Co-Design of Water Distribution Systems with Behind-the-Meter Solar ^†

Abstract

The design of water distribution systems (WDSs) is crucial for ensuring a resilient water supply for the future. To improve the energy efficiency of WDSs, behind-the-meter (BTM) solar has been considered as an option. Due to the complex water–energy relationship between WDSs and their associated BTM solar systems, the co-design of the integrated systems that considers the combined performance of both systems is required. Moreover, the design of WDS also needs to anticipate potential changes in the future due to their long service life, as both future water demand and potential solar PV technology development can have an impact on system performance over time. This study aims to develop an approach for the co-design of WDSs and the BTM solar systems under long-term water demand and solar PV technology development uncertainty.

1. Introduction

Water distribution systems (WDSs) are essential components of water supply infrastructure. To provide sufficient pressure to water users, a significant amount of energy is consumed by pump operation in WDSs [1]. Recently, behind-the-meter solar photovoltaic (BTM solar PV) systems have been identified as an effective method to decarbonize WDSs and improve their overall performance, considering the relatively lower cost and near-zero emissions of BTM solar PV systems [2,3]. Due to the high variability in water demand and intermittency in solar resources, there is a temporal mismatch between the energy required by pumping and that supplied by BTM solar systems. Therefore, in this study, the design of WDSs and their associated BTM solar systems are considered together to account for the water–energy nexus within the integrated systems.

WDSs are usually designed to serve for a long period of 50–100 years. In addition, the capital cost of the WDS and the cost of construction are relatively high. Therefore, the design of WDSs needs to anticipate potential changes in the future. Under the long-term drivers of climate change, population growth, and urbanization, the water demand of WDSs in the future is highly uncertain [4]. Solar PV systems are also expected to become cheaper as well as more efficient in terms of energy conversion in the future, considering their potential development. Therefore, this study focuses on the co-design of a robust WDS and its associated BTM solar systems that can maintain their performance over time no matter what future demand and technology may be realized. The rest of this paper is structured as follows: Section 2 illustrates the general methodology developed and the methods applied in this study. In Section 3, the results and discussion are presented, and Section 4 concludes the paper.

2. Methods

2.1. General Methodology

The co-design of WDSs integrating BTM solar systems considering multiple sources of long-term uncertainty mainly consists of two steps, as shown in Figure 1. In the first step, both the WDS and the BTM solar systems are designed through optimization under each future scenario. This first step leads to several sets of optimal design solutions. In the second step, all the optimal design solutions are re-evaluated under all the future scenarios using the hydraulic simulation model. The robustness of these optimal design solutions is then evaluated using a robustness matrix, and those design solutions that remain non-dominated considering their robustness values are identified as robust design solutions.

The co-design problem is formulated as a multi-objective optimization problem. The first objective is the minimization of the total life cycle cost by the integrated systems:

$$TC=CC+PV\left(RC\right)+PV\left(OC\right)$$

(1)

where $CC$ is the capital cost including the capital cost for WDS components and solar PV systems at the design starting point; $PV\left(RC\right)$ and $PV\left(OC\right)$ are the present value of the replacement cost for pumps and solar PV systems and the operational cost by the WDS.

The second objective is to minimize the total grid energy consumption by the WDS:

$$TEC=\sum {TEC}_t$$

(2)

where ${TEC}_t$ is the grid energy consumption at time step t.

In this study, three robustness metrics, i.e., mean-variance, optimism–pessimism, and undesirable deviations [5], have been selected considering their different risk attitudes.

2.2. Case Study

A modified Anytown network has been considered in this study as the case study network, and water is pumped directly from the water source to the demand nodes. A 60-year design period is considered for the WDS. The sizing of pipes is designed for the whole period, while pumps and the BTM solar PV systems are sized every 20 years to account for their standard service life.

The combined impact of water demand changes and potential solar PV technology development are characterized using a total of 15 future scenarios. Water demand of the WDS is assumed to change by −30%, +0%, +30%, +60%, and +100% by the end of the design period compared to the design starting point, which forms 5 water demand trajectories (i.e., D1, D2, D3, D4, D5, respectively). Three solar PV technology development trajectories are considered, which correspond to no development, conventional technology development, and advanced technology development (i.e., T1, T2, T3).

3. Results and Discussion

To investigate the impact of solar PV technology development on the WDS’s resilience to a range of uncertain future water demand conditions, the identified robust design solutions have been summarized in terms of their optimization conditions across two groups of scenarios, namely 5 water demand growth scenarios and all 15 future scenarios. The results are demonstrated in

Table 1. Summary of percentage of robust design solutions identified under 5 water demand growth scenarios (assuming no solar PV technology development, i.e., T1).

Robustness Matrix	Mean-Variance					Optimism–Pessimism					Undesirable Deviations
Water demand trajectory	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5
Percentage (%)	0	0	0	0	100	0	26	0	20	54	0	0	0	0	100

and

Table 2. Summary of percentage of robust design solutions identified under each scenario (optimization and evaluation conducted across all 15 scenarios).

Solar Technology Trajectory		T1					T2					T3
Mean-variance	Water demand trajectory	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5
	Percentage (%)	0	0	0	0	0	0	0	0	25	27	0	0	1	0	47
Optimism–pessimism	Water demand trajectory	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5
	Percentage (%)	0	0	0	0	0	0	0	0	0	0	18	0	30	0	52
Undesirable deviations	Water demand trajectory	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5	D1	D2	D3	D4	D5
	Percentage (%)	0	0	0	0	0	0	0	0	16	50	0	0	17	0	17

.

As shown in Table 1, when water demand uncertainty is considered the only source of uncertainty in the co-design of the integrated systems, the majority of robust design solutions are obtained from optimal solutions optimized under the largest water demand growth scenario. However, when all 15 scenarios are considered, more optimal design solutions obtained under lower-water-demand growth scenarios are identified as robust design solutions. This indicates that solar PV system integration enhances the WDS’s resilience to changing future water demand conditions.

To further explain the impact of solar PV integration and its development in the future on the design performance of WDSs, a comparison of the performance of two typical optimal design solutions is demonstrated in Figure 2. The boxplots show the distribution of TC and TEC of the optimal design solutions across all future scenarios. It is clear that the design solution obtained under the development of the advanced solar PV technology has almost identical average TC and variability of TC across all future scenarios compared to the solution obtained under no development scenario. This implies that installing larger solar PV systems will not increase the overall life cycle cost by the WDS. More importantly, such design is considered a more robust design in terms of energy efficiency, as it leads to a reduction in average grid energy consumed by the WDS and a narrower range of grid energy consumption across all future scenarios.

4. Conclusions

In this paper, the co-design of WDSs integrating BTM solar systems under long-term uncertainty has been investigated. It is concluded that BTM solar PV system integration improves WDSs’ performance under changing water demand conditions in the future, and it also increases WDSs’ resilience to future changes. BTM solar PV system integration reduces the risk of oversizing the WDS.