A Framework for Optimal Placement of Rooftop Photovoltaic: Maximizing Solar Production and Operational Cost Savings in Residential Communities

Solar power is one of the most popular clean energy technologies [1], and it has immense potential to satisfy building energy demands. Photovoltaics (PVs) are able to produce on-site electricity without energy supply concerns or environmental harm [2], making them very desirable. Combined with decreasing costs, rooftop PV is spreading rapidly. Rooftop-deployed PV has advantages over ground-mounted PV—it can avoid the cost of land use and be integrated within the building’s roof structure, reducing additional material and labor costs [3].

In addition to the aforementioned benefits, climate and energy targets have led to increased deployment of rooftop solar PV. Extensive recent literature has shown that integrating PV systems in residential neighborhoods is currently the most feasible and practical option for meeting these targets [4–6]. Because of this, analyzing the solar potential of individual buildings and neighborhoods is critical to informing future adaptive energy policies and utility planning [7].

Our implementation goals for analyzing PV generation and solar potential in residential communities can be divided into two analysis objectives:

1. Maximizing PV generation: Here, we focus on the science of sustainable urban context to quantify the amount of solar access [8], because mutual shading in residential neighborhoods has a large influence on solar energy production. For example, solar radiation for building rooftops in Osaka, Japan, is reduced by 13.7% when shadows from surrounding buildings are considered, and an additional 7.7% reduction when obstacles on the rooftop are taken into account [9,10]. Based on estimates from Navigant Consulting, only 8% of residential rooftops in the United States are flat [11]. Because of this, self-shading from roof structures has a significant impact when calculating the solar radiation absorbed by PV on available roof surfaces. Therefore, considering the shading effect from rooftop obstruction and surrounding context is crucial when simulating the solar radiation overall in United States residential communities.

2. Balancing building energy demand with PV generation: Mismatch of supply and demand leads to unwanted power flow between the household and the grid. This is abundant in residential neighborhoods, even in buildings with equal annual generation and consumption. The daily PV generation and electricity consumption profiles are different, which means buildings need to export a portion of the generated energy back to the grid [12]. This situation has introduced management difficulties for the electric grid. It also contributes to a significant financial loss to the end user when the price paid for the consumed energy is higher than the price of energy sold back to the grid. Therefore, it is important to maximize self-consumption of the generated energy [13]. In addition, residential energy consumers are charged based on different utility rate structures. To reduce consumers’ electricity bills in net zero energy homes and communities, expensive batteries are deployed to reduce the electricity fed from the grid during peak hours [14]. Although this seems to be an attractive solution, optimizing placement of PV panels can minimize operational energy cost while avoiding the financial burden of expensive and large-sized batteries.

Despite abundant literature evaluating the solar potential of individual buildings and urban areas, studying the spatial deployment of PV panels to satisfy the aforementioned objectives has not yet been addressed. Brownsword et al. estimated the PV resources for rooftops in Leicester city, considering only south-west to south-east oriented roofs and taking 75% of total roof area as an efficient area to install PV panels [15]. Lund analyzed the potential deployment of PV panels on roofs by simulating the generation of only 50% of the available roof area and neglecting shading effects [16]. Energy demand was calculated using a load distribution function based on the location. Wegertseder et al. combined solar mapping of roof surfaces with energy consumption patterns of the building stock in Concepcion, Chile, to calculate net power flows in the urban electric grid [17]. In a more recent attempt, Brito et al. carried out a techno-economic analysis of the feasibility of building-integrated PV in different areas in Portugal by coupling LiDAR and Typical Meteorological Year weather data. The demand is estimated using a top-down approach, where the average per capita electricity demand is multiplied by the estimated number of inhabitants [18].

All these approaches attempted to calculate the net energy profile. However, these studies relied on simplified assumptions to define areas for efficient rooftop PV application. They also relied on top-down approaches that cannot address different scenarios in terms of energy demand that require a bottom-up approach [19]. To fill in the literature gap, this paper introduces workflows that use a bottom-up approach to inform engineers, urban designers, residential project managers, and residential homeowners on the optimal placement of rooftop PV panels, taking into account economic and efficiency targets.

Our approach presents an automated framework to identify the optimal location of rooftop PV panels. The framework is implemented by combining multiple workflows, including energy and environmental simulation, parametric modeling, and optimization to identify the optimal number and location of PV panels on individual buildings for balancing the energy demand and supply at a building and community scale. These workflows are linked in the visual scripting interface grasshopper in rhinoceros cad software. The algorithms include two user-identified targets for optimal PV placement: (a) maximizing PV panel efficiency, where users aim to maximize the total energy generation, and (b) minimizing operational energy cost, where best panels are selected considering different utility rates for operational energy cost.

The workflows were demonstrated on a residential community in Fort Collins, Colorado. The developed workflows were implemented to find the optimal rooftop PV placement for each of the two targets. Results from the workflows are discussed in this paper, illustrating the effect of PV location and orientation on solar energy production efficiency and operational energy cost.

In Ref. [20], we described an earlier iteration of our workflow that informed the deployment of PV panels for individual buildings. We have since fine-tuned our analysis, understanding the application of workflows in an urban setting is key to inform energy-efficient design at the community level. This paper, therefore, develops workflows for optimal deployment of PV panels at both a building and community scale. At a community level, the workflows aim to find PV panel locations that enhance efficiently while saving cost for the community as a whole; at the building level, deployment of PV panels for each building aims to optimize savings for each individual homeowner.

The rest of the paper is organized as follows: Sec. 2.1 describes the community model generation. Section 2.2 describes the energy models and simulation of the demand energy profile. Section 2.3 presents a workflow for optimal PV sizing based on panel efficiency. Section 2.4 presents an optimization workflow for selecting panels to minimize operational energy cost. Section 3 compares the results of the implemented workflows and explores urban-scale implementation of each of the workflows. Section 4 discusses the details of the optimization workflow, the alternative optimization tools, and the corresponding solar ownership model for each analysis scenario.

Matching annual PV production to annual community energy demand is subject to the feasibility and efficiency constraints of deploying PV panels on roof surfaces. In this process, we simulated the community total demand profile. Then, we developed two different workflows to find optimal PV placement, each with a specific objective.

The site plan, along with detailed architectural drawings for each building type in the community, was provided by the project manager and used to develop the community model. The development of the community model included two steps: (1) establishing the model for individual building types and (2) positioning the single-building models spatially according to the site plan. The community has five major building types: duplex, three-storey townhome, two-storey townhome, cottage, and a single-family detached home. Also, each building type has unique variations in terms of room configuration, window configuration, and roof type.

We developed the urban-scale modeling of the community in Fort Collins using rhino3d cad software. For each building type, a model is developed based on the construction drawings that refer to its associated boundary and perimeter geometry (exact roof and envelope geometry). Then each of these single-building models is spatially positioned in the site plan, according to their corresponding labels, to create a three-dimensional site model for the whole community. This digital massing model provides geometric and spatial information of the built urban environment and is processed using the Grasshopper tool (a visual scripting plug-in for rhino3d cad software) for our analysis. Figure 1 shows part of the site plan and the different building types spatially placed into this model. Each color represents a different building type.

The energy consumption profiles for each building type were simulated using BEopt^™ software [21], taking into account the different orientations, occupancy levels, and construction properties.

Construction information was provided by the developer of the community. All building types share similar construction properties. Information regarding each building’s orientation and mutual shading was derived from the three-dimensional community model. Finally, occupancy information was estimated based on the number of bedrooms. All this information is used to generate a collection of BEopt prototype models with different orientations. These models are then used to simulate individual buildings” loads.

Afterwards, the community total building loads are generated by aggregating the building loads from all the prototype models in the community. An Actual Meteorological Year weather file of Fort Collins with historical data from 2017 was used to run the simulation, and an hourly community aggregate load was generated.

This workflow aims to find the most efficient placement of PV panels to be laid on building roofs in the community, based on surface efficiency and feasibility. This process is divided into two steps: (1) selection of most efficient panels and (2) PV energy simulation.

• Step 1: Selecting PV panels to maximize solar radiation gains. The first step is divided into three main parts, illustrated in Fig. 2 and detailed in the following paragraphs.

  • First, an automated PV panel layout algorithm is developed to geometrically lay out specific PV panels on complex roof geometry. The PV panel size is defined to be 1686 mm × 1016 mm, based on the PV module selected by the home builders. Based on the PV panel size, the geometric algorithm fits the maximum number of panels on any complex roof geometry. To reduce the computational time of the workflow, the algorithm disregards north surfaces because they are inefficient for PV implementation. Surfaces smaller than 15 m² are also disregarded to ensure the spatial feasibility of placing a PV panel. The functionality and output of this algorithm are illustrated in Fig. 2 subplot (a).

  • After populating the roof surfaces with the maximum number of panels, a solar radiation analysis for direct and indirect radiation is performed on all the panels. The Fort Collins weather file with historical data for 2017 was used for this study. This weather file was used to model a cumulative sky matrix by using Radiance’s gendaymtx function to calculate the sky’s radiation for each hour of the year. Figure 3 shows a visualization of the sky matrix generated from the weather file. Three sky domes are illustrated; the first dome shows the total radiations, the second dome shows diffused radiations, and the third dome shows only direct radiations.

    Using the generated sky matrix, the amount of absorbed radiations (kW h/m²) per year is calculated for all laid panels. In this process, several test points are assigned on each panel, and an average radiation result is returned for each panel. Figure 2 subplot (b) shows a radiation study for panels laid on the roof of a single-family detached building. Again, to reduce the computational time of the workflow, the algorithm disregards north-facing surfaces because they are inefficient for PV implementation. Surfaces smaller than 15 m² are also disregarded to ensure the spatial feasibility of placing a PV panel. The solar radiation analysis allows the user to quantify the amount of energy collected by each panel, as well as the number of direct sunlight hours received.

  • Based on the retrieved radiation data for each panel, the best panels are automatically identified by assigning a threshold for a solar radiation value. All panels that have an average radiation below the assigned threshold are considered inefficient and are disregarded. The user can now study different scenarios by assigning different efficiency thresholds. The output of this process is illustrated in Fig. 4: based on a defined threshold, the red colored panels were selected as the most efficient panels.

• Step 2: PV energy simulation. In the second step, the electrical energy produced by the selected PV panels is calculated using National Renewable Energy Laboratory’s PVWatts calculator for crystalline silicon (c-Si) and thin-film PV [22]. The inputs and assumptions for this model are summarized in Tables 1 and 2.

  The annual shading for each PV panel is calculated to evaluate the losses due to shading. The annual shading output is based on the method developed by Vignola [23]. Figure 5 visualizes the annual alternating current (AC) energy percentage of a single panel for each hour of the year. These results are used to account for the shading losses of each panel.

This workflow can be applied to individual buildings or a group of buildings. Following the simulation process, users can select different efficiency thresholds and compare the results. For instance, users can test different thresholds to investigate the trade-off between efficiency and the number of rooftop panels. When a high threshold is set, fewer panels are selected and the building or the community may fall short of meeting the generation target. To address this issue, additional land area might be needed to deploy the community PV or a lower threshold might be set to increase the number of the selected roof panels. In some cases, additional land area might not be available due to the space or cost constraint, forcing the user to deploy more rooftop PV panels at less efficient locations.

This workflow utilizes a genetic optimization algorithm to find the optimal placement of PV panels with the objective of minimizing operational energy cost. The overall process is illustrated in Fig. 6 and consists of four steps: parametric modeling, simulation, processing results, and optimization.

In the parametric modeling step, the panel layout algorithm, described in Sec. 2.3 (Fig. 2), is implemented. Then a method is developed and used to select all the possible combinations of a targeted number of panels. The number of panels is specified by users, because this decision depends on the amount of rooftop PV panels the homeowner or community managers decide to invest in. The panel combinations are the genomes input to be investigated by the optimization algorithm.

After, the selected PV panel surfaces are simulated in step 2 using the PV simulation model described in Sec. 2.3 to generate an hourly annual energy generation profile.

During step 3 (processing results), the PV generation profile is subtracted from the energy consumption profile to calculate a net energy hourly profile. Then a utility cost with a time-of-use rate structure is used to calculate the hourly annual energy cost and total operational energy cost for the whole year. Users should specify 8760 hourly values representing utility rates for both the export and import of electricity. This allows users to test and compare different utility rate structure scenarios such as (1) net metering scenario, where the assigned rate for purchasing electricity is equal to the sell-back (export) rate; (2) no-sell-back incentive, where residents do not get any financial incentive from giving back excess electricity generated from PV; and (3) specific feed-in tariff, where the users-specified utility rate for the import of electricity is different from the rate of electricity export.

Finally, using a genetic optimization algorithm, each combination of PV panels (genome) is evaluated based on the total operational energy cost value (fitness value) for the corresponding genome. The algorithm searches for the optimal option that minimizes the operational energy cost value. However, users can also set a threshold for the fitness value and the solver will stop when the threshold value is reached.

Figure 7 shows the output of a solver editor, called Galapagos [24], when this workflow was applied to a single building. In this example, two panels were specified as inputs to the panel combination algorithm. Also, a utility rate structure with no-sell-back incentive is used as an input in the processing step. The optimal panels option with the least operational energy cost is then selected for deployment. While the “best” option is automatically selected, users can use Galapagos editor to search and select other options of interest. The best option is illustrated in the panel configuration in Fig. 7: one panel was selected to be deployed on the south-facing roof, while the other was selected to be deployed on the west.

This workflow can be applied at a building scale or at a community scale to test different PV deployment scenarios. When the objective is to maximize the operational energy cost for individual homeowners, the workflow should be implemented on each building using the corresponding load profile and roof geometry. When the objective is to decrease the total operational energy cost for the community instead of individual homeowners, the input to the workflow would be the roof geometries of all buildings and the aggregate load profile of the community.

Using the developed workflow, users can now perform analyses for optimal PV placement at both a community and building scale. A sample of the results from both proposed methods is analyzed at a building scale in Sec. 3.1, followed by a discussion of urban-scale implementation and analysis in Sec. 3.2.

The developed workflows were tested using Fort Collins, Colorado, as a case study. Figure 8 illustrates three options for selecting optimal PV panel placement for a single-family house in this community. All of these options fall in the top 10% fit genomes when workflow 2 was implemented with an objective to reduce operational energy cost. From these three options, option 2 was selected to be the optimal option when workflow 1 was implemented, where the most efficient placement was identified to maximize PV generation.

The demand profile for the illustrated single-family house is simulated using BEopt. A default schedule for residential occupancy and behavioral schedules [25] was used for this simulation.

Figure 9 shows the demand profile plotted against the PV generation profiles for each of the three options. Based on Fig. 9, option 1 provides energy generation covering the largest timeframe (6 a.m. until 8 p.m.). Option 2 provides the highest amount of total energy generation; however, electricity generation drops dramatically starting at 3 p.m. and stops at 6 p.m. when the sun completely shifts to the west. Deploying both panels on the west (option 3) generates a smaller amount of total electricity compared to option 2, but this option provides the highest amount of electricity produced during afternoon hours (4–8 p.m.).

When investigating the solar potential of PV panels, both the demand and generation profiles should be taken into account along with the utility rate structure. For example, when considering a time-of-use billing plan, west-facing solar panels could help avoid paying the higher peak rates by providing more energy when the electricity cost is higher. However, with a net metering or other utility rate structure that provides financial incentive when exporting electricity back to the grid, south-facing panels might provide the most net financial benefit. Moreover, the geographic location and mutual shading of buildings are also important factors to be considered in this investigation, because they define the shape of the generation profile. The developed workflows can be used as tools to investigate the solar potential of rooftop PV panels while taking into account all of the aforementioned factors.

One example of such investigation is illustrated in Fig. 10. For each defined option, three different utility rate structure scenarios are tested by comparing the resulting net operational energy cost. The figures illustrate profiles representing hourly annual averaged operational energy cost and document the net annual cost values for each option in a scenario. The three tested scenarios are:

1. Net metering scenario, where electricity import and export utility rates are equal.

2. Feed-in tariff scenario, where utility rates for electricity export are half the utility rates of electricity import.

3. Scenario representing no economic incentive for electricity sell back, where users do not receive any economic benefit for giving back excess energy to the grid.

Referring to Fig. 10, results show that option 2 has the lowest net cost when net metering is applied. The user in this case is selling back excess electricity generation at an equal rate of consumed energy; therefore, maximizing the total PV generation is the best strategy to decrease the net annual cost. As a result, the optimal option is when both panels are deployed at the south-facing roof.

Option 1 is the optimal option, however, when no-sell-back incentive is applied. In this case, setting one panel on the south and another on the west will work best because the south-facing panel is reducing the grid energy consumption during midday hours, while the west-facing panel reduces the high cost of peak energy demand.

A similar conclusion is observed in the third graph of Fig. 10. In this scenario, the sell-back rate was set to be half the import rate. Overall, options 1 and 3 have similar results, with lower operational energy cost compared to option 2.

In this section, two analysis scenarios were computed to showcase the developed workflows application at a community scale. Workflows 1 and 2 were implemented to determine the number and location of PV panels to be deployed for the whole community such that the net zero energy goal is satisfied. Results from each workflow application are discussed and compared. The total annual energy consumption for the community is 6400 MW h. This value was set as a target for sizing the PV panels in the community to meet the net zero energy requirement.

In this scenario, workflow 1 was implemented to select the best PV panels to be deployed in the community to meet net zero energy goals.

As shown in Fig. 11, the efficiency increases significantly past 1650 kW h/m². At this threshold, the selected rooftop panels were not sufficient to match the annual energy consumption of the community, and additional community PV was needed to meet the net zero energy goal. Unlike rooftop PV, the community PV deployment is not constrained by a specific tilt and orientation. Therefore, an optimal tilt and orientation of the panels was used to calculate the community PV energy generation, thereby capturing maximum sunlight energy.

Based on these results, a threshold of 1800 kW h/m² was selected to identify the amount and location of the rooftop panels. The community rooftop system size was determined to be 3761 kW AC, which produces 5900 MW h of energy per year. Community PV with a system size of 252 kW was added to generate an additional 500 MW h to meet the total PV generation target (6400 MW h). The Coef for this scenario was calculated to be 1.58. Figure 12 shows a 3D view of the deployed PV panels.

In this scenario, workflow 2 was implemented to optimally place the PV panels in the community and minimize the operational energy cost, while taking into account two utility rate options: (1) using Fort Collins Utilities import and export rate structures and (2) using Fort Collins Utilities rates for import with no economic incentive for exporting excess energy to the grid. The tariff rates for electricity import are described in Fig. 13. Based on the figure, we can make two observations. First, on-peak prices are significantly higher than off-peak prices (approximately three times higher). Second, winter and summer schedules are different in duration and timing; the former has on-peak periods from 5 to 9 p.m. (4 h), and the latter from 2 to 7 p.m. (5 h).

The optimization algorithm described in Sec. 2.3 was applied to all buildings in the community. The demand profile of each building was used as an input. Then the algorithm identified the optimal locations of the assigned PV panels such that the operational cost was minimized. The total number of panels deployed in the community was determined based on the net zero energy goal.

Results of both scenarios are compared in Fig. 14. Based on these results, applying workflow 2 shows additional savings in the annual energy cost. The top figure compares the aggregated community demand profile with the community total generation profile from each workflow. In both scenarios, the total PV generation was 6400 MW h, meeting the net zero energy goal. However, the generation profile computed using workflow 2 aligned better with the building loads during the afternoon peak hours. When workflow 2 was applied, more panels were selected to be west-oriented whenever applicable. This reduces the grid electricity consumption during summer afternoon peak hours and lowers the overall energy cost. The metric Coef, as defined in Eq. (1), decreased from 1.58 to 1.46 in scenario 2. Since some panels were selected to be west-facing instead of south-facing, the solar production decreased while the operational cost savings increased.

The other figures show the hourly cost profile averaged over one year for each of the utility rate options. With the implementation of workflow 2, the community cost per day decreased from 1034 to 956 when no-sell-back was considered and from 373 to 286 when both the import and export rates of Fort Collins Utilities were imposed. This shows that the community, under its current utility rate structure, can gain up to 23% of additional operational cost savings when strategically deploying the panels using workflow 2. This translates to about 636,000 of additional cost savings over the life span of the PV panels.

For this paper, Grasshopper, a plug-in for a CAD tool called Rhinoceros developed by Robert McNeel & Associates,² was used. Grasshopper contains plug-ins that allow users to use various functions within the tool. This feature allows users to seamlessly integrate different functions by eliminating the need to transfer geometric information to different software tools. To calculate the solar radiation and PV simulation, the Ladybug plug-in³ was used. This plug-in includes components that utilize the PVWatts calculator and Radiance as under-the-hood engines for PV generation and solar irradiance simulation, respectively.

Regarding the optimization workflow, a Grasshopper tool called Galapagos—an evolutionary-based genetic optimization algorithm—was used [24]. Other optimization algorithms can be used as a substitute to Galapagos in this workflow. Among these is the Pareto algorithm, through which users can set a multi-objective function and a threshold value for each of the objectives to be met. For example, users can define a specific cost value and a specific efficiency target, in which the optimization algorithm will find the best PV panel location that yields an efficiency factor and an operational energy cost value closest to the specified thresholds.

Integrating geometric analysis with optimization tools and environmental simulation tools (that estimate solar energy generation) proves valuable for investigating the performance of different scenarios to find the most efficient and cost-effective deployment of PV panels. This workflow allows urban designers, project developers, and other urban stakeholders to design energy-efficient communities with well-studied PV deployment strategies that yield high energy cost savings, while taking into account a variety of key factors, such as contextual shading, land/rooftop area availability, utility rate structures, and buildings’ energy demand profiles.

Furthermore, the developed workflows can be used to test different optimization scenarios, as well as different solar ownership models. Following are examples of two different analysis scenarios:

1. Finding the optimal deployment of PV panels for each building in the community to increase the cost savings for each homeowner individually. In this scenario, the optimization workflow should be run for each building in the community, taking into account the household’s unique load profile.

2. Finding the optimal PV panel locations to increase the cost savings for the whole community. This approach aims at smoothing the aggregate community load profile. Currently, a large portion of homeowners who want to benefit from solar generation take advantage of third-party ownership. For example, this includes participating in a solar lease arrangement, where a third party installs and owns the solar systems on the rooftop of the homeowners. In this type of solar ownership model, the project manager has the flexibility to test a holistic approach to implement the PV panels, where all rooftops in the community are considered in the analysis. This approach allows the user to better match the total demand profile of the whole community, while still satisfying the needs of individual buildings.

This paper presents a novel framework for optimal PV placement on residential rooftops. Workflows are introduced as tools within the Grasshopper plug-in for rhinoceros cad software. We demonstrate the capabilities of the presented workflows through a case study in Fort Collins, Colorado. Utilizing these workflows, users can investigate solar potential at both building and community scales.

This analysis reveals the effectiveness of the proposed workflows in informing engineers, urban designers, and homeowners on the optimal placement of rooftop PV panels, considering both economic and efficiency goals. These bottom-up workflows aim to scale renewable energy analysis and are crucial to improving solar penetration into the United States building stock.

This work was authored by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding is provided by U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Building Technologies Office and Solar Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes. The authors would like to gratefully acknowledge Fort Collins Utilities for providing the distribution system model and design criteria, AMI data and collaborative discussions. The authors also thank Thrive Home Builders for providing the building floor plans and the site plan of the community.

There are no conflicts of interest.

The authors attest that all data for this study are included in this paper. Data provided by a third party are listed in Acknowledgement.