Source-linked AI summary
Modelling and Characterisation of Flexibility\\from Distributed Energy Resources
Shariq Riaz, Pierluigi Mancarella
TL;DR
Aggregated DER flexibility lacks a clear description of its steady-state and dynamic features under network constraints and market requirements. The paper introduces a nodal operating envelope framework, built using OPF and visualized in active-reactive power space, to characterize flexibility. Canonical and real-network studies illustrate its applicability to modelling flexibility and market services.
Problem
DER aggregation flexibility lacks a clear description of steady-state and dynamic features and their relation to network constraints and market requirements.
Source: §I · p. 1Method
The framework defines capacity, ramp, duration, and cost metrics and uses consistent nodal operating envelopes, derived through OPF, to represent flexibility features.
Source: §I · p. 2Results
Canonical and real Australian-network studies demonstrate the framework's applicability; technical NOEs reflect service potential, while commercial NOEs can support bid-stack construction.
Source: §V · p. 11Takeaways & Limitations
Comparing NOEs provides insights into stakeholder roles and use cases in developing distributed energy marketplaces.
Source: §V · p. 11
Abstract
from arXiv · showhide
Harnessing flexibility from distributed energy resources (DER) to participate in various markets while accounting for relevant technical and commercial constraints is essential for the development of low-carbon grids. However, there is no clear definition or even description of the salient features of aggregated DER flexibility, including its steady-state and dynamic features and how these are impacted by network constraints and market requirements. This paper proposes a comprehensive DER flexibility modelling and characterisation framework that is based on the concept of nodal operating envelope (NOE). In particular, capacity, ramp, duration and cost are identified as key flexibility metrics and associated with different but consistent NOEs describing capability, feasibility, ramp, duration, economic, technical and commercial flexibility features. These NOEs, which conceptually arise from a Venn diagram, can be built via optimal power flow (OPF) analysis, visualised in the active-reactive power space, and used by different stakeholders. Results from a canonical test system and a real distribution system illustrate the value and applicability of the proposed framework to model and characterise provision of flexibility and market services from DER for different use cases.
I. INTRODUCTION
DER aggregation flexibility lacks a clear account of steady-state and dynamic features under network constraints and market requirements. The paper proposes a nodal operating envelope framework to characterize these features and assess market participation.
I. INTRODUCTION
- DER aggregation capacity and constraints for multi-market participation are rarely discussed, and flexibility features under network and market constraints lack clear definition.Dynamic limits such as ramp rate and energy availability may affect market participation.Source: §I · p. 1
- Capacity, ramp, duration, and cost are the key metrics, distinguishing steady-state capability from dynamic flexibility features.The framework classifies capability, feasibility, ramp, duration, economic, technical, and commercial flexibility.Source: §I · p. 2
- The framework uses a Venn-diagram-based mathematical description and consistent terminology to represent flexibility features as nodal envelopes in active-reactive power space.The envelopes represent features at different aggregation levels.Source: §I · p. 2
- OPF analysis quantifies flexibility features while accounting for operational and network limits, activation costs, and market requirements.Representing features as linear constraints is proposed to support scalability.Source: §I · p. 2
- The framework supports multi-market bid-stack creation and is illustrated with canonical and real Australian distribution-network case studies.The studies demonstrate its use in modelling DER flexibility features.Source: §I · p. 2
II. KEY CONCEPTS AND DEFINITION
The paper uses nodal operating envelopes (NOEs) to represent downstream DER operating regions at a chosen aggregation point, with virtual or physical network constraints. It characterises flexibility through capacity, ramp, duration, and cost, and illustrates the concepts with a canonical DERA example.
A. Nodal operating envelope (NOE)
- An NOE represents the aggregated operating region of downstream DER relative to a reference node, which can be virtual or a physical network node.NOEs can be represented in P-Q space or with linear constraints; the reference point can move across aggregation levels to suit the study.Source: A. Nodal operating envelope (NOE) · p. 2
B. Flexibility characterisation and definitions
- The flexibility quadruplet is capacity, ramp, duration, and cost, represented by capability or feasibility, ramp, duration, and economic NOEs, respectively.Technical and commercial flexibility additionally account for specific service requirements.Source: B. Flexibility characterisation and… · p. 3
1) Illustrative canonical example:
- The canonical example uses a diesel generator, a battery energy storage system, and a 0.47 MW, 0.22 MVAr load, with the reference node at the transformer primary.The transformer thermal limit is 1.14 MVA; the BESS is assumed charged to 2.1% of maximum energy, and both resources are dispatched at zero active and reactive power.Source: 1) Illustrative canonical example · p. 3
2) Capability:
Capability describes viable aggregated P-Q operating points for a virtual DERA, while feasibility restricts dispatch points to those compatible with the physical network. Thermal and voltage limits illustrate how network constraints shape the feasible operating region.
2) Capability:
- Aggregating the generator and BESS produces a larger capability NOE than their individual P-Q regions.The virtual DERA capability NOE is obtained by Minkowski summation of individual DER P-Q capability sets.Source: 2) Capability · p. 3
3) Feasibility:
- For a physical aggregation, thermal and voltage network constraints restrict the DERA's network-feasible P-Q dispatch points.The feasibility NOE represents the resulting operating region after accounting for those constraints.Source: 3) Feasibility · pp. 3–4, Figure 4 · p. 4
4) Ramp and duration (dynamic) flexibility:
Ramp and duration envelopes capture dynamic flexibility around a dispatch point, while the economic envelope captures the cost of deviations. Their boundaries vary with response time, service length, and allowable cost.
4) Ramp and duration (dynamic) flexibility:
- Ramp flexibility limits dispatch deviations by response time, while duration flexibility limits them by how long the response can be sustained.Ramp capability, commitment status, dispatch point, and DER energy content shape these envelopes.Source: 4) Ramp and duration (dynamic)… · p. 4
- RFE grows with response time, whereas DFE shrinks with service length because energy-constrained resources cannot sustain the same deviation for longer.The test DERA is shown under virtual and physical aggregation arrangements.Source: 4) Ramp and duration (dynamic)… · p. 4, Figure 6 · p. 4
5) Economic flexibility:
- The EFE bounds deviations by cost and reflects DER financial willingness to deviate from dispatch, with the envelope increasing proportionally to allowable cost.Deviation costs can include fuel, maintenance, lost opportunity, storage buy-back, and other factors.Source: 5) Economic flexibility · p. 4
6) Technical and commercial (market specific) flexibility:
Technical and commercial flexibility describe service-specific participation limits beyond a DERA’s general flexibility potential. They incorporate technical requirements and, for commercial flexibility, economic restrictions.
6) Technical and commercial (market specific) flexibility:
- Capability, feasibility, ramp, duration, and economic NOEs describe flexibility potential independently of a particular service requirement.Technical and commercial flexibility instead address participation in a particular service or market segment.Source: 6) Technical and commercial (market… · pp. 4–5
- Technical flexibility measures deviation from current dispatch under service-specific constraints, represented here by response time and call length.The paper notes that other relevant constraints should be included for a specific service.Source: 6) Technical and commercial (market… · p. 5
- Commercial flexibility combines technical limits with economic restrictions, using response time, service duration, and anticipated clearance price.Its five-dimensional representation includes active power, reactive power, response time, duration, and cost; iso-cost contours can reflect short-run marginal cost for a service.Source: 6) Technical and commercial (market… · p. 5, Figure 9 · p. 5
C. Flexibility features and use cases
The paper describes how stakeholders can use NOEs in markets and across timescales, and how the approach scales through network aggregation levels. It also outlines set-based aggregation for virtual DERAs and the added complexity of physical networks.
C. Flexibility features and use cases
- Aggregators can send capability NOEs to the DSO for network capacity allocation, then use allocated capacity to plan market participation and inform bids and dispatch.Commercial NOEs can support bid-stack construction, while technical NOEs communicate service limitations.Source: C. Flexibility features and use cases · pp. 5–6, Figure 11 · p. 6
D. Implementation timescales and use cases
- NOEs can be calculated per market clearance interval and extended from contingency analysis and real-time operation to operational and long-term planning.Examples include FCAS allocation, next-day hosting-capacity allocation, and system adequacy studies spanning a week to years.Source: D. Implementation timescales and use… · p. 6
E. Scalability and applications of the NOE approach
- NOEs can scale from individual DER and feeders to higher-voltage aggregation points, with feasibility envelopes representing time-varying hosting capacity.The three-feeder example aggregates feeder envelopes, then combines them with a generator to form the system feasibility NOE.Source: E. Scalability and applications of the… · p. 6, Figure 12 · p. 6
III. NODAL OPERATING ENVELOPE MODELLING FRAMEWORK
- Virtual DERA envelopes can be formed by Minkowski summation of individual DER operating regions, whereas physical-network envelopes face nonlinear coupling constraints.The paper illustrates Minkowski addition in P-Q space.Source: §III · p. 6
A. General modelling options considering network
The framework extends optimization-based NOE modelling to multiple flexibility features, while contrasting it with Monte Carlo estimation. Its optimization procedure finds power limits and traces the envelope boundary using AC-OPF.
A. General modelling options considering network
- AC-OPF optimization finds the minimum and maximum active and reactive import limits, then samples boundary points or active-power ranges across reactive-power intervals.Four initial runs establish the NOE’s minimum bounding box.Source: A. General modelling options… · p. 7
- Monte Carlo estimation discards power-flow points violating network constraints and takes the convex hull of the remaining points, but accurate estimation can be time-demanding.The number of power-flow instances grows exponentially with DER count and parameters of interest, while few sampled points lie on the boundary.Source: A. General modelling options… · p. 7
- The framework extends optimization-based modelling to build coherent NOEs for feasibility, ramp, duration, economic, technical, and commercial flexibility.Earlier network-aware methods addressed feasibility NOEs only, according to the paper.Source: A. General modelling options… · pp. 6–7
1) Objective function:
- The optimization objective minimizes or maximizes active or reactive DERA power import, with parameter choices depending on the required NOE granularity.The framework’s inputs include DER dispatch, deviation, response-time, call-length, and cost parameters.Source: 1) Objective function · p. 7
2) Constraints:
The constraints represent network operating limits and DER capabilities alongside bounds on resource deviations, storage energy, and deviation costs.
2) Constraints:
- AC power flow, line thermal, bus-voltage, and branch-angle limits constrain the model, alongside DER active/reactive power, power-factor, and inverter-rating bounds.DER bounds include generator capability maps and battery charge/discharge rates.Source: 2) Constraints · p. 7
- Storage deviations must preserve energy for the market commitment and sustain the deviated operating point for the maximum service duration.The state-of-charge constraint keeps storage within its minimum and maximum limits during service.Source: 2) Constraints · p. 7
- Resource deviation costs are captured per MWh or MVArh, with a maximum cost associated with deploying a specified flexibility amount.The constraints applicable to each NOE are listed in Table II.Source: 2) Constraints · p. 7, Table II · p. 8
C. Methodology to build NOEs for various flexibility features
The method estimates NOE boundaries in P-Q space through repeated optimisation, with sampling granularity and market parameters shaping the resulting envelopes.
C. Methodology to build NOEs for various flexibility features
- For a given combination of response time (τ), call length (ψ), and cost (c), the methodology generates 4 + 2K P-Q boundary points, each obtained using AC-OPF and relevant NOE constraints.The parameters can be selected based on market specifications; other market-specific constraints beyond response time and call length can be added as required.Source: C. Methodology to build NOEs for… · p. 8
- The procedure first solves four optimisations for extreme P-Q points, then selects K equidistant intermediate reactive-power points to set envelope granularity.K can be chosen to achieve the required number of points per MVAr.Source: C. Methodology to build NOEs for… · p. 8
- For each intermediate reactive-power value, the method minimises active-power import, repeats the optimisation to find its maximum, and estimates one operating snapshot.The optimisation runs can be parallelised.Source: C. Methodology to build NOEs for… · p. 8
IV. CASE STUDY APPLICATIONS
The case study applies the framework to a real distribution network and considers market services, including symmetric reserve, to demonstrate the NOE methodology.
A. Test Network
- The real Australian medium-voltage network has 93 nodes at 22 kV, 3,136 customers, rooftop PV at 695 customers, and eight 1.1-MVA diesel units.The network has 2.3 MVA of rooftop PV and average storage of 1 MWh per MW of installed PV.Source: A. Test Network · p. 8
- The demonstration assumes offline diesel generators, batteries at 30% average state of charge, and negligible rooftop-PV generation; one aggregator controls all DER.The assumed load demand is 7.4 MW and 3.1 MVAr, with nominal voltage bounds of ±5%.Source: A. Test Network · p. 8
1) Symmetric reserve:
- In symmetric reserve markets, all participants must provide equal upward and downward flexibility; Fig. 15 presents boundary points, associated linear constraints, and resulting feasibility NOE for K = 10 and K = 20.Source: 1) Symmetric reserve · p. 8, Figure 15 · p. 9
3) Contingency frequency controlled ancillary services (FCAS):
The case study illustrates how market requirements shape technical and commercial flexibility envelopes, while the scalability analysis quantifies a potential computation-time reduction through distributed calculation.
3) Contingency frequency controlled ancillary services (FCAS):
- The FCAS markets require responses within 6, 60, or 300 seconds, sustained for 60 seconds, 5 minutes, or 10 minutes, respectively.These response and sustain times apply to fast, slow, and delayed FCAS, respectively.Source: 3) Contingency frequency controlled… · p. 9
C. Scalability and accuracy of the approach
- For 20 replicated feeders (1,860 nodes), distributed calculation reduces total computation time from 116 s to about 23 s in this case study.The reported distributed calculation takes 13 s per feeder and another 10 s for the substation NOE; benefits require case-by-case assessment.Source: C. Scalability and accuracy of the… · p. 9
D. Flexibility features and NOEs discussion
- Technical envelopes define DERA market-segment participation capability; in this case, FCAS is ramp-limited while demand response is duration-limited.Fig. 18 presents technical envelopes for symmetric reserve, demand response, and FCAS.Source: D. Flexibility features and NOEs… · pp. 9–10, Figure 18 · p. 9
- Delayed-raise FCAS commercial envelopes match economic envelopes, while 4-hour long-DR is more constrained and costlier because batteries lack energy for maximum output.For delayed raise FCAS, ramp and duration are nonbinding; for long-DR, the cheaper batteries cannot sustain maximum output for the full call length.Source: D. Flexibility features and NOEs… · p. 10
- Commercial NOEs can support bid-stack construction for individual market segments, but the methodology does not optimise a DERA’s participation across multiple markets.The bid-stack example covers long-DR and delayed-raise FCAS.Source: Figure 20 · p. 10
V. CONCLUSION
The paper presents an NOE-based framework for assessing DER flexibility while accounting for reactive power and network constraints. Its case studies show how distinct NOEs capture service and market features and support different stakeholder use cases.
V. CONCLUSION
- The framework represents capability, feasibility, ramp, duration, economic, technical, and commercial flexibility through constraints and P-Q operational maps built using OPF-based methodologies.The paper identifies virtual and physical DER aggregations as its starting distinction.Source: §V · p. 10
- Feasibility, ramp, duration, and economic NOEs show impacts of network constraints, response time, call length, and cost; capability measures overall capacity, while technical and commercial NOEs represent service potential and bid stacks.The NOE comparison also offers insights for stakeholders and use cases in distributed energy marketplaces.Source: §V · pp. 10–11
- Further work includes detailed NOE modeling for unbalanced LV networks and incorporating uncertainty into the framework.The paper notes Monte Carlo simulations, robust optimisation, and multiparametric programming as potential approaches to uncertainty.Source: §V · p. 11
A. Ramp flexibility NOE
- Ramp flexibility NOE (RFE) measures the speed of operating-point changes across active power, reactive power, and response time while considering network constraints.Intersections with response-time planes form iso-ramp contours.Source: A. Ramp flexibility NOE · p. 11, Figure 21 · p. 11
- Duration flexibility NOE (DFE) describes the ability to sustain a response across active power, reactive power, and service duration while considering network constraints.Intersections with service-duration planes form iso-duration contours.Source: B. Duration flexibility NOE · p. 11, Figure 22 · p. 11
C. Economic flexibility NOE
- Economic flexibility NOE (EFE) reflects the cost of deviating from the operating point across active power, reactive power, and cost while considering network constraints.Intersections with cost planes form iso-cost contours.Source: C. Economic flexibility NOE · p. 11, Figure 23 · p. 11