Flexibility Models

2015

Ulbig & Andersson

Analyzing operational flexibility of electric power systems

Assess flexibility of hydro storage lake and overall power system operation

Optimization using the power node model to determine feasible operating regions and ramping capabilities

Implementation:

DOI:
10.1016/j.ijepes.2015.02.028

Asset Types:
renewable generation, conventional generation, grid infrastructure

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, ramp-rate, energy

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical

2020

Chicco et al.

Flexibility from distributed multienergy systems

Characterisation and quantification of flexibility from distributed multi-energy systems

Optimization (extended power node model and multi-energy nodes, flexibility maps)

Implementation:

DOI:
10.1109/JPROC.2020.2986378

Asset Types:
multi-energy system, CHP units, heat pumps, thermal energy storage, distributed generation

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
reactive power

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical, service-guarantees

2018

Pedersen et al.

Modeling and Managing Energy Flexibility Using FlexOffers

Market participation using FlexOffers for distributed energy resources

Forecasting and specific FlexOffer extraction algorithms (flexibility envelope construction from time series)

Implementation:

DOI:
10.1109/SmartGridComm.2018.8587605

Asset Types:
electric vehicles, flexible loads

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
reactive power

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, economic

2014

Dvorkin et al.

Assessing flexibility requirements in power systems

Flexibility requirements analysis for power systems with variable generation

Time series analysis (TSA) of net load and optimization-based assessment of flexibility requirements

Implementation:

DOI:
10.1049/iet-gtd.2013.0720

Asset Types:
renewable generation, conventional generation

Classification:
envelope

Flexibility:
requirement

Type:
probabilistic

Metric:
active power, ramp-rate, ramp duration

Uncertainty:
yes

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
economic

2009

Makarov et al.

Operational impacts of wind generation on California power systems

Flexibility requirements analysis for California power systems under high wind penetration

Scenario analysis combined with the “swinging door” algorithm for net load segmentation and ramping requirement estimation

Implementation:

DOI:
10.1109/TPWRS.2009.2016364

Asset Types:
renewable generation

Classification:
envelope

Flexibility:
requirement

Type:
probabilistic

Metric:
active power, ramp-rate, ramp duration

Uncertainty:
yes

Aggregation:
no

Time:
discrete

Resolution:
long-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
none

2017

Müller et al.

Aggregation and disaggregation of energetic flexibility from distributed energy resources

Market participation via aggregation and disaggregation of energetic flexibility from distributed energy resources

Set-based envelope modelling using zonotopes and algorithms for aggregation and disaggregation of flexibility (feasible set approximations)

Implementation:

DOI:
10.48550/arXiv.1705.02815

Asset Types:
distributed generation, flexible loads, battery storage systems

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, economic

2022

Nalini et al.

OpenTUMFlex: A flexibility quantification and pricing mechanism for prosumer participation in local flexibility markets

Prosumer participation in local flexibility markets

Optimization (MILP/Linear Programming, Energy Management System)

Implementation:
https://github.com/tum-ewk/OpenTUMFlex

DOI:
10.1016/j.ijepes.2022.108382

Asset Types:
renewable generation, distributed generation, battery storage systems, flexible loads, electric vehicles

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, energy, cost

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical, economic, service guarantees

2011

Menemenlis et al.

Thoughts on power system flexibility quantification for the short-term horizon

Operations planning (with balancing reserves) – short-term flexibility quantification

Scenario-based analysis of system adequacy and reserve requirements under uncertainty

Implementation:

DOI:
10.1109/PES.2011.6039617

Asset Types:
renewable generation, conventional generation

Classification:
metric

Flexibility:
potential

Type:
probabilistic

Metric:
energy, ramp-rate, economics

Uncertainty:
yes

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, economic

2012

Lannoye et al.

Evaluation of Power System Flexibility

Generation planning and assessment of system flexibility adequacy

Time series analysis with the insufficient ramping resource expectation (IRRE) metric for flexibility assessment

Implementation:

DOI:
10.1109/TPWRS.2011.2177280

Asset Types:
renewable generation, conventional generation

Classification:
metric

Flexibility:
requirement

Type:
probabilistic

Metric:
active power, ramp-rate

Uncertainty:
no

Aggregation:
no

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical

2025

Tiemann et al.

Amplify: Multi-purpose flexibility model to pool battery energy storage systems

peak shaving, uninterrupted power supply, self-consumption optimization, use for frequency containment reserve (FCR)

Optimization and conflict detection

Implementation:
https://gitlab.com/offis-dai/models/amplify

DOI:
10.1016/j.apenergy.2024.125063

Asset Types:
battery storage systems

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, ramp-rate, energy

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, service guarantees

2012

Bertsimas et al.

Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

Unit Commitment / Economic Dispatch with security constraints

Adaptive robust optimization formulation of security-constrained unit commitment (two-stage robust optimization with uncertainty sets)

Implementation:

DOI:
10.1109/TPWRS.2012.2205021

Asset Types:
conventional generation, grid infrastructure

Classification:
envelope

Flexibility:
requirement

Type:
deterministic

Metric:
active power

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
none

2021

Riaz & Mancarella

Modelling and Characterisation of Flexibility from Distributed Energy Resources

Market participation (distributed energy resource aggregate)

Optimization-based characterization of nodal operating envelopes and DER flexibility regions

Implementation:

DOI:
10.48550/arXiv.2107.05144

Asset Types:
distributed generation, renewable generation, battery storage systems, flexible loads

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, reactive power

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical, economic, service guarantees

2013

Ma et al.

Evaluating and planning flexibility in sustainable power systems

Evaluate and plan system flexibility for integrating large-scale wind generation in sustainable power systems

Simulation-based generation scheduling and planning (unit construction/commitment) combined with flexibility indices and long-term time series analysis

Implementation:

DOI:
10.1109/PESMG.2013.6672221

Asset Types:
renewable generation, conventional generation

Classification:
metric

Flexibility:
potential

Type:
deterministic

Metric:
active power, ramp-rate

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical

2015

Zhao et al.

A Unified Framework for Defining and Measuring Flexibility in Power System

Situational awareness tool for operator (is system flexibility sufficient?)

Flexibility metric / indicator function derived from optimization of the largest uncertainty range the system can accommodate under network and operational constraints

Implementation:

DOI:
10.1109/TPWRS.2015.2390038

Asset Types:
renewable generation, conventional generation, grid infrastructure

Classification:
metric

Flexibility:
potential

Type:
deterministic

Metric:
time, actions, cost

Uncertainty:
no

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, economic

2016

MacDougall et al.

Applying machine learning techniques for forecasting flexibility of virtual power plants

Residential virtual power plant flexibility analysis

Machine learning forecasting using multivariate linear regression and artificial neural networks on historical bidding and portfolio state data

Implementation:

DOI:
10.1109/EPEC.2016.7771738

Asset Types:
distributed generation, flexible loads

Classification:
machine learning model

Flexibility:
potential

Type:
deterministic

Metric:
duration

Uncertainty:
no

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical

2018

Förderer et al.

Modeling flexibility using artificial neural networks

Enable operator to find suitable load profiles

Machine learning using artificial neural networks as surrogate flexibility models to classify feasibility, generate and repair load profiles

Implementation:

DOI:
10.1186/s42162-018-0024-4

Asset Types:
flexible loads

Classification:
machine learning model

Flexibility:
potential

Type:
deterministic

Metric:
active power

Uncertainty:
no

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, economic

2012

Wang et al.

A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid

Storage sizing for integrating renewable energy sources into the power grid

Stochastic network calculus to derive probabilistic bounds on energy and buffer requirements

Implementation:

DOI:
10.1109/JSAC.2012.120703

Asset Types:
renewable generation, battery storage systems, grid infrastructure

Classification:
envelope

Flexibility:
requirement

Type:
probabilistic

Metric:
energy

Uncertainty:
yes

Aggregation:
yes

Time:
both

Resolution:
any

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
service guarantees

2012

Wu et al.

A stochastic calculus for network systems with renewable energy sources

Studying QoS guarantees in networked systems with renewable energy sources

Stochastic network calculus for performance and service-guarantee analysis

Implementation:

DOI:
10.1109/INFCOMW.2012.6193470

Asset Types:
renewable generation, grid infrastructure

Classification:
envelope

Flexibility:
requirement

Type:
probabilistic

Metric:
energy

Uncertainty:
yes

Aggregation:
yes

Time:
both

Resolution:
any

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
economic

2021

Xu et al.

Unit commitment of power system with large-scale wind power considering multi time scale flexibility contribution of demand response

Unit Commitment with large-scale wind power considering multi time scale flexibility contribution of demand response

Unit commitment model with technical constraints and probabilistic treatment of wind and demand response contributions

Implementation:

DOI:
10.1016/j.egyr.2021.10.025

Asset Types:
renewable generation, flexible loads

Classification:
envelope

Flexibility:
both

Type:
deterministic

Metric:
active power, ramp-rate

Uncertainty:
no

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
technical, economic

2018

Chen et al.

Aggregating flexibility of heterogeneous energy resources in distribution networks

Provide capacity reserves to the transmission system from distribution networks

Optimization-based aggregate flexibility modeling of heterogeneous energy resources

Implementation:

DOI:
10.23919/ACC.2018.8431445

Asset Types:
distributed generation, flexible loads

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power

Uncertainty:
no

Aggregation:
no

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical

2018

Huo et al.

Flexibility Envelopes for Distribution Networks

Assess flexibility requirements for distribution networks

Shift factors combined with probabilistic modeling to derive distribution-level flexibility envelopes

Implementation:

DOI:
10.1109/PESGM.2018.8586668

Asset Types:
grid infrastructure, distributed generation

Classification:
envelope

Flexibility:
requirement

Type:
probabilistic

Metric:
active power, voltage

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
no

Constraints:
none

2020

Huo et al.

Spatio-temporal flexibility management in lowcarbon power systems. IEEE Trans Sustain Energy

Unit Commitment and Economic Dispatch in low-carbon power systems with flexibility constraints

Time series analysis with probabilistic modeling of renewable generation and flexibility requirements

Implementation:

DOI:
10.1109/TSTE.2020.2967428

Asset Types:
conventional generation, renewable generation

Classification:
envelope

Flexibility:
requirement

Type:
probabilistic

Metric:
active power

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
no

Constraints:
none

2023

Lechl et al.

Aggregating multi-time-scale flexibility potentials of battery storages based on open data – a potential analysis

System-wide potential analysis – replacing gas-fired power plants with BESS flexibility

Multi-time-scale flexibility model + temporal and spatial aggregation (open data)

Implementation:

DOI:
10.1186/s42162-023-00273-4

Asset Types:
battery storage systems

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, energy, ramp-rate

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
technical, economic

2023

Wang et al.

A robust flexibility evaluation method for distributed multi-energy microgrid in supporting power distribution system

Assessment of the flexibility capability of distributed multi-energy microgrids (MEMG) to support the distribution grid

Virtual “MG Flexibility Bus” + Flexibility Parameters (MG-FPs) + 2-stage Adaptive Robust Optimization

Implementation:

DOI:
10.3389/fenrg.2022.1021627

Asset Types:
multi-energy system, CHP units, heat pumps, thermal energy storage

Classification:
envelope

Flexibility:
potential

Type:
probabilistic

Metric:
active power, heat, energy

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical, economic

2023

Muessel et al.

Accurate and scalable representation of electric vehicles in energy system models: A virtual storage-based aggregation approach

System-wide planning/simulation – realistic aggregation of EV flexibility

Virtual energy storage – flexibility as a deviation from an inflexible reference charging curve; aggregation of many EVs

Implementation:

DOI:
10.1016/j.isci.2023.107816

Asset Types:
electric vehicles

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, energy

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical, economic

2025

Öztürk et al.

A python toolbox for flexibility aggregation and disaggregation: PyFlexAD

Generic aggregation/disaggregation of DER flexibility

Quantity-based flexibility representation

Implementation:
https://github.com/erc-fhv/PyFlexAD

DOI:
10.1016/j.segan.2025.102033

Asset Types:
battery storage systems, flexible loads, distributed generation

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, energy

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical

2025

Li et al.

Research on Multi-Time Scale Flexible Resource Aggregation and Evaluation for New Power Systems

Aggregation and evaluation of flexibility resources in “new power systems”

Multi-dimensional flexibility “polymerization” process

Implementation:

DOI:
10.3390/inventions10010008

Asset Types:
renewable generation, conventional generation, grid infrastructure

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, energy, ramp-rate

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
technical, economic

2024

Ai et al.

Multi-scenario flexibility assessment of power systems considering renewable energy output uncertainty

System-wide flexibility assessment (planning/operation) in systems with a high proportion of wind/PV

Scenario-based flexibility analysis + improved hierarchical cluster analysis + flexibility indicators

Implementation:

DOI:
10.3389/fenrg.2024.1359233

Asset Types:
multi-energy system, CHP units, heat pumps, thermal energy storage

Classification:
metric

Flexibility:
requirement

Type:
probabilistic

Metric:

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
yes

Mediator:
no

Constraints:
technical, economic

2024

Zhao et al.

Real-Time Economic Dispatching for Microgrids Based on Flexibility Envelopes

Real-time economic dispatch of microgrids

Flexibility envelope-based dispatch model + comparison with heuristic control strategy

Implementation:

DOI:
10.3390/pr12112544

Asset Types:
distributed generation, battery storage systems, flexible loads

Classification:
envelope

Flexibility:
potential

Type:
deterministic

Metric:
active power, energy, cost

Uncertainty:
no

Aggregation:
yes

Time:
discrete

Resolution:
short-term

Multi-Time-Scale:
no

Mediator:
yes

Constraints:
technical, economic, service guarantees

2024

Abbà et al.

Assessing flexibility in networked multi-energy systems: A modelling and simulation-based approac

Assessment of flexibility in networked multi-energy systems

Modeling of network restrictions and coupling elements, definition of flexibility indicators

Implementation:

DOI:
10.1016/j.egyr.2023.11.049

Asset Types:
distributed generation, renewable generation, battery storage systems, flexible loads

Classification:
metric

Flexibility:
both

Type:
deterministic

Metric:

Uncertainty:
yes

Aggregation:
yes

Time:
discrete

Resolution:
any

Multi-Time-Scale:
no

Mediator:
no

Constraints:
technical, economic

List of Publications about Flexibility Models