# Achieving Optimal Value of Solar: A Municipal Utility Rate Analysis

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Value of Solar (VOS)

_{2}). VOS is presented as energy-normalized ($/kWh) or capacity-normalized (annual $/kW).

#### 2.2. Load Characterization

#### 2.3. PV Optimization and Uncertainty

#### 2.4. Alternate Rate Structures

#### 2.5. Financial Analysis

## 3. Results and Discussion

#### 3.1. VOS Optimization

_{2}components remain relatively constant as PV energy increases, while the T&D and losses components of VOS have an intermediate reduction, as they are proportional to both the displaced energy and capacity credit of the PV system.

#### 3.2. Orientation Optimization

#### 3.3. Investment Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ATB | Annual Technology Baseline |

CAPEX | Capital Expenditures |

CC | Combined Cycle |

CT | Combustion Turbine |

CF | Capacity Factor |

DF | Debt Fraction |

FCR | Fixed Charge Rate |

FOM | Fixed Operation and Maintenance |

IR | Interest Rate |

LAC | Levelized Annual Cost |

LCOE | Levelized Cost of Energy |

LDC | Load Duration Curve |

MACRS | Modified Accelerated Cost Recovery System |

NPV | Net Present Value |

NREL | National Renewable Energy Lab |

PV | Photovoltaic |

RES | Renewable Energy Systems |

RLDC | Residual Load Duration Curve |

RMSE | Root Mean Square Error |

ROU | Rate-of-Use |

RROE | Rate of Return on Equity |

SCMU | Sioux Center Municipal Utilities |

SSW | South-Southwest |

T&D | Transmission and Distribution |

TOUm | Time-of-Use midday |

TOUe | Time-of-Use evening |

TMY | Typical Meteorological Year |

TR | Tax Rate |

U.S. EIA | United States Energy Information Administration |

VOM | Variable Operation and Maintenance |

VOR | Value of Resource |

VOS | Value of Solar |

WACC | Weighted Average Cost of Capital |

WWSIS | Western Wind and Solar Integration Study |

## Appendix A

**Figure A1.**PV optimization system model diagram showing input data of electric load/demand and PV Power. Two iterative processes are leveraged. First, the energy production model is calibrated to best fit the PV production data. Then, the PV system orientation is optimized to maximize energy cost savings.

**Figure A2.**Comparative conventional generation Levelized Cost of Energy (LCOE) for base, intermediate, and peak loads based on the Load Duration Curve (LDC). Costs are broken down into categories of capital expenditures (CAPEX), fixed operations and maintenance (FOM), fuel, and variable operations and maintenance (VOM). CAPEX and FOM fixed costs represent an increasing portion of the total cost for intermediate and peak generation. The calculated cost ratios of 1.4 for intermediate to base and 2.1 for intermediate/peak to base agree well with published time-of-use rate structures [39,40].

**Figure A3.**Hourly energy consumption broken down into base, intermediate, and peak types from the Load Duration Curve (LDC). Graph (

**A**) is the entirety of the five years of load data, while graph (

**B**) shows the increased commercial/industrial load on weekdays. Graphs (

**C**,

**D**) demonstrate the increased peak demand from late spring to early fall, peaking specifically in July.

**Figure A4.**Verification and validation regression plots for 16, 29, 41, and 65° tilt, south-facing production data. The production model is calibrated and verified with 16, 41, and 65° tilt data and then validated with the 29° tilt production data.

**Figure A5.**Convergence of the Monte-Carlo simulation as runs are increased from 100 to 800 for each of the 0.1, 4, 10, and 25% PV energy contribution scenarios. Results are plotted as percent difference of Monte Carlo simulation mean compared to nominal annual cost savings. Value of Solar (VOS) and Demand/Energy (D/E) rate have a negative bias in simulation savings beyond the 0.1% PV energy marginal scenario, while the Time-of-Use (TOU) and Rate-of-Use (ROU) have slight positive bias. The 90% confidence interval error bars are greater for VOS and D/E rate due to their cost sensitivity to instances of peak demand. The span of VOS and D/E confidence interval also decreases with increased PV energy contribution as a higher portion of total cost savings is attributed to energy than demand.

**Table A1.**Annual production (kWh/kW) for installed PV compared to PVWatts Typical Meteorological Year (TMY) prediction. PVWatts DC losses were lowered to 11% from the default 14% to best match the annual production. Also included for comparison to the raw data is the production data model of annual production.

Configuration | Data Annual Energy [kWh/kW] | TMY Annual Energy [kWh/kW] | TMY to Data Difference | Production Data Model Annual [kWh/kW] | Model to Data Difference |
---|---|---|---|---|---|

South, 16° Tilt | 1383 | 1390 | +0.5% | 1400 | +1.2% |

South, 29° Tilt | 1459 | 1464 | +0.3% | 1465 | +0.4% |

South, 41° Tilt | 1476 | 1479 | +0.2% | 1475 | −0.1% |

South, 65° Tilt | 1366 | 1359 | −0.5% | 1355 | −0.8% |

One-Axis Tracking | - | 1616 | - | 1571 | - |

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**Figure 1.**Load Duration Curve (LDC) and Residual LDC (RLDC) curves illustrating peak/intermediate/base load determination based on 15–60% relative durations. RLDC plots with solar contribution show the resulting capacity credit, reduced capacity factor (CF), and overproduction impacts of increasing PV energy contribution.

**Figure 2.**Value of Solar (VOS) for south-facing 41° tilt (41S), horizontal one-axis tracking (One-Axis), and optimal fixed orientation (Optimal) systems. VOS is broken down into fuel, variable operation and maintenance (VOM), capacity credit, fixed operations and maintenance (FOM), transmission and distribution (T&D), transmission losses, and environmental carbon credit (CO

_{2}). The optimal fixed orientation produces highest energy-normalized VOS in most cases.

**Figure 3.**Capacity normalized annual ($/kW) combined Value of Solar (VOS), Levelized Annual Cost (LAC), and net value (VOS—LAC) for south-facing 41° tilt (41S), horizontal one-axis tracking (One-Axis), and optimal fixed orientation (Optimal) systems. VOS is broken down into fuel, variable operation and maintenance (VOM), capacity credit, fixed operations and maintenance (FOM), transmission and distribution (T&D), transmission losses, and environmental carbon credit (CO

_{2}).

**Figure 4.**Difference in Value of Solar (VOS) for the production data model versus Typical Meteorological Year (TMY) solar prediction. Differences in category (fuel, VOM, capacity, etc.) are plotted as negative or positive, with positive indicating that production model VOS is higher than TMY prediction.

**Figure 5.**Residual Load Duration Curve (RLDC) conventional generation capacities for the optimal Value of Solar (VOS) fixed orientation system. Solar capacity credit is above 60% for PV energy contribution less than 4% but decreases to below 15% for 25% PV energy contribution. Base generation is most significantly reduced at 25% PV energy contribution.

**Figure 6.**Comparison of optimal azimuth (plot (

**A**)) and tilt (plot (

**B**)) angles for production data model and Typical Meteorological Year (TMY) for Value of Solar (VOS), as well as demand/energy (D/E), Time-of-Use midday (TOUm), TOU evening (TOUe), and Rate-of-Use (ROU) energy rate structures. With small differences in specific azimuth angles, in general, the trends remain the same: VOS and D/E favor a south-southwest-facing system with an optimal azimuth that decreases with increasing PV energy contribution, while TOU rate structures maintain a constant optimal azimuth with the TOUe favoring a more southwest direction than TOUm. Tilt is less of an orientation factor than azimuth as all the optimal configurations lie between 30 and 40° tilt. However, there is a consistent trend where the optimal production data tilt is 3–5° less than the corresponding TMY optimization.

**Figure 7.**Optimal fixed orientation annual cost savings capacity normalized ($/kW) for Demand/Energy (D/E), Time-of-Use midday (TOUm) and evening (TOUe), and Rate-of-Use (ROU) energy structures compared to the Value of Solar (VOS) benchmark. D/E and ROU savings trend down with increasing PV energy similar to VOS, while TOU savings remains flat. ROU savings are consistently the highest. Error bars represent 90% confidence intervals from Monte Carlo simulations.

**Figure 8.**Comparison of annual cost savings for the production data model and Typical Meteorological Year (TMY) solar prediction. The 90% confidence interval uncertainty confirms a statistically significant savings difference for Value of Solar (VOS) and demand/energy (D/E), which are most dependent on PV production during specific instances of peak demand. Time-of-Use midday and evening (TOUm, TOUe) show little difference since they are more dependent on total annual energy production which was intentionally equalized. The high 25% PV energy contribution shows a negative difference due to increased PV overproduction as the TMY production tends to be more levelized day-to-day.

**Table 1.**Value of Solar (VOS) categories characterized as the sum of net benefits in five major categories and listed alongside the calculation method employed for seven components of net benefits in this study.

Category | Net Benefit | Calculation Method |
---|---|---|

Energy | Avoided fuel and variable costs | LDC-RLDC (1) Fuel Costs, (2) VOM |

Generation Capacity | Avoided fixed costs of new generation | LDC-RLDC (3) Capacity Credit, (4) FOM |

T&D Capacity | Avoided cost of building and maintaining T&D infrastructure | (5) T&D Levelized cost on Capacity plus T&D Variable cost on Energy |

T&D Losses | Avoided losses from remote generators | (6) Transmission Loss Multiplier on PV generation |

Environmental | Reduced air emissions | (7) CO_{2} social cost 39 $/ton |

Months | Demand Plus Transmission [$/kW] | Energy [$/kWh] |
---|---|---|

DEC, JAN, FEB | 22.00 | 0.0315 |

MAR, APR, MAY | 16.50 | |

JUN, JUL, AUG | 27.00 | |

SEP, OCT, NOV | 16.50 |

**Table 3.**Economic analysis inputs, assumptions, and calculated rates following the model of NREL’s annual technology baseline [37]. The Weighted Average Cost of Capital (WACC) is the discount rate used in the net present value analysis. Inflation is the difference between nominal and real rates (nominal includes inflation). The fixed charge rate (FCR) is used in calculating the value of PV capacity credit in the annual savings, and depreciation is calculated with a 5-year Modified Accelerated Cost Recovery System (MACRS) model.

Parameter | Value | |
---|---|---|

Assumptions/ Inputs | Inflation (i) | 2.5% |

Debt Interest Rate (IR) | 5% | |

Rate of Return on Equity (RROE) | 10% | |

Debt Fraction (DF) | 60% | |

Tax Rate, federal + state (TR) | 27% | |

Loan Term, years | 10 | |

Period of Analysis, years (t) | 25 | |

Depreciation | MACRS-5 | |

Annual PV degradation | 0.60% | |

Calculated | WACC, Nominal | 6.2% |

WACC, Real | 3.6% | |

Fixed Charge Rate (FCR) | 6.5% |

**Table 4.**Time-of-Use (TOU) and Rate-of-Use (ROU) energy costs for base, intermediate, and peak energy. Energy costs were calculated to generate revenue equivalent to the existing demand/energy rate (D/E) structure over the five years of analysis. Resulting rates are similar for TOU and ROU structures at 0.06–0.07 $/kWh for base energy and 0.013–0.014 $/kWh for peak energy.

Rate Structure | Equivalent Revenue Rate [$/kWh] | ||
---|---|---|---|

Base | Intermediate | Peak | |

TOU midday (TOUm) | 0.063 | 0.089 | 0.133 |

TOU evening (TOUe) | 0.066 | 0.066 | 0.139 |

ROU | 0.067 | 0.094 | 0.141 |

**Table 5.**Investment analysis and rate-of-return for PV investment. A simple payback was calculated based on total PV installation costs and annual cost savings. A zero net present value (NPV) analysis was run to calculate the Rate-of-Return on Equity (RROE) and corresponding Weighted Average Cost of Capital (WACC) over the 25-year period of performance. The 4% PV energy contribution has the shortest simple payback and highest RROE and WACC. The RROE of the 25% PV energy contribution is negative to achieve a zero NPV.

PV Energy Contribution | Simple Payback [yr] | RROE | WACC Nominal | WACC Real |
---|---|---|---|---|

0.1% | 16 | 8% | 5.3% | 2.7% |

4% | 13 | 13% | 7.5% | 4.9% |

10% | 16 | 7% | 4.9% | 2.5% |

25% | 22 | −2% | 1.3% | −1.0% |

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## Share and Cite

**MDPI and ACS Style**

Saarloos, B.A.; Quinn, J.C.
Achieving Optimal Value of Solar: A Municipal Utility Rate Analysis. *Solar* **2022**, *2*, 99-119.
https://doi.org/10.3390/solar2020007

**AMA Style**

Saarloos BA, Quinn JC.
Achieving Optimal Value of Solar: A Municipal Utility Rate Analysis. *Solar*. 2022; 2(2):99-119.
https://doi.org/10.3390/solar2020007

**Chicago/Turabian Style**

Saarloos, Benjamin A., and Jason C. Quinn.
2022. "Achieving Optimal Value of Solar: A Municipal Utility Rate Analysis" *Solar* 2, no. 2: 99-119.
https://doi.org/10.3390/solar2020007