinated ESS usage and accounting for the rate of WE usage in the TOU environment can significantly improve the economics of peak-shaving in the power system. Te prices of coal consumption are similar in all scenarios, and the large calculated decrease of the peak-tovalley diference in the grid's net load caused by optimizing the grid-connected power of WE at all times is the main contributor to the lower costs of the power system. Tis reduces the net load peak-to-valley diference as well as the frequency with which TPUs enter DPRO, signifcantly cutting the cost of oil investment and the cost of TPU life loss. Tis implies that, in contrast to the operational efects of scenarios 1 and 3, the peak output of wind power should be rationalized to ensure the secure and reliable operation of the power system. Specifcally, WE utilization should be planned on the basis of the need for low-carbon, economical wind power consumption.

Conclusion
Te main contributions of this study include the following: (1) It is verifed that rational wind power curtailment can efectively improve the overall economy of the power system, and new evidence for the economical uptake of WE is presented. (2) A mathematical model for solving the optimal gridconnected wind power throughout the day is constructed. Compared with previous models, it has greater signifcance for practical guidance on realizing the economical consumption of WE. Simulated data vividly illustrate the favorable efect of rational energy curtailment on the thermal power peaking cost and grid net load fuctuation.
(3) Te results of the operational simulations show that the peak-shaving cost of the strategy devised in this study is 4,025,300 CNY. Compared with the scheduling model in which wind power is completely integrated into the grid, the overall costs are decreased by 1,267,900 CNY, the costs of carbon are decreased by 207,200 CNY, and the costs of DPR for TPUs are decreased by 1,100,800 CNY. Te overall peak-shaving cost of the system can be reduced by up to 23.95%, and the TP DPR cost can be reduced by up to 90.06%.
To further explore the economical consumption of WE and improve the safety and economy of the operation of new power systems, future research could focus on the following: (1) Incorporation of the wind power output forecast error, which is not studied in this study. Tis would enhance the practical signifcance of the proposed method.
(2) Consideration of the infuence of the capacity confguration of the ESS or other attributes on the participation of wind power in optimal dispatch, as the capacity of the ESS in this study is a fxed value

Data Availability
All data, models, and code generated or used during the study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.