Optimal Sizing and Techno-Economic Evaluation of a Utility-Scale Wind–Solar–Battery Hybrid Plant Considering Weather Uncertainties, as Well as Policy and Economic Incentives, Using Multi-Objective Optimization

Abstract

This study presents an optimization framework for a utility-scale hybrid power plant (HPP) that integrates wind power plants (WPPs), solar power plants (SPPs), and battery energy storage systems (BESS) using historical and probabilistic weather modeling, regulatory incentives, and multi-objective trade-offs. By employing multi-objective particle swarm optimization (MOPSO), the study simultaneously optimizes three key objectives: economic performance (maximizing net present value, NPV), system reliability (minimizing loss of power supply probability, LPSP), and operational efficiency (reducing curtailment). The optimized HPP (283 MW wind, 20 MW solar, and 500 MWh BESS) yields an NPV of $165.2 million, a levelized cost of energy (LCOE) of $0.065/kWh, an internal rate of return (IRR) of 10.24%, and a 9.24-year payback, demonstrating financial viability. Operational efficiency is maintained with <4% curtailment and 8.26% LPSP. Key findings show that grid imports improve reliability (LPSP drops to 1.89%) but reduce economic returns; higher wind speeds (11.6 m/s) allow 27% smaller designs with 54.6% capacity factors; and tax credits (30%) are crucial for viability at low PPA rates (≤$0.07/kWh). Validation via Multi-Objective Genetic Algorithm (MOGA) confirms robustness. The study improves hybrid power plant design by combining weather predictions, policy changes, and optimizing three goals, providing a flexible renewable energy option for reducing carbon emissions.

1. Introduction

The global push toward decarbonization and energy security has accelerated the adoption of renewable energy technologies, particularly wind and solar power [1]. Over the past decade, significant drops in the prices of wind turbines, photovoltaic (PV) modules, and battery storage systems [2], along with power electronics, have allowed plant owners to combine different energy sources to create hybrid power plants (HPPs) that connect to the grid at one point [3,4], making it easier to use variable renewable energy (VRE) on a large scale. While extensive research has addressed small-scale hybrid microgrids [5], utility-scale HPP remains relatively understudied despite its critical role in grid decarbonization. Additionally, co-located HPPs take advantage of different energy generation patterns, share infrastructure, and use energy storage to reduce fluctuations, lower energy waste, and increase profit potential [3,6,7].

However, making utility-scale HPPs work well is a complex engineering problem that involves carefully balancing different goals: spending less money upfront versus making more money in the long run, ensuring the system is reliable while also being efficient, and achieving good technical performance while following regulations [8]. Poor sizing decisions can lead to either significant underutilization of assets or substantial lost revenue opportunities, with even marginal (1–3%) improvements in configuration potentially translating to millions in additional project value [9].

The existing literature reveals diverse approaches to HPP optimization [10], each with notable limitations (summarized in Table 1). For instance, Das et al. [11] employed mixed-integer linear programming (MILP) to maximize net present value (NPV) but overlooked multi-objective considerations. Similarly, Silva and Estanqueiro [12] applied genetic algorithms to optimize aging wind power plants hybridized with solar and storage but acknowledged the lack of robust trade-off mechanisms. González-Ramírez et al. [13] developed regression models for wind–solar integration but relied on static financial parameters, limiting adaptability to dynamic market conditions. Other studies, like the one by Duchaud et al. [14], used multi-objective particle swarm optimization (MOPSO) to reduce costs and the chance of losing power supply (LPSP), but they did not consider important investment measures like net present value (NPV) and return on investment (ROI). Commercial tools like HOMER Pro and REopt are helpful for initial evaluations, but they do not have advanced multi-objective algorithms and do not consider the unpredictable nature of renewable energy generation [15]. While tools like HyDesign [16] improve sizing capabilities but still exclude crucial reliability indicators like LPSP or capacity credit. A recurring gap in the literature is the narrow focus on single metrics, either cost or reliability, without adequately addressing their interdependencies. For example, Al-Shereiqi et al. [17] optimized wind–solar configurations for grid stability but neglected financial performance indicators.

Furthermore, many studies overlook the impact of policy and market dynamics, despite evidence that incentives like tax credits can alter project NPV by 20–40% [18]. Grimaldi et al. [19] demonstrated how curtailment and battery degradation affect profitability but did not link these to policy-driven financial mechanisms. Similarly, Street and Prescott [20] analyzed regulatory incentives for HPPs in Brazil but focused narrowly on network charges without integrating reliability trade-offs. While some research, such as by Rocha et al. [21], explore regulatory frameworks, few integrate these factors into the core optimization process. Power purchase agreements (PPAs) are recognized for enhancing financial stability [22], but their interplay with reliability metrics remains underexplored.

Table 1. Comparative analysis of optimization approaches for utility-scale hybrid power plants, highlighting methods, objectives, policy considerations, and key limitations.

References	Method Used	Objectives	Policy Support	Key Limitations
[8]	Genetic algorithm (GA)	Physical design and layout	None	No technical–financial integration
[11]	MILP optimization	Maximize NPV	None	Lacks multi-objective handling and dynamic financial modeling
[12]	MILP with Genetic algorithm	Optimal sizing, efficiency, and economic viability	Feed-in Tariff	Limited trade-off analysis; static parameter assumptions
[13]	Multilevel regression model	Optimal size, Max NPV	None	Fixed financial parameters; lacks market adaptability
[14]	MOPSO	Minimize average service cost and LPSP	None	No investment metrics (NPV, ROI)
[15]	HyDesign (two-tiered approach)	Minimize COE, maximize NPV	None	Excludes reliability metrics (LPSP, capacity credit); ignores forecasting uncertainty
[17]	Genetic algorithm, Iterative algorithm	Grid stability	None	No financial metrics included
[19]	MILP	Max NPV, min curtailment and battery degradation	Assumption FIT	Lacks detailed inclusion of economic and policy metrics
[20]	-	Exploration of complementary, renewable generation profiles	Network access charge (incentives)	No detailed analysis
[21]	Multi-objective	Max NPV, min LCOE	None	No technical integration
[22]	HOPP	Max NPV	PPA	No detailed analysis
[23]	Monte Carlo Simulation	Sizing and loss of load expectation	None	Lacks financial integration and full technical analysis
[24]	HOPP (hybrid optimizer)	Spatial-constrained hybrid sizing (e.g., Power-to-X systems)	None	Lacks integrated financial-reliability trade-offs
[25]	HOMER Pro and REopt (commercial tools)	Evaluate NPV, NPC, LCOE, Payback	None	Single-objective, deterministic, limited to fixed profiles
[26]	NSGA-II, CCP	Minimize system cost, reliability	None	No detailed analysis

NSGA: Non-dominated sorting genetic algorithm; HOPP: Hybrid optimization and performance platform; HOMER: Hybrid optimization of multiple energy resources; REopt: Renewable energy integration and optimization; CCP: Chance constrained programming.

Table 1. Comparative analysis of optimization approaches for utility-scale hybrid power plants, highlighting methods, objectives, policy considerations, and key limitations.

References	Method Used	Objectives	Policy Support	Key Limitations
[8]	Genetic algorithm (GA)	Physical design and layout	None	No technical–financial integration
[11]	MILP optimization	Maximize NPV	None	Lacks multi-objective handling and dynamic financial modeling
[12]	MILP with Genetic algorithm	Optimal sizing, efficiency, and economic viability	Feed-in Tariff	Limited trade-off analysis; static parameter assumptions
[13]	Multilevel regression model	Optimal size, Max NPV	None	Fixed financial parameters; lacks market adaptability
[14]	MOPSO	Minimize average service cost and LPSP	None	No investment metrics (NPV, ROI)
[15]	HyDesign (two-tiered approach)	Minimize COE, maximize NPV	None	Excludes reliability metrics (LPSP, capacity credit); ignores forecasting uncertainty
[17]	Genetic algorithm, Iterative algorithm	Grid stability	None	No financial metrics included
[19]	MILP	Max NPV, min curtailment and battery degradation	Assumption FIT	Lacks detailed inclusion of economic and policy metrics
[20]	-	Exploration of complementary, renewable generation profiles	Network access charge (incentives)	No detailed analysis
[21]	Multi-objective	Max NPV, min LCOE	None	No technical integration
[22]	HOPP	Max NPV	PPA	No detailed analysis
[23]	Monte Carlo Simulation	Sizing and loss of load expectation	None	Lacks financial integration and full technical analysis
[24]	HOPP (hybrid optimizer)	Spatial-constrained hybrid sizing (e.g., Power-to-X systems)	None	Lacks integrated financial-reliability trade-offs
[25]	HOMER Pro and REopt (commercial tools)	Evaluate NPV, NPC, LCOE, Payback	None	Single-objective, deterministic, limited to fixed profiles
[26]	NSGA-II, CCP	Minimize system cost, reliability	None	No detailed analysis

NSGA: Non-dominated sorting genetic algorithm; HOPP: Hybrid optimization and performance platform; HOMER: Hybrid optimization of multiple energy resources; REopt: Renewable energy integration and optimization; CCP: Chance constrained programming.

Perhaps most notably, there remains a substantial disconnect between technical optimization and policy considerations, with most frameworks treating crucial financial mechanisms as external factors rather than integrated variables. This fragmented analytical approach fails to capture the complex interdependencies that characterize real-world hybrid power plant operations, where economic viability, system reliability, and policy constraints must be simultaneously evaluated to develop truly optimal configurations.

Therefore, the motivation of this research is to develop a robust and practical sizing framework for utility-scale HPPs that realistically captures renewable resource uncertainty, regulatory and market policy impacts, and critical techno-economic trade-offs. The main contributions of this work are as follows:

• Development of an integrated, probabilistic, Multi-Objective Particle Swarm Optimization (MOPSO) framework that simultaneously optimizes economic performance, reliability (LPSP), and curtailment.
• Clear inclusion of changing policy tools, like tax credits and power purchase agreements, as internal limits in the optimization process.
• Cross-validation of the proposed MOPSO results with a Multi-Objective Genetic Algorithm (MOGA) to demonstrate solution robustness.

Together, the above contributions provide practical insights for developers, planners, and policymakers working towards cost-effective, reliable, and policy-compliant hybrid renewable energy systems.

This study chooses MOPSO because it is effective and adaptable for tackling complicated sizing problems that involve continuous variables. Unlike GA or NSGA-II, which usually need more computing power to keep a variety of solutions, MOPSO uses swarm intelligence and Pareto dominance sorting to find solutions more quickly and spread them out better in complex search areas. This makes it especially suitable for optimizing hybrid renewable systems under probabilistic uncertainty and policy incentives.

2. Methodology

2.1. System Description

The core components of co-located HPPs considered in the study typically include a WPP, SPP, and BESS, as shown in Figure 1. WPP and SPP are the main power generators that convert wind speed and solar irradiance, respectively, into electricity. BESS helps manage energy by saving extra power when it is available and using it when there is not enough, and it includes systems like inverters that change direct current (DC) to alternating current (AC) and the other way around to work with the grid.

2.2. Hybrid Power Plant Components Model

The following section outlines the mathematical formulations governing power generation from wind turbines and photovoltaic arrays, the operational dynamics of BESS, and integrated energy modeling for the HPP.

2.2.1. Wind Turbine Model

The wind speed at the desired hub height, $v_2$, is calculated using the power law as given in Equation (1) [27].

$${\displaystyle \frac{v_2}{v_1}}={\left({\displaystyle \frac{h_2}{h_1}}\right)}^{\alpha }$$

(1)

where $h_2$ is the desired hub height; $v_1$ is the measured wind speed at height $h_1$; and $\alpha$ is the power law exponent.

The power output of the wind turbine at wind speed $v$ is determined by the power curve, as shown in Equation (2), whereas the turbine output is further bounded by rated power and cut-in/cut-off wind speeds, as described in Equation (3) [27].

$$P_{wt}=\left\{\begin{array}{c}P\left(t\right), v_{cut-in}\le v<v_r \\ P_r, v_r\le v\le v_{cut-off}\\ 0, otherwise\end{array}\right.$$

(2)

$$P\left(t\right)=P_r\left({\displaystyle \frac{v^3}{v_r^3-v_{cut-in}^3}}\right)-P_r\left({\displaystyle \frac{v_{cut-in}^3}{v_r^3-v_{cut-in}^3}}\right)$$

(3)

where $P_{wt}$ is the power output from the wind turbine; $P_r$ is the rated power; $v_{cut-in}$ is the cut-in wind speed; $v_{cut-off}$ is the cut-off wind speed; $v_r$ is the rated wind speed; and $v$ is the actual wind speed.

The total power output of the WPP, $P_{wpp}$, is expressed in Equation (4) as the product of the number of turbines and the output per unit.

$$P_{wpp}=N_{wt}·P_{wt}$$

(4)

where $N_{wt}$ is the total number of wind turbines.

Many conventional wind turbine models simplify generation by assuming a linear relationship between wind speed and power output or alternatively, in the case of wind speed extrapolation, across different altitudes under the same selected power law exponents, most frequently in the case of the 1/7th power law (α = 0.1429). However, the 1/7th exponent may not reflect local atmospheric conditions well, which can result in an incorrect wind speed value being computed and, subsequently, an inaccurate turbine performance. Another drawback of linear power generation is that it does not take into account the non-linear power curve characteristics of the turbine (cut-in, rated, and cut-out wind speed). In this paper, these shortcomings are overcome by employing hourly historical wind speed data and imposing a realistic, site-specific power law exponent on wind speed to bring it to hub height, as well as the real non-linear turbine power curve to more accurately predict generation under various wind conditions.

2.2.2. Solar Photovoltaic Model

The output power of a single solar PV panel $P_{pv}$ is calculated using irradiance and temperature conditions, as shown in Equation (5) [28].

$$P_{pv}=P_{Npv}·{\displaystyle \frac{G· S_f}{G_{ref}}} ·\left[1+k\left(\left(T+\left(0.0256·G\right)\right)-T_{ref}\right)\right]$$

(5)

where $P_{Npv}$ is the nominal power of a solar PV panel; G is the solar irradiance; $G_{ref}$ is the reference solar irradiance; k is the temperature coefficient; T is the ambient temperature; $T_{ref}$ is the reference temperature; and $S_f$ is the shading factor.

The total power output of the SPP, $P_{spp}$, is expressed in Equation (6) as the product of the number of panels and the power per unit solar PV panel.

$$P_{spp}=N_{pv}·P_{pv}$$

(6)

where $N_{pv}$ represent the numbers of the PV panels.

Many existing PV models simplify system performance by assuming constant average daily or monthly irradiance while ignoring short-term fluctuations throughout the day. They often neglect the effect of shading caused by surrounding structures, which can significantly reduce the actual energy output. This study addresses these limitations by capturing diurnal and seasonal variability more realistically using hourly historical solar irradiance and ambient temperature data. A shading factor is applied to correct the effective irradiance for typical partial shading losses.

2.2.3. Battery Storage System

Batteries allow for energy shifting, where excess energy generated during off-peak production times is stored and used later during peak demand periods [28,29]. In HPP that uses WPPs, SPPs, and BESS, the system is represented by equations that explain how the batteries charge and discharge, as well as the least amount of battery storage needed [30]. This integration optimizes energy management and enhances the overall efficiency and reliability of the HPP.

The battery charging energy at time t, $E_{charge}\left(t\right)$, is calculated as shown in Equation (7) based on surplus generation and demand.

$$E_{charge}\left(t\right)=E_{charge}\left(t-1\right)·\left(1-\sigma \right)+\left(E_{Total}\left(t\right)-{\displaystyle \frac{E_{Load}\left(t\right) }{{\eta }_{inv}}}\right) ·{\eta }_b$$

(7)

where $E_{charge}\left(t\right)$ is the stored charge at time t; $E_{charge}\left(t-1\right)$ is the stored charge at time t − 1; $E_{Total}\left(\mathrm{t}\right)$ is the total generation; $E_{Load}\left(t\right)$ is the total grid demand; σ is the battery self-discharge rate; and ${\eta }_{inv}$ is the inverter’s efficiency.

The battery discharging energy at time t, $E_{discharge}\left(t\right)$, is determined as shown in Equation (8) to meet the load deficit.

$$E_{discharge}\left(t\right)=E_{discharge}\left(t-1\right)·\left(1-\sigma \right)-\left({\displaystyle \frac{E_{Load}\left(t\right)}{{\eta }_{inv}}}-{\displaystyle \frac{E_{Total}\left(t\right)}{{\eta }_b}}\right)$$

(8)

where $E_{discharge}\left(t\right)$ is the battery discharge at time t; $E_{discharge}\left(t-1\right)$ is the battery discharge at time t − 1.

The minimum battery storage capacity at time t, $E_{min}$(t) is updated according to the energy balance equation given in Equation (9).

$$E_{min}\left(t\right)=\left(1-DOD\right)·S_b$$

(9)

where DOD is the depth of discharge and $S_b$ is the nominal capacity.

In many studies, battery storage models are mainly created for microgrid use, usually assuming constant charge and discharge rates and round-trip efficiency, which means they do not account for changes in SOC as well as long-term wear and tear. These simplifications should be used with caution, as realistically, they can result in inaccurate estimates of storage capacity use and system reliability, especially at large scales. This paper represents the BESS with practical SOC limitations, dynamic charge and discharge power boundaries, and efficiency. This detailed modeling provides a more accurate representation of the battery’s role in storing excess energy, supplying power during peak demand, and ensuring reliable system performance for utility-scale HPPs.

While various energy storage technologies are emerging, lithium–ion batteries are widely adopted in current HPP systems due to their mature technology, high energy density, and declining costs. A detailed discussion on various energy storage technologies is beyond the primary scope of this work. However, a comparison of Li-ion batteries, supercapacitors, and reversible solid-oxide cell (RSOC) systems is provided in Appendix A 

Table A1. Lithium–ion battery vs. Supercapacitor vs. RSOC.

Feature	Lithium–Ion Battery [47,48]	Supercapacitor [47,48]	Reversible Solid-Oxide Cell (RSOC) [47,48,49,50]
Energy Storage Mechanism	Electrochemical storage via ion intercalation	Electrostatic storage between electrodes	Electrochemical storage and conversion; operates reversibly as an electrolyzer and a fuel cell
Energy Density (Wh/kg)	High (80–200 Wh/kg)	Very low (~5 Wh/kg)	High (200–500 Wh/kg)
Power Density (W/kg)	Moderate to high	Very high (up to 10,000 W/kg)	Moderate
Efficiency (%)	85–97%	~90%	High (60–80% for each mode)
Response Time	Fast (<1 ms)	Instantaneous (µs–ms)	Moderate (minutes to hours)
Cycle Life	1000–10,000 cycles	Very high (>500,000 cycles)	Moderate (~10,000 cycles)
Self-Discharge Rate	Low (~0.1%/day)	High (~40%/day)	Very low
Operating Temperature	–20 °C to 60 °C	Wide (–40 °C to 70 °C)	High (600–1000 °C)
Capital Cost ($/kWh)	$900–1300	$1000–2500	High (~$1000–2000)
Maintenance Requirements	Low	Low	High (due to high temp operation)
Advantages	High energy density, mature, scalable	Extremely fast response, high power density	Dual-mode (H2 production and power), high round-trip efficiency
Disadvantages	Potential thermal runaway, recycling challenges	Very low energy storage capacity, high self-discharge, costly for bulk storage	High operating temperature, complex system, high capital cost
Typical Applications	Grid-scale energy storage, EVs, renewables	Short-term voltage smoothing, power bursts, regenerative braking	Long-duration seasonal storage, power-to-gas-to-power integration

of this paper for easy reference. This comparison highlights the key technical and economic characteristics, illustrating the relative advantages and disadvantages of each storage technology.

2.3. Wind and Solar Uncertainties

2.3.1. Wind Speed Uncertainties

To account for the variability in wind resources, the study models wind speed using the Weibull probability density function (PDF). This approach effectively captures the asymmetric and site-specific nature of wind data through its two parameters: scale (α) and shape (β). Monte Carlo Simulation (MCS) implements the model to generate synthetic wind speed distributions over various time periods. This method ensures probabilistic accuracy in estimating wind power potential under stochastic weather conditions.

The PDF of wind speed, $f\left(v\right)$, is defined using the Weibull distribution in Equation (10).

$$f\left(v\right)={\displaystyle \frac{\mathrm{\beta }}{\mathrm{\alpha }}}{v}^{\mathrm{\beta }-1}exp\left[-{\left({\displaystyle \frac{v}{\mathrm{\alpha }}}\right)}^{\mathrm{\beta }}\right]$$

(10)

where v is the wind speed; β is the Weibull shape parameter; and α is the Weibull scale parameter.

The CDF for wind speed, $F\left(v\right)$, is derived from the PDF and is given in Equation (11) [27,31].

$$F\left(v\right)=1-exp\left[-{\left({\displaystyle \frac{v}{\mathrm{\alpha }}}\right)}^{\mathrm{\beta }}\right]$$

(11)

Wind power output is then estimated by applying turbine power curves to each simulated wind speed, incorporating turbine cut-in, rated, and cut-off speeds as mentioned in Equation (2).

2.3.2. Solar Irradiance Uncertainties

Solar irradiance uncertainty is modeled using a lognormal distribution, which reflects the positively skewed nature of solar radiation data. This distribution is well suited for capturing the variability in solar availability, as solar irradiance tends to fluctuate significantly and can change rapidly. The PDF for solar irradiance, $f\left(G\right)$, is modeled using the lognormal distribution, as shown in Equation (12) [31].

$$f\left(G\right)={\displaystyle \frac{1}{G{\sigma }_s\sqrt{2\pi }}}exp\left[-{\displaystyle \frac{{\left(lnG-{\mu }_s\right)}^2}{2{\sigma }_s^2}}\right] for G>0$$

(12)

where G is the solar irradiance; ${\mu }_s$ is the mean of the logarithm of irradiance; and ${\sigma }_s$ is the standard deviation of the logarithm of irradiance.

2.4. Energy Management System

Energy management strategies are critical for enhancing system performance while ensuring reliability. This study illustrates the implemented energy management strategy in Figure 2. The process begins by calculating power generation using uncertain weather data, grid demand, and component specifications. A rule-based control algorithm is integrated into the MOPSO framework to manage energy flow. WPPs and SPPs serve as the primary energy sources, with BESS playing a supportive role. When renewable energy generation exceeds PPA demand, the excess power is used to charge the battery storage. If the BESS reaches its SOC, any additional surplus power is curtailed. Conversely, the system deploys the stored battery energy to meet load requirements when renewable generation falls short of demand. In scenarios where both renewable resources and battery storage are insufficient to meet grid demand, the system calculates the LPSP to assess reliability.

The energy management system (Figure 2) integrates three operational strategies to minimize curtailment while maintaining reliability: battery arbitrage (storing excess generation to avoid curtailment), rule-based dispatch (prioritizing renewable utilization over grid exports), and SOC management (preventing overcharging, which leads to curtailment).

2.5. Optimization Problem Formulation

2.5.1. Objective Function

The primary aim of this research is to determine the most effective configuration of HPP components that can simultaneously meet grid demand, ensure economic viability, maintain system reliability, and minimize energy curtailment. Given the stochastic nature of renewable energy sources, particularly the variability in solar irradiance and wind speed, the system must be designed to effectively manage both overgeneration and shortfalls. To address this complex challenge, the study employs a multi-objective Pareto optimization approach with three key objectives:

Economic performance: Maximize NPV, which is a vital indicator of the project’s financial appeal and long-term economic sustainability.

System reliability: Minimize LPSP, which evaluates the system’s capacity to meet energy demand consistently.

Curtailment minimization: Minimize the percentage of curtailed energy, particularly from solar PV and wind sources, which often occurs when generation exceeds grid demand or storage capacity. Curtailment not only represents wasted energy but also reduces the overall efficiency and economic return of the HPP system. Therefore, managing curtailment ensures optimal utilization of WPPs and SPPs and enhances the overall grid contribution.

The combination of these objectives ensures a balanced optimization strategy that accounts for economic gains, operational reliability, and energy efficiency within an uncertainty-aware framework. The tri-objective optimization problem, combining economic, reliability, and operational objectives, is mathematically formulated in Equation (13).

$$f=\left[f_1,-f_2,-f_3\right]$$

(13)

where $f$ is the objective function vector; $f_1$ is the NPV; $f_2$ is the LPSP; and $f_3$ is the curtailment ratio.

The multi-objective framework in this study considers the inherent trade-offs and mutual incentives between economic performance (maximizing NPV), system reliability (minimizing LPSP), and operational efficiency (minimizing curtailment). These objectives are not always aligned: The higher the degree of reliability, the greater the degree of oversizing of generation, storage capacity, and, therefore, capital expenditure, while also possibly harming the NPV due to higher capital costs in the beginning. On the other hand, economic optimization results in leaner sizing of the system, which might result in higher LPSP and loss of load during periods of low generation. Reducing the curtailment is beneficial for integrated renewable energy use and revenue; however, in most cases, it requires flexible storage or grid export, causing additional expenditures. This interrelationship directly affects the way in which the constraints are turned into a fitness function, as well as the way in which the MOPSO algorithm balances between exploration and exploitation to find a set of Pareto-optimal solutions that become an acceptable compromise between all these conflicting goals.

The proposed three objectives are mathematically dependent on the main system sizing parameters $P_{wpp}$, $P_{spp}$, and $P_{BESS}$. Specifically, increasing $P_{wpp}$ or $P_{spp}$ raises the total renewable generation, directly impacting energy revenue and, therefore, the NPV. Likewise, a larger $E_{BESS}$ allows surplus generation to be stored and later dispatched to meet the grid demand, which helps reduce LPSP and curtailment by balancing supply fluctuations. The objective function is designed to reflect these clear connections, making sure that the optimization algorithm works together to achieve economic, reliability, and efficiency goals.

2.5.2. Constraints

The multi-objective optimization was carried out while considering the limitations and constraints for decision-making parameters. The system constraints for power balance, component capacity, and operational limits are defined in Equation (14).

$$\begin{array}{c}{P}_{wpp}\ge 0\\ P_{spp}\ge 0\\ P_{BESS}\ge 0\\ E_{BESS}\ge 0\\ 0.1\le SOC\le 0.9\\ LPSP\le 0.15\\ Curtailment\le 0.15\end{array}$$

(14)

where $P_{wpp}$ is the capacity limit for WPP; $P_{spp}$ is the capacity limit for SPP; $P_{BESS}$ is the capacity limits for BESS; $E_{BESS}$ is the energy limits for BESS; and $SOC$ is the BESS’s state of charge.

2.6. Performance Metrics and Indicators

2.6.1. Loss of Power Supply Probability

The LPSP measures the reliability of the HPP, ranging from 0 to 1. A value of 1 indicates a load unmet, while 0 means the load is always satisfied. The LPSP is mathematically quantified in Equation (15) [28].

$$LPSP={\displaystyle \frac{{{\displaystyle \sum }}_1^T{E}_{unmet}\left(t\right)}{{{\displaystyle \sum }}_1^T{E}_{demand}\left(t\right)}}$$

(15)

where $P_{unmet}$ is the total unmet load energy [kWh] and $E_{demand}$ is the total energy demand [kWh].

2.6.2. Net Present Value

To evaluate economic viability, this study utilized NPV as a key indicator of economic performance. Although it is often difficult to appropriately model all the financial considerations, this study approximated simple revenue. Investment is considered worthwhile if the NPV is zero or positive [32]. The NPV is calculated using the discounted cash flow approach as given in Equation (16).

$$NPV={{\displaystyle \sum }}_{t=0}^T{\displaystyle \frac{C{F}_t}{{\left(1+r\right)}^t}}$$

(16)

where $r$ is the discount rate; $t$ is the time in years; and $C{F}_t$ is the net cash flow in year t.

The net cash flow, $C{F}_t$ at time $t$, is computed using revenue and costs, as shown in Equations (17) and (18).

$$C{F}_t=Revenu{e}_t-cos{t}_t$$

(17)

$$Revenu{e}_t=P_{HPP}·C_{PPA}$$

(18)

where $Revenu{e}_t$ is the revenue at time t; $cos{t}_t$ is the total cost at time t; $P_{HPP}$ is the total generated power form HPP; and $C_{\mathrm{PPA}}$ is the price of the PPA per kWh.

The ASC is calculated using cost components, as given in Equation (19).

$$ASC={{\displaystyle \sum }}_{k=1}^{N_{component}}{N}_k·T{C}_k$$

(19)

where $N_k$ represents the components such as WTs, PVs, and battery packs, while $T{C}_k$ is the total cost associated with $N_k$. The $T{C}_k$ includes capital costs, operating costs, and replacement costs.

2.6.3. Curtailment

Curtailment refers to the portion of available renewable energy (from wind or solar sources) that cannot be utilized due to limitations such as storage capacity, grid constraints, or overgeneration relative to the load. It is a key performance indicator in HPP, as high curtailment reduces overall energy efficiency and economic returns. Minimizing curtailment ensures better utilization of generated power and improved integration of renewables into the grid. Curtailment is mathematically defined as the ratio of unused renewable energy to total available generation in Equation (20).

$$E_{curtailed}={\displaystyle \frac{{{\displaystyle \sum }}_{t=1}^{8760}{E}_{surplus}\left(t\right)}{{{\displaystyle \sum }}_{t=1}^{8760}{E}_{WPP+SPP}\left(t\right)}}$$

(20)

where $E_{curtailed}$ is the curtailed energy; $E_{surplus}\left(t\right)$ is the surplus energy; and $E_{WPP+SPP}\left(t\right)$ is the total available renewable energy.

A curtailment value close to 0 indicates near-complete utilization of generated renewable power, which is desirable. Higher curtailment suggests under-utilization and possible oversizing of generation components or insufficient storage integration.

2.7. Solution Method

2.7.1. Multi-Objective Particle Swarm Optimization

To address multi-objective optimization challenges, this study implemented the particle swarm optimization developed by Kennedy and Eberhart [33], known as MOPSO, which was later advanced as MOPSO by Coello et al. [34]. This algorithm tackles multi-objective optimization challenges by integrating a unique approach that employs a crowding mechanism to determine optimal particle positioning and uses a dominance-based approach to filter less favorable solutions. Through this process, MOPSO successfully manages and balances the trade-offs between conflicting objectives [35]. The general flow diagram is illustrated in Figure 3 [36]. MOPSO is modified from the original PSO algorithm, which mimics the collective behavior of bird flocking. In this approach, each particle represents a potential solution, and the particles dynamically adjust their search patterns based on personal experience and collective group learning.

The velocity update rule for each particle in MOPSO is given in Equation (21).

The algorithm updates particle velocity ($V_i)$ and position ($X_i$) using two fundamental equations highlighted below.

$$V_i\left(t+1\right)=\omega ·V_i\left(t\right)+C_1·R_1·\left(p_{besti}\left(t\right)-X_i\left(t\right)\right)+C_2·R_2·(g_{besti}\left(t\right)-X_i\left(t\right)$$

(21)

where $V_i$ is the particle velocity; $\omega$ is the inertia weight; $C_1$ and $C_2$ are the cognitive and social acceleration coefficients; $R_1$ and $R_2$ are random numbers between 0 and 1; $p_{best}$ is the personal best position; and $g_{best}$ is the global best position.

The position update for each particle is defined using Equation (22).

$$X_i\left(t+1\right)=X_i\left(t\right)+V_i\left(t+1\right)$$

(22)

where $X_i$ is the particles’ position.

All particles must iterate their X_i position, i.e., move towards the population best ($p_{best}$) and globe best ($g_{best}$). A general pseudocode for MOPSO is shown in

Table 2. Pseudo-code for the MOPSO algorithm.

Begin for each particle (i) in the swarm do         Initialize Vi with zero         Initialize xi  end for for each particle (i) in the swarm do         Evaluate the fitness function f(xi)         Assign xi to Pbest,i end for         Initialize non-dominated particles in an external repository         Determine domination & keep only non-dominated members         Select a leader         Update Vi and position (xi) for each particle using Equations (21) and (22)         Check if maximum iterations or termination criteria are met repeat         until maximum iterations or termination criteria are satisfied         Select the best solution from the repository end

.

The overall performance of the MOPSO was studied using two methods such as using historical data (1 h resolution) and incorporating uncertainty. In this study, stochastic modeling serves as the foundation for representing the uncertainty in wind and solar resource availability, utilizing probability distributions and random sampling to simulate their temporal variability. The general flowchart for these two methods is shown in Figure 4.

2.7.2. Advantages and Novelty of the Proposed MOPSO Algorithm

The MOPSO framework suggested in this study has several improvements that make it especially useful for sizing complex hybrid power plants, more so than other methods like conventional GA and NSGA-II. Firstly, MOPSO uses a combination of swarm intelligence, a system for keeping track of the best solutions, and a method for managing how crowded the solutions are, which helps it create a well-spread set of optimal solutions with less computing power than GA or NSGA-II. The combination ensures faster convergence and robust exploration in high-dimensional, continuous-variable search spaces typical of renewable energy sizing problems. Secondly, the framework includes likely weather conditions (using Monte Carlo method to create synthetic wind and solar data) and internal policy rules (like tax credits and power purchase agreements) directly into the objective function, allowing for realistic trade-offs that consider policies. Finally, the strength and reliability of the proposed MOPSO implementation are verified by comparing it with a MOGA, showing that it consistently finds the best solutions even when there is uncertainty. These features position the enhanced MOPSO algorithm as an efficient and flexible tool for real-world, hybrid, renewable energy planning.

3. Case Study

3.1. Assessment of the Study Area

The case study focuses on an optimal HPP location (Figure 5) near Lexington, Oregon (45.56° N, −119.634° W), chosen for its exceptional renewable resources and supportive policy environment. The site benefits from strong complementary wind and solar patterns (Figure 6), with wind speeds averaging 6.9 m/s at a height of 100 m (extrapolated from 50 m NASA POWER data) and peaking at 21.92 m/s. Solar irradiance averages at 247.62 W/m² daily, with peaks reaching 1285.31 W/m² [37]. Wind turbine operational thresholds are carefully characterized, with generation initiating at a 3 m/s cut-in speed (occurring 96.3% of hours), reaching a rated capacity at 12 m/s, and shutting down at a 25 m/s cut-out speed (never triggered in the 2023 dataset). Temperature data show an annual average of 11.38 °C, ranging from −11.34 °C in February to 39.36 °C in August. The location’s advantages are further enhanced by Oregon’s progressive renewable energy policies, including a mandate for 100% clean electricity by 2040 with interim targets of 80% by 2030, alongside existing incentives like 30% state tax credits and PPA mechanisms [38]. Situated in the Columbia River Gorge wind corridor, the site leverages existing transmission infrastructure that reduces interconnection costs by approximately 15% compared to undeveloped locations. The study uses detailed 2023 NASA POWER weather data collected every hour, showing a strong seasonal relationship between resources (correlation index −0.82), which helps lower the need for storage. The proposed HPP configuration is designed to deliver 1730 GWh annual output under PPA terms.

Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 present the key meteorological conditions recorded at the case study site, including wind speed, solar irradiance, and ambient temperature. Similarly, Figure 12 illustrates the calculated power output profiles for a single wind turbine and a single solar PV unit, respectively. The wind turbine’s power output profile reflects the expected operating regimes based on hub-height wind speeds, illustrating periods of zero output (cut-in and cut-out conditions) and full-rated output during high wind intervals. Similarly, the solar PV unit power profile depicts how irradiance and temperature variations affect the real-time power generation of a typical panel, highlighting diurnal and seasonal trends. These plots provide clear evidence of the dynamic relationship between site-specific weather data and the operational behavior of each component in the hybrid energy system.

3.2. Assumptions and Parameters

3.2.1. Assumptions

To balance computational tractability with technical realism, the study adopts the following assumptions across system components and operational parameters:

• In line with this study’s objectives, the authors have explicitly focused on reviewing and incorporating optimization approaches relevant to utility-scale HPPs only. Other small-scale or microgrid-focused optimization literature has not been considered, as it falls outside the defined scope and scale of the presented system.
• The study employed aggregated modeling approaches to represent utility-scale WPPs, SPPs, and BESS with hundreds of wind turbines, thousands of solar panels, and hundreds of battery packs, effectively reducing computational effort and system complexity.
• Performance degradation of solar panels, wind turbines, and batteries over time is not considered, implying consistent energy output throughout the system lifetime.
• Costs related to land leasing, insurance, and taxation are excluded from the financial model to maintain simplicity.
• The SPP power calculation estimated temperature-induced losses using a linear model with respect to ambient temperature and irradiance. Shadowing losses are not explicitly modeled in the PV output calculation. The simulation assumes full-sky exposure with no obstruction or shading.
• Inverter and DC-DC converter efficiencies are fixed at 96%.
• Annual degradation is modeled as a 0.5% linear loss in usable battery capacity.
• The battery and inverter are assumed to respond instantaneously to charge/discharge decisions.
• The simulation considers real-time knowledge of load/generation without forecast errors, dispatch errors, or control delays.
• Wake effects, grid import, reactive power dynamics, auxiliary system losses, and ancillary services are not included to preserve model simplicity and computational tractability.
• The study incorporates sensitivity analysis based on widely implemented policy instruments, including PPAs, investment subsidies, tax credits, and interest rates. Additional mechanisms such as carbon trading schemes, renewable energy certificates, net metering, and performance-based incentives are not considered to maintain a generalized and policy-agnostic modeling framework.

3.2.2. Parameters

The key parameters of the MOPSO algorithm used in this study are outlined in

Table 3. Parameters for MOPSO algorithm.

Parameters	Value
Population size	100
Repository size	200
Intertia weight	0.5
Personal learning coefficient	1.5
Global learning coefficient	1.5
Number of grids	20
Maximum velocity	5%
Maximum number of generations	50

.

Table 4. Economic parameters for the proposed HPP [42].

Description	Parameter	Value	Unit
Wind Turbine	CAPEX	1544	$/kW
	OPEX	30	$/year
	Replacement cost	1544	$/kW
Photovoltaic Panel	CAPEX	1456	$/kW
	OPEX	21	$/year
	Replacement cost	1456	$/kW
Battery Storage	CAPEX	1390	$/kWh
	OPEX	31	$/year
	Replacement cost	1390	$/kWh

also summarizes the techno-economic parameters for the HPP components. Cost data for utility-scale onshore WPPs, SPPs, and BESS were obtained from the National Renewable Energy Laboratory (NREL) database [42]. Based on NREL’s Annual Technology Baseline (ATB), large-scale utility wind, solar PV, and battery storage systems are expected to achieve a 30-year operational lifespan by 2030. Accordingly, this study adopts a conservative project lifetime of 30 years for economic and performance assessments.

The techno-economic model developed in this study incorporates a comprehensive bottom-up cost estimation approach for each component of the HPP [43,44,45]. Capital costs reflect total installed costs (equipment, construction, electrical infrastructure, and labor), while annual O&M costs cover maintenance, monitoring, and replacements. A 30% tax incentive is included in the baseline calculations, and an average discount rate of 6% is applied, consistent with U.S. market conditions. The analysis assumes a 30-year PPA at a fixed price of $63/MWh, derived from blended wind and solar PPA benchmarks [46].

4. Result and Discussion

The output power of the WPP and SPP is estimated based on uncertain wind speed and solar irradiance, which are modeled using probabilistic distributions. A Weibull distribution represents wind speed, while a lognormal distribution models solar irradiance (Figure 13). Synthetic time-series data is generated through Monte Carlo simulation, forming the basis for assessing system performance under uncertainty (Figure 13). For illustration purposes, only 1000 samples are presented in Figure 13 and Figure 14.

MOPSO is used to determine the optimal sizing of the hybrid WPP, SPP, and BESS, considering the uncertainty of power output with 100 particles and a maximum of 50 iterations to balance computational efficiency and solution accuracy. The optimization framework evaluates five key aspects: optimization results, energy management analysis, economic evaluation, and sensitivity analysis.

4.1. Optimal Solution

The Pareto front (Figure 15) and

Table 5. Selected optimal results from MOPSO for HPP.

Parameters	Max NPV	Min LPSP	Min Curtailment
WPP (MW)	283	350	281
SPP (MW)	20	45	39
BESS (MWh)	500	523	500
NPV ($ million M)	165.2	83.561	43.19
LPSP (%)	8.26	2.5	7.828
Curtailment (%)	3.79	18.24	4.49

show important trade-offs between NPV, LPSP, and curtailment for different HPP setups. High-NPV solutions (like $150–165 million) show that you can have good financial returns along with moderate reliability (LPSP 8–14%) and very little curtailment (<1%). However, aiming for very high reliability comes with a big cost: setups with very low LPSP (1.73%) have high curtailment (18.93%) and a much lower NPV ($14.09 million), showing the financial downsides of trying to achieve almost perfect reliability. High-NPV solutions (e.g., $150–165 million) demonstrate that strong financial returns can coexist with moderate reliability (LPSP 8–14%) and minimal curtailment (<1%). However, pursuing extreme reliability comes with a steep cost: configurations with ultra-low LPSP (1.73%) suffer from high curtailment (18.93%) and greatly reduced NPV ($14.09 million), highlighting the economic penalty of over-sizing for near-perfect reliability. Conversely, systems prioritizing curtailment often sacrifice either reliability or profitability. These trade-offs underscore why multi-objective optimization is indispensable; the optimal HPP configuration balances all three objectives rather than maximizing any single metric. The suggested balanced-optimization HPP shows strong financial health with a net present value of $165.2 million, a levelized cost of electricity of $0.065 per kilowatt–hour, an internal rate of return of 10.24%, and a payback period of 9.24 years. Operational performance remains efficient, with curtailment below 4% and LPSP at 8.26%.

Based on the multi-objective optimization results, the optimal configuration of the proposed utility-scale HPP consists of 283 MW of WPP, 20 MW of SPP, and 500 MWh of BESS. This optimized sizing (with maximum NPV) is used as the baseline for all subsequent behavior analysis, economic analysis, and sensitivity assessments.

4.2. Energy Dispatch Behavior

The proposed HPP’s operational behavior was analyzed through a full-year simulation, with Figure 16 illustrating a representative 24 h dispatch profile that reveals key system dynamics. During the early morning hours (1–6), except for hour 2, WPP generation frequently exceeds demand, enabling battery charging with minimal curtailment; however, hour 2 requires brief battery discharge to address a supply deficit. The system reaches its first operational constraint from hours 7 to 9 when the battery achieves full charge (SOC = 90%), forcing the complete curtailment of surplus generation. A critical stress period emerges between 10 h and 12 when neither renewable generation nor stored energy can meet demand, resulting in an unmet load and a sharp SOC decline. Partial recovery occurs from hours 13 to 16 as wind generation improves and battery charging resumes, though hour 17 again demonstrates system limitations with concurrent battery discharge and unmet load. The evening period (18–24) shows restored operational balance, with adequate wind generation progressively recharging the battery. The SOC curve’s evolution precisely mirrors these phases, rising during charging periods (2–6, 13–16, 18–24), plateauing at full capacity (7–9), and dropping sharply during deficit conditions (10–12, 17). This profile shows how well the system handles the ups and downs of renewable energy, while also pointing out key times when energy production and storage are not enough, with the battery’s SOC clearly showing the overall balance of the system.

The 24 h dispatch profile demonstrates an effective dynamic response to renewable variability. However, occasional unmet load and curtailment indicate potential for storage and dispatch optimization.

Table 6. Annual energy dispatch in GW/GWh.

Grid Demand	WPP	SPP	BESS Discharge	BESS Charge	Curtailed	Unmet Load
1730.2	1670.9	32.457	296.13	256.19	64.559	142.91

complements this analysis with annual performance metrics, revealing system-wide energy balance and storage utilization patterns across the full operating year.

4.3. Economic Assessment of the HPP

The primary challenge for utility-scale HPPs is to achieve economic viability while integrating capital-intensive components such as WPP, SPP, and BESS. The financial evaluation presented in

Table 7. Economic parameters from MOPSO for HPP.

ASC ($ Million)	LCOE ($/kWh)	IRR (%)	Payback (%)
104.44	0.065	10.24	9.24

demonstrates the proposed system’s strong performance across four key metrics:

The system demonstrates strong economic performance, with an IRR of 10.24%, indicating a substantial financial return relative to total expenditure. The system achieves a payback period of 9.24 years, which is considerably shorter than the project lifetime, thereby enhancing its attractiveness for stakeholders and investors. The ASC of the HPP, incorporating all capital, replacement, and operational expenditures, is estimated at $104.44 million per year. From an energy pricing perspective, the LCOE is calculated to be $0.0658/kWh, positioning the system competitively against conventional fossil fuel-based power plants, which typically range between $0.07 and $0.12/kWh under current U.S. utility-scale cost structures.

4.4. Comparative Analysis with Other Algorithms

Table 8. Comparison of selected optimal result with highest NPV.

Parameters	MOPSO (Uncertainty)	MOPSO (Deterministic)	MOGA (Uncertainty)
WPP (MW)	283	221	271
SPP (MW)	20	26	41
BESS (MWh)	500	515	522
NPV ($ million)	165.2	75.15	128.36
LPSP (%)	8.26	20.13	9.36
Curtailment (%)	3.79	2.35	3.01
LCOE($/kWh)	0.065	0.075	0.07
ASC ($ million)	104.44	100.87	110.78

provides a systematic comparison of optimal HPP configurations derived from various optimization approaches: MOPSO with probabilistic distribution, deterministic MOPSO, and MOGA with probabilistic distribution. The analysis emphasizes configurations that maximize NPV to facilitate consistent economic evaluation across methodologies while considering reliability (LPSP) and curtailment trade-offs. Key findings indicate significant variations in system design and performance. MOPSO with uncertainty identifies a WPP-dominant configuration (283 MW WPP, 20 MW SPP, 500 MWh BESS), while deterministic MOPSO lowers WPP capacity (221 MW) to slightly increase SPP (26 MW) and BESS (515 MWh). MOGA finds a balance with renewables (271 MW WPP, 41 MW SPP) and the largest BESS (522 MWh).

In terms of cost performance, MOPSO with uncertainty also achieves the LCOE at $0.065/kWh and maintains a moderate ASC of $104.44 million per year. By comparison, the deterministic result shows a slightly higher LCOE of $0.075/kWh but achieves the lowest ASC at $100.87 million per year, albeit with significantly lower NPV and much higher unreliability. MOGA offers an intermediate LCOE of $0.070/kWh and the highest ASC at $110.78 million, while delivering strong reliability and moderate curtailment.

In terms of reliability, MOPSO with uncertainty achieves the lowest LPSP at 8.26%, outperforming both MOGA (9.36%) and the deterministic result (20.13%). Although the deterministic system achieves the lowest curtailment (2.35%), it does so at the expense of high unreliability and reduced economic benefit. MOGA maintains curtailment at a balanced level (3.01%) while offering a good compromise between cost, reliability, and economic return. Overall, MOPSO with uncertainty delivers the most cost-effective and reliable system configuration, confirming the benefit of integrating uncertainty and policy factors within the optimization framework. The comparative Pareto front for these configurations is illustrated in Figure 17.

4.5. Sensitivity Analysis

Given the high capital costs and long operational lifespan of HPP projects, understanding parameter sensitivity provides crucial insights into financial resilience during market fluctuations. Given the high capital costs and long operational lifespan of HPP projects, understanding parameter sensitivity provides crucial insights into financial resilience during market fluctuations. This section presents a sensitivity analysis using MOPSO with probabilistic methods for the optimal configuration (WPP of 283 MW, SPP of 20 MW, and BESS of 500 MWh) for further analysis.

4.5.1. Economic Parameters with Tax Credit

A.

Power Purchase Agreement Sensitivity

In utility-scale HPPs, PPAs serve as long-term contracts that define the rate at which the produced electricity is sold to the grid. Given the capital-intensive nature of HPPs, small variations in PPA prices can significantly impact economic viability. The analysis evaluated PPA prices ranging from $0.05/kWh to $0.12/kWh. As the PPA price increased from $0.05 to $0.12/kWh, the NPV shifted from negative values to a highly profitable $1.22 billion (Figure 16). Correspondingly, the payback period decreased from 22.5 years to 5.5 years, while the IRR improved from 1.95% to 18.08%, indicating enhanced investment attractiveness. In contrast, both the LCOE and ASC remained constant across all PPA levels, as they depend on system cost rather than revenue.

A further sensitivity analysis incorporated a 30% federal tax credit on capital expenditures (CAPEX) alongside varying PPA rates. Without tax credits, the project was economically unviable at lower PPAs; at $0.05/kWh, the NPV was –$665 million, with a payback period exceeding 32 years. With tax credits, the NPV improved to –$316 million, and the payback shortened to 22.5 years, significantly mitigating financial risk. At $0.08/kWh, the tax credit increased the NPV by over $348 million and reduced the payback period by more than four years. At $0.12/kWh, the project became highly profitable in both cases, but the IRR increased to 18.08% with the tax credit compared to 12.36% without.

Figure 18 illustrates that while LCOE and ASC remain constant without incentives, applying a 30% tax credit significantly reduces both metrics: LCOE drops from approximately $0.065/kWh to $0.045/kWh, and ASC decreases from $104.51 million to $73.15 million. Most importantly, the results demonstrate that at lower PPA rates (≤$0.07/kWh), the project is only viable if supported by tax incentives.

B.

Discounted Interest Rate

The analysis of how sensitive project economics are to changes in the discount rate (Figure 19) reveals profound impacts. As rates climb from 3% to 7%, NPV plummets by 74.7% from $486.66 millionto −$118.45 million, while LCOE escalates by 49% to $0.0715/kWh, and ASC grows by 50% to $114.45 million. Tax credits dramatically mitigate these effects: at 7% rates, they boost NPV by 294% to $230.32 million, reduce LCOE by 30% to $0.05/kWh, and lower ASC by 30% to $80.11 million. Notably, payback periods (improving from 13.82 to 9.67 years) and IRR (increasing from 5.96% to 9.70%) remain rate-independent but consistently benefit from incentives. These results demonstrate that while rising rates severely threaten viability, tax credits maintain attractiveness, transforming even a 7% scenario from loss-making to profitable. The stability of IRR and payback metrics suggests their utility for evaluating renewable investments across financial climates.

C.

Cost Projection Scenario Analysis

This evaluation looks at how well the system can work under three different technology cost paths (conservative, moderate, and advanced) using NREL’s 2024 ATB projections [38], with specific cost details shown in

Table 9. Cost projection under three scenarios (* [43]; ** [44]; *** [45]).

Scenario	Wind *		Solar ***		BESS **		Tax Credit
	CAPEX	O&M	CAPEX	O&M	CAPEX	O&M
Year 2025
Conservative	1632.639	31.868	1540.628	21.503	2159.943	49.595	No
Moderate	1569.099	31.251	1491.64	21.001	1711.403	38.777	No
Advanced	1544.244	30.145	1456.24	20.602	1390.744	31.043	No
Year 2035
Conservative	1522.152	30.291	1189.247	17.962	1717.701	38.929	No
Moderate	1344.692	28.261	895.321	15.022	1347.396	29.997	No
Advanced	1258.799	23.834	682.896	12.764	1028.712	22.311	No

CAPEX: $/kWh, O&M: $/kW year.

. The conservative scenario assumes historical learning rates and minimal cost reductions. The moderate scenario relies on engineering and bottom-up scaling models that reflect typical current projections. The advanced scenario incorporates aggressive cost-reduction assumptions based on accelerated learning and deployment.

Technological advancement (Figure 20) is transformative; the advanced scenario with tax credits delivers optimal performance with a $624.55 million NPV, $0.0347/kWh LCOE, 14.32% IRR, and a 6.86-year payback period, representing a 52% reduction in BESS CAPEX from 2025 levels. Tax credits are particularly crucial for near-term viability, boosting 2025 economics by reducing LCOE by up to 30% and converting negative NPV scenarios into break-even or profitable cases. While all scenarios show improved 2035 performance due to projected cost declines (solar CAPEX falling by 53% in advanced cases), conservative trajectories without incentives remain financially unviable even in 2035. This study demonstrates that while long-term technology cost reductions enhance economic attractiveness, policy support is essential to enable near-term deployment and ensure financial sustainability across all market conditions. The results highlight the sensitivity of HPP costs and the compounding benefits of combining technological advancement with supportive policies.

4.5.2. Technical Parameter

A.

Constant Grid Demand Scenario

The constant demand analysis evaluates system performance independently of load fluctuations, revealing that the best-optimized configuration (450 MW WPP, 200 MW SPP, 500 MWh BESS) achieves strong reliability (8.45% LPSP) with modest curtailment (4.29%). Financially, the system demonstrates robust viability with a $366.6 million NPV and 8.31% IRR (exceeding the discount rate), supported by competitive metrics including $0.0532/kWh LCOE and $128.1 million ASC. The 10.94-year payback period further confirms investment attractiveness.

Table 10. Comparison of optimal results from constant demand with variable demand from previous methods.

Metrics	Constant Demand	Variable Demand	Change (%)
WPP (MW)	450	284	+58.5
SPP (MW)	20	20	-
BESS (MWh)	500	500	-
NPV ($million)	366.6	165.2	+122
LPSP (%)	8.45	8.26	+2.3
Curtailment (%)	4.29	3.79	+7.3
LCOE ($/kWh)	0.0532	0.065	−18.2
ASC ($ million)	128.1	104.44	−18.5
IRR (%)	8.31	10.24	−18.8
Payback (Years)	10.94	9.24	+18.4

’s comparison of constant and variable grid demand scenarios reveals that constant demand significantly enhances the economic performance of the HPP. While keeping similar reliability (LPSP 8.26% vs. 8.45%), the constant demand scenario needs 58.5% more wind capacity (450 MW) and results in a 122% higher NPV ($366.6 million vs. $165.2 million), along with an 18.2% lower LCOE (0.0532/kWh vs. 0.065/kWh). However, this improvement comes with trade-offs: the larger wind investment reduces capital efficiency, yielding an 18.8% lower IRR (8.31% vs. 10.24%), an 18.5% reduction in ASC, and an 18.4% longer payback period (10.94 vs. 9.24 years). The systems show comparable curtailment rates (4.29% vs. <4%), though the constant demand case exhibits 7.3% more energy surplus due to reduced load flexibility.

Figure 19 shows how this setup keeps operations steady compared to the 300 MW constant load, with battery usage effectively managing the ups and downs of renewable energy while keeping waste low. In contrast to Figure 16, the constant demand case (Figure 21) exhibits smoother dispatch behavior, with minimal unmet load and consistently high SOC. However, this is achieved through a significantly oversized wind power plant, resulting in substantial curtailment during periods of surplus generation.

B.

Wind Resource Quality

Given that the WPP is the primary energy source in the proposed HPP configuration, its variability critically influences system performance (

Table 11. Comparison of optimal results based on wind resources.

Parameters	Wind Resources
	Low-Moderate	Good	Excellent
WPP (MW)	450	411	327
SPP (MW)	73	27	24
BESS (MWh)	500	527	538
NPV ($ million)	−163.197	−126.23	92.097
LPSP (%)	29.60	4.10	2.81
Curtailment (%)	1.70	16.19	12.33
LCOE ($/kWh)	0.111	0.076	0.068
ASC ($ million)	134.774	126.655	115.827
IRR (%)	100	5.14	6.66
Payback (Years)	−150.82	15.12	12.85
Capacity factor (%)	26.61	43.32	54.63

). A sensitivity analysis was conducted by varying the average wind speed across three realistic site categories: moderate (~5.75 m/s), good (~8.60 m/s), and excellent (~11.60 m/s). Analysis across these three wind regimes reveals dramatic improvements at higher wind speeds, transitioning from economically infeasible (−$163.2 million NPV) at moderate sites (5.75 m/s) to highly profitable ($92.1 million NPV) at excellent sites (11.6 m/s). Superior wind resources enable a 27% more compact system (327 MW vs. 450 MW WPP) while doubling the capacity factor to 54.6%, confirming efficient asset utilization and reducing LCOE by 39% to $0.068/kWh. The excellent wind scenario achieves outstanding reliability (2.81% LPSP) with reasonable curtailment (12.33%) and attractive payback (12.85 years). In comparison, average wind locations need much bigger setups (450 MW WPP + 73 MW SPP) but still perform poorly (29.6% LPSP, 26.6% capacity factor) without major financial support or high-power purchase agreements. These results point out the urgent need for site-specific wind resource assessments in HPP planning to ensure economic feasibility.

C.

BESS C-Rate

Table 12. Comparison of optimal results based on BESS C-rate.

Parameters	BESS C-Rate
	0.5C	0.75C	1C
WPP (MW)	318	318	335
SPP (MW)	41	68	74
BESS (MWh)	513	500	500
NPV ($ million)	88.97	77.262	77.47
LPSP (%)	3.49	3.29	2.44
Curtailment (%)	11.62	13.05	16.76
LCOE ($/kWh)	0.068	0.069	0.070
ASC ($ million)	113.539	115.327	118.674
IRR (%)	6.66	6.56	6.66
Payback (Years)	12.86	12.98	13
Capacity factor (%)	53.14	49.58	47.1

presents the impact of the BESS charge/discharge rate (C-rate) on system flexibility and techno-economic performance. A sensitivity analysis was performed for three scenarios: 0.5C, 0.75C, and 1C. Results show that increasing the C-rate from 0.5C to 1C enhances the system’s ability to respond to load fluctuations and absorb surplus renewable generation, reducing LPSP by 30% (3.49%→2.44%) and enabling higher renewable integration (WPP increases from 5% to 335 MW). However, the change comes with a 44% surge in curtailment (11.62%→16.76%) as faster cycling outpaced storage capacity. Economically, the 0.5C configuration proves optimal, delivering a 15% higher NPV ($88.97 million vs. $77.47 million at 1C) and marginally better LCOE (0.068 vs. 0.070/kWh), despite requiring slightly larger storage (513 MWh). The stability of IRR (~6.6% across scenarios) suggests that C-rate primarily affects capital efficiency rather than long-term returns. Notably, higher C-rates reduce the capacity factor by 11.4% (53.14%→47.1%), indicating increased operational stress on components. These results demonstrate that while faster BESS response improves reliability, the 0.5C rate offers the best balance of economic and technical performance for this HPP configuration.

D.

BESS SOC

The evaluation of different SOC operating ranges (

Table 13. Comparison of optimal results based on BESS SOC.

Parameters	BESS SOC (socmin–socmax%)
	20–80%	30–70%	10–90%
WPP (MW)	343	337	332
SPP (MW)	55	62	37
BESS (MWh)	500	500	500
NPV ($ million)	99.08	89.74	115.77
LPSP (%)	2.40	2.56	3.06
Curtailment (%)	17.27	16.36	14.15
LCOE ($/kWh)	0.0695	0.0696	0.0676
ASC ($million)	117.287	115.327	113.427
IRR (%)	6.70	6.63	6.84
Payback (Years)	12.79	12.88	12.61
Capacity factor (%)	48.48	48.28	51.95

) demonstrates significant impacts on system performance and economics. Three SOC bands were analyzed: 20–80%, 30–70%, and 10–90%. The results indicate that wider SOC operating windows enhance battery flexibility, leading to improved renewable energy utilization and superior economic outcomes. When operating within a 10–90% SOC range, the system achieved the best financial performance, with an NPV of $115.77 million, approximately 28.9% higher than the $89.74 million achieved under the narrower 30–70% SOC range. The wider SOC range allowed for more effective battery usage, reducing curtailment to 14.15%, a 13.5% improvement over the 30–70% case. Additionally, the payback period decreased to 12.61 years, and the LCOE slightly improved to $0.0676/kWh.

In contrast, the 30–70% case exhibited a higher SPP capacity requirement (62 MW) to maintain system reliability due to reduced usable BESS capacity. This resulted in a higher ASC of $115.33 million and a lower NPV. The middle 20–80% SOC range showed good results, with an NPV of $99.08 million, an IRR of 6.70%, and an LPSP of 2.40%, suggesting a good balance between technical strength and financial success.

E.

Grid Import

Table 14. Comparison of optimal results based on BESS degradation rate.

Metrics	Grid Import	No Grid Import
WPP (MW)	253	283
SPP (MW)	20	20
BESS (MWh)	500	500
NPV ($million)	123.00	165.2
LPSP (%)	1.89	8.26
Curtailment (%)	0.95	3.79
LCOE ($/kWh)	0.0615	0.065
ASC ($million)	104.43	104.44
IRR (%)	7.83	10.24
Payback (Years)	9.22	9.24
Capacity factor (%)	70.1	48.28

compares the optimal performance of the HPP under two operational strategies: with and without grid import support. The results demonstrate that enabling the grid significantly enhances system reliability and operational flexibility. With grid support, the system achieves a substantially lower LPSP of 1.89% and a curtailment rate of only 0.95%, compared to 8.26% and 3.79%, respectively, without grid import. Additionally, despite a reduced WPP capacity of 253 MW (compared to 283 MW without grid support), the system’s capacity dramatically improves from 48.28% to 70.1%, indicating better resource utilization. However, these technical improvements are accompanied by economic trade-offs. The NPV declines from $165.2 million to $123.00 million, and the IRR decreases from 10.24% to 7.83%. Nonetheless, the LCOE improves from $0.065/kWh to $0.0615/kWh, while the ASC remains nearly identical. The payback period remains largely unchanged at approximately 9.2 years. Overall, while grid import significantly enhances technical performance and reliability, it slightly compromises economic returns.

The dispatch profiles (Figure 22) highlight substantial differences in HPP behavior under scenarios with grid import. When grid import is available, external support allows for smoother load following, minimal unmet load, and reduced curtailment, despite a smaller wind capacity. The BESS SOC remains relatively low and stable, reflecting reduced operational stress. In contrast, without grid import (Figure 16), the system depends only on its own power generation and BESS, which results in noticeable times when it cannot meet the load, more fluctuations in SOC levels, and a higher reliance on battery use. As a result, the system without grid import needs a bigger WPP capacity and faces a bit more curtailment, showing that it has more operational difficulties and needs more infrastructure.

F.

Comparative System Performance Analysis

The optimization framework evaluated three distinct hybrid configurations to identify the most viable solution for utility-scale deployment, as shown in

Table 15. Comparative analysis of hybrid configurations.

Metrics	Wind–Battery	Wind–Solar	Wind–Solar–Battery
WPP (MW)	350	328	283
SPP (MW)	0	24	20
BESS (MWh)	500	0	500
NPV ($ million)	157.50	94.50	165.20
LPSP (%)	2.82	20.59	8.26
Curtailment (%)	16.38	30.94	3.79
LCOE ($/kWh)	0.0678	0.0361	0.0650

. Standalone wind/solar systems are fundamentally limited by intermittency, making them unsuitable for reliable utility-scale deployment without storage or hybridization.

The optimization results demonstrate that the proposed wind–solar–battery HPP system achieves superior techno-economic performance compared to alternative configurations. While the wind–battery system (350 MW WPP, 500 MWh BESS) provides high reliability (LPSP = 2.82%), it suffers from significant curtailment (16.38%) due to wind overgeneration, limiting its NPV ($157.5 million). Conversely, the wind–solar hybrid system (328 MW WPP, 24 MW SPP) exhibits unacceptable reliability (LPSP = 20.59%) and extreme curtailment (30.94%), resulting in suboptimal economics (NPV = $94.5 million). In contrast, the full hybrid system (283 MW WPP, 20 MW SPP, 500 MWh BESS) optimally balances these trade-offs, achieving the highest NPV ($165.2 million), lowest curtailment (3.79%), and acceptable LPSP (8.26%), while maintaining a competitive LCOE ($0.065/kWh). However, a solar–battery-only system proved infeasible. These findings validate that wind-dominated hybridization represents the only viable solution, meeting all operational constraints (LPSP < 10%, curtailment < 5%, NPV > 0) while maintaining a competitive LCOE ($0.065/kWh) for the given resource profile (6.9 m/s wind, 247 W/m² irradiance).

4.5.3. Policy Analysis

A.

Regional Policy Analysis

The comparative analysis of the U.S. and India’s economic metrics for baseline scenarios (

Table 16. Economic metrics for baseline scenarios for selected countries.

Metrics	USA	India
NPV ($million)	344.93	64.06
LCOE($/kWh)	0.059	0.04
IRR (%)	9.21	7.74

) reveals how policy structures fundamentally shape the HPP system viability. This scenario models market-driven conditions using country-specific parameters: a fixed PPA rate of 0.065/kWh with a 6% interest rate is applied to the United States, while 0.0487/kWh and 11% are applied for emerging markets like India to account for higher capital costs. The policy parameters for the USA and India are shown in Appendix A 

Table A2. Available policy support economic parameters in India and USA for HPP.

Policy Metrics	Values	References
India
Interest rate (%)	11	[51,52]
Interest rate subsidy (%)	Max 3	[51]
Accelerated depreciation (%)	40	[51]
Auction PPA/FIT ($/kWh)	0.0487	[52]
Viability gap funding (Varies with state)	30%	[52]
Generation-based incentives ($/kWh)	0.008	[51]
USA
PTC ($/kWh) *	0.026	[53]
ITC (%) *	30	[53]
PPA ($/kWh)	0.065	[22]

* Maximum 10% bonus available [54].

.

In the U.S., market-driven mechanisms, including a fixed PPA ($0.065/kWh) combined with the Production Tax Credit (PTC, $0.026/kWh) and Investment Tax Credit (ITC, 30%), delivered robust financial performance (NPV: $344.93 million, IRR: 9.21%). However, the moderate IRR reflects reliance on time-limited incentives and competitive market pressures. In contrast, India’s subsidy-intensive model featuring a lower auction-based PPA ($0.0487/kWh) but layered support (interest rate subsidies, 40% accelerated depreciation, 30% viability gap funding, and generation-based incentives) achieved a competitive IRR (7.74%) despite higher capital costs (11% interest rate). Notably, India’s lower LCOE ($0.04/kWh vs. $0.059/kWh in the U.S.) did not translate to higher NPV due to structural constraints, including elevated financing risks and revenue limitations. These results underscore that while mature markets benefit from streamlined, high-impact incentives (e.g., tax credits), emerging economies require comprehensive, multi-tiered policy support to offset inherent disadvantages. The findings emphasize the critical role of tailored policy frameworks in enabling HPP deployment across diverse regulatory environments, with implications for designing region-specific support mechanisms to enhance bankability.

B.

Uncertainty policy

HPP projects are highly cost-intensive and highly dependent on government support mechanisms. However, such policies are susceptible to budget cuts, political transitions, and evolving regulatory agendas. To evaluate HPPs’ exposure to these uncertainties, the study conducted a scenario-based simulation analyzing three policy support conditions: (1) stable, (2) moderately reduced, and (3) withdrawn (see

Table 17. Scenario-based simulation.

Scenario	Description
	USA	India
Stable (Case 1)	PTC support for lifetime	GBI support for lifetime
Moderate (Case 2)	PTC drops 50% after year 5	GBI drops 50% after year 5
Withdrawn (Case 3)	PTC removed after year 10	GBI removed after year 10

).

The policy uncertainty analysis (

Table 18. Economic metrics using policy uncertainty for the U.S.

Metrics	Case 1	Case 2	Case 3	Change % (Case 1)
				With Case 2	With Case 3
USA
NPV ($ million)	369.85	185.85	123.11	−49%	−66.71%
IRR (%)	9.43	7.88	7.40	−16.4%	−21.5%
India
NPV ($ million)	29.81	−26.67	−44.66	−189.48%	−249.78%
IRR (%)	7	6.03	5.65	−13.85%	−19.28%

) reveals stark contrasts in how U.S. and Indian HPP projects withstand support mechanism changes. In the U.S., market-driven structures demonstrate moderate resilience—complete withdrawal of the Production Tax Credit (PTC) after 10 years reduces NPV by 66.7% (from $369.85 million to $123.11 million) and IRR by 21.5% (9.43% to 7.40%), yet projects remain viable due to stable PPAs ($0.065/kWh) and the 30% Investment Tax Credit. In contrast, India’s subsidy-dependent model shows extreme fragility: a 50% reduction in Generation-Based Incentives (GBI) after 5 years plunges NPV into negative territory (−$26.67 million), while complete GBI withdrawal causes a catastrophic 249.78% NPV collapse (−$44.66 million) and renders projects unbankable. This divergence stems from structural differences. U.S. projects benefit from lower capital costs (6% interest) and market mechanisms, whereas Indian ventures rely on layered subsidies (interest rate support, viability gap funding) to offset high financing costs (11% interest) and constrained PPA rates ($0.0487/kWh). The results underscore that while mature markets can absorb phased policy reductions, emerging economies require long-term, legally guaranteed support (15+ years) to mitigate investment risks.

4.6. Comparison with Previous Studies

In

Table 19. Comparison with literature on utility scale.

Metrics	Das et al. [4]	Stanley & King [8]	Leon et al. [15]	Current Study
WPP (MW)	171	301	264	283
SPP (MW)	378	42.9	300	20
BESS (MWh)	271	0	228	500
NPV ($ million)	93.52 *	37.08	347.63 *	165.2
LPSP (%)	-	-	-	8.26
Curtailment (%)	2	-	0	3.79
LCOE ($/kWh)	0.045 *	0.037	0.022 *	0.065
ASC ($ million)	-	-	-	104.44
IRR (%)	9	-	0.151	10.24
Payback (Years)	-	-	-	9.24
Capacity factor (%)	46	-	-	48.28

* Converted to $ or $/KWh from euro (1 Euro = 1.14$ as of 27 April 2025).

, the current study is compared to previous works by Das et al. [4], Stanley & King [8], and Leon et al. [15] on HPP performance. The comparison centers on key techno-economic performance indicators across various optimization methods and approaches. Even though it is difficult to directly compare HPP optimization studies because of differences in system setups, energy demands, weather, and financial assumptions, consistent techno-economic trends can still be observed across key parameters.

This study’s HPP configuration demonstrates significant advancements compared to previous research (Table 13). Unlike solar-heavy designs (e.g., Das et al.’s [4] 378 MW SPP system) or storage-less approaches [8], the current wind-dominated HPP achieves a balanced economic profile with a $165.2 million NPV and a 10.24 IRR versus a $37.08 M NPV by Stanley and King [7] and Leon et al.’s [15] aggressive strategy of $347.63 million NPV. While the LCOE of the current study ($0.065/kWh) is slightly higher, it reflects realistic operating conditions and moderate renewable resource availability. The inclusion of ASC ($104.44 million) and explicit LPSP (8.26%) optimization addresses a significant gap in the existing literature, providing a more holistic assessment framework. The 9.24-year payback period further demonstrates balanced performance, particularly when compared to storage-less configurations that may show shorter returns but higher operational risks. This comparison highlights how the new method improves HPP design by tackling three important but often conflicting goals at the same time: making it cost-effective, ensuring the system is reliable, and integrating renewable energy, all while being clear about the main performance measures.

5. Conclusions and Recommendation

5.1. Conclusions

This study created a strong plan for improving large-scale HPPs by looking at the balance between economic, reliability, and operational goals while considering uncertainties and policy incentives. Key findings demonstrate the following:

• The tri-objective MOPSO approach yields a high-performing configuration (284 MW WPP, 20 MW SPP, 500 MWh BESS) with competitive economics ($165.2 million NPV), reliability (8.26% LPSP), and operational efficiency (3.79% curtailment), validating the need for a holistic design.
• The system maintained an LCOE of $0.065/kWh, an IRR of 10.24%, and a payback period of 9.24 years, demonstrating strong financial viability.
• Enabling grid imports significantly enhance reliability (LPSP: 1.89%) but require trade-offs in NPV ($123 million), which emphasizes the value of a market-aware design.
• Wind quality significantly influences system viability, as excellent sites (11.6 m/s) achieve 54.6% capacity factors and a 39% lower LCOE compared to moderate sites.
• Tax credits reduce LCOE by 30% and enable feasibility at low PPAs, underscoring their role in bridging cost gaps.

Similarly, when individual optimization priorities were emphasized:

• Maximizing NPV resulted in a slight reduction in battery sizing and moderate curtailments (3–4%), prioritizing cost savings over absolute reliability.
• Minimizing LPSP necessitated a larger battery size and increased grid imports, enhancing system resilience while slightly decreasing profitability.
• Minimizing curtailment drove a configuration featuring enhanced battery discharge capacity and a larger wind plant size, improving utilization, albeit at a higher initial capital cost and a slightly extended payback period.

The optimization results were checked by a separate method called MOGA, which shows that the best setups found are strong and trustworthy.

5.2. Recommendation

This study recommends that future HPP developments strategically incorporate limited grid imports to enhance system reliability, as demonstrated by a reduction of more than 75% in LPSP. However, such grid interactions should be carefully evaluated against electricity import prices and carbon footprint considerations to ensure overall project viability. Furthermore, policy incentives, including tax credits and a stable PPA, are critical to de-risk hybrid investments, particularly under high weather variability. For future research, it is advisable to extend the optimization framework by integrating alternative forms of storage, such as supercapacitors, RSOCs, and the upcoming hybrids of these storage configurations. This approach can help identify configurations with improved sustainability, cycle life, and system resilience under different grid conditions and maximize revenue stacking and operational flexibility. The energy management system inherently minimizes curtailment through battery storage utilization, rule-based surplus energy allocation, and SOC management. However, future work could also be integrated into the EMS framework in future implementations.

The proposed optimization framework is designed for broad applicability and can be adapted to other regions by incorporating local policy structures (e.g., feed-in tariffs, auctions) and site-specific resource data. To implement the framework in new contexts, users need to update three key inputs: (1) region-specific wind/solar profiles, (2) local incentive mechanisms, and (3) local economic boundaries (PPA rates, discount rates). This flexibility ensures the framework remains viable across diverse regulatory and geographic settings, enabling stakeholders to tailor solutions to regional energy transition goals. Future work could automate this adaptation process by integrating global renewable energy databases and policy libraries into the optimization tool.