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Emergency Control of Transmission Voltages by Coordinating DERs From Multiple Substations

Francisco Escobar, Gustavo Valverde

arXiv:2609.36094v1eess.SYcs.SY

TL;DR

Long-term voltage stability can be threatened when a weakened transmission network cannot supply demanded power, while DER-based emergency support must contend with regulator interactions, coordination, and communication constraints. The paper proposes a hierarchical MPC coordinating DER aggregations and LTCs across substations; simulations report successful coordination, maintained stability, and better performance than model-free local control.

  • Problem

    DER-based support for long-term voltage stability must address interactions with legacy regulators, intersubstation coordination, and real-time communication limits.

    Source: §I · p. 1

  • Method

    A hierarchical MPC coordinates substation LTCs with DN power requests that aggregators broadcast to downstream DERs.

    Source: §I · pp. 1–2

  • Results

    Simulations on a realistic transmission network showed successful DER–LTC coordination while maintaining long-term voltage stability and better performance than model-free local control.

    Source: §V · p. 15

  • Takeaways & Limitations

    The scheme can smoothly move the system to a new steady state after a disturbance and is robust to predictor inaccuracies in the tested simulations.

    Source: §V · p. 15

Abstract

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Voltage stability can be endangered in transmission networks that operate under high strain and exhibit a large separation between generators and loads. During emergencies associated to voltage instability, one promising supporting countermeasure is to control large populations of Distributed Energy Resources (DERs) connected to medium- and low-voltage networks, so that they locally reduce the net load by modifying their power generation or consumption. However, it is challenging to achieve this control while anticipating interactions with legacy voltage regulators, coordinating efforts across substations, and exchanging small amounts of information with DERs. In this paper, we propose a control scheme that coordinates DER aggregations with the load tap changers of substation transformers, asks them to contribute power depending on the substation they are connected to, and relies on lightweight communication. Our simulations show that the proposed control can successfully coordinate DERs and load tap changers to enhance long-term voltage stability.

I. INTRODUCTION

The introduction frames DER-based support for long-term voltage stability as a coordination and communication challenge, then proposes a hierarchical MPC scheme spanning transmission and distribution resources. The following discussion explains how local voltage-regulator actions and DER interactions can compound instability across substations.

I. INTRODUCTION

  • DER control must account for interactions with slow LTCs, coordinate actions across substations, and limit real-time communication with large device populations.Existing approaches described in the section do not jointly address all three requirements.Source: §I · p. 1
  • A hierarchical controller uses transmission-level LTC actions and DN power requests, which aggregators broadcast as signals to downstream DERs.Individual DER disaggregation is outside the paper’s scope.Source: §I · p. 1
  • The MPC coordinates resources across substations, embeds a stability indicator, and uses system-wide information to scale and sign remedial actions.The paper contrasts this model- and measurement-informed MPC with a comparable model-free local-control scheme.Source: §I · p. 2

A. The Need for Coordination

  • After a fault, LTCs restoring their own MV voltages can restore load power, depress HV voltage, and contribute to voltage collapse without intersubstation coordination.The described Nordic-system response also links successive loss of diagonal dominance to a positive-feedback mechanism.Source: A. The Need for Coordination · pp. 2–3
  • DER reactive support can raise MV voltage and restore voltage-sensitive loads, increasing active demand; depending on system physics and control, this hidden effect may precipitate instability.The discussion distinguishes the effects of individual and cumulative tap changes on HV and MV voltages.Source: A. The Need for Coordination · p. 3

B. Real-Time Detection of Voltage Instability

The section introduces the New LIVES Index (NLI) for detecting voltage instability when voltage measurements alone are insufficient. It derives the indicator from boundary-bus PMU measurements and explains its relationship to corridor transfer limits.

B. Real-Time Detection of Voltage Instability

  • The NLI is used because instability detection may require more than voltage measurements, particularly with high DER shares.The passage assumes PMUs are installed at boundary buses of the weak area.Source: B. Real-Time Detection of Voltage… · p. 3
  • At each boundary bus, the procedure derives imported active power and conductance from PMU voltage and current measurements before defining the instantaneous NLI.The imported current aggregates flows from adjacent sending buses.Source: B. Real-Time Detection of Voltage… · p. 3
  • At the corridor power-transfer limit, an increase in conductance does not increase active power, making the NLI nonpositive.Moving averages can suppress fast transients, and OEL states elsewhere can be used to reset NLIs.Source: B. Real-Time Detection of Voltage… · p. 3

III. PROPOSED CONTROL

The controller coordinates DER aggregations and LTCs through an MPC that uses transmission-level measurements and simplified distribution models. Aggregators broadcast compact active- and reactive-power requests to downstream DERs.

A. Control Architecture

  • Each transformer’s aggregator broadcasts a common signal with independent integer-valued active- and reactive-power requests, without receiving individual DER participation reports.Requests are issued every few seconds; injection is positive, consumption negative, and zero denotes inaction.Source: B. MPC and Aggregator Interaction · p. 4

B. MPC and Aggregator Interaction

  • The MPC represents downstream DERs as a fast fictitious aggregate and loads as an aggregate voltage-sensitive exponential model.The model parameters can be estimated, and the inherent MPC feedback is intended to compensate for simplified models.Source: B. MPC and Aggregator Interaction · p. 4

III. PROPOSED CONTROL

  • The MPC uses measured LTC ratios and estimated DER contributions as manipulated variables, while monitoring transformer-side voltages and the transmission-network stability indicator.DER contributions are estimated because boundary measurements also reflect distribution losses and voltage-sensitive load restoration.Source: B. MPC and Aggregator Interaction · p. 4

C. MPC Formulation

The formulation predicts voltages and stability indicators from manipulated-variable changes, then optimizes control efforts under physical and operating constraints. It switches between emergency support and restoration objectives, with soft voltage and stability limits to preserve feasibility.

C. MPC Formulation

  • Predicted voltages and NLIs use a linearization at the post-disturbance operating point and topology, with closed-loop MPC compensating for model or sensitivity errors.Sensitivities may come from a power-flow model or measurements and can be updated infrequently.Source: C. MPC Formulation · p. 5
  • The objective minimizes abrupt control changes during an emergency, then can steer DER powers and other manipulated variables toward their pre-disturbance values during restoration.Mutually exclusive mode parameters select emergency or restoration; slack variables can render the constrained problem feasible.Source: C. MPC Formulation · p. 5
  • Tap-movement and boundary-power limits are physical or contractual constraints, while voltage and NLI limits are soft constraints to avoid infeasibility after large disturbances.Voltage and NLI bounds may be tightened progressively along the prediction horizon.Source: C. MPC Formulation · p. 5
  • LTC tap ratios remain continuous during optimization, and their changes are accumulated until they exceed a physical tap step, when that step is enacted.The MPC therefore avoids integer decision variables for discrete LTC actions.Source: C. MPC Formulation · p. 5
  • The resulting convex quadratic program scales with the number of coordinated substations, not the number of DERs, because the MPC controls DER aggregations.The paper anticipates coordination mainly within weak areas, where voltage problems are primarily local.Source: C. MPC Formulation · pp. 5–6
  • The formulation keeps constant DER bounds because the authors assume limited distribution-network knowledge and do not prioritize DN operational constraints during an emergency.Compensation schemes for DER participation are outside the paper’s scope.Source: C. MPC Formulation · p. 6
  • For reactive-only requests, DERs may use P-priority, which makes available reactive power depend on nominal capacity and active-power output.If aggregate reactive support is insufficient, the paper describes possible compensation to encourage Q-priority operation.Source: C. MPC Formulation · p. 6
  • A planning cost-benefit analysis may determine how many DERs participate per substation, potentially prioritizing larger units to maximize impact.The stated scalability chiefly depends on communication infrastructure for transmitting signals.Source: C. MPC Formulation · p. 6

D. Sequence of Events

After a large disturbance, the controller initializes the MPC in emergency mode, updates sensitivities when topology changes, and repeatedly measures, optimizes, and enacts the first control change. It deactivates when safe operation is reached, restoring prior settings only when safe to do so.

D. Sequence of Events

  • A detected disturbance starts the controller, which configures the prediction matrices and emergency objective; topology changes or major outages trigger a sensitivity-matrix update.At each iteration, the controller estimates manipulated variables, collects outputs, solves the optimization, and enacts only the first change.Source: D. Sequence of Events · p. 6
  • Once operation is safe, the controller can deactivate or restore DERs and LTCs toward pre-disturbance settings if other sources can take over or the triggering disturbance is resolved.If safe restoration is not possible, it continues minimizing control effort and deactivates once safe operation returns.Source: D. Sequence of Events · p. 6

E. Computation of NLI Sensitivities

The method estimates NLI sensitivity using power-flow studies and constructs a static NLI from fictitious tap-ratio perturbations. It accounts for voltage-sensitive load behavior, while treating aggregate DER output as voltage-independent for approximation.

E. Computation of NLI Sensitivities

  • The static NLI is defined from fictitious small transformer-tap perturbations, using the lowest resulting NLI as the indicator for the current operating point.Tap perturbations change boundary-bus active power and conductance.Source: E. Computation of NLI Sensitivities · p. 7
  • NLI sensitivity to each manipulated variable is approximated by running two successive power-flow studies.The method treats the NLI as non-static because its definition depends on changing active power and conductance.Source: E. Computation of NLI Sensitivities · p. 7
  • For improved accuracy, NLI computation retains voltage-sensitive load dependence; aggregate DER output may be approximated as voltage-independent.An exponential load model can be incorporated into power-flow mismatch equations and the Jacobian.Source: E. Computation of NLI Sensitivities · p. 7

IV. SIMULATION RESULTS

The simulations use a stressed Nordic test-system central area with aggregated DERs and detailed models of slow devices. Scenarios compare uncontrolled and alternative control strategies after a critical line outage.

IV. SIMULATION RESULTS

  • The central area connects through four transformers between 400 kV and 130 kV systems, with LTC-equipped step-down transformers and six substations.Autonomous LTCs use a 1 ± 0.01 pu deadband, with randomized initial and subsequent delays.Source: §IV · p. 7
  • Aggregated DERs supply 20% of distribution-network consumption and have 20% nominal-capacity headroom for support.They initially operate at unity power factor; in the stated setup, they follow reactive-power setpoints without curtailing active power.Source: §IV · p. 7
  • The simulations use 1 ms time steps and include detailed LTC and overexcitation-limiter models, but omit slow self-restoring loads.Potential interactions with secondary frequency control are also excluded because the scenarios do not involve generation/load tripping.Source: §IV · p. 7
  • The scenarios compare no control, local LTC blocking, the LC benchmark, and proposed MPC variants after line 4032–4044 trips.Reactive-power support is used through the initial comparisons; active-power support is considered separately.Source: §IV · pp. 7–8

A. Response Without Control

Without control, autonomous LTC actions temporarily restore distribution-side voltages but ultimately contribute to declining voltages and collapse. Sensitivities remain fairly stable after the outage in this scenario, though stress may change them.

A. Response Without Control

  • The collapse occurs about 30 s later than in [25, Fig. 3] because enlarged loads increase voltage sensitivity; DER effects on collapse timing can vary with share and control mode.The load enlargement causes voltage declines to reduce load power, slightly improving stability in this scenario.Source: A. Response Without Control · p. 8
  • The uncontrolled system collapses after LTC actions and OEL support withdrawals drive voltages downward and NLIs negative.DERs provide no reactive support in this case; the simulation ends with voltage collapse at HV bus 1042 and MV bus 2.Source: Figure 8 · p. 8, A. Response Without Control · p. 8
  • Sensitivity signs and magnitudes remain fairly constant after the outage, supporting infrequent MPC updates, but this may not hold under stressed conditions.The outage is outside the central area; sensitivities are examined from before the disturbance through shortly before collapse.Source: A. Response Without Control · p. 8

B. Response Under Local LTC Blocking

Local LTC blocking avoids simulated collapse but leaves weak voltages and negative stability indicators. The LC benchmark coordinates local voltage goals with DER support, yet its actions produce oscillatory, antagonistic effects across substations.

B. Response Under Local LTC Blocking

  • Local blocking uses a 0.9 pu HV-side threshold sustained for 3 s, but neighboring active LTCs continue pulling voltages down after the first block.Only buses 41, 47, and 51 reenter the LTC deadband, at the expense of neighbors; several machines reach field-current limitation and NLIs are negative.Source: B. Response Under Local LTC Blocking · pp. 8–9, Figure 10 · p. 9

C. Response Under an LC scheme

  • The LC scheme anchors an L-shaped voltage region after an alarm, steering tap ratios and downstream DER reactive-power ramps toward its operating region.In this implementation, the first sign-changing NLI triggers all 11 transformer schemes simultaneously; the anchored region uses δ = 0.01 pu and ε = 0.02 pu.Source: C. Response Under an LC scheme · pp. 9–10, Figure 11 · p. 10
  • After the first NLI turns negative, the 11 LC schemes request reactive support, but the resulting voltage dynamics are oscillatory as local LTC actions affect neighboring voltages.The bus 42 LTC acts twice between 2 and 3 minutes; the response is less smooth than, which divides the central load among 144 transformers rather than 11.Source: C. Response Under an LC scheme · pp. 10–11, Figure 12 · p. 10

D. Response Under MPC

The MPC coordinates LTCs and DER reactive-power requests using sensitivities, operational constraints, and aggregator signals. In simulation, these joint actions improve stability and return voltages to the prescribed band.

D. Response Under MPC

  • The MPC uses a 10 s sampling period, a three-step prediction horizon, and a post-disturbance sensitivity matrix computed once with 10% model-parameter error.Tap ratios and reactive powers are constrained, while NLIs must remain positive and voltage deadbands are softly enforced.Source: D. Response Under MPC · p. 11
  • The controller overwrites NLI sensitivities to DER reactive power with zero, separating NLI control through tap ratios from voltage control through reactive injections.The design addresses the competing effects of tap ratios and reactive power on distribution voltages and NLIs.Source: D. Response Under MPC · p. 11
  • Aggregators map MPC requests to bounded, discretized broadcast signals using estimated downstream DER capacity, and DERs translate signals into reactive-power setpoints.Capacity-estimation error is modeled with zero mean and a standard deviation of 10% of installed capacity; signals are issued every second.Source: D. Response Under MPC · p. 11
  • Joint MPC actions improve voltage stability enough to reset the NLI to 0.1 and return voltages to the 1 ± 0.025 pu band after DER deployment.The MPC moves LTCs and requests reactive power according to DER size and location; G14 later exceeds its thermal limit only slightly, delaying OEL action.Source: D. Response Under MPC · p. 11, Figure 13 · p. 12

E. Response Under MPC in a T-D system

The T-D test system extends the Nordic network across transmission and medium-voltage levels using replicated distribution networks. Under MPC, its voltage and stability-indicator responses closely match the previous scenario, with smaller DERs providing limited reactive power.

E. Response Under MPC in a T-D system

  • The test system disaggregates the Nordic system's 11 medium-voltage loads using replicas of a 76-bus radial distribution network.DERs are spread over 15% of load buses, with outputs summing to the original DER share.Source: E. Response Under MPC in a T-D system · p. 12
  • The 2,624-bus T-D system connects replicated medium-voltage distribution networks through the existing 11 transformers and includes 339 DER A instances.Only 50 buses and 50 DERs are monitored to reduce computational burden.Source: E. Response Under MPC in a T-D system · p. 12
  • The simulated voltage and NLI responses essentially match the previous scenario, while DERs respond with no more than 2.5 Mvar.The smaller DER size accounts for the minor differences; MPC parameters remain unchanged.Source: E. Response Under MPC in a T-D system · p. 12, Figure 14 · p. 12

F. Scenario Comparison and Sensitivity Analysis

The scenario comparison finds that MPC avoids oscillations and requests sufficient reactive power, while sensitivity tests show adaptation to availability and settings. The outcomes are assessed using averages over time and across system elements.

Performance measures

Scenario comparison

  • The four-scenario comparison shows that MPC avoids voltage and tap-ratio oscillations, requests sufficient reactive power, and relies less on synchronous machines than the local-control scheme.The T-D case shows a slight stability improvement attributed to the constant-impedance load component from explicit distribution-network modeling.Source: F. Scenario Comparison and Sensitivity… · p. 13

Prediction horizon sensitivity

DER availability

Voltage deadband sensitivity

  • Halving the MV-side voltage half-deadband from 0.030 pu to 0.015 pu increases reactive-power effort tenfold, while the tighter settings incur voltage-constraint slacks.The MPC focuses more on voltage control, lowering average NLI in the 0.015 pu and 0.020 pu cases.Source: F. Scenario Comparison and Sensitivity… · p. 14, Table IV · p. 14

DER penetration sensitivity

G. Response Under MPC Including Active-Power Support

Simulations show that the proposed scheme coordinates DERs and LTCs to maintain long-term voltage stability, and performs better than model-free local control. In the active-power-support scenario, additional DER support is requested as the stability indicator becomes negative; the authors frame the scheme as an emergency first line of defense.

G. Response Under MPC Including Active-Power Support

  • The active-power-support case assumes inverter-based DERs with available headroom and circular capability, limits changes to ±5 MW per sampling period, and prices them ten times above reactive power.Flexible loads and more complex power-priority modes are also identified as possible active-power sources or controls.Source: G. Response Under MPC Including… · p. 14
  • When the NLI becomes negative, MPC requests active power; the added support leads to further active-power requests and tap-ratio increases, alleviating synchronous machines.The active-power injections are ramp-limited, and may reduce reactive power; the bus 47 DER's initial reactive contribution was about 25 Mvar, reaching 120% of its 31.25 MVA capacity.Source: G. Response Under MPC Including… · pp. 14–15, Figure 16 · p. 15
  • Active-power use may deplete battery storage or synchronize thermostatically controlled loads, so the scheme is framed as a first line of emergency defense.The authors expect network operators to respond with more sustainable countermeasures before these effects arise.Source: G. Response Under MPC Including… · p. 15

V. CONCLUSION

  • Simulations on a realistic transmission network show successful DER–LTC coordination and long-term voltage stability, with better performance than model-free local control.The scheme is also reported to be robust to predictor inaccuracies and to drive the system smoothly to a new steady state after disturbance.Source: §V · p. 15
  • Future work includes adapting MPC weights and horizons using historical measurements, strengthening aggregator knowledge, and exploring intrasubstation DER coordination and participant incentives.The authors also identify compensation strategies for DERs participating in emergency control as future work.Source: §V · p. 15
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