Dynamic Ancillary Services in Power Systems

• Dynamic ancillary services are specialized, time-sensitive support functions defined by grid-code prescribed capability curves to maintain stability amid disturbances.
• They enable precise control of active and reactive power through transfer function approaches that translate time-domain performance curves into stable controllers.
• This methodology outperforms traditional droop and virtual inertia schemes by ensuring exact ramp response, rigorous grid-code adherence, and robust system stability.

Dynamic ancillary services are specialized, time-sensitive support functions provided to modern electric power systems to ensure system stability, security, and performance in the face of rapid disturbances or operating changes. They are characterized by explicit grid-code requirements on dynamic trajectories—such as specific delay, ramp-rate, and setpoint-following properties—in response to frequency or voltage excursions. Unlike static reserves, dynamic ancillary services are critical in systems dominated by converter-interfaced resources where time-domain step response and frequency-domain shaping (via transfer functions) determine grid compliance and stability under high renewable penetration (Häberle et al., 2023).

1. Specification via Time-Domain Capability Curves

Modern grid codes prescribe dynamic ancillary services (e.g., Fast Frequency Response (FFR), Frequency Containment Reserve (FCR), voltage regulation) through piecewise linear, time-domain step-response "capability curves." These curves precisely delineate the desired output—active power for a frequency step $\Delta f(t)$, reactive power for a voltage step $\Delta v(t)$—including breakpoints for latency, ramp-rate, and settling time:

• For each service, normalized unit-step trajectories are specified as breakpoints $\{(t_0=0, y_0=0), (t_1,y_1), ..., (t_N,y_N)\}$ connected by straight lines, with segment-wise equations $P_i(t)$ or $Q_i(t)$ parameterized via slopes and plateaus.
• FCR example: $P(t)=0$ for $0\leq t\leq t_i$, $P(t)=y_p\frac{t-t_i}{t_a-t_i}$ for $t_i\leq t\leq t_a$, $P(t)=y_p$ for $t\geq t_a$, where $y_p=|\Delta p^{\eta}_{\mathrm{fcr}}|=1/D_p$ (Häberle et al., 2023).
• Each segment is constrained by grid-code parameters (e.g., $t_i\leq T_{i,\max}$, $t_a\leq T_{a,\max}$, ramp rates), enabling derivation of performance limits such as $t_{90}\leq T_{90,\max}$, $y_{90}\leq t_{90}R_{\max}^\varphi$ for voltage responses.

The time-domain specification imposes nontrivial implementation challenges for converter-dominated systems, necessitating systematic translation to implementable, grid-compliant controllers.

2. Time-to-Frequency Domain Translation: Rational Transfer Function Approach

To realize prescribed dynamic behavior in power electronic converters, a generalized constructive method translates time-domain segments into a rational transfer function $G(s)$ in the Laplace domain:

• Each piecewise segment is Laplace-transformed, giving $$Y_{ij}(s) = [y_i/s + d/s^2]e^{-t_is} - [y_j/s + d/s^2]e^{-t_js}$$.
• The impulse response is obtained via $T_{ij}(s)=sY_{ij}(s)$, capturing dynamic shaping near each breakpoint.
• Exponential delays $e^{-ts}$ are rationalized using Padé approximants of order $n$: $e^{-ts}\approx(1-ts/(2n))^n / (1+ts/(2n))^n$.
• The aggregate desired transfer function is assembled: $G_P(s;\alpha)=\sum_{\text{segments}}T_{ij}(s)$ for active, and $G_Q(s;\alpha)$ for reactive responses, yielding a rational realization with direct correspondence to the original time-domain requirements.

This method ensures that each slope $d_i$, delay $t_i$, and amplitude $y_i$ enters $G(s)$ as zeros and poles at analytically predictable locations, precisely shaping both transient and steady-state system trajectories. The steady-state gain at $s=0$ enforces the correct asymptotic response (Häberle et al., 2023).

3. Controller Synthesis and Implementation in Converter Systems

Realization of the derived $G(s)$ in practical converter-based generation leverages cascade control architecture:

• Standard Voltage Source Converter (VSC) control employs high-bandwidth inner $d$-$q$ current, outer active and reactive power loops, and phase-locked loop synchronization.
• The required power-loop controller (e.g., $C_P(s)=K_p^P+K_i^P/s$) is synthesized so that $C_P(s)\cdot P_p(s)\approx G_P(s;\alpha)$, where $P_p(s)$ models primary plant and DC-link dynamics, and $G_P(s;\alpha)$ encodes the full grid-code trajectory.
• Outer-loop PI gains are matched to the desired $G_P(s)$ by equating low-order coefficients (typically, proportional and integral) derived from the transfer function quotient $G_P(s;\alpha)/P_p(s)$.
• Similar procedures apply to the reactive/voltage loop for $G_Q(s;\alpha)$.

This design guarantees precise tracking of grid-code envelopes, enforces device-level constraints (e.g., DC-link limitations, current saturation), and allows full traceability from code to implementation (Häberle et al., 2023).

4. Comparative Analysis with Classical Droop and Virtual Inertia Schemes

Classical droop and virtual inertia controllers—typically of the form $\Delta p(s)=-[M s+1/D_p]/(τ_f s+1)\Delta f(s)$—demonstrate inherent limitations:

Scheme Type	Ramp Delay Matching	Device Constraints	Grid Code Compliance
Droop + Inertia	Poor	Risk of saturation for aggressive τ_f	Overshoot/settling time errors $>$ 50%; steady-state error up to 10%
Transfer Function-Based (proposed)	Exact	Explicitly Enforced	Always satisfied (by design)

• High ramp-rate droop control ($τ_f\ll1$s) can violate device limits due to large reference excursions, while slower $τ_f$ fails to reach required output plateaus within grid-code timeframes.
• The transfer function methodology introduces additional zeros/poles, providing sufficient degrees of freedom to match segmented time-response curves, which classical approaches cannot do structurally.
• Simulation results confirm that only the TF-based design maintains trajectories above the "grid-code limit" across all segments, without overshoot or lag (Häberle et al., 2023).

5. Stability and Robustness Considerations

Rigorous stability and robustness are ensured by construction:

• Each Padé-approximated segment $T_{ij}(s)$ is stable (no right-half-plane zeros or poles).
• The cascaded control architecture with time-scale separation (high inner-loop bandwidth, low outer-loop bandwidth) enables standard small-gain arguments for overall loop stability.
• Empirical closed-loop implementations exhibit $>10$ dB gain margin and $>40^\circ$ phase margin.
• Device constraints (e.g., DC-link time constant, current limitation) are incorporated directly, ensuring physical realizability without recourse to ad hoc anti-windup or limit-projection logic.

This systematic approach results in a quantitatively robust and certifiably grid-compliant dynamic ancillary services provider (Häberle et al., 2023).

6. Applicability, Grid-Code Compliance, and System Impact

Grid-code testing (EU, Fingrid, EirGrid) and parameter selection directly in the transfer function framework produce the following properties:

• Fast Frequency Response: Full response times $t_a$ as low as $2$s and ramp rates up to $R_{\max}=32.6$ p.u./s achievable and verifiable.
• Voltage Regulation: $t_{90}\leq5$s, $t_{100}\leq60$s, $R^{\varphi}_{\max}=150$ p.u./s, with compliance maintained for every regulatory segment.
• The controller accommodates device-level limitations and grid-code segmentation simultaneously, outperforming classical schemes across all compliance metrics.

This method is extensible to emerging grid code designs, including those specifying dynamic ancillary services in frequency domain envelopes or with stricter transient and robustness constraints.

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References:

• "Dynamic Ancillary Services: From Grid Codes to Transfer Function-Based Converter Control" (Häberle et al., 2023)