Fast Adaptive Reactive-Power Compensation Control for Renewable Power Plants Considering Dynamic Active-Power–Voltage Coupling

Abstract

Renewable power plants connected to low-system-strength grids are increasingly dominated by inverter-based resources (IBRs). Their point of common coupling (PCC) voltage is therefore shaped not only by reactive-power support but also by active-power ramps, network impedance, short-circuit capacity, and converter limits. Conventional Q-V droop control, fixed power-factor control, Volt/VAR control, and fixed active-power/reactive-power (P/Q) decoupling schemes often absorb active-power excursions into the voltage error, which can drive excessive reactive-power injection during fault clearing, post-fault power recovery, and phase-angle disturbances. Here, an active-power–voltage-coupling-aware reactive-power compensation (APVQ-RC) method is proposed for plant-level voltage control. The method estimates local P-V and Q-V voltage sensitivities online, reconstructs an effective voltage error, and produces a capacity-constrained reactive-power reference through smooth coupling activation. The reduced-order evaluation includes estimator conditioning, excitation screening, sensitivity-estimation error and empirical 95% estimator-error intervals, sensitivity to the smoothing factor and window length, measurement noise, converter capability saturation, and computational timing. Under P-V-coupled transients, APVQ-RC reduces voltage overshoot and reactive-power compensation energy while retaining Q-V-like support during voltage-sag-dominated events. Compared with the best scanned fixed P/Q baseline, it reduces overshoot, reactive-power compensation energy, and reactive-power peak by 42.03%, 60.35%, and 8.90%, respectively; the representative single-step calculation time is 0.0188 ms within a 1 ms control cycle. These results indicate millisecond-scale plant-level feasibility within the reduced model, while electromagnetic-transient, hardware-in-the-loop, and field validation remain necessary before deployment.

1. Introduction

Power systems with high renewable penetration are moving from distributed interconnection towards plant-level aggregation of inverter-based resources (IBRs). As synchronous machine capacity is displaced, lower system strength and reduced inertia make the PCC voltage more sensitive to current injection, impedance angle, and converter controls [1,2,3,4]. In this setting, voltage regulation is no longer governed by reactive power alone; it is also affected by active-power trajectories and converter operating limits.

Utility-scale renewable plants contain heterogeneous assets, including wind turbines, photovoltaic inverters, energy storage systems, static var generator (SVG) units, static synchronous compensators (STATCOMs), and plant-level controllers. Active-power fluctuations, post-fault recovery ramps, power limits, and changing reactive-power headroom can all perturb PCC voltage [1,2,3,4,5,6,7]. In low-system-strength grids, the resulting voltage response is a coupled P-V/Q-V process rather than a purely reactive-power regulation problem.

The linearized weak-grid power-flow relation contains both the RΔP and XΔQ components of PCC-voltage variation. As the short-circuit ratio (SCR) decreases, the R/X ratio increases, or post-fault active-power recovery becomes faster, the active-power term can be comparable with the reactive-power term. Active power is therefore a dynamic state that can reshape local voltage, not a slow independent variable that can be ignored in reactive-power compensation.

At the system level, renewable-rich integrated energy systems are also exposed to uncertainty from renewable generation, hydrogen-powered vehicle demand, and coupled microgrid-transportation operation [8]. Such uncertainty appears at the plant controller as time-varying active-power ramps, variable converter headroom, and shifting operating points. This reinforces the need for online P-V/Q-V sensitivity estimation rather than a fixed feedforward coefficient.

Existing studies have examined system-strength assessment based on SCR, impedance modeling, inverter synchronization stability, phase-locked-loop (PLL) interactions, grid-forming and grid-following control, Q-V droop, Volt/VAR curves, SVG/STATCOM support, inverter current limiting, and plant-level reactive-power coordination [5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. These studies establish that renewable-rich voltage control depends on network strength, impedance characteristics, converter dynamics, and available reactive-power capacity.

Three gaps remain. First, conventional voltage controllers may conflate external voltage faults with active-power-induced voltage offsets. Second, fixed P/Q decoupling or fixed active-power feedforward is sensitive to SCR, R/X, and the operating point. Third, impedance-based stability analysis has not been translated into a lightweight online error-reconstruction law that can be embedded in a plant-level reactive-power controller. APVQ-RC is developed to close this control-oriented gap.

2. Materials and Methods

2.1. Equivalent Weak-Grid Model

A reduced-order discrete weak-grid equivalent is adopted to represent the local dynamic relation between the renewable plant and the external grid. The model is not intended to replace a detailed electromagnetic-transient (EMT) model; instead, it isolates the millisecond-scale PCC-voltage response to active-power variation, reactive-power variation, and exogenous voltage disturbance [28].

The renewable plant is represented as an aggregated grid-connected source. The PCC-voltage increment is driven jointly by active-power increments, reactive-power increments, and unmeasured external disturbances. Equation (1) defines the incremental model used throughout the analysis:

$$\Delta V(k)=S_{VP}(k)\Delta P(k)+S_{VQ}(k)\Delta Q(k)+d(k),$$

(1)

$$SCR={\displaystyle \frac{S_{SC}}{S_N}},$$

(2)

$$y_W=X_W\theta +{\eta }_W,\theta ={\left[\begin{array}{cc}{S}_{VP}& S_{VQ}\end{array}\right]}^T,$$

(3)

$$\widehat{\theta }={(X_W^T{X}_W+\mu I)}^{-1}{X}_W^T{y}_W,$$

(4)

In Equation (1), k is the discrete sampling index; ΔV(k) denotes the PCC voltage variation during the k-th sampling interval; ΔP(k) and ΔQ(k) denote active- and reactive-power increments, respectively; d(k) represents external disturbances that cannot be directly explained by plant power, such as voltage sags, phase-angle jumps, or fault clearing; and S_VP(k) and S_VQ(k) are the local sensitivities of PCC voltage to active- and reactive-power increments. Voltage is expressed in p.u., P in MW, and Q in MVar; consequently, S_VP and S_VQ have units of p.u./MW and p.u./MVar in the reported simulations. Equation (2) defines SCR = S_sc/S_N, where S_sc is the short-circuit capacity at the grid-connection point and S_N is the plant power base used for SCR calculation. In Equations (3) and (4), y_W is the voltage-increment observation vector within window W, X_W is the regression matrix composed of ΔP and ΔQ, $\theta$ = [S_VP S_VQ]^T is the parameter vector, ${\eta }_W$ represents measurement noise and unmodeled residuals, and $\mu$ is the Tikhonov regularization coefficient, which stabilizes the least-squares estimate when the regression matrix is ill conditioned. The regression is solved after numerical normalization, so $\mu$ is dimensionless in the implemented normal equation.

A larger absolute S_VP indicates that a given active-power perturbation produces a larger equivalent voltage deviation at the PCC, whereas a larger absolute S_VQ indicates stronger reactive-voltage sensitivity. Lower SCR and larger R/X increase the relative importance of active-power effects. The SCR and R/X scans therefore test whether APVQ-RC remains effective across different levels of grid strength and impedance coupling.

2.2. Baseline Controllers

Two representative baselines are used. Conventional Q-V control maps the PCC-voltage error to a reactive-power command through a proportional–integral channel. The fixed P/Q decoupling baseline augments Q-V control with a constant active-power feedforward term. These baselines are deliberately simple and broadly used, which makes them appropriate references for isolating the effect of online sensitivity-based error reconstruction.

$$Q_{QV}(k)=Q_0+K_v\left[V_{ref}-V(k)\right]+K_i{\displaystyle \sum _{i=0}^k\left[V_{ref}-V(i)\right]}{T}_s,$$

(5)

$$Q_{dec}(k)=Q_{QV}(k)+K_{dec}\Delta P(k),$$

(6)

In Equation (5), Q_QV(k) is the reactive-power reference generated by conventional Q-V control, Q₀ is the steady-state reactive-power base value, K_v is the voltage proportional gain, K_i is the integral gain, V_ref is the reference voltage, V(k) is the measured PCC voltage, and T_s is the sampling period. In Equation (6), Q_dec(k) is the reactive-power reference of the fixed P/Q decoupling controller, and K_dec is the fixed decoupling coefficient.

The Q-V controller converts voltage error directly into reactive-power support. It is effective during voltage-sag-dominated events, but can overreact when active-power ramps dominate the measured voltage deviation.

The fixed P/Q decoupling baseline acknowledges that active-power variation affects voltage control, but represents this effect with a single constant coefficient. Because S_VP and S_VQ vary with SCR, R/X, operating point, and controller state, a fixed K_dec cannot remain locally optimal across disturbance types. The K_dec scan therefore tests the limits of a nonadaptive feedforward approximation.

2.3. APVQ-RC Adaptive Reactive-Power Compensation Controller

APVQ-RC acts by reconstructing the voltage error before the reactive-power target is updated. At each sampling instant, it estimates the active- and reactive-power contributions to PCC-voltage variation and removes the active-power-induced equivalent voltage component from the raw error when the P-V channel is dominant. The control kernel consists of a sliding-window least-squares estimator, a scalar activation law, and a capacity-limited PI channel, making it suitable for periodic plant-level control.

At each sample, the controller measures V(k), P(k), and Q(k), forms ΔP(k), ΔQ(k), and ΔV(k), and estimates S_VP and S_VQ over the accepted sliding window. It then computes λ_PV(k) and α(k), reconstructs the effective voltage error in the reactive-control direction, and updates the APVQ-RC reactive-power reference. The sliding window is updated at every sample, so the controller does not wait for a full window before issuing the 1 ms reactive-power reference.

The online APVQ-RC update procedure is implemented at every sampling instant as follows: (i) sample V(k), P(k), and Q(k); (ii) compute ΔP(k), ΔQ(k), and ΔV(k); (iii) update the sliding window and retain only samples satisfying the voltage-jump and excitation criteria; (iv) solve the regularized estimator in Equation (4), reject the update when cond $(X_W^T{X}_W+\mu I)$ > 10¹² or the minimum singular value of X_W is below 1 × 10⁻⁴, and otherwise project and smooth S_VP and S_VQ; (v) compute λ_PV(k), α(k), and the effective error e_eff(k); (vi) update the leaky PI state with anti-windup; (vii) enforce the instantaneous P-Q capability curve with active-power priority and reactive-power saturation; and (viii) send Q_ref(k) to the plant-level reactive-power actuator while storing the accepted states for the next sample.

During the first W samples, the estimator uses all available valid increments after at least eight accepted samples have been collected; before that point, nominal weak-grid sensitivities are used. Samples are admitted only when the voltage jump is below 0.04 p.u. and the window contains sufficient P/Q excitation. The condition number of the regularized normal matrix and the minimum singular value of the regression matrix are monitored; ill-conditioned updates are rejected and the previous bounded estimate is retained.

The estimator does not assume unconditional invertibility. Numerical robustness is obtained by Tikhonov regularization, excitation screening, condition-number rejection, projection, and exponential smoothing. Thus, poorly excited or noise-dominated windows do not force an unreliable matrix inversion; they hold the last admissible sensitivity estimate until informative data become available.

$${\lambda }_{PV}(k)={\displaystyle \frac{\left|S_{VP}(k)\Delta P(k)\right|}{\left|S_{VQ}(k)\Delta Q(k)\right|+{\epsilon }_0}},$$

(7)

$$\alpha (k)={\displaystyle \frac{{\lambda }_{PV}(k)}{1+{\lambda }_{PV}(k)}},$$

(8)

$$e_{eff}(k)=e_{raw}(k)-\alpha (k)S_{VP}(k)\Delta P(k),e_{raw}(k)=V_{ref}-V(k),$$

(9)

$$Q_{APVQ}^{*}(k)=Q_0+K_v{e}_{eff}(k)+K_i{\displaystyle \sum _{i=0}^k{e}_{eff}}(i)T_s,$$

(10)

$$P{(k)}^2+Q_{ref}{(k)}^2\le S_{rated}^2,$$

(11)

In Equation (7), ${\lambda }_{PV}(k)$ is a coupling-strength index for measured P- and Q-channel voltage components. The numerator $\left|S_{VP}(k)\Delta P(k)\right|$ estimates the active-power contribution to PCC-voltage variation, whereas the denominator $\left|S_{VQ}(k)\Delta Q(k)\right|+{\epsilon }_0$ represents the reactive-power contribution with zero-avoidance regularization. Equation (8) maps λ_PV(k) to the continuous activation factor $\alpha (k)$, and Equation (9) defines the effective voltage error from the raw error $V_{\mathit{ref}}-V(k)$.

Equation (7) is not used as a stand-alone fault classifier. The unmeasured disturbance d(k) is excluded from the denominator because it is not a controllable measured input. Large exogenous voltage jumps are handled by sample screening, while the raw Q-V path remains active during voltage-sag-dominated events. Under mixed disturbances, λ_PV quantifies the filtered P-channel contribution to the measured voltage variation rather than the physical origin of every voltage component. Near-zero ΔQ is regularized by ${\epsilon }_0$ and constrained by the P-Q capability limiter, whereas sign-inconsistent or rapidly varying sensitivity estimates are bounded by projection, smoothing, and condition-number rejection.

A larger λ_PV indicates that the measured transient is dominated by the active-power channel; a smaller λ_PV indicates voltage-sag dominance or insufficient reactive support.

A continuous activation law is used instead of a hard threshold because active-power ramps and voltage faults often overlap in plant operation. Smooth activation avoids threshold chatter and preserves continuity of the reactive-power command.

The sign in Equation (9) follows the adopted reactive-control convention. Positive ΔP denotes increasing active-power injection from the plant to the grid, and positive ΔQ denotes increasing capacitive reactive-power injection. Under the weak-grid equivalent, positive S_VPΔP raises the active-power-related PCC-voltage component; this component should therefore be removed from the voltage error seen by the reactive-power channel. APVQ-RC consequently uses $e_{eff}(k)=e_{raw}(k)-\alpha (k)S_{VP}(k)\Delta P(k)$.

Bounded operation is enforced by three mechanisms. First, $\alpha (k)$ is constrained between zero and unity, preventing unbounded amplification of the active-power correction. Second, the integral state uses activation-dependent leakage, magnitude limiting, and rollback anti-windup under saturation. Third, the reactive-power reference is clipped by the instantaneous P-Q capability envelope, so the command remains physically feasible for the converter.

The sliding-window estimator has only two regressors, ΔP and ΔQ. With a 50-sample window, the computation is a small regularized least-squares problem followed by scalar updates. The window length affects variance and smoothing, but not the 1 ms update cadence of the reactive-power reference [24].

When active-power disturbances dominate the voltage variation, λ_PV increases, α approaches unity, and the active-power-induced equivalent voltage component is removed from the raw error. When voltage sag dominates or active power is nearly steady, λ_PV approaches zero and the controller smoothly reverts toward Q-V support. This continuous reversion avoids threshold-induced chatter while preserving fast low-voltage support.

A representative online calculation is reported at 1.020 s in the active-power step-down case, where no external voltage disturbance is applied. At this instant, ΔP and ΔQ are −0.479 MW and 0.067 MVar, and the measured ΔV is −0.001107 p.u. The 50-sample estimator has a regularized condition number of 1649.99. The smoothed estimates are S_VP = 0.000705 p.u./MW and S_VQ = 0.001020 p.u./MVar, giving active- and reactive-channel voltage components of −0.000337 p.u. and 6.84 × 10⁻⁵ p.u. The resulting ${\lambda }_{PV}$ and α are 4.86 and 0.82934, respectively. The effective PI input changes from e_raw = 0.023223 p.u. to e_eff = 0.023503 p.u., illustrating the sample-level P-V correction.

The Q-V-like operating region is defined by the activation level. For α < 0.1, the corresponding coupling index satisfies λ_PV < 0.111. Under the nominal SCR = 2 and R/X = 1.0 condition, the median sensitivities are S_VP = 0.0016 p.u./MW and S_VQ = 0.0027 p.u./MVar. Thus, for a simultaneous 30 MVar reactive-power increment, active-power variation below approximately 5.63 MW per control sample keeps the controller in the Q-V-like region.

2.4. Evaluation Metrics

In Equation (12), $O_V$ is the maximum voltage overshoot and reflects the degree to which the voltage exceeds its reference after fault clearing. In Equation (13), $E_Q$ is the reactive compensation energy and measures the intensity of reactive resources mobilized during a disturbance; a smaller $E_Q$ indicates less reactive-power misoperation and less reactive-power tailing. In Equation (14), $Os{c}_V$ is the post-clearing oscillation index, which evaluates the accumulated voltage deviation from the reference during a time interval after fault clearing.

$$O_V={\max }_{t\ge t_0}(V(t)-V_{ref})\times 100\%,$$

(12)

$$E_Q={\displaystyle {\int }_{t_0}^{t_1}|}{Q}_{ref}(t)-Q_0|dt,$$

(13)

$$Os{c}_V={\displaystyle {\int }_{t_c}^{t_c+0.3}|}V(t)-V_{ref}|dt,$$

(14)

This study also reports the recovery time T_rec, defined as the time required for the PCC voltage to recover to 0.9 per unit (p.u.). Recovery time quantifies practical low-voltage support speed within the reduced-model setting. Overshoot and $Os{c}_V$ describe recovery quality, $E_Q$ describes reactive-power control cost, and the four metrics together avoid one-sided conclusions based on a single indicator.

3. Simulation Setup

The test design covers four control properties: voltage-sag support, adaptation beyond a fixed feedforward coefficient, millisecond-scale computational feasibility, and engineering boundaries requiring higher-fidelity validation. The cases include fault recovery, disturbance-type comparison, weak-grid and fixed-baseline scans, noise robustness, plant-parameter uncertainty, and timing tests.

The tests are mechanism-oriented. The reduced-order weak-grid equivalent is used to compare error reconstruction and reactive-power overcompensation under controlled conditions; EMT, hardware-in-the-loop, and field tests are required for deployment-level validation.

3.1. Parameter Settings

The test system uses a 1 ms sampling period over 2 s. The base apparent power is S_b = 100 MVA, with P₀ = 100 MW, Q₀ = 0 MVar, and V₀ = V_ref = 1.0 p.u.; S_b is used for per-unit normalization and SCR calculation, not as the instantaneous converter rating. The default grid is SCR = 2 and R/X = 1.0, and the scans use SCR = [1.5,2,3,5] and R/X = [0.1,0.5,1.0]. The converter rating is S_rated = 135 MVA with an active-priority P-Q capability limit.

The dynamic plant model used to generate P(k), Q(k), and V(k) is a first-order discrete equivalent. Active power tracks its disturbance command with time constant τ_P; reactive-power output tracks Q_ref with time constant τ_Q; and PCC voltage follows the weak-grid static operating point with time constant τ_V. A P-Q capability check is applied at every sample with active-current priority, so the reactive-power command is saturated to the remaining apparent-power headroom.

To assess real-time feasibility, the test was designed with 100,000 repeated controller updates using double precision. The reported time includes only the control-law calculation and excludes sampling, communication, and actuator delays; end-to-end latency must be verified on the target platform. Table 1 reports 0.0188 ms as the representative single-step time. A repeated timing run gave a mean of 0.0156 ms, a 95th percentile of 0.0194 ms, a 99th percentile of 0.0374 ms, and a maximum of 1.4151 ms, with the maximum attributed to operating-system scheduling jitter rather than deterministic arithmetic workload.

Table 1. Control-cycle and response-speed indices.

Indicator	Value	Meaning
Control period, Ts (ms)	1	Online update
Single-step time, tc (ms)	0.0188	1.9% of the period
Recovery time, Trec (ms)	12	Tens-of-milliseconds support
Measured inputs	VPCC, P, Q	Standard plant measurements

The parameter values were selected for implementability, interpretability, and preservation of low-voltage support, rather than to reproduce a single favorable waveform. K_v and K_i retain the response speed of conventional Q-V control. The window length W, smoothing factor β, projection bounds, and regularization coefficient μ suppress sensitivity-estimation noise. The zero-avoidance term ${\epsilon }_0$ and the P-Q capability limiter avoid numerical singularity and infeasible commands. Table 2 lists the resulting settings.

Table 2. APVQ-RC implementation parameters.

Parameter	Value	Role
Sampling period, Ts (ms)	1	Control-period setting
Estimation window, W	50	Sensitivity estimation
Smoothing factor, β	0.95	Noise suppression
Regularization/screening, μ/ε0/σmin	1 × 10−6/1 × 10−6/1 × 10−4	Conditioning/zero avoidance/excitation
PI gains, Kv/Ki	85/260	Error-to-Q mapping
Converter rating, Srated (p.u.)	1.35	P-Q capability, active priority

3.2. Baselines and Robustness Tests

The baselines are conventional Q-V control, fixed P/Q decoupling, and APVQ-RC. The fixed coefficient K_dec is scanned over [0, 0.005, 0.012, 0.02, 0.04, 0.08] under the same capacity and anti-windup constraints, and the best value is selected separately for each metric. Thus, the comparison represents a single-coefficient, nonadaptive feedforward baseline.

Robustness tests vary SCR, R/X, fixed K_dec, measurement noise, actuator time constants, and P-Q capability stress. Here, σ_V, σ_P, and σ_Q are the standard deviations of voltage, active-power, and reactive-power measurement noise; τ_P and τ_Q are first-order actuator time constants; and RMSE is the root-mean-square error between estimated and known reduced-model sensitivities. Under high noise, APVQ-RC keeps lower mean O_V and E_Q than Q-V control (4.743% and 7.961 MVar·s versus 9.419% and 21.508 MVar·s). The S_VP/S_VQ estimator RMSEs are 5.11 × 10⁻³ and 1.85 × 10⁻³, and the median/95th-percentile condition numbers are 87.0 and 8.15 × 10⁴, indicating that ill-conditioned windows are screened before estimation.

Sensitivity to β and W is evaluated with β = 0.85, 0.90, 0.95, and 0.98 and W = 30, 50, 80, and 100. Across the 16 combinations, T_rec remains 12 ms, O_V changes only from 5.238% to 5.570%, E_Q from 8.424 to 8.621 MVar·s, and peak Q from 61.834 to 63.540 MVar. Therefore, β and W mainly tune estimator smoothness and delay, while the 1 ms command update is retained.

4. Results and Discussion

4.1. Default Weak-Grid Fault-Recovery Case

The default case isolates the interaction among fault clearing, active-power recovery, voltage overshoot, and reactive-power tailing. Figure 1 resolves the voltage, power, activation, sensitivity, and error-reconstruction dynamics.

Figure 1. Fault-recovery mechanism of APVQ-RC under low-system-strength conditions.

Figure 1a indicates that APVQ-RC preserves low-voltage support during the fault and suppresses post-clearing overshoot during active-power recovery. Figure 1b,c link this overshoot to the active-power ramp and reactive-power tailing, confirming that the measured voltage error contains a P-channel component.

Figure 1d–f show that λ_PV and α provide event-dependent activation. S_VP and S_VQ set the local scale for error reconstruction, allowing the controller to replace the raw voltage error with an effective error aligned with the required reactive-power support. In Figure 1d, λ_PV^* denotes the normalized P-V coupling index, i.e., λ_PV/max(λ_PV); it is plotted for direct comparison with α(k), whereas APVQ-RC evaluates the activation law using the unnormalized coupling index.

4.2. Response Comparison Under Different Disturbance Types

Figure 2 defines the disturbance-dependent operating boundary of APVQ-RC. Under a voltage-sag-dominated event, Figure 2a shows smooth reversion toward conventional Q-V support. Under active-power steps, phase-angle disturbances, and fault recovery, Figure 2b–d show that error reconstruction suppresses reactive-power overcompensation.

Figure 2. Event-dependent APVQ-RC responses under representative disturbances.

The results indicate that APVQ-RC preserves necessary reactive-power support when λ_PV is small. When the P-channel contribution increases, the controller separates the active-power-related voltage component from the Q-V loop, thereby reducing overshoot and reactive-power cost.

4.3. Metric Comparison and Control Cost

Figure 3 benchmarks voltage overshoot, reactive-power compensation energy, post-clearing oscillation, and recovery speed. The metric set indicates that APVQ-RC reduces P-V-coupling-induced overcompensation while keeping recovery on a tens-of-milliseconds time scale.

Figure 3. Metric-level benchmarking and real-time feasibility in the default case.

Figure 3a–c show that uncompensated Q-V action can convert active-power recovery into overshoot, additional reactive energy, and post-clearing oscillation. Figure 3d provides the real-time baseline, showing that recovery remains compatible with plant-level online control.

4.4. Fixed Decoupling Parameter Scan

Figure 4 quantifies the range over which a fixed feedforward gain can compensate P-V coupling. Because Q_dec = Q_QV + K_decΔP, K_dec is a reactive-power-per-active-power coefficient with units of MVar/MW. The tested interval K_dec = [0, 0.08] represents a same-sign damping feedforward range under the adopted sign convention, rather than a full signed gain-scheduling search. The nearly horizontal curves indicate that a single fixed coefficient has limited adaptability across the tested operating conditions.

Figure 4. Fixed P/Q feedforward-gain scan.

The fixed-gain comparison is restricted to a representative single-coefficient feedforward baseline. More elaborate fixed-control designs, including negative-gain scans, piecewise K_dec, offline optimized K_dec, gain scheduling, adaptive feedforward control, and model-predictive voltage control, may perform better when tuned under matched constraints. The contribution of APVQ-RC is the online estimation of S_VP/S_VQ, smooth activation by λ_PV and α, and effective-error reconstruction during fault recovery.

The quantitative comparison is therefore limited to the reduced-order benchmarks with identical constraints and tuning objectives. Within this scope, the results support the adaptability of APVQ-RC against the representative baselines considered here; broader comparisons require matched converter limits, delays, disturbance profiles, and tuning objectives.

4.5. Coupling Relation, Control Trade-Off, and Model Consistency

Figure 5 connects coupling strength, control cost, and reduced-model consistency. Figure 5a relates the P-V coupling ratio to performance improvement, Figure 5b gives the recovery-speed/reactive-power-cost trade-off, and Figure 5c compares simulated voltage increments with equivalent-model predictions. This consistency check supports the reduced-order implementation but does not replace nonlinear EMT, hardware-in-the-loop, or field validation.

Figure 5. Coupling strength, control cost, and reduced-model consistency.

Figure 5 further indicates that S_VP/S_VQ is a local measure of P-V participation rather than a stand-alone predictor of performance gain. The results support local sensitivity-based error reconstruction within the discrete equivalent controller, while independent nonlinear converter-grid studies remain necessary for deployment-level claims.

The EMT-dependent phenomena most likely to alter the response are PLL bandwidth, converter current limiting and priority logic, inner current-loop saturation, PWM and switching delay, measurement filtering, communication delay, protection blocking, and multi-converter interactions. These effects can change the apparent S_VP/S_VQ, introduce phase lag among P, Q, and V, or clip the reactive-power command at the capability limit.

5. Comparison with Existing Methods and Methodological Advantages

The results in Section 4 show that APVQ-RC differs from Q-V control, fixed P/Q decoupling, and optimization-based methods in error construction, parameter adaptability, smooth reversion to Q-V support, and real-time implementation. By estimating the active-power contribution before issuing the reactive-power command, APVQ-RC reduces overcompensation and parameter-mismatch risk with low computational burden.

Unlike conventional Q-V control, APVQ-RC separates the active-power-induced equivalent voltage component before reactive-power regulation. Figure 1 and Figure 3 show lower overshoot and reactive-power compensation energy with millisecond-scale recovery. Compared with the best scanned fixed P/Q baseline in the default reduced-order benchmark, APVQ-RC reduces O_V, E_Q, Q_peak, and Osc_V by 42.03%, 60.35%, 8.90%, and 7.40%, respectively. Online voltage-sensitivity estimation and adaptive activation therefore avoid the mismatch of a single K_dec across SCR, R/X, and disturbance types within the tested constraints.

APVQ-RC also provides event-dependent activation and smooth reversion to Q-V support. Figure 2a shows Q-V-like support during a voltage-sag-dominated event, whereas Figure 2b–d show that error reconstruction activates when P-V coupling strengthens. The 0.0188 ms single-step time in Table 1 provides computational margin within a 1 ms control cycle.

Relative to published impedance-reshaping, PLL-stability-enhancement, Volt/VAR optimization, and data-driven dispatch methods [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], APVQ-RC is a local plant-level correction rather than a network-wide optimizer. It requires only V_PCC, P, and Q measurements, solves a two-regressor regularized estimator, and retains an explicit Q-V support path. The quantitative claims are therefore confined to the identical reduced-order benchmarks reported here.

6. Conclusions

This study develops a fast adaptive reactive-power compensation method for renewable power plants under dynamic active-power–voltage coupling. The main conclusions are as follows.

(1)

In low-system-strength grids, PCC voltage is affected by reactive-power support, post-fault active-power recovery, phase-angle disturbances, and plant-output variation. APVQ-RC estimates local P-V/Q-V sensitivities online and converts the active-power-related voltage component into an effective-error correction for reactive-power compensation.

(2)

Compared with conventional Q-V control and the representative fixed P/Q baseline, APVQ-RC reconstructs the voltage error according to the coupling state. When active-power disturbances participate in the transient, it reduces post-clearing voltage overshoot and reactive-power compensation energy while maintaining recovery on a tens-of-milliseconds time scale under identical reduced-model constraints.

(3)

APVQ-RC provides event-dependent activation and smooth reversion to Q-V support. During voltage-sag-dominated events, the coupling factor remains low and the response stays close to Q-V control; during active-power steps, phase-angle disturbances, or fault recovery, error reconstruction becomes active.

(4)

Multi-disturbance, weak-grid, fixed-parameter, noise, uncertainty, and timing tests support the conclusions within the equivalent model. APVQ-RC updates the reactive-power reference every 1 ms, with a representative single-step calculation time of 0.0188 ms and a 95th-percentile repeated-run time of 0.0194 ms. Estimator-error diagnostics, condition-number monitoring, excitation screening, sensitivity scanning of the smoothing factor and window length, and P-Q capability handling define the present applicability boundary. Further validation using nonlinear EMT models, hardware-in-the-loop tests, and field data is required for deployment.