Economic Operation Scheme of Cascade Pump Station Group Under the Power Market Situation—Taking the Yellow River to Qingdao Project as an Example

Abstract

To solve the problems of s arehigh operating costs and excessive electricity consumption of cascade water supply pump stations in large-scale water transfer projects, this paper develops three optimized operation models for pump station group. Model 1 aims to minimize the daily total electricity cost, Model 2 aims to minimize the daily total electricity consumption, and Model 3 considers both time-of-use electricity prices and regulation and storage of canal section. The dynamic programming algorithm was employed to solve the optimized models. Taking the cascade pump station group of the Yellow River to Qingdao Water Regulation Project in China as an example, application research was conducted under average daily pumping flow of 8 m³/s; 16 m³/s; 24 m³/s; and 32 m³/s. Results indicate that all models exhibit excellent economic performance. Among them, the best performance was achieved by the Model 3 scenario, which consumed 98,700 kWh, 195,600 kWh, 293,400 kWh, and 394,500 kWh of electricity, and reduced the operating costs by 37,100, 38,100, 34,300, and 4400 USD, respectively, compared with the fixed-flow condition.

1. Introduction

Cascade pump stations serve as the primary power source for water regulation projects. These stations elevate water in a series configuration, overcoming topographical constraints to facilitate long-distance water conveyance, thereby effectively alleviating the uneven spatial and temporal distribution of water resources [1]. However, the process of water conveyance results in substantial energy consumption, with electricity usage accounting for more than 95% of the total consumption [2]. To comply with the directives of the ‘Work Plan for Energy and Resource Conservation in Public Institutions’, it is necessary to investigate optimized schemes for cascade pump stations, with the objective of achieving energy savings and emission reductions [3].

The objective of optimal regulation in cascade pump station water conveyance systems is to identify the most energy-efficient operational strategy while adhering to the constraints of pipe loss, flow rate, and head range under specified flow conditions. Zhang et al. [4] proposed an optimized regulation method for cascade pump stations based on the improved Harris Hawks algorithm and established a model for the water diversion system in Beijing, which effectively enhanced the operational efficiency of the cascade pump station system and reduced the operational costs. Gao et al. [2] took head, time-of-use electricity pricing, and control frequency into account, constructing a flow distribution model for the Bozhou pump station group, which effectively decreased the operational expenses. Guo et al. [5] developed a two-layer daily economic optimization model for single-stage pump stations, consisting of a daily economic optimization model and an operational efficiency optimization model, which effectively reduced the operational costs by 18%. Xu et al. [6] developed a flow optimization allocation model for the Liyuzhou pumping station to address the insufficient reliability and practicality of flow optimization allocation schemes caused by flow monitoring errors during the pumping process. The model revealed the response patterns of the number of pump stations and overall efficiency to flow monitoring errors and identified sensitive areas for the optimal number of pump stations. To improve the economic efficiency of the pumping station, Michał [7] analyzed the relationship between the operating electricity cost and electricity price of the pumping station by predicting and analyzing energy consumption and obtained a scientific profit ratio of the pumping station system for different periods. Aiming at the significant energy consumption of water supply pump stations annually, Chen et al. [8], based on a dynamic level feedback control method and NSGA-II algorithm, established a simulated two-stage system for water intake and supply pump stations, which can effectively decrease the total energy consumption and carbon dioxide emissions. Aimed to enhance the economic efficiency of pump station operations in Ningbo, China, Chen et al. [9] applied a fuzzy optimization method to optimize the effective volume of the pump station reservoir by integrating daily electricity costs, pump start-stop frequencies, and submergence depths, providing theoretical support for the economic operation of drainage pump stations. In these studies, dynamic programming, as a powerful optimization tool, has been widely used in the field of economic operation of terrace pump stations.

Synthesizing the existing research results, the exploration in the field of economic operation of pumping stations covers the following key areas: (1) algorithm improvement, such as the Harris Hawks algorithm [4], Runge–Kutta algorithm [10], and sparrow search algorithm [11]; (2) comprehensive consideration, which includes factors such as head, time-of-use electricity pricing, control frequency [2], inverter and motor losses [12], dynamic water level adjustments over short periods [1], erosion of the pump station outlet pool by outflow [13], characteristics of pipe loss [14], and calculation of the optimal startup combination [15]; (3) multi-layer models, such as two-layer model (daily economic optimization model and operational efficiency optimization model [5], flow distribution prediction model and coordinated dynamic planning model [16]), three-layer model (flow optimization model of single stage unit, flow optimization model of pump station, and daily economic operation model of pump station group [17]); (4) other aspects, such as identifying the sensitive areas for the optimal number of operational pumps [6].

The above research has made some progress in reducing the operating costs of pumping stations. However, further investigation remains necessary in the following areas: (1) How to appropriately consider historical operation data in the process of model construction? (2) How to achieve the joint regulation of gates and pumps in an open channel? (3) How to coordinate the competitive contradictions of multiple objectives to obtain a reasonable operation scheme and conduct a detailed analysis of the optimal scheme.

The Yellow River to Qingdao Water Regulation Project (YQWRP) in Shandong Province, China, is a critical infrastructure project that ensures the security and allocation of water resources for the Jiaodong region. YQWRP includes six consecutive pump stations along its open channel [18]. Shandong Province has implemented spot electricity market trading, including the time-of-use electricity pricing policy for industrial and commercial users [19]. By optimizing the intraday operational patterns of each pump station and coordinating the interaction between stations, the total pumping costs of the project could be effectively reduced [20]. Currently, however, the hydraulic structures along the canal sections of YQWRP are primarily controlled by the subjective experience of the management personnel. The application of economic operation for pump stations has not been systematically implemented [21]. Aiming at the problem of high operation costs of water supply pumping stations in large-scale water conservancy regulation projects, this study took the YQWRP as an example and conducted systematic research on the operation optimization of its pumping station group. First of all, by conducting an in-depth analysis of the historical operation data of the pump station group, the relationship between the efficiency and flow rate of each pump station unit under different working conditions was studied. On this basis, three optimized operation models for the pump station group were developed to solve the problems of high operating costs and excessive electricity consumption of cascade water supply pump stations in large-scale water transfer projects.

2. Study Area and Data

2.1. Study Area

Shandong Province has implemented spot trading in the electricity market, exhibiting pronounced intraday variations in electricity price. The electricity price structure is segmented into the following periods: from 00:00 to 10:00 represents the flat rate period, from 10:00 to 16:00 represents the valley rate period, and from 16:00 to 24:00 represents the peak rate period, as illustrated in Figure 1.

Taking YQWRP as an example for a case study. The YQWRP is a large-scale, long-distance, cross-basin water regulation project in Shandong Province, China, which transfers the water resources of the Yellow River to Qingdao City and provides strong support for the industrial and agricultural development of Qingdao City [22]. The geographical location and distribution of pump stations for the research area are shown in Figure 2. The project comprises six pump stations. The operational parameters of each pump station are shown in

Table 1. Parameters of pumping stations for YQWRP.

Pump Station	Name	Design Flow	Design Water Level	Design Net Head
pump station 1	Dayuzhang	36.0 m3/s	11.24/16.6 m	3.02 m
pump station 2	Wangdao	36.0 m3/s	1.90/4.45 m	2.55 m
pump station 3	Songzhuang	34.5 m3/s	1.80/10.51 m	8.71 m
pump station 4	Wangnou	31.1 m3/s	2.0/12.05 m	10.05 m
pump station 5	Tingkou	29.2 m3/s	6.26/13.04 m	6.78 m
pump station 6	Jihongtan	28.0 m3/s	4.02/12.0 m	7.98 m

.

Figure 2 illustrates the upstream and downstream layout of the step pumping station, where the upstream pumping station raises the water level and supplies water to the downstream pumping station, thus creating a continuous water flow delivery system. This layout optimizes the distribution and use of water resources while improving energy efficiency.

The YQWRP is characterized by huge energy consumption, multiple objectives, and multiple water conservancy facilities [23].

(1)

Huge energy consumption: The pumping stations and gates along YQWRP are currently controlled on-site based on the subjective experience of the management personnel, resulting in high operational costs. By optimizing the intraday operational strategies of each pump station and enhancing the coordination of the pumping station group, the time-of-use electricity pricing strategy that delineates peak and off-peak intervals can be optimally utilized, ultimately resulting in a decrease in total pumping costs. Furthermore, the participation of the gates between canal sections in hydraulic control facilitates the pumping head management. This strategy would facilitate the operation of all pump stations along the channel predominantly during periods of low electricity prices, thereby further decreasing the operational energy consumption.

(2)

Multiple objectives: To reduce the energy consumption of actual operation, the regulation objectives include minimizing electricity consumption, minimizing power consumption, and minimizing the number of regulation times.

(3)

Multiple water conservancy facilities: This project has 5 formal pump stations and 1 temporary pump station, starting from Dayuzhang pump station, passing through Wangdao pump station, Songzhuang pump station, Wangnou pump station, Tingkou pump station, Jihongtan pump station, and reaching Baisha Water Plant, with a total length of 291 km [24].

The Yellow River to Qingdao Water Regulation Project (YQWRP), selected for this study, is a highly representative case. YQWRP not only demonstrates the optimal regulation of pumping stations under specific conditions, but also reflects the general challenges of achieving energy efficiency and cost control in large-scale water resource allocation. Therefore, the case study of YQWRP not only provides in-depth empirical insights, but also provides valuable references and lessons for similar projects.

2.2. Analysis of Historical Regulation Scenarios

By analyzing the historically measured operational data of pump stations, under specific head conditions, the efficiency of each pump unit reaches its maximum value, with the flow distribution shown in Figure 3 and the power distribution shown in Figure 4. Operational parameters for each pump unit are presented in

Table 2. Operation parameters of pump unit.

Pump Station	Unit	1	2	3	4	5	6	7	8	9
Dayuzhang	Head (m)	2.20	2.20	2.20	2.20	2.20	/	/	/	/
	Min flow (m3/s)	7.70	7.70	7.70	7.70	7.70	/	/	/	/
	Max flow (m3/s)	10.75	10.75	10.75	10.75	10.75	/	/	/	/
	Min efficiency	0.3623	0.3623	0.3623	0.3623	0.3623	/	/	/	/
	Max efficiency	0.4488	0.4488	0.4488	0.4488	0.4488	/	/	/	/
Wangdao	Head (m)	1.60	1.60	1.60	1.60	1.60	1.60	/	/	/
	Min flow (m3/s)	5.00	5.00	5.00	10.00	10.00	10.00	/	/	/
	Max flow (m3/s)	10.00	10.00	10.00	10.00	10.00	10.00	/	/	/
	Min efficiency	0.6014	0.6014	0.6014	0.6014	0.6014	0.6014	/	/	/
	Max efficiency	0.6014	0.6014	0.6014	0.6014	0.6014	0.6014	/	/	/
Songzhuang	Head (m)	7.50	7.50	7.50	7.50	7.50	7.50	7.50	7.50	7.50
	Min flow (m3/s)	5.80	5.80	5.80	5.80	5.80	5.80	5.80	2.00	2.00
	Max flow (m3/s)	5.80	5.80	5.80	5.80	5.80	5.80	5.80	2.00	2.00
	Min efficiency	0.7133	0.7133	0.7133	0.7133	0.7133	0.7133	0.7133	0.5850	0.5850
	Max efficiency	0.7133	0.7133	0.7133	0.7133	0.7133	0.7133	0.7133	0.5850	0.5850
Wangnou	Head (m)	8.80	8.80	8.80	8.80	8.80	8.80	8.80	8.80	/
	Min flow (m3/s)	4.95	4.95	7.75	7.75	7.75	7.75	2.35	2.35	/
	Max flow (m3/s)	7.75	7.75	7.75	7.75	7.75	7.75	2.35	2.35	/
	Min efficiency	0.7600	0.7600	0.7600	0.7600	0.7600	0.7600	0.7275	0.7275	/
	Max efficiency	0.7600	0.7600	0.7600	0.7600	0.7600	0.7600	0.7275	0.7275	/
Tingkou	Head (m)	6.78	6.78	6.78	6.78	/	/	/	/	/
	Min flow (m3/s)	6.80	6.80	6.80	6.80	/	/	/	/	/
	Max flow (m3/s)	9.55	9.55	9.55	9.55	/	/	/	/	/
	Min efficiency	0.6945	0.6945	0.6945	0.6945	/	/	/	/	/
	Max efficiency	0.6334	0.6334	0.6334	0.6334	/	/	/	/	/
Jihongtan	Head (m)	7.50	7.50	7.50	7.50	7.50	7.50	7.50	/	/
	Min flow (m3/s)	5.80	5.80	7.00	7.00	7.00	2.60	2.60	/	/
	Max flow (m3/s)	8.55	8.55	7.00	7.00	7.00	2.60	2.60	/	/
	Min efficiency	0.6225	0.6225	0.6559	0.6559	0.6559	0.6559	0.6559	/	/
	Max efficiency	0.6225	0.6225	0.6559	0.6559	0.6559	0.6559	0.6559	/	/

.

Through in-depth analysis of the historical data, the optimal combination allocation scheme for each flow condition is derived, i.e., intra-station optimization, and then the optimal flow allocation table is formed. These data will be used in the subsequent model construction process to achieve inter-station optimization. First, the maximum and minimum flow values of the pump station group are extracted from the historical data to serve as the constraints of the model. Secondly, in the process of model construction, the flow distribution scheme of the pump station group is calculated based on the historical data, i.e., the specific distribution method for each flow unit, which can be directly obtained from the flow distribution table. This method effectively links intra-station and inter-station optimization, forming a two-stage optimization process that constitutes the main innovation of this study.

2.3. Data Sources

The geographical locations, design parameters of the pumping stations, and historical measures involved in the study were provided by the Jiaodong Water Diversion Bureau of Shandong Province.

3. Construction of Optimization Regulation Model for Cascade Pump Stations

Considering the actual conditions of the spot electricity market trading in Shandong Province, three optimization regulation models for cascade pump stations were constructed.

(1)

Model 1: The main objective of Model 1 is to minimize the total daily electricity cost and the number of pumping station adjustments. The model assumes that gates between channels are not involved in the regulation and storage of water resources.

(2)

Model 2: The main objective of Model 2 is to minimize electricity consumption and the number of pump station adjustments. The model assumes that gates between channels are not involved in the regulation and storage of water resources.

(3)

Model 3: Model 3 aims to minimize the total daily electricity cost and the number of pumping station adjustments. Regulators should implement regulations to make sure the hydraulic transmission times between consecutive pump stations align with integer multiples of 24-h cycles. This strategy would facilitate the operation of all pump stations along the channel, predominantly during periods of low electricity prices.

3.1. Model 1

(1)

Objective function: The regulation objective is to minimize the total daily electricity cost of the cascade pumping station group and minimize the number of pump station adjustments, given a specific daily average flow.

$$\mathrm{Minimize} \mathrm{electricity} \mathrm{cost}: \min F={\displaystyle \sum _{i=1}^6{\displaystyle \sum _{j=1}^T{c}_j{N}_{ij}\Delta t}}={\displaystyle \frac{Q_{ij}\times H\times \rho \times g}{\eta \times 1000}}$$

(1)

$$\mathrm{Minimize} \mathrm{number} \mathrm{of} \mathrm{unit} \mathrm{adjustments}: \mathrm{minN}={\displaystyle \sum _{i=1}^6{\displaystyle \sum _{k=1}^x{n}_{i,k}}}$$

(2)

where c_j is the electricity price for pumping during the j-th time period; N_ij is the pumping power of the i-th pump station in the j-th time period; Δt is the interval between time periods; Q_ij is the pumping flow of the i-th pump station during the j-th time period; H is operation head; ρ is water density; g is gravitational acceleration; n is operation efficiency of the pumping station; T is the number of regulation time periods; N is the total number of unit adjustments; n_i,k is the adjustment number of the i-th pump station of k-th pump unit.

(2)

Constraints:

(1)

Pumping flow constraint: The pumping flow of each pump unit does not exceed its maximum operation flow and does not fall below the minimum operation flow:

Q_i,k,min ≤ Q_i,k ≤ Q_i,k,max

(3)

where Q_i,k is the pumping flow of the k-th pump unit of the i-th pump station; Q_i,k,min is the minimum value of operation flow of the k-th pump unit of the i-th pump station; Q_i,k,max is the maximum value of operation flow of the k-th pump unit of the i-th pump station.

(2)

Pumping power constraint: The pumping power of each pump unit does not exceed its maximum operation power and does not fall below the minimum operation power:

P_i,k,min ≤ P_i,k ≤ P_i,k,max

(4)

where P_i,k is the pumping power of the k-th pump unit of the i-th pump station, P_i,k,min is the minimum value of the operation power of the k-th pump unit of the i-th pump station; P_i,k,max is the maximum value of the operation power of the k-th pump unit of the i-th pump station.

(3)

Constraint of total water regulation volume: The total pumping flow of the pump station group is less than the total water regulation volume:

$$0<{\displaystyle \sum _{i=1}^6{Q}_{i,k}<Q}$$

(5)

where Q is the total water regulation volume.

3.2. Model 2

(1)

Objective function: The objective of the regulation is to minimize the electricity consumption and minimize the number of pump station adjustments (same as Formula (2)):

$$\mathrm{Minimize} \mathrm{electricity} \mathrm{consumption}: \min C={\displaystyle \sum _{i=1}^6{\displaystyle \sum _{j=1}^T{N}_{ij}\times \Delta t}}$$

(6)

where H is total power consumption of cascade pumping station group.

(2)

Constraints: Constraints are the same as (3)–(5).

3.3. Model 3

(1) Objective function: The objective function is the same as (1) and (2).

(2) Constraints: In Model 3, a constraint on hydraulic transmission time is added to control the hydraulic transmission time between successive pump stations to be an integer multiple of 24 h, facilitating the operation of all pump stations along the channel predominantly during periods of low electricity prices.

$$T_{i-(i+1)}=24,48,72,\dots$$

(7)

where T_i−(i+1) is the hydraulic propagation time between the i-th pump station and the (i + 1)-th pump station.

The other constraints are the same as (3)–(5).

3.4. Model Solution

The model was solved using dynamic programming. The principle of dynamic programming involves transforming a multi-stage decision-making problem into a series of inter-related single-stage decision-making problems that are solved stage by stage [25]. The optimal solution for each stage is determined first, and then, by employing a recursive algorithm, the optimal solution path for the complex problem can be obtained ultimately [26]. Dynamic programming is known for its reliability and wide use, applied in many areas such as water resources allocation [27], hydropower station dispatching [28], optimal reservoir operation [29], and agricultural management [30]. In the intra-station-inter-station two-phase regulation problem, dynamic programming improves the efficiency of the algorithm by efficiently utilizing the results of previous computations and avoiding repeated computations.

The basic equation of the dynamic programming algorithm is founded on the principle of optimality, which assumes that to solve an optimization problem, n decision variables D₁, D₂, …, D_n must be made sequentially. If this sequence of decision variables is optimal, then for any integer k, (1 < k < n), the subsequent optimal decision variables will only depend on the current state determined by the previous decision variables. Consequently, the subsequent decision variables D_k+1, D_k+2, …, D_n will also be optimal [27].

From the principle of optimality, the following relationship can be derived:

$$f_k(s_k)=\underset{d_k(x_k)\in D_k(s_k)}{\max }[{\displaystyle \sum _{k=1}^j{\nu }_k(s_k,d_k)}]$$

(8)

where v_k (s_k, d_k) is the stage indicator.

Formula (9) can be expressed as follows:

$$f_k(s_k)=\underset{d_k(s_k)\in D_k(s_k)}{\max }[{\nu }_k(s_k,d_k)+f_{k+1}(s_{k+1})]$$

(9)

where f_k (s_k) is the optimal value function for the entire strategy.

Assuming the initial cost is:

$$f_1(s_1)={\nu }_1(s_1,d_1)$$

(10)

Then, Equations (9) and (10) are used to calculate the value function of the strategy, and they are referred to as the basic equations of dynamic programming. The principle of the dynamic programming algorithm solution is illustrated in Figure 5.

3.5. Research Process

The research flowchart is shown in Figure 6.

(1)

Data preparation: This phase involves the collection and analysis of historical operational data, design parameters, and real-time flow conditions to provide a solid foundation for model development.

(2)

Model construction: This phase involves three optimization regulation models for the cascade pumping station to alleviate its operating costs and excessive electricity consumption.

(3)

Result analysis: This phase involves comparing the optimized operational schemes with traditional fixed-flow methods to highlight the benefits of the proposed models in terms of cost savings, energy efficiency, and overall system performance.

4. Result and Analysis

4.1. Results of Optimization Regulation Model

Research was conducted on the application of Model 1, Model 2, and Model 3 under four operating conditions with daily average pumping flows of 8 m³/s, 16 m³/s, 24 m³/s, and 32 m³/s. The flow results of the optimal regulation scheme are presented in Figure 7. The power results of the optimal regulation scheme are presented in Figure 8.

4.2. Result Analysis

(1)

Analysis of target and actual water regulation volume

The comparative analysis between the target and the actual water regulation volume is shown in

Table 3. Analysis of target and actual water regulation volume.

Flow Condition	Target Water Volume (104 m3)	Actual Water Regulation Volume (104 m3)				Water Regulation Completion Rate (%)
		Fix Flow	Model2	Model1	Model3	Fix Flow	Model2	Model1	Model3
8 m3/s	69.12	67.39	68.92	69.05	69.06	97.50	99.71	99.90	99.92
16 m3/s	138.24	134.78	138.05	138.17	138.11	97.50	99.87	99.95	99.91
24 m3/s	207.36	200.45	207.28	207.26	207.31	96.67	99.96	99.95	99.97
32 m3/s	276.48	267.84	276.48	276.45	276.48	96.88	100.00	99.99	100.00

.

According to Table 3, all optimized schemes can achieve good regulation results. The water regulation completion rate of the optimized schemes is higher than that of the fixed flow scheme.

(2)

Analysis of total and unit electricity cost

The comparative analysis between the total and unit electricity costs is shown in

Table 4. Analysis of total and unit electricity cost.

Flow Condition	Electricity Cost (104 CNY RMB)				Unit Electricity Cost (CNY RMB/m3)
	Fix Flow	Model1	Model2	Model3	Fix Flow	Model1	Model2	Model3
8 m3/s	6.93	5.75	6.27	3.22	0.1028	0.0833	0.0910	0.0467
16 m3/s	13.73	12.13	13.27	9.92	0.1019	0.0878	0.0961	0.0718
24 m3/s	20.15	19.05	20.06	16.72	0.1005	0.0919	0.0968	0.0807
32 m3/s	26.46	27.03	27.42	26.02	0.0988	0.0978	0.0992	0.0941

.

The data in Table 4 show that all optimization scenarios achieved significant results in reducing the operating costs of the pumping station. Model 1 effectively reduces the energy consumption during the high electricity price hours by optimizing the operation time and power allocation of the pumping station, which significantly reduces the total electricity cost and unit electricity cost under different flow conditions. For example, under the flow condition of 8 m³/s, the unit electricity cost of Model 1 is reduced by 18.9% compared with the fixed flow scenario, which shows a strong economic performance.

However, the optimization strategy of Model 3 is more advanced. It not only considers the optimization of pumping station operations, but also incorporates the regulation and storage capacity of channel gates into the overall regulation scheme. This integrated optimization strategy enables the pumping station to fully utilize channel water storage during low tariff periods and reduce operation demand during high tariff periods, thus further reducing the electricity cost. Under the same 8 m³/s flow condition, the unit of electricity cost of Model 3 is only RMB 0.0467/m³, which is 43.9% and 44.3% lower compared to Models 1 and 2, respectively, showing its significant advantage in economy. This demonstrates that Model 3 not only achieves lower operating costs but also enhances the flexibility and stability of the system through synergistic optimization of pumping stations and gates, providing a better solution for the economic operation of large-scale water transfer projects.

(3)

Analysis of total and unit electricity consumption

The comparative analysis between the total and unit electricity consumption is shown in

Table 5. Analysis of total and unit electricity consumption.

Flow Condition	Electricity Consumption (104 kWh)				Unit Electricity Consumption (kWh/m3)
	Fix Flow	Model1	Model2	Model3	Fix Flow	Model1	Model2	Model3
8 m3/s	9.85	9.72	9.69	9.87	0.1462	0.1408	0.1406	0.1429
16 m3/s	19.54	19.46	19.39	19.56	0.1450	0.1409	0.1405	0.1416
24 m3/s	28.67	29.36	29.12	29.34	0.1430	0.1417	0.1405	0.1415
32 m3/s	37.65	39.44	39.14	39.45	0.1406	0.1426	0.1416	0.1427

.

According to Table 5, all the optimized schemes demonstrate significant improvements in reducing the operating consumption of the pump stations, highlighting the effectiveness of the proposed optimization models. Specifically, Model 3’s regulation scheme stands out as it achieves a more pronounced reduction in electricity consumption compared to Model 1 and Model 2. This is evident across all tested flow conditions.

(4)

Innovation analysis

This research delves into the optimization of pumping stations, revealing strategies for enhancing their operational efficiency under varying flow conditions. Traditional operation modes often overlook the synergistic potential of pumping stations, leading to an all-or-nothing approach—stations either run at full capacity or shut down entirely when flow demands fluctuate. This gap in systematic optimization is addressed by the proposed new operation mode, which fine-tunes the start-up combinations of pumping stations based on real-time flow requirements. This innovative approach not only maximizes the synergy between pumping stations but also significantly boosts their operational efficiency, offering robust theoretical support for the economic management of cascade pumping systems.

Moreover, the study explores the temporal coordination in pumping station operations. Without considering time-of-day tariffs, stations typically fail to capitalize on the variability of electricity prices to minimize costs. By incorporating time-of-day tariffs into the operational strategy, this research optimizes the regulation of pumping stations to prioritize operation during off-peak hours when tariffs are lower. By employing this meticulous time management, the pumping stations can ensure uninterrupted water supply while achieving maximum cost-effectiveness. This approach provides a novel framework for the optimal regulation of cascade pumping stations, balancing operational efficiency with economic sustainability.

4.3. Discussion

(1)

Limitations of the Study

Firstly, this study does not incorporate ecological factors, such as the impact of water transfer on local ecosystems or the potential for environmental protection measures. Additionally, this study does not fully consider real-time constraints like equipment failures, or emergency situations, which could affect the practical implementation of the proposed strategies. Lastly, the models do not account for the impacts of climate change on water availability and demand, which is increasingly important for long-term water resource planning.

(2)

Application prospects

The data used in this study are limited to the YQWRP in Shandong Province, China, but the model construction approach is also applicable to the economic operation of cascade pumping stations in large-scale water regulation projects around the world. The optimized regulation scheme of Model 2 achieves a significantly higher reduction in operational cost compared to that of Model 1. However, Model 2 necessitates the collaborative involvement of regulators for hydraulic regulation, thus making it more applicable to research areas where control structures are well-established.

5. Conclusions

To reduce the operational costs of cascade pump stations in large-scale water regulation projects, this study takes the YQWRP as a case study and develops three optimization regulation models. Model 1 aims to minimize the daily total electricity cost, Model 2 aims to minimize the daily total electricity consumption, and Model 3 considers both time-of-use electricity prices and regulation and storage of canal sections. A dynamic programming algorithm was employed to solve for the optimal operation scheme of each pumping station. The main research conclusions are as follows:

(1)

Analysis of Historical Data: The YQWRP has been constructed for more than 30 years. There are deviations between the actual operational conditions of the project and its design values. The constraint design of this study is determined based on the measured historical operation data of the pump station group, which is more in line with the actual regulation process. This study proposes an innovative optimization method for pump station operation that covers both intra-station and inter-station regulation levels. At the intra-station level, the method breaks the traditional all-open or all-stop operation mode of pumping stations through a systematic optimization scheme, and achieves effective synergy between pumping stations. At the inter-station level, the study optimizes the operation strategy of the pumping station in different tariff periods by considering the time-sharing tariff factor, allowing the pumping station to operate during the lowest-cost periods, thus ensuring the safety of water supply while significantly improving the economic rationality. This optimization method, which integrates intra- and inter-station regulation, provides a new theoretical framework and practical guidance for the economic operation of step pumping stations.

(2)

Advantages and suggestions of joint regulation of pump stations and gates: The optimization regulation scheme of Model 3, which considers both time-of-use electricity pricing and regulation and storage of water resources, is the most economical operation scheme. Under various average daily pumping flow conditions, the reduction in operational costs for Model 3 is significantly higher than that of Model 1 and Model 2. However, due to the requirement of Model 3 for the collaborative involvement of gates in hydraulic control, it is recommended for application in research areas where hydraulic installations are well-developed.

(3)

Application effect: All models can fully utilize the intraday peak-valley time-of-use electricity pricing policy, effectively reducing the operational costs of the pump station group in the water regulation project. Results indicated that Model 3 scheme performs the best. The application was conducted under conditions of average daily pumping flows of 8 m³/s, 16 m³/s, 24 m³/s, and 32 m³/s, respectively. The operating costs of Model 3 were reduced by 37,100, 38,100, 34,300, and 4400 CNY RMB, respectively, compared to the fixed flow condition.