Grid-Forming Mode-Based Allocation (GFM-BA)

• GFM-BA is an optimization framework that dynamically balances inverter control modes to enhance cost efficiency and maintain grid stability.
• It integrates a stochastic unit commitment model with mixed-integer second-order cone programming to manage GFM and GFL operations under security constraints.
• The framework demonstrates significant economic benefits and improved grid performance, validated on a modified IEEE 30-bus system with wind farms and synchronous generators.

Grid-Forming Mode-Based Allocation (GFM-BA) is an optimization framework designed to optimally allocate the control modes of inverter-based resources (IBRs)—specifically, the choice between Grid-Forming (GFM) and Grid-Following (GFL) operation—in power systems with high penetration of power electronics. GFM-BA is embedded within a stochastic unit commitment (SUC) problem, enabling dynamic scheduling of GFM and GFL resources to achieve minimum system cost while satisfying both small-signal stability and frequency-security constraints. The approach explicitly accounts for the headroom requirements of GFM units, network stability parameters, and security requirements, and solves the resulting mixed-integer second-order cone program (MISOCP) for operational setpoints and mode allocations at each scheduling interval (Cui et al., 2023).

1. Context: GFM Versus GFL in Modern Power Grids

In power systems undergoing transformation due to increasing inverter-based generation (e.g., wind, solar), traditional synchronous generators are being displaced. Grid-Forming (GFM) control is proposed to replace conventional Grid-Following (GFL) operation in order to maintain grid strength and mitigate small-signal instability, especially in weak grid scenarios. GFM devices regulate their terminal voltage and can provide grid support functions such as synthetic inertia, whereas GFL devices synchronize to the prevailing grid voltage and frequency without contributing to system strength. However, GFM units must operate with reduced active and reactive power output (i.e., reserve headroom) to provide these services, potentially causing suboptimal steady-state utilization.

2. Mathematical Formulation of GFM-BA

GFM-BA is formulated as a stochastic unit commitment (SUC) problem, where decisions must be made regarding:

• The status and dispatch of synchronous generators,
• The partitioning of each wind farm’s converter fleet between GFM and GFL operation (expressed via a continuous allocation variable $\alpha_{j,s} \in [0,1]$ for farm $j$ in scenario $s$),
• All nodal setpoints for active and reactive power,
• Ancillary system parameters central to frequency and stability security.

The key decision variables and parameters include:

• $P_{g,s}$: active power dispatched from synchronous generator $g$ in scenario $s$,
• $u_{g,s}, d_{g,s}$: unit commitment (start-up/shut-down) indicators,
• $x_{g,s}$: binary generator on/off status,
• $\alpha_{j,s}$: fraction of wind farm $j$ in GFM mode,
• $P_{0,nj,s}, Q_{0,nj,s}$: GFM unit (n,j) steady-state active/reactive power setpoints,
• $\Delta P^{GFM_WS}_{n,j,s}$: wind-shed (deloaded) power serving as GFM headroom,
• $P^{sh}_{b,s}$: load shedding at bus $b$.

The objective is to minimize the expected system cost: $$Z = \sum_{s \in S} \pi(s)\Bigg[\sum_{g \in G} \big( c^m_g P_{g,s} + c^{su}_g u_{g,s} + c^{sd}_g d_{g,s} + c^p_g x_{g,s} \big) + \sum_{j \in F} \sum_{n \in N_j} c^{ws} \Delta P^{GFM_WS}_{n,j,s} + \sum_{b \in B} c^{sh} P^{sh}_{b,s} \Bigg]$$ subject to constraints on commitment logic, generation and current/fault limits, wind-farm nameplate partitioning, GFM headroom (for frequency support and phase-jump), network power balance, and system-level stability indicators such as frequency-nadir, RoCoF, and generalized SCR (short-circuit ratio).

3. Modeling Power System Security Constraints

GFM-BA incorporates a comprehensive security constraint set:

• Active and Reactive Reserve: GFMs must reserve both active power (for inertia/frequency/phase support) and reactive power (for fault current and voltage support), limiting their continuous energy delivery and necessitating wind-shedding penalties.
• Frequency Security: System-wide frequency nadir and RoCoF limits are enforced, requiring combined synchronous and synthetic (GFM) inertia to exceed minimum threshold levels in every scenario.
• Grid Strength (SSC Constraint): Small-signal stability is encoded using a linearized generalized SCR, $gSCR_{L,s}$, formed as an affine function of both SG and GFM unit commitment variables and auxiliary bilinear indicators. The coefficients in $gSCR_{L,s}$ are obtained by off-line regression over a scenario dataset; the constraint $gSCR_{L,s} \geq CgSCR$ is imposed.

All nonlinearities—including those arising from power flow, stability metrics, and reserve formulations—are reformulated either as convex second-order cone (SOC) constraints or as mixed-integer linear terms, resulting in a MISOCP suitable for solution by commercial solvers.

4. Wind-Farm Control Mode Allocation Mechanism

The mechanism for allocating control modes in each wind farm is centered around the variable $\alpha_{j,s}$, which can be interpreted as the fraction of the farm’s converter fleet running in grid-forming configuration in scenario $s$. The allocation is dynamically optimized in every scheduling interval with respect to:

• The cost/benefit of deloading wind to provide headroom for GFM operation versus running more synchronous (fuel-based) units,
• The need for GFMs to provide synthetic inertia and maintain RoCoF/nadir below limits,
• The minimum system grid strength as encoded by the gSCR constraint,
• Network power flow feasibility and limits (omitted for brevity in the original source).

System-level dynamic allocation of $\alpha_{j,s}$ allows the SUC to trade off between maximizing renewable utilization and security-provided flexibility.

5. Numerical Case Study: IEEE 30-Bus System

The GFM-BA framework was validated on a modified IEEE 30-bus system featuring three wind farms (located at buses 1, 23, and 24) and seven synchronous generators (at buses 2, 3, 4, 5, 26, and 30), with loads ranging from 230 to 620 MW and a largest credible disturbance $\Delta P_L$ of 50 MW. Key findings include:

• Wind-abundant intervals: When wind power is plentiful, $\alpha_j$ is driven close to 1.0 (all or nearly all wind machines in GFM mode), maximizing synthetic inertia and providing frequency support through GFM units.
• Intermediate-wind intervals: The SUC increases $\alpha_j$ preferentially in the most effectively-located wind farm while selectively committing additional synchronous units as necessary for SSC compliance.
• Wind-scarce intervals: $\alpha_j \rightarrow 0$ (GFM operation largely suspended) and synchronous generators supply both energy and inertia, maintaining grid strength.

6. Economic Implications and Trade-offs

GFM-BA yields significant operational cost benefits by optimizing GFM/GFL mode splits. Fixing $\alpha_j$ a priori (e.g., at 0.6) yields an average cost of approximately 6.5 k£/h, while allowing the SUC to dynamically optimize $\alpha_j$ reduces average cost to 5.9 k£/h (a savings of about 10%). The optimizer avoids excessive wind-shed penalty at high $\alpha_j$ and avoids unnecessary synchronous unit commitment at low $\alpha_j$, attaining a system-level trade-off between grid support headroom and inertia services versus steady-state renewable utilization.

7. Significance, Applications, and Limitations

GFM-BA represents an advance in operational scheduling by tightly integrating converter control-mode allocation with security-centric system operations. It enables software-defined grids to dynamically offer grid-forming services where they are most cost- and stability-effective. The resulting approach is applicable to modern power systems with high renewable penetration and is adaptable to system evolution without fixed GFM quota policies. A plausible implication is that future implementations may further integrate additional grid services and network-aware mode allocations for real-time adaptive operation (Cui et al., 2023).