**5. Case Analysis**

#### *5.1. Basic Data and Scene Settings*

This paper takes a wind farm in Gansu as an example to simulate and verify the effectiveness of the proposed model. The system includes 3 wind farms with installed capacities of 300 MW, 500 MW, and 700 MW; the energy-intensive load consists of 12 smelting furnaces, with a single operating power of 17.5–21.5 MW, oven power of 10.5 MW, and longest oven time of 2 h; wind curtailment cost is 300 yuan/MW·h. The energy-intensive load, energy storage system, and related parameter information of conventional units are shown in Tables 2–4 and the system load curve and forecasting curve of wind farms are shown in Figure 8.

**Table 2.** Energy-intensive load parameters.


**Table 3.** Energy-intensive load parameters.


**Table 4.** Conventional unit parameters.


**Figure 8.** Curve of system load and forecasting power of wind farms.

In order to analyze the impact of wind power uncertainty and the addition of energyintensive load and energy storage system on wind power consumption, this paper mainly considers the following four cases.

Case 1: Without considering the uncertainty of wind power, only energy-intensive load participates in regulation.

Case 2: Considering the uncertainty of wind power, only energy-intensive load participates in the regulation.

Case 3: Without considering the uncertainty of wind power, energy-intensive load and energy storage system work together.

Case 4: Considering the uncertainty of wind power, energy-intensive load and energy storage system work together.

#### *5.2. Result Analysis*

5.2.1. Analysis of Storage Capacity Configuration Results

For case 3 and 4, the energy storage capacity is configured with the lowest investment cost of the energy storage system as the goal, and the particle swarm algorithm is used to solve the problem [29]. The population size is 25, and the number of iterations is 50. The operation results are shown in Figure 9 and Table 5.

**Figure 9.** (**a**) Case 3 convergence result; (**b**) Case 4 convergence result.


**Table 5.** Energy storage system capacity configuration results.

It can be seen from Figure 9 that the operation results of case 3 and 4 converge in the 12th and 14th generations, respectively, and the best fitness values are 7437 and 9366, respectively. At the same time, the analysis in Table 5 shows that when case 4 considers the uncertainty of wind power, the energy storage capacity is increased compared to case 3 since, at this time, the risk constraints of wind power and energy-intensive load are considered, and the energy-intensive load regulation will be to reduce wind curtailment, and the capacity and power of energy storage will increase.

#### 5.2.2. Analysis of Coordinated Dispatching Results

In this paper, the NSGA-II algorithm is used to solve the model established in the paper, and the distribution of the Pareto solution set in the four cases obtained in the objective function space is shown in Figure 10.

**Figure 10.** Pareto solution set distribution in different cases.

It can be seen from Figure 10 that the wind power curtailment volume and the operation cost of the system have previously shown an inverse proportional relationship. When the wind power curtailment volume decreases, the operation cost of the system will increase, which is not conducive to the economic indicators of the system. When the operation cost of the system decreases, the wind power curtailment volume will increase, which is not conducive to wind power consumption. Therefore, this paper selects the solution with the highest degree of satisfaction according to the multi-objective compromise strategy. Table 6 presents the two sets of solutions with the smallest wind power curtailment volume and the lowest system operating cost and the optimal compromise solution selected from the Pareto solution set.


**Table 6.** Comparison of Pareto optimal solutions in different cases.

In addition, Table 7 shows the overall system operating costs, energy-intensive load costs, energy storage costs, expected curtailment of wind, and energy-intensive load increments in the four cases.


**Table 7.** Comparison of results in different cases.

As can be seen from Table 7, the system operation cost in case 2 is reduced by 23,980 yuan compared with case 1. This is due to the fact that the introduction of risk constraints restricts the regulation of energy-intensive load and reduces the load increment, and the output of conventional units will also be reduced, so the system operation cost will be reduced. However, due to the impact of risk constraints, the expected curtailment of wind in case 2 has increased by 11.6 MW compared with case 1. Compared with case 1, the system operation cost of case 3 increased by 48,591 yuan. This is due to the fact that the energy storage system is introduced to participate in wind power consumption, and the energy storage cost is high, so the system operation cost increases. However, the energy storage system is adjusted flexibly and rapidly, the expectation of wind curtailment is significantly reduced, which is 31.27% lower than that in case 1, and the level of wind power consumption is significantly improved. The system operation cost of case 4 is slightly lower than that of case 3. This is due to the fact that the uncertainty of wind power has been taken into account, the risk of the load side has been further avoided, and the increment of energy-intensive load has been reduced. Meanwhile, the increase of energy storage capacity is conducive to the consumption of more wind power. It can be seen that the expected curtailment of wind is reduced by 19.4 MW·h compared with case 3. It can be seen from the comparison of different cases that through the effective cooperation between energy-intensive load and energy storage system, the expected curtailment of wind is significantly reduced and the consumption level of congested wind power is effectively improved. And through the risk constraints of energy-intensive load, enterprises can adjust the load in a targeted manner, which can effectively avoid the risk of mismatch between the adjustment increment of energy-intensive load and the wind power output, so as to greatly reduce the overall operating cost of the system. Moreover, with the reduction of the conventional units output, the startup and shutdown times of units are also relatively reduced, which increases the stability of unit operation. The specific operation conditions under different cases are analyzed below.

#### (1) Operation result analysis of case 1

In case 1, the uncertainty of wind power is not considered, and the wind power is consumed by adjusting energy-intensive load. Figure 11 shows the wind power curtailment expectation curve, load power plan curve, upper and lower boundaries of ARWP before and after energy-intensive load participates in the regulation, and system dispatching curve.

As can be seen from Table 7 and Figure 11, since the uncertainty of wind power output is not considered in case 1, in order to consume more wind power, energy-intensive load enterprises will increase load regulation as much as possible. It also increases the operating cost of energy-intensive load while reducing wind curtailment. Since the discretely adjustable energy-intensive load cannot be adjusted continuously in a short time, when the predicted output of wind power is higher but the actual output is lower, it will cause the problem of a mismatch between the load increment and the power generation increment, resulting in a higher risk of load shedding. In order to meet the constraints of system power balance and to try and avoid the risk of load shedding due to the uncertainty of wind power, conventional units will increase output, so the overall operating cost of the system will increase.

**Figure 11.** (**a**) Curves of expected curtailment of wind; (**b**) Curves of electricity plan of load; (**c**) ARWP boundary of power grid; (**d**) System coordination dispatching diagram.

#### (10) Operation result analysis of case 2

In case 2, the uncertainty of wind power is considered, and the wind power is consumed by adjusting the high load energy load. Figure 12 shows the wind power curtailment expectation curve, load power plan curve, upper and lower boundaries of ARWP before and after energy-intensive load participates in the regulation, and system dispatching curve.

In case 2, the risk constraints of wind power and energy-intensive load are considered. The increment of energy-intensive load is reduced by 44.38 MW·h compared with case 1, and the operation cost of corresponding energy-intensive load is reduced by 25,296 yuan. At the same time, the cost of conventional units is reduced by 2164 yuan, so the comprehensive operation cost of the system is slightly lower than that in case 1. It can be seen that due to the influence of risk constraints, the wind curtailment expectation of case 2 has increased by 11.6 MW·h compared with case 1. In addition, after the energy-intensive load participates in coordinated dispatch, the total ARWP upper boundary of the grid has increased by 499.29 MW·h the lower boundary of ARWP has increased by 9.96 MW·h, and the total amount of APWP has increased by 489.33 MW·h, which greatly improves the acceptance capacity of the power grid for wind power and effectively promotes the consumption of wind power.

**Figure 12.** (**a**) Curves of expected curtailment of wind; (**b**) Curves of electricity plan of load; (**c**) ARWP boundary of power grid; (**d**) System coordination dispatching diagram.

It can be seen from Figure 12 that due to the increased risk constraints of wind power and energy-intensive load, compared with the original plan for energy-intensive load, the time period during which the adjusted high-energy load power increases generally corresponds to the time when wind power is relatively curtailed. This indicates that in the coordinated dispatching process of energy-intensive load and wind power, the addition of risk constraint makes the energy-intensive load tend to adjust electricity consumption in the period of more wind curtailment so as to avoid the economic risks brought by wind power shortage to the load side.

In addition, according to Table 7, the increment of energy-intensive load before and after coordination is not equal to the expected reduction of wind abandoning, nor is it equal to the increase of the upper and lower boundary width of the grid ARWP. The reason is that the three are not the same. The load increment is *E<sup>u</sup> i*,*t* (*w<sup>u</sup> i*,*t* ), the expected reduction of wind curtailment is *E<sup>u</sup> i*,*t* (*wu*,*add <sup>i</sup>*,*<sup>t</sup>* ) <sup>−</sup> *<sup>E</sup><sup>u</sup> i*,*t* (*w<sup>u</sup> i*,*t* ), and the upper boundary increase of ARWP is *wu*,*add <sup>i</sup>*,*<sup>t</sup>* <sup>−</sup> *<sup>w</sup><sup>u</sup> i*,*t* .

(11) Operation result analysis of case 3

In case 3, the uncertainty of wind power is not considered, and wind power is consumed through the joint adjustment of energy-intensive load and energy storage system. Figure 13 show the wind power curtailment expectation curve, load power plan curve, upper and lower boundaries of ARWP before and after energy-intensive load participates in the regulation, charging and discharging conditions and energy storage system SOC change, and system dispatching curve.

**Figure 13.** (**a**) Curves of expected curtailment of wind; (**b**) Curves of electricity plan of load; (**c**) ARWP boundary of power grid; (**d**) Charging and discharging of energy storage system; (**e**) Energy storage system SOC; (**f**) System coordination dispatching diagram.

After adding the energy storage system in case 3, it can be seen that the output of conventional units has been significantly decreased, and the start and stop of some conventional units have been reduced, saving the cost of conventional units. At the same time, when the system load is low, the excess electric energy can be stored in the energy storage system. When the load is high, the discharge of the energy storage system can make up for the insufficient wind power output. This shows that the energy storage system can assist the operation of the power system and optimit.

#### (12) Operation result analysis of case 4

In case 4, the uncertainty of wind power is considered, and wind power is consumed through the joint adjustment of energy-intensive load and energy storage system. Figure 14 shows the wind power curtailment expectation curve, load power plan curve, upper and lower boundaries of ARWP before and after energy-intensive load participates in the regulation, energy storage system SOC change and charging and discharging conditions, and system dispatching curve.

**Figure 14.** (**a**) Curves of expected curtailment of wind; (**b**) Curves of electricity plan of load; (**c**) ARWP boundary of power grid; (**d**) Charging and discharging of energy storage system; (**e**) Energy storage system SOC; (**f**) System coordination dispatching diagram.

It can be seen from Table 7 that when considering the uncertainty of wind power, the increase in energy-intensive load is reduced by 12.99 MW·h compared with case 3, and the capacity configuration of the energy storage system is increased by 26 MW. The energy storage system can convert part of the wind power waste into chemical energy and store it in the energy storage system when wind power is generated. Therefore, the conventional unit output in case 4 is the smallest among the four cases. In the comparison of different cases, case 4 is the optimal operation scenario, with the lowest expectation of wind curtailment and the most significant effect of wind power consumption.

Through the analysis of different cases, it can be seen that energy-intensive load and the energy storage system can effectively reduce the wind power curtailment volume, decrease the total system operation cost, and reduce the output fluctuation of conventional units while increasing the operation stability of the power system.

#### 5.2.3. Influence of Conservative Degree Change of Energy-Intensive Load on Consuming Results

In this paper, the concept of conservatism is introduced to restrict the adjustment of energy-intensive load power under wind power uncertainty. The selection of conservatism parameters will affect the results of wind power consumption. Table 8 and Figure 15 show the results of energy-intensive load and energy storage system participating in wind power consumption in each case under different conservative parameters.


**Table 8.** Energy storage system capacity configuration results.

From the analysis of Table 8 and Figure 15, it can be seen that when the wind curtailment expectation is certain, the lower the conservative level of the load, the greater the load increment. When the conservative degree is greater than or equal to 1, the load increment is less than or equal to the expected wind curtailment before coordination; when the conservative degree is less than 1, it is understood that the load side is willing to take a certain risk during the coordination process, so the load increment is greater than the expected wind curtailment before coordination. This shows that the introduction of risk constraints can help the load side choose the amount of risk it can bear according to its own characteristics (such that the dispatching method of power grid can meet the needs of load enterprises with different operation tendencies).

**Figure 15.** Results of congested wind power consumption under different conservative degrees.

#### **6. Conclusions**

In order to deal with the mismatch between the electricity plan of the load, the output caused by the uncertainty of wind power, and the fact that the discretely adjustable energyintensive load cannot be continuously adjusted in a short time in the process of consuming congested wind power, a bi-level optimization model research for an energy-intensive load and energy storage system (considering congested wind power consumption) is proposed, and the effectiveness of this model is verified by a practical example. The specific results of his research are as follows:


**Author Contributions:** Conceptualization, S.Z. and K.Z.; methodology, K.Z.; software, S.Z.; validation, S.Z., K.Z. and G.Z.; formal analysis, S.Z.; investigation, C.F. and W.B.; resources, G.Z.; data curation, J.W.; writing—original draft preparation, S.Z. and K.Z.; writing—review and editing, S.Z., K.Z. and G.Z.; visualization, T.X. and J.W.; supervision, T.X.; project administration, G.Z.; funding acquisition, G.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Key Research and Development Plan of Shaanxi Province (2018-ZDCXL-GY-10-04), Natural Science Basic Research Program of Shaanxi (Program No.2019JLZ-15).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**



#### **References**


**Miftah Altwieb 1, Rakesh Mishra 2, Aliyu M. Aliyu 2,\* and Krzysztof J. Kubiak <sup>3</sup>**


**Abstract:** Multi-tube multi-fin heat exchangers are extensively used in various industries. In the current work, detailed experimental investigations were carried out to establish the flow/heat transfer characteristics in three distinct heat exchanger geometries. A novel perforated plain fin design was developed, and its performance was evaluated against standard plain and louvred fins designs. Experimental setups were designed, and the tests were carefully carried out which enabled quantification of the heat transfer and pressure drop characteristics. In the experiments the average velocity of air was varied in the range of 0.7 m/s to 4 m/s corresponding to Reynolds numbers of 600 to 2650. The water side flow rates in the tubes were kept at 0.12, 0.18, 0.24, 0.3, and 0.36 m3/h corresponding to Reynolds numbers between 6000 and 30,000. It was found that the louvred fins produced the highest heat transfer rate due to the availability of higher surface area, but it also produced the highest pressure drops. Conversely, while the new perforated design produced a slightly higher pressure drop than the plain fin design, it gave a higher value of heat transfer rate than the plain fin especially at the lower liquid flow rates. Specifically, the louvred fin gave consistently high pressure drops, up to 3 to 4 times more than the plain and perforated models at 4 m/s air flow, however, the heat transfer enhancement was only about 11% and 13% over the perforated and plain fin models, respectively. The mean heat transfer rate and pressure drops were used to calculate the Colburn and Fanning friction factors. Two novel semiempirical relationships were derived for the heat exchanger's Fanning and Colburn factors as functions of the non-dimensional fin surface area and the Reynolds number. It was demonstrated that the Colburn and Fanning factors were predicted by the new correlations to within ±15% of the experiments.

**Keywords:** heat exchanger; heat transfer; louvred fins; heat transfer effectiveness; Fanning friction factor; Colburn factor
