A review of optimization modeling and solution methods in renewable energy systems

doi:10.1007/s42524-023-0271-3

Front. Eng

2023, Vol. 10

Issue (4) : 640-671 https://doi.org/10.1007/s42524-023-0271-3

REVIEW ARTICLE

A review of optimization modeling and solution methods in renewable energy systems

Shiwei YU(

), Limin YOU, Shuangshuang ZHOU

Center for Energy Environmental Management and Decision-making, China University of Geosciences, Wuhan 430074, China; School of Economics and Management, China University of Geosciences, Wuhan 430074, China

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Abstract

The advancement of renewable energy (RE) represents a pivotal strategy in mitigating climate change and advancing energy transition efforts. A current of research pertains to strategies for fostering RE growth. Among the frequently proposed approaches, employing optimization models to facilitate decision-making stands out prominently. Drawing from an extensive dataset comprising 32806 literature entries encompassing the optimization of renewable energy systems (RES) from 1990 to 2023 within the Web of Science database, this study reviews the decision-making optimization problems, models, and solution methods thereof throughout the renewable energy development and utilization chain (REDUC) process. This review also endeavors to structure and assess the contextual landscape of RES optimization modeling research. As evidenced by the literature review, optimization modeling effectively resolves decision-making predicaments spanning RE investment, construction, operation and maintenance, and scheduling. Predominantly, a hybrid model that combines prediction, optimization, simulation, and assessment methodologies emerges as the favored approach for optimizing RES-related decisions. The primary framework prevalent in extant research solutions entails the dissection and linearization of established models, in combination with hybrid analytical strategies and artificial intelligence algorithms. Noteworthy advancements within modeling encompass domains such as uncertainty, multienergy carrier considerations, and the refinement of spatiotemporal resolution. In the realm of algorithmic solutions for RES optimization models, a pronounced focus is anticipated on the convergence of analytical techniques with artificial intelligence-driven optimization. Furthermore, this study serves to facilitate a comprehensive understanding of research trajectories and existing gaps, expediting the identification of pertinent optimization models conducive to enhancing the efficiency of REDUC development endeavors.

Keywords renewable energy system bibliometrics mathematical programming optimization models solution methods

Corresponding Author(s): Shiwei YU

Just Accepted Date: 10 October 2023 Online First Date: 22 November 2023 Issue Date: 07 December 2023

Cite this article:

Shiwei YU,Limin YOU,Shuangshuang ZHOU. A review of optimization modeling and solution methods in renewable energy systems[J]. Front. Eng, 2023, 10(4): 640-671.

URL:

https://academic.hep.com.cn/fem/EN/10.1007/s42524-023-0271-3
https://academic.hep.com.cn/fem/EN/Y2023/V10/I4/640

AI	Artificial intelligence
AHP	Analytic hierarchy process
APSO	Adaptive particle swarm optimization
BESS	Battery energy storage system
BP	Bilevel programming
CCHP	Combined cooling, heating, and power
CDPSO	Chaotic Darwinian particle swarm optimization
CVaR	Conditional value-at-risk
DDRO	Data-driven robust optimization
DE	Differential evolution
DEA	Data envelopment analysis
DL	Deep learning
DNP	de Novo programming
DP	Dynamic programming
DPPO	Distributed proximal policy optimization
DR	Demand response
DRG	Distributed renewable generation
DRL	Deep reinforcement learning
DROCCP	Distributed robust optimization chance constraint programming
DSM	Demand-side management
DSO	Distribution system operator
EFI	Ecological footprint index
ELECTRE	Elimination et choice translating reality
EV	Electric vehicle
FCP	Fuzzy compromising
FIT	Feed-in tariff
FL	Fuzzy logic
FMCDA	Fuzzy multicriteria decision analysis
GA	Genetic algorithm
GEP	Generation expansion planning
GHG	Greenhouse gas
GP	Goal programming
GRG	Generalized reduced gradient
GTEP	Generation and transmission expansion planning
HRES	Hybrid renewable energy system
IoT	Internet of Things
KKT	Karush?Kuhn?Tucker
LCA	Life cycle assessment
LCOE	Levelized cost of electricity
LP	Linear programming
LPSP	Loss of power supply probability
MADM	Multiattribute decision making
MC	Markov chain
MCDM	Multicriteria decision making
MCS	Monte Carlo simulation
MILP	Mixed integer linear programming
MINLP	Mixed integer nonlinear programming
ML	Machine learning
MO	Multiobjective
MODM	Multiobjective decision making
MOGA	Multiobjective genetic algorithm
MOGSO	Multiobjective glow-worm swarm optimization
MOGWO	Multiobjective gray wolf optimizer
MOPs	Multiobjective optimization problems
MOPSO	Multiobjective particle swarm optimization
MOWDO	Multiobjective wind-driven optimization
MPEC	Mathematical program with equilibrium constraints
NLP	Nonlinear programming
NPV	Net present value
NSGA	Nondominated sorting genetic algorithm
OPF	Optimal power flow
PDF	Probability distribution function
PPO	Proximal policy optimization
PSO	Particle swarm optimization
QPP	Quadratic programming problem
RE	Renewable energy
REDUC	Renewable energy development and utilization chain
RES	Renewable energy system
RL	Reinforcement learning
RO	Robust optimization
RPS	Renewable portfolio standard
SAE	Stacked autoencoder
SAIFI	System average interruption frequency index
SD	System dynamics
SP	Stochastic programming
SQP	Sequential quadratic programming
SVR	Support vector regression
TEP	Transmission expansion planning
TOPSIS	Technique for order of preference by similarity to ideal solution
UC	Unit commitment
WOS	Web of Science
WPM	Weighted product model
WSM	Weighted sum model

List of abbreviations

Fig.1 Components of the renewable energy system (RES) and subsystems.

Fig.2 General procedure and flowchart of RES optimization.

Tab.1 Research results from the WOS search

Fig.3 (a) Publications, (b) Citations, and article type (pie chart) and citation of a single article on average (point and line) in (a).

Fig.4 (a) The most popular journals by publications and citations; (b) Most popular research areas, JCR rank, and most popular keywords.

Fig.5 (a) Network visualization occurrences; (b) Overlay visualization average publication per year occurrence for author keywords in all fields.

Fig.6 RES modeling in the optimal planning and operation of subsystems.

Decision objective	Criteria/Constraint	Description
Economic	Total annual cost or annual system cost (Xuan et al., 2021)	All costs for capital, installation, operation, and delivery
	Net present value (NPV) (Li et al., 2016; Tezer et al., 2017)	The sum of lifetime incoming and outgoing cash in the form of discounted present values
	Levelized cost of electricity (LCOE) (Memon et al., 2021; Chennaif et al., 2022)	For generation: The ratio of total antioxidant capacity (TAC) to the total generated energy For storage: Costs and energy consumed per operating hour
	Life cycle cost (Tezer et al., 2017; Chennaif et al., 2022)	All expenses are expected to occur, except manufacturing and disposal costs
	Life cycle unit cost (Tezer et al., 2017)	Unit energy cost is calculated by dividing life cycle cost by the total energy produced
	Cumulative savings (Afful-Dadzie et al., 2017)	Sum of money saved due to fuel saving
	Fuel consumption (Gbadamosi et al., 2018; Xu et al., 2020)	The total amount of energy consumption by nonrenewable plants
	Learning rate (Yu et al., 2022)	The cost reduction path of RES-related technologies
Technical	Loss of power supply probability (LPSP) (Feng et al., 2018; Memon et al., 2021)	The probability of load deficit over total energy produced
	Difference in net loads (Feng et al., 2018)	Load shifting capacity to smooth the difference between load peaks and valleys
	Loss of load risk (Sinha and Chandel, 2015)	The probability of failure to meet daily energy demand for RE generation
	Loss of energy or load hours expectation (Tezer et al., 2017)	The excepted number of hours for energy or load deficit, exceeding available generation capacity, excluding breakdown and maintenance time
	Unmeet load (Sinha and Chandel, 2015; Dehghan and Amjady, 2016)	The ratio of unsatisfied load to total load after consuming power generation and storage
	Loss of power produces probability (Feng et al., 2018)	Expected probability of energy surplus
	Variable renewable energy (VRE) curtailment rate (Peker et al., 2018; Xu et al., 2020)	Maximum VRE share allowed to be curtailed
	Renewable energy penetration (Liu et al., 2022a)	The ratio of energy generated from RE to total load demand
Social	Job creation (Al-Falahi et al., 2017; Atabaki and Aryanpur, 2018)	Job amounts created by RES, including manufacturing, installation, and operation and maintenance (O&M), throughout the lifetime of components
	Human Development Index (Al-Falahi et al., 2017)	A country development indicator considering life expectancy at birth, years of schooling, and average national income, related to power consumption
	Herfindahl–Hirschman Index (HHI) or Shannon–Weiner Index (Grubb et al., 2006)	Describe diversification of the energy matrix
	Social acceptance (Stigka et al., 2014)	Social performance evaluation criteria to consider social resistance to the installation of RES
	Social cost of carbon (Koltsaklis et al., 2014; Xu et al., 2020)	An additional cost is imposed on society
Environmental	Total CO₂ or fuel emission (Atabaki and Aryanpur, 2018; Hu et al., 2019)	The total amount of CO₂ emissions produced by the system
	Land use (Wang, 2023)	The area of renewable power related land
	Ecological footprint index (EFI) (Fakher et al., 2023)	The comprehensive resource pressure of environmental degradation
	Life cycle assessment (Li et al., 2011; Yu et al., 2019)	The cost includes pollution, health effects, and environmental impacts

Tab.2 Summary of evaluation criteria in RES modeling

Fig.7 Framework of optimization models in RES.

Fig.8 Principle of programming models in RES.

Fig.9 Dynamic programming models in RES.

Fig.10 Bilevel optimization models in RES.

Fig.11 MADM and MODM models in the RE system.

Fig.12 Game models in RES.

Fig.13 Hybrid models and interrelationships in RES.

Models		Advantages	Limitations
Programming models	LP	·Most widely used in every corner of RES ·Have mature solvers	·Limited linear relation and expression ·Strictly rely on data accuracy
	NLP	·Iteration methods and lots of heuristic algorithms ·Optimal power flow question	·Local optimum ·Possible severe scarcity by means of linearization
	MILP	·Decision on integer results ·Help decide whether to do, e.g., RE facility location problem	·High requirements for algorithm accuracy ·Hard to solve large-scale models by an exact algorithm
	DP	·Widely used in optimization with risks and uncertainties ·Solve problems with multistage attribute	·Curse of dimensionality ·Large space requirement
	SP	·Uncertainty decisions in RESs ·Flexible and alternative models	·Difficult to analyze the running time ·Unknown probability of getting an incorrect solution
	BP	·Interaction between different decision-makers ·Suitable with different energy sectors or subsystems of RES	·Difficult to guarantee the optimal solution ·May only get the strong stationary solution
MCDM models	MODM	·Economic, technical, environmental, and social perspectives ·Suitable with conflicts in energy management and decision	·Hard to deal with inconsistent units among objectives ·Optimal Pareto fronts are hard to obtain
MCDM models	MADM	·Evaluate the characteristic properties comprehensively ·Compare or rank for schemes	·Strong subjectivity to determine the weight ·Unable to provide new alternatives for decision-making
Games models	Noncooperative game	·Players make decisions independently	·Individual rationality ·Statistical decision and equilibrium process
	Cooperative game	·Profit maximization and distribution of RES	·Collective rationality ·Statistical decision and equilibrium process
	Evolutionary game	·Dynamic equilibrium process ·Relaxes “rational man” and “complete information” assumptions	·Evolutionary stable strategy derivation limitation ·Unable to characterize the uncertain decision
Hybrid models	With prediction/simulation/assessment models	·Higher applicability and validity ·Complements theory for the optimization mechanism ·Data and result evaluation support	·Complexity of system and information exchange ·Difficult to link and balance different models

Tab.3 Comparison of different models

Fig.14 Solution methods for the optimization model in RES.

Tab.4 Comparison of different types of solution methods

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