Hybrid renewable power plants consisting of collocated wind, solar photovoltaic (PV), and lithium-ion battery storage connected behind a single grid connection can provide additional value to the owners and society in comparison to individual technology plants, such as those that are only wind or only PV. The hybrid power plants considered in this article are connected to the grid and share electrical infrastructure costs across different generation and storing technologies. In this article, we propose a methodology for sizing hybrid power plants as a nested-optimization problem: with an outer sizing optimization and an internal operation optimization. The outer sizing optimization maximizes the net present values over capital expenditures and compares it with standard designs that minimize the levelized cost of energy. The sizing problem formulation includes turbine selection (in terms of rated power, specific power, and hub height), a wind plant wake loss surrogate, simplified wind and PV degradation models, battery degradation, and operation optimization of an internal energy management system. The problem of outer sizing optimization is solved using a new parallel “efficient global optimization” algorithm. This new algorithm is a surrogate-based optimization method that ensures a minimal number of model evaluations but ensures a global scope in the optimization. The methodology presented in this article is available in an open-source tool called HyDesign. The hybrid sizing algorithm is applied for a peak power plant use case at different locations in India where renewable energy auctions impose a monetary penalty when energy is not supplied at peak hours. We compare the hybrid power plant sizing results when using two different objective functions: the levelized cost of energy (

A hybrid power plant (HPP) consisting of collocated wind, photovoltaic (PV), and lithium-ion battery storage connected behind a single grid connection point can provide better returns on investment than individual-source (wind or solar) plants in locations where the wind and solar resources are comparable and for electricity markets in which fixed power purchase agreement electricity prices are not possible. HPPs can be designed to have operational flexibility in terms of dispatchability and ancillary service provision that makes them closer to traditional power plants in terms of achieving additional profitability in markets with time-varying electricity prices under grid connection constraints and that have reduced costs due to the shared infrastructure

Sizing of HPPs is a multi-disciplinary design analysis and optimization (MDAO) problem that requires detailed modeling of the wind and solar resources as well as the wind, PV, and storage performance, costs, and operation

A detailed energy management system (EMS) is required to determine the operation of the battery, given the time series of wind and solar generation and the battery's capacity. EMS optimization will determine when to charge and discharge the battery with the objective of maximizing the revenue obtained by the HPP. Several articles focus on formulating EMS optimization problems and propose different formulations

Furthermore, HPP sizing requires solving the long-term performance of the different components through the lifetime of the HPP; this implies modeling the degradation in the performance of the individual components. Li-ion (lithium-ion) batteries, wind turbines, and PV cells have significant degradation over time. Several models of PV degradation exist

Typically, battery cells have to be replaced when their capacity degrades beyond a manufacturer-defined safety threshold. The higher costs due to battery replacement play a dominant role in total battery costs. Therefore, considering battery degradation when sizing HPPs can optimize the use of batteries, extending battery lifetime and reducing costs. Battery degradation is a complicated chemical process. Theoretical studies

To the authors' knowledge, there is no available sizing methodology for the design of utility-scale grid-constrained hybrid power plants considering all the above-mentioned characteristics. This article presents a general methodology for hybrid plant sizing as a nested optimization, including several novel aspects: (1) turbine selection, (2) PV and wind degradation, (3) internal EMS operation optimization, and (4) battery degradation based on resulting load cycles. We apply the methodology and report the detailed result of the hybrid plant design in three different locations in India for sites with the following characteristics: (a) good solar, (b) good wind, and (c) bad solar and bad wind. The research objective is to build a framework for optimization of hybrid power plants that is flexible, is modular, and can be extended to solve the sizing and physical design of HPPs.

India is a large market in which HPPs could become important because of the need to provide renewable energy that supports the demand patterns and because of the intermediate solar and wind resources. For this reason, Indian sites are used as example cases in this article.

HPP sizing as a nested optimization. XDSM diagram.

The design of an HPP is an optimization problem that involves several sub-optimization problems such as WT selection, wind power plant (WPP) siting and layout optimization, PV array sitting, EMS operation optimization coupled with battery degradation, and electrical infrastructure optimization. HPP sizing optimization focused on maximizing the viability of an HPP installation in a given location requires a simplified approach. The XDSM (eXtended Design Structure Matrix) diagram of the proposed nested optimization for HPP sizing is presented in Fig.

The HPP sizing optimization problem consists of minimizing

Generic wind turbine surrogate:

A lookup table is built based on DTU's (Technical University of Denmark) PyWake generic turbine model

WPP example of generated layouts.

A database of wind power plants is generated using circular plant borders and a simplified layout optimization that maximizes the distance between the turbines. Two example layouts are presented in Fig.

Example wake losses as a function of the number of turbines, installation density, and WT's specific power.

Detailed wake losses as a function of wind speed and wind direction are simulated for multiple WPP layouts with the same number of turbines (

ERA5

The mean wind speed from the Global Wind Atlas 2 (GWA2) is used for correcting ERA5's mean wind speed following the approach presented in

ERA5-Land is used as a reanalysis of the hourly global horizontal irradiance time series (

The wind generation time series (

Wind turbine degradation is modeled as a mixture of two performance degradation mechanisms: (a) a shift in the power curve towards higher wind speeds represents blade degradation and increasing friction losses

Power conversion uses pvlib

The PV degradation model has a loss factor that follows a prescribed PV degradation curve

EMS comparison in an example HPP for two different battery fluctuation penalty factors

The electricity price time series in the spot market (

The energy management system optimization model determines the optimal amount of battery charge or discharge and power curtailment that maximizes the revenue generated by the plant over a period of time, including a possible penalty for not meeting the requirement of energy generation and a penalty for battery power ramping to control the number of battery load cycles (see Eq.

The revenue is given by the product of electricity price (

The penalty (

The battery fluctuation penalty (

The constraints in the optimization force a minimum level of energy in the battery (

The battery degradation model includes a linear degradation rate as a function of load cycles and a non-linear degradation due to the solid electrolyte interphase (SEI) film formation process in the early stage of the battery life. The rainflow-counting algorithm

Battery degradation comparison in an example HPP for two different battery fluctuation penalty factors

The linear degradation rate (

The non-linear part of the degradation given in Eq. (

Finally, the time series of the degrading energy capacity of the battery is

A ruled-based EMS is implemented to account for battery, PV, and wind degradation and forecast errors in estimated wind and solar generation. The correction model consists of the following general principles: (1) try to follow the resulting operation obtained in the EMS described in Sect.

The implementation consists of computing the reduction in charging power due to the different available generations, as presented in Eq. (

A simple WPP cost model consists of estimating the total capital expenditure (CAPEX) costs (

A simple PV plant cost model consists of estimating the total capital expenditure (CAPEX) costs (

The battery plant cost model consists of estimating the total capital expenditure (CAPEX) costs (

A simple electrical infrastructure cost model consists of estimating the total capital expenditure (CAPEX) costs (

A simple financial model uses the weighted average cost of capital (WACC) for wind, PV, and battery as a discount rate (see Eq.

The financial model then estimates the yearly incomes (

Surrogate-based optimization is used as the outer sizing optimization to reduce the number of full model evaluations during a gradient-based optimization

An updated version of the parallel efficient global optimization (EGO)

Parallel EGO algorithm for exploring and refining.

Location of the three example sites.

Assumptions for the HPP sizing optimization with two scenarios for battery costs. O&M: operation and maintenance.

Design variable in the optimization setup.

Three locations in India are selected as study cases (see Fig.

Hourly statistics per month for wind speed and direct normal irradiance on the three locations.

The detailed results of the hybrid plant sizing optimization based on minimizing

On the site with good solar, an HPP of PV and storage is obtained for the

On the site with good wind, a single wind plant with minimal over-planting is obtained for the

Example of 10

On the site with bad solar and bad wind, a PV plant with a storage plant is obtained for the

HPP sizing optimization results in the example sites with respect

Figure

Hybrid power plants with storage are obtained across India with

Battery degradation plays an important role in HPP sizing as the additional costs of replacing the battery one or two times will change the financial viability of the project.

The sizing optimization prioritizes cheaper turbines for the

The proposed nested-optimization approach ensures realistic HPP operation and at the same time allows for having non-linear sizing optimization. In the proposed framework, both EMS models are necessary since it is not computationally feasible to solve the internal EMS optimization for varying degradation states for the full lifetime within an outer sizing optimization. Instead, the rule-based long-term EMS is used to account for component degradation in a computationally efficient way. Hybrid power plants should be designed considering a realistic representation of the technologies, including their degradation.

The

Future work will look into integrating stochastic optimization with internal operation optimization to have operation strategies that are robust to the forecast errors. Furthermore, HPP sizing optimization under cost and future spot price uncertainties is planned.

Sensitivity of some key outputs for

HyDesign is an open-source code for the design and control of a utility-scale hybrid power plant (HPP) based on wind and solar storage. The documentation and interactive examples are available at (

JPML is responsible for the model development, overall implementation, and the article. HH implemented the rule-based correction method. MFM contributed to the implementation of the parallel EGO algorithm. MG contributed to the improvement of the EMS formulation. RZ contributed to the initial implementation of the battery degradation model. KD provided funding and supervision. All authors contributed to the article.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

Part of the research was performed within the REALISE project funded by EUDP (journal no. 64021-2049) and as part of the Indo-Danish project “HYBRIDize” (

This research has been supported by the EUDP-funded REALISE project (grant no. 64021-2049) and the IFD-funded HYBRIDize project.

This paper was edited by Jennifer King and reviewed by two anonymous referees.