**3. Methods**

Here we develop an integrated water-energy systems framework that utilizes a top-down approach to estimate electric load projections for LADWP's water network for the reference year (average between 2010–2015) through 2050 in 5-year increments. We also propose a method to study the relative significance of key factors impacting electricity demand for the utility's evolving water supply over time. Methodological details are described in this section.

### *3.1. Integrated Water-Energy System Framework*

A block diagram of LADWP's water supply stages is plotted in Figure 2 to illustrate the water supply system sources (inputs) and discharges (outputs) considered in this analysis. Our control volume includes the stages involved with supplying water (i.e., surface water supply and recycled water systems). Thus, wastewater managemen<sup>t</sup> stages (i.e., wastewater collection, wastewater treatment and discharge) are excluded from study boundaries because these processes are managed by a separate entity (i.e., the Los Angeles Bureau of Sanitation), but the water cycle stages involving recycled water production (i.e., additional treatment and distribution) are included in the study as they contribute to LADWP's water supply. For each year studied, we utilize energy intensity values (*EIi* in kWh/m<sup>3</sup> for each stage of *i*) and annual water supply volumes (*Vj* in m<sup>3</sup> per year) from each water source of *j* to calculate the total annual electricity demand for the system (*E<sup>t</sup>* in kWh per year), using Equation (1):

$$E^t = \sum\_{i}^{n} \sum\_{j}^{m} EI\_i V\_j^t \tag{1}$$

The energy intensity values of the various water supplies and treatment processes applied within this framework are presented in Table 1. When available, we use *EI* values reflecting those received by a communication with LADWP or from LADWP's UWMP [7]; otherwise we use *EI* values from literature [17,34,35]. To address issues related to uncertainty in *EI* values, we provide electricity demand estimates based on a range of *EI* values that reflect values in the literature. Otherwise, when no ranges were available, we apply ±20% to nominal *EI* values. These high and low *EI* value bounds are noted in parentheses in Table 1.



*Energies* **2020**, *13*, 5589

1 The lower and higher EI values are obtained by applying 20% to listed nominal EI values.

Since LADWP's imported water travels long way to arrive to the city, some of LADWP's water infrastructure, including pumping and raw water treatment, is provided electricity by other utilities. Thus, the electricity-supplier for each energy consuming water facility was determined according to its geographic location based on publicly available documents from LADWP (see Table 1). Two distinct tags (i.e., LADWP and non-LADWP) were applied to distinguish the electric loads supplied by LADWP versus those supplied by other neighboring electric utilities, typically within California Independent System Operator (CAISO).

Other assumptions were made to estimate water-related electricity demands. For example, we assumed no losses in water across each individual water supply stage; in other words, the volume of water entering each facility/stage equals the volume of water exiting that stage, which transfers to the subsequent stage that follows. However, water losses (including firefighting and mainline flushing to improve water quality) are accounted for as non-revenue generating water demands in LADWP's projected total water demand. Thus, we do not make further assumptions regarding to potable water lost to the environment. We understand that ignoring water losses may cause an overestimation of electricity demand, but given the low fractions of water losses in LADWP (the real water losses accounted for 3.8% of total supplied water in 2013/2014 [7]) and the fact that most electricity consumed for water supply occurs upstream of the water distribution system, the significance of this potential overestimation of annual electricity consumption is likely small. Additionally, we assume water leaving the treatment stage is potable and is distributed uniformly across LADWP consumers, regardless of the source or location of treatment and consumption. In terms of recycled water, we consider the marginal energy needs of treating the effluent exiting wastewater treatment facilities to meet recycled water standards, as well as the energy needed for recycled water distribution pumping [36]. We also account for the electricity needed for producing recycled water that is used for beneficial reuse (namely for environmental uses), even though this water is eventually discharged into the environment without offsetting end-use water demand.

**Figure 2.** Block diagram of the general components of a water supply system. The dashed box indicates the boundaries of this study.
