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Grid-side Flexibility of Power Systems in Integrating Large-scale Renewable Generations: A Critical Review on Concepts, Formulations and Solution Approaches

Jia Li, Feng Liu, Zuyi Li, Chengcheng Shao, Xinyuan Liu

arXiv:1805.12452v2math.OC

TL;DR

Uncertain renewable generation makes power-system security and economics challenging, while grid-side operational flexibility has not been fully investigated. This review defines and explains the concept, then surveys formulations and solution approaches for operation and planning. It also outlines future research directions and challenges, including nonlinear and time-scale issues in multi-energy co-optimization.

  • Problem

    Grid-side operational flexibility has not been fully investigated, despite challenges to power-system security and economics from uncertain renewable generation.

    Source: §1 · p. 1

  • Method

    The review defines grid-side flexibility, explains it physically and mathematically with geometric examples, and surveys operational and planning formulations and solution approaches.

    Source: §1 · p. 3

  • Results

    The review presents conceptual examples of grid-side flexibility’s impacts and surveys two major formulation types and their solution approaches.

    Source: §2.4 · pp. 12–13, §4.2.1 · p. 17, §6 · p. 22

  • Takeaways & Limitations

    The review identifies future research directions and challenges for grid-side flexibility, including multi-energy co-optimization’s nonlinear constraints and differing operational time scales.

    Source: §6 · p. 22, §5.5 · p. 22

    Multi-energy co-optimization remains difficult because of massive nonlinear constraints and distinct energy-system time scales, requiring careful accuracy–tractability trade-offs for approximations.

    Source: §5.5 · p. 22

Abstract

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Though considerable effort has been devoted to exploiting generation-side and demand-side operational flexibility in order to cope with uncertain renewable generations, grid-side operational flexibility has not been fully investigated. In this review, we define grid-side flexibility as the ability of a power network to deploy its flexibility resources to cope with the changes of power system state, particularly due to variation of renewable generation. Starting with a survey on the metrics of operational flexibility, we explain the definition from both physical and mathematical point of views. Then conceptual examples are presented to demonstrate the impacts of grid-side flexibility graphically, providing a geometric interpretation for a better understanding of the concepts. Afterwards the formulations and solution approaches in terms of grid-side flexibility in power system operation and planning are reviewed, based on which future research directions and challenges are outlined.

1. Introduction

Variable renewable generation creates security and economic challenges, while existing generation- and demand-side flexibility has received more attention than grid-side flexibility. The review introduces grid-side flexibility and surveys its concepts, formulations, solution approaches, and research challenges.

1. Introduction

  • Renewable generation’s intermittency and low predictability create security and economic challenges that require power-system flexibility.Source: §1 · p. 1
  • Grid-side flexibility has received less attention than generation- and demand-side flexibility, despite network constraints creating congestion and voltage-stability concerns.Renewable output deviations can raise operating risk or congestion, increase costs, and limit other flexibility resources; reactive-power needs add voltage-instability risk.Source: §1 · pp. 2–3
  • Prior reviews address flexibility potentials, supply- and demand-side approaches, and flexibility impacts, but the authors identify a lack of comprehensive reviews on grid-side flexibility.Source: §1 · p. 3
  • The review introduces grid-side flexibility’s physical and mathematical concepts, geometric interpretation, operational and planning formulations, solution approaches, and future challenges.It presents the concept as a supplement to generation- and demand-side flexibility for accommodating uncertainty.Source: §1 · pp. 2–3

2. Concepts of Grid-side Flexibility

The section reviews power-system flexibility metrics, explains grid-side flexibility from physical and mathematical perspectives, and uses visualizations to illustrate resource impacts.

2. Concepts of Grid-side Flexibility

  • The section surveys metrics of power-system flexibility before explaining grid-side flexibility.Source: §2 · p. 4
  • It explains grid-side flexibility from both physical and mathematical perspectives.Source: §2 · p. 4
  • Straightforward visualizations provide an intuitive view of the impacts of different grid-side flexibility resources.Source: §2 · p. 4

2.1. Literature Review of Flexibility Metrics

Existing flexibility metrics cover operational and planning questions, but the review finds no comprehensive metric that explicitly quantifies grid-side flexibility with respect to renewable generation. It surveys operational measures and planning metrics, while noting that network topology, parameters, and resource constraints shape grid-side flexibility.

2.1. Literature Review of Flexibility Metrics

  • No comprehensive metric explicitly quantifies grid-side flexibility with respect to renewable generation, and flexibility depends on network and generation- and demand-side constraints.Source: §2.1 · p. 4

2.1.1. Power System Operation

  • Operational metrics range from generator ramping and reserve measures to feasible flexibility regions and multidimensional capacity, ramp-rate, and energy characterizations.Some measures account for security criteria or renewable uncertainty; the cited metrics include flying-brick, flexibility cube, and flexibility envelope concepts.Source: §2.1.1 · pp. 5–6

2.1.2. Power System Planning

  • Planning metrics include IRRE and PFD for flexibility adequacy, and transmission-expansion measures based on expected unserved load or branch distribution factors weighted by margins.IRRE highlights time horizons of possible flexibility shortfalls, while a smaller value of the cited network metric indicates greater flexibility.Source: §2.1.2 · pp. 6–7
  • Transmission constraints significantly affect the use of operational flexibility resources.Source: §2.1.2 · p. 6

2.2. Physical Explanation of Grid-side Flexibility

The paper defines grid-side flexibility as a network’s use of flexibility resources to respond to volatile changes in system state. It distinguishes discrete topology controls from continuous power-flow controls and reviews their use individually and in combination.

2.2. Physical Explanation of Grid-side Flexibility

  • Grid-side flexibility is a network’s ability to deploy flexibility resources to cope with volatile changes in power-system state.Operational flexibility is framed as responding to changes in net load, the system load remaining after variable generation.Source: §2.2 · p. 7

2.2.1. Discrete Flexibility Resources

  • Line switching changes network topology and power-flow distribution to alleviate congestion, but its discrete control has limited accuracy and adds N-1 contingency complexity.It has been studied for corrective flow violations, contingency security, congestion management, and uncertainty-aware optimization.Source: §2.2.1 · p. 9

2.2.2. Continuous Flexibility Resources

  • FACTS and HVDC provide continuous grid-side control; FACTS can rapidly regulate transmission parameters, while VSC-HVDC enables faster, reversible, decoupled active- and reactive-power control.The review describes applications of FACTS and HVDC to renewable integration, congestion mitigation, and post-disturbance control.Source: §2.2.2 · pp. 9–10

2.2.3. Combination of Discrete and Continuous Flexibility Resources

  • Combining discrete and continuous resources may better exploit grid-side flexibility, and studies include FACTS or HVDC in transmission planning.FACTS may reduce or defer the need for new transmission lines.Source: §2.2.3 · p. 10

2.3. Mathematical Definition of Grid-side Flexibility

The mathematical formulation represents grid-side flexibility through controllable network variables and the uncertain injections they can accommodate. Its region is the additional admissible injection space relative to a case without grid-side flexibility.

2.3. Mathematical Definition of Grid-side Flexibility

  • Grid-side resources add controllable variables to network constraints to control power flow, within an extended steady-state security region defined using injections, line availability, voltage, and network constraints.The formulation includes active and reactive injections and constraints covering steady-state operation, economic dispatch, transmission expansion, and line switching.Source: §2.3 · p. 10
  • An admissible region contains uncertain active and reactive injections for which at least one choice of controllable injections and line availability satisfies the extended security region.The controllable variables include reference-bus and other flexibility-resource injections; the uncertain injections represent renewable generation.Source: §2.3 · p. 11
  • The grid-side flexibility region is the additional admissible region compared with the corresponding region when grid-side flexibility is omitted.Fixing grid-side resource variables and considering only economic-dispatch constraints makes the extended security region equivalent to the conventional steady-state security region.Source: §2.3 · p. 11
  • The grid-side flexibility region may be discrete or continuous and is associated with mixed-integer nonlinear, non-convex constraints.Its discrete or continuous character depends on the uncertain injection variables.Source: §2.3 · p. 11

2.4. Geometric Interpretation

A modified three-bus DC system illustrates how grid-side flexibility resources change admissible regions for uncertain renewable injections. The examples compare a FACTS device, a new line, and line switching.

2.4. Geometric Interpretation

  • The example uses a modified three-bus system with DC power flow and constructs admissible regions using Fourier-Motzkin elimination.It compares regions for different grid-side flexibility resources under specified line and injection limits.Source: §2.4 · pp. 11–12, Figure 2 · p. 12
  • The extended steady-state security region is represented by a gray hexagonal region in Figure 2.The passage identifies the region's shape and color but does not specify its underlying boundary values.Source: §2.4 · p. 12
  • A series FACTS device expands the admissible range of P1 for any given P2 by regulating flow through line 1-3.The example assumes a 0.5 p.u. FACTS capacity on line 1-3.Source: §2.4 · pp. 12–13
  • A new line expands the admissible range of P1 further than FACTS, but within a slightly smaller range of P2.The example doubles corridor 1-3 transmission capacity.Source: §2.4 · p. 13
  • Line switching makes the admissible region concave by taking the union of regions for line 1-3 on and off.The resulting two triangular grid-side flexibility regions depend on system parameters and operational state.Source: §2.4 · p. 13

3. Problem Formulations Corresponding to Grid-side Flexibility

The review organizes grid-side flexibility formulations by how they represent uncertainty, covering stochastic programming and robust optimization approaches. It surveys representative modeling variants and their uses in operation and transmission planning.

3. Problem Formulations Corresponding to Grid-side Flexibility

  • Stochastic programming assumes the uncertainty probability distribution is available and generally minimizes expected total cost.The review introduces scenario-based, point-estimation, and chance-constrained variants.Source: §3 · p. 13, §3.1 · p. 13

3.1.1. Scenario-Based Model

  • Scenario-based models generate discrete realizations from a presumed distribution, trading solution accuracy against computational burden and possible intractability.Applications include wind spillage minimization with FACTS, multi-period OPF with an offshore wind farm and LCC-HVDC, and transmission expansion planning.Source: §3.1.1 · p. 14

3.1.2. Point-Estimation-Based Model

  • Point-estimation methods approximate statistical information of functions associated with random variables for transmission expansion and probabilistic OPF planning.The reviewed work includes two-point estimation and an approximate (2m+1)-scheme.Source: §3.1.2 · p. 14

3.1.3. Chance-Constrained Programming Model

  • Chance-constrained programming permits constraint violations with a predefined small probability and is applied to renewable uncertainty, controllable power flows, and line switching.Reviewed applications include OPF, HVDC and multi-terminal HVDC, and transmission expansion planning.Source: §3.1.3 · pp. 14–15

3.2. Robust Optimization

  • Robust optimization uses uncertainty sets without requiring probability distributions and protects against all realizations within the set, but may be over-conservative.The review describes its information needs as moderate, such as means and ranges of uncertain variables.Source: §3.2 · p. 15

3.2.1. Uncertainty-Set-Based Model

  • Uncertainty-set-based robust models use polyhedral sets and minimize worst-case costs or regret in transmission expansion planning and line switching.The reviewed frameworks include single-stage and two-stage models.Source: §3.2.1 · p. 15

3.2.2. Taguchi’s Orthogonal-Array-Testing-Based Model

  • Taguchi orthogonal-array testing selects representative worst-case scenarios from approximate uncertainty-space corners to reduce the number of tests.The review cites a robust transmission expansion planning method considering load and renewable uncertainty.Source: §3.2.2 · p. 15

3.2.3. Information-Gap-Decision-Theory-Based Model

  • Information-gap decision theory bounds the allowable objective-function range by an uncertainty budget to find a robust feasibility region.The reviewed transmission-planning framework models capital-cost and electricity-demand uncertainty and explicitly represents robustness cost.Source: §3.2.3 · p. 15

4. Solution Approaches

The section reviews solution approaches used to solve the formulations introduced in Section 3.

4. Solution Approaches

  • The section surveys methods for solving the grid-side flexibility problems formulated in Section 3.Source: §4 · p. 15

4.1. Stochastic Programing

The review summarizes solution techniques for stochastic formulations, including scenario-based, point-estimation, and chance-constrained models.

4.1.1. Scenario-Based Model

  • Stochastic programming models can use commercial solvers for NLP or MILP formulations, while decomposition and sequential approximation address computational efficiency or two-stage planning.Benders decomposition adds cuts to a master problem; Dantzig-Wolfe adds columns, and sequential approximation iteratively solves a two-stage stochastic problem.Source: §4.1.1 · p. 16

4.1.2. Point-Estimation-Method-Based Model

  • NSGA II is used for point-estimation stochastic transmission expansion planning with nonlinear and mixed-integer features.The algorithm ranks Pareto fronts and uses tournament selection, crossover, and mutation to form successive populations.Source: §4.1.2 · p. 16

4.1.3. Chance-Constrained Model

  • Chance constraints can be transformed into deterministic nonlinear constraints under a normality assumption and solved with KNITRO.Source: §4.1.3 · p. 16
  • Sample average approximation estimates constraint-satisfaction probability from sampled scenarios for chance-constrained line switching.Other reviewed approaches use scenario-based minimum-volume sets followed by robust optimization, or a two-step genetic algorithm for transmission expansion.Source: §4.1.3 · pp. 16–17

4.2. Robust Optimization

The review surveys robust-optimization solution approaches for grid-side flexibility, covering uncertainty-set-based, Taguchi orthogonal-array-testing-based, and information-gap-decision-theory-based models. It summarizes the associated formulations and solution approaches.

4.2.1. Uncertainty-Set-Based Model

  • Two-stage uncertainty-set robust models use decomposition or metaheuristics, with C&CG’s primal cuts improving computational performance over Benders but enlarging the master problem more per iteration.The added variables and constraints can make the master problem intractable after many iterations; adaptive Tabu search and a greedy-search/PSO hybrid are alternative approaches.Source: §4.2.1 · p. 17

4.2.2. Taguchi’s Orthogonal-Array-Testing-Based Model

  • A Taguchi orthogonal-array-testing-based robust transmission-planning model is solved with a genetic algorithm whose initial population represents different testing scenarios.A scheme set stores checked plans and results to avoid rechecking candidates across random generations.Source: §4.2.2 · pp. 17–18

4.2.3. Information-Gap-Decision-Theory-Based Model

  • For robust transmission planning using information-gap decision theory, an augmented ε-constraint method uses lexicographic optimization to set effective objective ranges and seeks Pareto-efficient solutions.The augmented method optimizes a main augmented objective selected from the objectives.Source: §4.2.3 · p. 18

4.2. Robust Optimization

  • Table 2 summarizes formulations and solution approaches from studies associated with grid-side flexibility.The review organizes robust approaches in three categories corresponding to the formulations in Section 3.2.Source: §4.2 · p. 17, Table 2 · p. 18, §4.2.3 · p. 18

5. Future Research Directions and Challenges

The review identifies open challenges in representing grid-side flexibility and coordinating it across resources and energy systems. It highlights computational, market-design, and multi-timescale issues that remain to be addressed.

5.1. Consideration of Power Network Topology and Parameter Changes

  • Topology and parameter changes such as line switching and N-k security introduce integer variables, making the resulting problem NP-hard.MILP linearizations may omit reactive-power constraints, and efficient methods for two-stage robust models with integer variables in both stages remain lacking; many studies place integers only in the first stage.Source: §5.1 · pp. 18–19

5.2. Consideration of Impacts of Reactive Power Flow

  • Accounting for reactive power requires AC OPF constraints, whose nonlinearity and non-convexity complicate optimization, especially with wide FACTS control ranges.Despite proposed methods, efficient algorithms to exploit grid-side flexibility in AC networks regardless of topology are still needed.Source: §5.2 · pp. 19–20

5.3. Market for Grid-side Flexibility

  • Current FACTS compensation may discourage frequent set-point changes, while FTR-style compensation for merchant transmission projects makes project-specific rights difficult to identify and depends on build order.The review calls for compensation schemes covering both continuous and discrete resources, renewable-uncertainty-aware FTR bidding, and market-power metrics and mitigation.Source: §5.3 · pp. 20–21

5.4. Coordination of Different Flexibility Resources

  • Coordinating flexibility across planning and operating timescales creates difficult multi-stage time-coupled optimization, while interactions among resources increase model scale and complexity.An intertemporal framework using characteristic time slices is cited, but it provides only qualitative results.Source: §5.4 · p. 21

5.5. Co-optimization of Multiple Energy Systems

  • Extending grid-side flexibility to multiple energy systems adds nonlinear constraints and differing operating timescales, requiring careful trade-offs between approximation accuracy and tractability.Electricity, gas, and heat processes may require coordination of distinct dynamics, potentially combining algebraic and differential equations.Source: §5.5 · pp. 21–22

6. Conclusions

The conclusion presents grid-side flexibility as a supplement to generation- and demand-side flexibility for renewable uncertainty. It emphasizes modeling topology and reactive power, developing efficient algorithms and market incentives, and coordinating resources and energy systems.

6. Conclusions

  • Grid-side flexibility complements generation- and demand-side flexibility in accommodating renewable-generation uncertainty.The review frames it as a means of supporting secure operation and economics as renewable penetration rises.Source: §6 · p. 22
  • Fully utilizing grid-side flexibility requires modeling topology changes and reactive power, producing mixed-integer nonlinear problems that need efficient solution algorithms.The conclusion also calls for effective market incentives and identifies coordination of flexibility resources and multiple energy systems as potential approaches to volatile renewable generation.Source: §6 · p. 22
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