# Study on Multi-Measures Joint Optimization Regulation of Temperature Control and Ice Melting for Water Conveyance Projects in Cold Regions

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Basic Principles of Ice-Melting Measures

#### 2.1.1. Solar Heating Gallery

#### 2.1.2. Heated Water Storage Tank

#### 2.1.3. Ice Melting in Water Conveyance Channels

#### 2.2. Single-Objective Function

#### 2.3. Genetic Algorithm

## 3. A Case Study

#### 3.1. Basic Data Description

#### 3.2. Objective Functions and Decision Variables

#### 3.2.1. Objective Functions

#### 3.2.2. Decision Variables

#### 3.2.3. Constraint Conditions

- (1)
- Constraints on the injection flow:$$CIn{Q}_{nc}^{min}\le CIn{Q}_{nc}\le CIn{Q}_{nc}^{max}$$$$\sum}{Q}_{initial}+CIn{Q}_{1}+CIn{Q}_{2}+\cdots CIn{Q}_{nc}\le {Q}_{max$$
- (2)
- Constraints on the injection water temperature:$$CIn{T}_{nc}^{min}\le CIn{T}_{nc}\le CIn{T}_{nc}^{max}$$
- (3)
- Constraints on the non-freezing length of each channel:$$PileNumbe{r}_{i+1}-PileNumbe{r}_{i}\le {L}_{s}^{i}$$
- (4)
- Equation (3) is used to calculate the non-freezing length and node water temperature, so that the length of each redivided channel meets the conditions, then the time–history change curve of the water temperature of the whole channel can be obtained. The constraints on the heating power of the heated water storage tank are as follows:$$CIn{T}_{nc}=\frac{2.291\times {10}^{-7}P{r}_{nc}}{CIn{Q}_{nc}}$$$$\sum}P{r}_{1}+P{r}_{2}+\cdots P{r}_{nc}\le P{r}_{total$$

#### 3.3. Model Solving Procedure

#### 3.4. Setting of the GA Optimization

## 4. Result and Discussion

#### 4.1. Analysis of Results of Different Comprehensive Satisfaction Rates

#### 4.2. Analysis of the Influence of Water Flow

#### 4.3. Analysis of the Influence of Downstream Depth before the Gate

#### 4.4. Multi-Factor Relationship Fitting

#### 4.5. Cost and Benefit Analysis

#### 4.5.1. Cost Comparison

#### 4.5.2. Benefit Analysis

^{3}/s, the comprehensive satisfaction rate is 100%, and the operating cost is CNY 0.8 million per day, then the total operating cost is nearly CNY 72 million, and the comprehensive total benefit is nearly CNY 220 million, which is about three times the operating cost. Through consulting the data, it is found that the installation cost of the heating gallery is 831.9 CNY$/{\mathrm{m}}^{2}$, and the installation cost of the heated water storage tank is 6710.1 $\mathrm{CNY}/{\mathrm{m}}^{3}$. The NPVs of the ice-melting measures can be calculated using the following equation:

## 5. Conclusions

- (i)
- Under the optimal regulation of the two ice-melting measures, the overall water temperature along the lines presents a “ladder shape”, and the average hourly flow and water temperature have the characteristics of overall unity and local complementarity. The higher the comprehensive satisfaction rate, the greater the average hourly operating cost, but when the comprehensive satisfaction rate is less than 56%, the change range of the operating cost slows down and has no obvious change. The decreasing trend in the water temperature of the channel with the heating gallery is much slower than that without the heating gallery, and the decrease range is 15%.
- (ii)
- With an increase in the water flow, the operating cost also increases, but under the strong control of the velocity of the flow, its growth rate slows down to a certain extent, and the average growth rate decreases from 18.3% to 13.1% when the water flow rate increases by 40 ${\mathrm{m}}^{3}/\mathrm{s}$. With a decrease in the downstream depth in front of the gate, the velocity of the flow increases, the heat transfer efficiency increases, and the operating cost decreases.
- (iii)
- Through the analysis of the costs and benefits of the ice-melting measures, with the decrease in the comprehensive satisfaction rate, their operating costs gradually becomes smaller, and the cost advantages of the ice-melting measures compared with other methods gradually diminish. In addition, the benefits of water transfer flow, power generation, and water saving are very considerable, far exceeding the operating costs, which shows that the ice-melting measures have broad prospects.
- (iv)
- The change in the operating costs of the ice-melting measures is a relatively dynamic process, which will vary with the change in the location and scale of the ice-melting measures. The research conclusions in this paper are only applicable to the research object in this paper, but the research method in this paper can be extended to other similar projects and has a good guiding significance.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PV | photovoltaic |

PV/T | photovoltaic–solar-thermal |

ITC | investment tax credit |

PTC | production tax credit |

WSPV | water surface photovoltaic |

PHS | pumped hydro storage |

CSA | crow search algorithm |

CSAAC-AP | CSA with an adaptive chaotic awareness probability |

GA | genetic algorithm |

PSO | particle swarm optimization |

IRPG | independent regional power grid |

NPV | net present value |

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**Figure 1.**Picture of ice-melting well of the Hongshanzui Power Station, in the southern margin of the Zhunge Basin, China.

**Figure 2.**Picture of photovoltaic panel laying in water conveyance channel [15].

**Figure 3.**The specific working principle of PV/T air solar panels [21].

**Figure 4.**The specific working principle of solar heating gallery [21].

**Figure 5.**The structure of the heated water storage tank [21].

**Figure 7.**Schematic diagram of the Hebei section in the Middle Route Project of South-to-North Water Conveyance Project.

**Figure 10.**Empirical distribution curves of total solar radiation, air temperature, and wind speed in Handan.

**Figure 11.**Probability density curves of total solar radiation, air temperature, and wind speed in Handan.

**Figure 12.**When the water flow is 101 ${\mathrm{m}}^{3}/\mathrm{s}$, the time–history variation of the outlet flow of the heated storage tank is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) 79%; (

**c**) 56%; and (

**d**) 37%.

**Figure 13.**When the water flow is 101 ${\mathrm{m}}^{3}/\mathrm{s}$, the time–history variation of the outlet water temperature of the heated storage tank is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) 79%; (

**c**) 56%; and (

**d**) 37%.

**Figure 14.**When the water flow is 101 ${\mathrm{m}}^{3}/\mathrm{s}$, the change process of the water temperature along the lines is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) 79%; (

**c**) 56%; (

**d**) 37%.

**Figure 15.**Three-dimensional diagram of temperature increase amplitudes in water injection nodes under different comprehensive satisfaction rates.

**Figure 16.**Amplitude variation in the water temperature and time variation in the water temperature of piles No.2 + 300 and No.2 + 800 under comprehensive satisfaction rates is 100%.

**Figure 17.**The change process of the hourly average flow and hourly average water temperature under different comprehensive satisfaction rates.

**Figure 18.**When the water flow is 140 ${\mathrm{m}}^{3}/\mathrm{s}$, the change process of the water temperature along the lines is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) 79%; (

**c**) 56%; and (

**d**) 37%.

**Figure 19.**When the water flow is 180 ${\mathrm{m}}^{3}/\mathrm{s}$, the change process of the water temperature along the lines is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) 79%; (

**c**) 56%; and (

**d**) 37%.

**Figure 20.**The change curve for the operating cost per kilometer of the channel under different water flow and different comprehensive satisfaction rates.

**Figure 21.**When the water flow is 101 ${\mathrm{m}}^{3}/\mathrm{s}$ and the downstream depth is 5 m, the change process of the water temperature along the lines is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) %; (

**c**) 56%; and (

**d**) 37%.

**Figure 22.**When the water flow is 101 ${\mathrm{m}}^{3}/\mathrm{s}$ and the downstream depth is 5.5 m, the change process of the water temperature along the lines is shown under different comprehensive satisfaction rates: (

**a**) 100%; (

**b**) 79%; (

**c**) 56%; and (

**d**) 37%.

**Figure 23.**Three-dimensional graph of the velocity, comprehensive satisfaction rate, and operating cost at the same velocity.

**Figure 24.**Variation curve of the operating cost per kilometer of channel under different downstream depths and different comprehensive satisfaction rates.

**Figure 25.**Relationship diagram of four factors: comprehensive satisfaction rate, water flow, downstream depth, and operating cost.

**Figure 26.**Residual results diagram of the mathematical relation in operation mode: red means greater error; green means less error.

**Figure 27.**(

**a**) Bar chart of the cost combination of ice-melting measures; (

**b**) savings rate fitting curve.

Design Flow for Ice Cover Operation | Velocity | Slope Coefficient | Water Depth | Bottom Width | Canal Length |
---|---|---|---|---|---|

78 m^{3}/s | 0.4 m/s | 2 | 6 m | 23.5 m | 30.4 m |

Name | Collector | Photovoltaic Panel | ||||
---|---|---|---|---|---|---|

Structure Parameters | Size/m | Efficiency | Air hole diameter/m | Heat collection efficiency | Temperature coefficient | Power generation efficiency |

Value | 2 × 1 × 0.22 | 65% | 0.18 | 65% | 0.4 | 17% |

Name | Water tank | Electric heating rod | ||||

Structure Parameters | Radius/m | Height/m | Number of coils | Height/m | Diameter/m | Total length/m |

Value | 3 | 6 | 8 | 3.6 | 0.3 | 75.48 |

City Name | Temperature Probability Density Function | Fit Degree | Wind Speed Probability Density Function | Fit Degree |
---|---|---|---|---|

Handan | $F\left({T}_{a}\right)=0.49+16.2{\mathrm{e}}^{-2{\left(\frac{{T}_{a}+35.63}{91.62}\right)}^{2}}$ | 0.97 | $F\left({v}_{w}\right)=0.74+26.48{\mathrm{e}}^{-2{\left(\frac{{v}_{w}-15.65}{13.76}\right)}^{2}}$ | 0.96 |

**Table 4.**Values of air temperature, wind speed, and radiation and corresponding comprehensive satisfaction rates under different cumulative probabilities.

Cumulative Probability (%) | 100 | 95 | 90 | 85 | 80 | 75 | 70 | 65 |
---|---|---|---|---|---|---|---|---|

$\mathrm{Temperature}(\xb0\mathrm{C})$ | −15 | −13.4 | −11.8 | −10.6 | −9.4 | −8.2 | −7 | −6.3 |

$\mathrm{Wind}\mathrm{speed}(\mathrm{m}/\mathrm{s}$) | 6.3 | 4.5 | 2.6 | 2.4 | 2.2 | 2.0 | 1.8 | 1.6 |

$\mathrm{Total}\mathrm{solar}\mathrm{radiation}(\mathrm{kJ}/{\mathrm{m}}^{2}$) | 1788 | 1788 | 1788 | 2039 | 2281 | 2523 | 2765 | 4234 |

Comprehensive satisfaction rate (%) | 100 | 93 | 79 | 67 | 56 | 46 | 37 | 30 |

**Table 5.**Calculation results of average hourly flow temperature and operating cost of heated water storage tank under different comprehensive satisfaction rates.

Ice-Melting Measures | Comprehensive Satisfaction Rates (%) | Average Hourly Flow $({\mathbf{m}}^{3}/\mathbf{s}\mathbf{\xb7}\mathbf{h}$) | Average Hourly Water Temperature $(\mathbf{\xb0}\mathbf{C}/\mathbf{h}$) | Average Hourly Operating Cost $(\mathbf{Yuan}/\mathbf{h}$) |
---|---|---|---|---|

Heating gallery + heated water storage tank | 100 | 0.57 | 3.42 | 24,262 |

93 | 0.58 | 3.16 | 24,068 | |

79 | 0.47 | 3.46 | 21,325 | |

67 | 0.54 | 3.34 | 21,272 | |

56 | 0.45 | 3.58 | 19,449 | |

46 | 0.49 | 3.37 | 19,343 | |

37 | 0.48 | 3.22 | 17,363 | |

30 | 0.44 | 3.23 | 17,257 |

**Table 6.**Changes in the velocities and operating costs of different flow channels with comprehensive satisfaction rates of 79% and 37%.

Comprehensive Satisfaction Rate (%) | 79 | 37 | ||||
---|---|---|---|---|---|---|

Flow (${\mathrm{m}}^{3}/\mathrm{s}$) | 101 | 140 | 180 | 101 | 140 | 180 |

Velocity of flow $(\mathrm{m}/\mathrm{s}$) | 0.47 | 0.66 | 0.83 | 0.47 | 0.66 | 0.83 |

Operating cost $(\mathrm{CNY}{10}^{5}$) | 5.62 | 6.61 | 7.39 | 4.67 | 5.64 | 6.61 |

Number | $\mathit{P}$ (%) | $\mathit{Q}$ $({\mathbf{m}}^{3}/\mathbf{s}$) | ${\mathit{H}}_{\mathit{g}}$ $(\mathbf{m}$) | Actual Value $(\mathbf{CNY}{10}^{5}$) | Predicted Value $(\mathbf{CNY}{10}^{5}$) | Error Rate (%) |
---|---|---|---|---|---|---|

1 | 62 | 167 | 5.8 | 9.12 | 9.04 | 0.9 |

2 | 76 | 147 | 5.8 | 9.53 | 9.09 | 4.9 |

3 | 80 | 144 | 5.4 | 8.58 | 9.01 | 4.8 |

4 | 84 | 174 | 5.6 | 9.25 | 9.53 | 2.9 |

5 | 48 | 123 | 5 | 7.57 | 7.95 | 4.8 |

**Table 8.**When the water flow is 101 ${\mathrm{m}}^{3}/\mathrm{s}$, the cost calculation results after single heating and ice-melting measures are shown for ice-free water conveyance.

Comprehensive Satisfaction Rate (%) | Single Heating Charge $({10}^{5}$ CNY/Day) | Cost after Regulating $({10}^{5}$ CNY/Day) | Cost Change $({10}^{5}$ CNY/Day) | Saving Rate |
---|---|---|---|---|

100 | 32.90 | 6.32 | 26.57 | 0.81 |

93 | 19.47 | 6.28 | 13.19 | 0.68 |

79 | 15.83 | 5.62 | 10.21 | 0.65 |

67 | 9.78 | 5.61 | 4.18 | 0.43 |

56 | 8.88 | 5.17 | 3.71 | 0.42 |

46 | 6.51 | 5.14 | 1.37 | 0.21 |

37 | 5.52 | 4.67 | 0.85 | 0.15 |

30 | 4.25 | 4.64 | −0.39 | −0.09 |

**Table 9.**Calculation results of the average water transfer flow benefit, power generation benefit, and water saving benefit generated by employing the ice-melting measures.

Flow (m ^{3}/s) | Flow Benefit $({10}^{6}$ CNY/Day) | Power Generation Benefit $({10}^{7}$ CNY/Year) | Water Saving Benefit $({10}^{6}$ CNY/Year) |
---|---|---|---|

101 | 0.31 | 4.84 | 4.07 |

140 | 0.84 | 4.84 | 4.33 |

180 | 1.38 | 4.84 | 4.76 |

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## Share and Cite

**MDPI and ACS Style**

Yang, D.; Lian, J.; Zhao, X.; Chen, Y.
Study on Multi-Measures Joint Optimization Regulation of Temperature Control and Ice Melting for Water Conveyance Projects in Cold Regions. *Water* **2024**, *16*, 1039.
https://doi.org/10.3390/w16071039

**AMA Style**

Yang D, Lian J, Zhao X, Chen Y.
Study on Multi-Measures Joint Optimization Regulation of Temperature Control and Ice Melting for Water Conveyance Projects in Cold Regions. *Water*. 2024; 16(7):1039.
https://doi.org/10.3390/w16071039

**Chicago/Turabian Style**

Yang, Deming, Jijian Lian, Xin Zhao, and Yunfei Chen.
2024. "Study on Multi-Measures Joint Optimization Regulation of Temperature Control and Ice Melting for Water Conveyance Projects in Cold Regions" *Water* 16, no. 7: 1039.
https://doi.org/10.3390/w16071039