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Real-Time Local Volt/VAR Control Under External Disturbances with High PV Penetration

Ankit Singhal, Venkataramana Ajjarapu, Jason. C. Fuller, Jacob Hansen

arXiv:1710.02551v3math.OC

TL;DR

High PV penetration makes local droop VVC vulnerable to poor parameter selection, instability, voltage oscillations, and steady-state error under changing disturbances. The paper proposes a two-layer, real-time adaptive local controller with theoretical convergence analysis, and reports accurate tracking, reduced flicker, and zero flicker and violation indices in stated tests. Its local design remains less effective for system-wide optimization.

  • Problem

    Local droop VVC needs parameter selection that remains effective under changing conditions while avoiding instability, voltage oscillations, and significant SSE.

  • Method

    The paper proposes a fully local, real-time adaptive droop VVC that dynamically dispatches control parameters and includes convergence analysis within the IEEE1547 framework.

  • Results

    The adaptive control accurately tracks set points, maintains a flat voltage profile under daily variation, and achieves zero flicker and violation indices under cloud disturbances.

  • Takeaways & Limitations

    Adaptive local VVC can provide tight voltage regulation and stability across the reported operating conditions while remaining compatible with utility standards and practices.

Abstract

from arXiv · show

Volt/var control (VVC) of smart PV inverter is becoming one of the most popular solutions to address the voltage challenges associated with high PV penetration. This work focuses on the local droop VVC recommended by the grid integration standards IEEE1547, rule21 and addresses their major challenges i.e. appropriate parameters selection under changing conditions, and the control being vulnerable to instability (or voltage oscillations) and significant steady state error (SSE). This is achieved by proposing a two-layer local real-time adaptive VVC that has two major features i.e. a) it is able to ensure both low SSE and control stability simultaneously without compromising either, and b) it dynamically adapts its parameters to ensure good performance in a wide range of external disturbances such as sudden cloud cover, cloud intermittency, and substation voltage changes. A theoretical analysis and convergence proof of the proposed control is also discussed. The proposed control is implementation friendly as it fits well within the integration standard framework and depends only on the local bus information. The performance is compared with the existing droop VVC methods in several scenarios on a large unbalanced 3-phase feeder with detailed secondary side modeling.

I. INTRODUCTION

Rising PV penetration creates voltage-rise and fluctuation challenges that conventional regulators cannot respond to quickly. The paper proposes a local, real-time adaptive droop VVC to address parameter selection, stability, and steady-state error under disturbances.

  • High PV penetration causes voltage rise and rapid cloud-driven voltage fluctuations, while traditional capacitors and tap changers are too slow for these transients.
  • Communication requirements, delays, and OPF solution times limit centralized and distributed approaches for second-scale disturbances such as cloud intermittency.
  • Conventional local droop VVC is widely adopted because it uses local bus information, but parameter choices can cause instability, voltage oscillations, or high steady-state error.
  • The proposed adaptive VVC self-adjusts parameters under changing conditions while achieving low SSE and control stability simultaneously.
  • The framework is theoretically analyzed, compatible with IEEE1547 droop controls, and evaluated using detailed unbalanced feeder models with house-level loads and heterogeneous inverters.

A. Stability Analysis

The stability analysis models local droop VVC as a feedback dynamical system and derives spectral-radius conditions for local stability. Because feeder sensitivities vary with operating conditions and topology, inverter slopes must adapt dynamically.

  • A. Stability Analysis: Local droop VVC is locally stable when every eigenvalue of the feedback Jacobian has magnitude below one.
  • A. Stability Analysis: The stability condition is ρ(MA) < 1, where M contains inverter slopes and A is the voltage sensitivity matrix with respect to reactive-power injections.
  • A. Stability Analysis: A conservative sufficient condition requires each row sum of MA to be less than one, providing a basis for selecting inverter slopes below critical values.
  • A. Stability Analysis: Cloud cover, load changes, and topology changes alter sensitivity entries and critical slopes, so fixed slopes can cause instability; longer rural feeder lines require more conservative settings.
  • A. Stability Analysis: Delayed droop can improve stability under normal conditions, but its non-adaptive and uncontrolled parameters remain vulnerable to disturbances and topology changes.

B. Steady State Error (SSE) Concerns

Droop control faces a fundamental trade-off between steady-state accuracy and stability. Higher slopes reduce disturbance-induced SSE but can violate the stability condition, leaving conventional methods unable to optimize both objectives.

  • B. Steady State Error (SSE) Concerns: An external voltage disturbance changes the initial equilibrium and drives subsequent reactive-power updates through the local droop feedback.
  • B. Steady State Error (SSE) Concerns: When the stability condition holds, the disturbance response converges through a geometric matrix progression to a new equilibrium voltage and corresponding SSE.
  • B. Steady State Error (SSE) Concerns: Higher inverter slopes reduce SSE for a given disturbance but can violate the stability condition, so conventional designs typically compromise SSE to preserve stability.
  • B. Steady State Error (SSE) Concerns: High SSE may remain within ANSI limits initially but can leave little margin for external disturbances to push voltages beyond those limits.
  • B. Steady State Error (SSE) Concerns: Delayed droop has the same SSE as conventional droop, despite improving stability performance under some conditions.

C. Illustration

A modified IEEE four-bus system illustrates how external disturbances and slope choices affect droop-VVC behavior. The setup contrasts conservative and non-conservative slopes while introducing solar generation and a topology change.

  • C. Illustration: The illustration uses a modified IEEE four-bus system with 600 kW load and 900 kW solar generation at node 3.
  • C. Illustration: A normally open switch adds node 4 to simulate feeder-topology change, while slopes m = 1 and m = 6 represent conservative and non-conservative settings.
  • C. Illustration: Solar generation begins at t = 20, allowing the example to observe voltage-profile responses around a reference voltage µ = 1 at node 3.
  • C. Illustration: The example is intended to expose how changing operating conditions, topology, and parameter selection create control challenges in systems with many independent inverter devices.

III. ADAPTIVE CONTROL STRATEGY

The proposed adaptive VVC uses a two-layer local framework that separates fast voltage control from slower parameter adaptation. Its parameters adjust in real time to reduce SSE while preserving stability using only local voltage information.

  • Two-layer adaptive framework: The two-layer controller decouples stability and low SSE: the inner loop performs fast VVC, while the outer loop adapts separate control parameters.The outer loop runs more slowly so the inner controller can settle before new parameters are dispatched, avoiding hunting and over-corrections.
  • Adaptive strategy I: The error-adaptive parameter q_p is updated to reduce steady-state voltage deviation by increasing or decreasing var support according to the signed error.Positive or negative updates depend on whether voltage settles below or above the set point.
  • Adaptive strategy I: An analytical q_p update can achieve zero SSE in one iteration, but it requires feeder-wide information unavailable to local controllers, motivating the proposed local update.The local strategy trades the one-iteration analytical solution for implementation using local bus information.
  • Adaptive strategy I: The outer loop estimates average SSE over each time horizon using local inverter-bus voltages and updates q_p at each outer-loop interval.SSE_avg,i is compared with a tolerance band around the voltage set point, and its signed value determines the update direction.
  • Adaptive strategy I: The adaptive droop curve changes with q_p, while q_p = 0 recovers the conventional droop control.A correction factor k_d affects convergence speed and can be selected from offline studies.
  • Adaptive strategy I: The proposed approach may require multiple iterations to approach zero SSE, unlike the analytical solution, while retaining local-information operation.The update can be made faster and more accurate if information from other nodes becomes available.

B. Adaptive Slope Control: Strategy II

Strategy II adapts droop slope parameters using voltage flicker regions, seeking stable operation while keeping fluctuations within IEEE 141 limits. It decouples slope adaptation from SSE correction and updates inverter limits using available PV capacity.

  • B. Adaptive Slope Control: Strategy II: The strategy targets both stability and IEEE 141 voltage-flicker limits by adapting slope and inverter operating parameters.Its control parameters include slope, reactive-power bounds, and voltage limits dispatched to the inner loop.
  • B. Adaptive Slope Control: Strategy II: Strategy II changes droop slope according to four flicker regions, using larger reductions in critical conditions and smaller reductions near the limit.No action is taken in the safe zone; the relaxed zone permits slope increases only when SSE is out of range.
  • B. Adaptive Slope Control: Strategy II: Slope adaptation and SSE correction are decoupled, allowing conservative slopes to protect stability while the reactive-power parameter addresses SSE.Conservative slopes may temporarily increase SSE, after which Strategy I adapts the SSE-related parameter.
  • B. Adaptive Slope Control: Strategy II: Reactive-power limits are updated each outer loop from inverter rating and average PV real-power generation during the previous interval.The method uses the previous interval’s PV output rather than a forecast for the next interval.

IV. CONVERGENCE OF THE PROPOSED LOCAL ADAPTIVE CONTROL ALGORITHM

The proposed two-layer controller is analyzed by separating inner-loop and outer-loop convergence. Its slope adaptation maintains the inner-loop stability condition, while the algorithm updates SSE and flicker-related parameters in real time.

  • IV. CONVERGENCE OF THE PROPOSED LOCAL ADAPTIVE CONTROL ALGORITHM: The convergence analysis treats the two-layer controller as separate inner and outer loops, assuming the inner loop reaches steady state within horizon T.The adaptive scheme measures voltage, calculates SSE and flicker, then updates error and slope parameters.
  • IV. CONVERGENCE OF THE PROPOSED LOCAL ADAPTIVE CONTROL ALGORITHM: The inner local control converges when selected slopes remain below critical values, which Strategy II maintains by keeping slopes conservative.This links slope adaptation directly to the sufficient inner-loop convergence condition.

A. Outer Loop Control Convergence

The outer adaptive loop is represented as a linear discrete feedback system whose SSE convergence depends on the correction-factor matrix. A spectral-radius condition guarantees convergence, while local diagonal updates trade speed for locality.

  • A. Outer Loop Control Convergence: The outer-loop SSE evolves as [S]_(t_o+1) = B[S]_(t_o), where B = I − [I + AM_p]^-1AK_d determines convergence behavior.The derivation reduces the outer-loop dynamics to SSE as the sole state variable.
  • A. Outer Loop Control Convergence: ρ(B) < 1 guarantees convergence to zero SSE for any initial SSE under the derived outer-loop model.The condition requires selecting K_d so that the feedback matrix’s spectral radius remains below one.
  • A. Outer Loop Control Convergence: A non-diagonal K_d can achieve zero SSE in one iteration, but it requires each node to use SSE values from all other nodes.The proposed local implementation instead accepts slower convergence to preserve locality.
  • A. Outer Loop Control Convergence: For the illustrative scalar system, k_d < 4.5 produces overdamped convergence, k_d = 4.5 reaches zero in one iteration, and 4.5 < k_d < 9 yields decaying oscillations.When k_d > 9, SSE diverges with non-decaying oscillations.

A. Small System Illustration

The small-system study compares adaptive VVC with delayed VVC under substation-voltage, cloud-cover, and topology disturbances. The broader evaluation uses a detailed 1500-node unbalanced IEEE 123-bus feeder model.

  • A. Small System Illustration: At a substation-voltage increase from 1.03 to 1.05, adaptive VVC re-tracks the set point within one iteration, whereas delayed VVC causes voltage violation.The comparison is shown for the disturbance scenarios in Fig. 11.
  • A. Small System Illustration: Under sudden cloud cover with non-conservative settings, adaptive VVC maintains a smooth voltage profile unlike delayed VVC.During the first 10 seconds after VVC activation, adaptive VVC has higher SSE because correction begins after the outer-loop horizon.
  • A. Small System Illustration: The large-feeder evaluation uses an unbalanced 1500-node expansion of the IEEE 123-bus feeder with detailed 120-volt secondary-side house-load modeling.The model contains 1280 residential houses and approximately 6 MW peak load.
  • A. Small System Illustration: The feeder simulation uses 24-hour total load and solar-PV profiles for its operating scenarios.The profile is identified in Fig. 13.

C. Performance Metrics

The proposed adaptive VVC is evaluated against conventional and delayed droop controls using set-point tracking, flicker, and voltage-violation metrics under static, daily, and sudden-disturbance conditions.

  • Static Load Conditions: The adaptive controller tracks a changed voltage set-point accurately, whereas conventional and delayed droop controls settle with high steady-state error.The comparison applies a set-point change from 1 to 0.96 pu under static load conditions.
  • Daily Load and Solar Variation: 31 to 5 OLTC tap counts: adaptive VVC maintained a flatter daily voltage profile while reducing tap operations relative to no var control.Non-adaptive controls failed to track the set point during daytime peak solar generation.
  • Daily Load and Solar Variation: Near-zero MSSE at conservative settings: the adaptive controller decoupled set-point accuracy from stability without making the system prone to flicker.The delayed controller’s high MSSE could be reduced with a higher slope, but that setting increases vulnerability to sudden disturbances.
  • Sudden External Disturbances: 6919 to 107 flicker violations: delayed droop reduced flicker relative to conventional control, but adaptive control achieved zero flicker and voltage-violation indices under cloud intermittency.The intermittent-solar comparison uses a two-hour window and reports the adaptive controller’s zero indices despite visible disturbance effects.
  • Sudden External Disturbances: Non-conservative droop settings caused voltage oscillations after sudden cloud cover because freed inverter capacity was used immediately.The adaptive controller instead adjusts its behavior under the disturbance, avoiding the reported oscillatory response.
  • Sudden External Disturbances: The proposed control also supports real-time restoration of set-point tracking under changing generation conditions.The paper connects this capability to applications involving sudden real-power changes, including virtual inertia support.

VI. CONCLUSION

The study proposes a real-time local adaptive VVC scheme for high-PV systems that addresses the steady-state-error and stability challenges of conventional droop control. Its scope is limited for system-wide optimization, although it can be combined with centralized approaches.

  • VI. CONCLUSION: The proposed adaptive VVC achieves high set-point tracking accuracy and control stability while adapting parameters to external disturbances in real time.It remains compatible with IEEE1547 and Rule 21 practices and is evaluated against existing droop methods on a large unbalanced distribution system.
  • VI. CONCLUSION: Local control may be less effective for system-wide optimization, but the framework can be combined with centralized approaches.The paper identifies supervisory integration and coordination with conventional regulators as future work.
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