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Data-driven Local Control Design using Optimization and Machine Learning Techniques

Stavros Karagiannopoulos, Petros Aristidou, Gabriela Hug

arXiv:1808.01009v2math.OC

TL;DR

Distribution networks often lack the monitoring and communication infrastructure needed for optimal coordinated control, leaving them dependent on suboptimal local schemes. This paper combines offline chance-constrained OPF, historical data, and machine learning to design local controls for multiple DERs. In the demonstrated unbalanced low-voltage network, the proposed controls outperform standard industry practice and mimic OPF-based control without communication.

  • Problem

    Distribution networks commonly lack monitoring and communication infrastructure, while standard local controls can use one-size-fits-all settings that create security and power-quality problems.

  • Method

    The method uses an offline three-phase, multi-period chance-constrained OPF on historical data to generate DER setpoints, then applies regression and classification machine learning to derive local controls.

  • Results

    The proposed local control mitigates overvoltages and overloads, improves balancing, and mimics OPF-based control without communication, outperforming standard industry practice.

  • Takeaways & Limitations

    Data-driven local controls can address security problems and optimize operation in an unbalanced distribution network without monitoring and communication infrastructure.

Abstract

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The optimal control of distribution networks often requires monitoring and communication infrastructure, either centralized or distributed. However, most of the current distribution systems lack this kind of infrastructure and rely on suboptimal, fit-and-forget, local controls to ensure the security of the network. In this paper, we propose a data-driven algorithm that uses historical data, advanced optimization techniques, and machine learning methods, to design local controls that emulate the optimal behavior without the use of any communication. We demonstrate the performance of the optimized local control on a three-phase, unbalanced, low-voltage, distribution network. The results show that our data-driven methodology clearly outperforms standard industry local control and successfully imitates an optimal-power-flow-based control.

I. INTRODUCTION

The paper addresses the lack of monitoring and communication infrastructure in distribution grids by designing optimized local DER controls from historical data, centralized optimization, and machine learning. It targets several DER types and uses a three-phase, multi-period chance-constrained OPF formulation that accounts for renewable uncertainty and unbalanced operation.

  • Motivation: Distribution networks increasingly need active DER-based operation, but existing local controls often use one-size-fits-all parameters and can create security and power-quality problems.Centralized schemes require costly infrastructure, while decentralized schemes avoid communication but may perform poorly across grids, generator types, and operating conditions.
  • Proposed approach: The proposed method uses historical data and offline centralized optimization to derive local controls that do not require real-time monitoring or communication.The offline process computes optimal DER setpoints for operating conditions, which machine-learning models then use to construct local control schemes.
  • Proposed approach: The methodology covers reactive power control, active power curtailment, controllable load shifting, and battery energy storage systems.Segmented regression, SVM regressors, and SVM classifiers are among the machine-learning techniques used for local control design.
  • Contributions: Its offline optimization is based on a tractable three-phase, multi-period chance-constrained OPF that incorporates renewable uncertainty and unbalanced operation.The formulation supports multiple DER models and generates the setpoints used to train local controls.
  • Evaluation: The paper evaluates the optimized controllers in a three-phase, unbalanced, low-voltage distribution-network case study and reports simulation results in Section IV.The paper extends earlier work on offline DER control design, controllable loads, and machine-learning-derived volt-var curves.

II. CENTRALIZED CHANCE-CONSTRAINED OPF

The centralized CC-OPF computes DER setpoints over the network and time horizon by minimizing control costs and network losses while representing DER power injections and flexible-load and battery actions. Its formulation uses active-curtailment and reactive-support terms, with reactive support prioritized through the assumed cost relationship.

  • 1) Objective function:: The OPF objective minimizes DER control costs and network losses across nodes, phases, branches, and the full time horizon.The objective includes active-power curtailment and reactive-power support terms weighted by their respective cost coefficients.
  • 1) Objective function:: The formulation computes curtailed DG power from maximum available generation and actual active-power injection, while reactive support is represented by the magnitude of DG reactive injection.These quantities connect DER operating decisions to the objective function and network power-balance constraints.
  • 1) Objective function:: Reactive-power support is prioritized over active-power curtailment by assuming CQ ≪ CP.CP represents the cost of active-power curtailment, while CQ represents the cost of reactive-power support.
  • 2) Power balance constraints:: Node power injections combine DG generation with flexible-load demand and battery charging or discharging actions.The active and reactive injection equations include flexible-load demand, load power factor, and BESS power terms.

3) Power flow constraints:

The power-flow formulation replaces nonlinear AC constraints with a single-iteration backward/forward sweep approximation for a three-phase, unbalanced network. It combines branch-current and voltage calculations with thermal and voltage constraints, while rotating phase voltages to avoid nonconvexity from minimum-voltage requirements.

  • 3) Power flow constraints:: The iterative backward/forward sweep method approximates the nonlinear AC power flow to make multi-scenario, multi-period OPF computation tractable.The formulation extends the sweep method to a three-phase, unbalanced distribution system and uses a single iteration in the OPF constraints.
  • 3) Power flow constraints:: The sweep maps bus injection currents to branch currents and voltage drops, then computes bus voltages while incorporating OLTC tap position.BIBC represents network topology, BCBV represents line impedances and mutual coupling, and ρt defines the tap position.
  • 3) Power flow constraints:: The convex formulation approximates nonlinear AC OPF, remains tractable for a three-phase model, and produces AC-feasible solutions that account for uncertainties.The stated properties support using the formulation to derive optimal setpoints under uncertain operating conditions.
  • 4) Thermal loading and voltage constraints:: Thermal and voltage constraints bound branch currents and bus-voltage magnitudes, with relaxation variables available when limits cannot be met.The current constraint uses branch thermal limits, while voltage constraints use upper and lower acceptable voltage limits.
  • 3) Power flow constraints:: Rotating the three voltage phases toward a common reference axis avoids the nonconvexity caused by minimum-voltage magnitude requirements.The rotation defines the same feasible-space treatment for each phase.

5) Balancing constraint:

The formulation balances three-phase voltages using a voltage-unbalance constraint and models controllable loads and battery storage subject to operational constraints.

  • 5) Balancing constraint:: The voltage-unbalance factor is constrained below an acceptable maximum, with a negative-sequence approximation used to avoid nonconvexity.The approximation assumes the positive voltage sequence is close to 1 pu.
  • 6) DER constraints:: Reactive and active-power limits represent inverter-based DG operating restrictions, including technical or regulatory power-factor limitations.These restrictions can link active and reactive power limits through a maximum power-factor value.
  • 6) DER constraints:: Flexible loads shift a fixed amount of consumption across time while maintaining the final total daily energy demand.The shift variable indicates whether demand increases, decreases, or remains unchanged relative to the initial demand.
  • 6) DER constraints:: Battery constraints track stored energy between fixed state-of-charge limits using charging efficiency, time intervals, and charging or discharging power.Binary variables ensure that the battery does not charge and discharge simultaneously.

B. Accounting for Uncertainty through Chance Constraints

Chance constraints incorporate PV generation uncertainty into voltage and current security limits, using an iterative tightening procedure to obtain a tractable formulation.

  • B. Accounting for Uncertainty through Chance Constraints: PV generation is treated as the uncertainty source, while load uncertainty could be included similarly.Chance constraints limit the probability of violating security constraints.
  • B. Accounting for Uncertainty through Chance Constraints: Voltage and current constraints are modeled as chance constraints that must hold with a selected probability 1−ε.For example, the maximum voltage magnitude must remain below its limit with probability at least 1−ε.
  • B. Accounting for Uncertainty through Chance Constraints: The resulting CC-OPF is solved iteratively by alternating deterministic optimization with tightened constraints and recalculation of the optimal tightenings.The procedure converges when the tightening values stop changing between iterations.

2) Uncertainty margin evaluation based on Monte Carlo Simulations:

Uncertainty margins are estimated by Monte Carlo simulation and fed back into an iterative tightened-constraint procedure until the margins converge.

  • 2) Uncertainty margin evaluation based on Monte Carlo Simulations:: Monte Carlo simulations evaluate uncertainty margins outside the OPF iterations while allowing nonlinear AC power flow and arbitrary uncertainty distributions.The margins are held constant within each OPF solution and then reevaluated.
  • 2) Uncertainty margin evaluation based on Monte Carlo Simulations:: Empirical voltage and current distributions are formed at each time step, and their 1−ε quantiles determine the constraint tightenings.Each tightening is the difference between the zero-error forecast and the corresponding empirical quantile.
  • 2) Uncertainty margin evaluation based on Monte Carlo Simulations:: The algorithm alternates deterministic OPF solutions with uncertainty-margin calculations and declares convergence when tightening changes fall below a threshold.The margins depend on the selected DER setpoints, requiring this iterative update.

C. Solution Algorithm

The solution algorithm combines a centralized CC-OPF with backward-forward-sweep power-flow updates and exact AC feasibility projection, iterating until convergence.

  • C. Solution Algorithm: The algorithm initializes uncertainty margins to zero and three-phase voltages to a flat profile before solving the centralized multi-period CC-OPF.The centralized scheme computes optimal DER setpoints.
  • C. Solution Algorithm: The BFS-OPF block uses a single backward-forward sweep to replace exact nonconvex AC power flow with a linearized approximation for setpoint optimization.The resulting setpoints are then evaluated with an exact power-flow algorithm.
  • C. Solution Algorithm: After exact power-flow projection, updated voltages are used for another BFS-OPF step, and the iterative procedure continues until all components converge.The optimization and uncertainty loops have separate iteration indices.
  • C. Solution Algorithm: Nonconvergent cases can cycle between points with different tightenings, so an acceleration factor reduces update aggressiveness at the cost of more iterations.The method is reported to converge after a few iterations when the OPF solution changes little between iterations.

III. OPTIMIZED LOCAL CONTROL DESIGN

The method generates optimal DER setpoints offline from seasonal historical data and uses them to train local controls that approximate optimal operation. Seasonal or topology-specific control schemes can maintain near-optimal behavior across changing operating conditions.

  • III. OPTIMIZED LOCAL CONTROL DESIGN: The workflow combines a distribution-network model, historical generation and consumption data, centralized optimization, and machine learning to derive local controls.The optimization accounts for renewable uncertainty and unbalanced three-phase operation.
  • III. OPTIMIZED LOCAL CONTROL DESIGN: Offline CC-OPF computes optimal DER setpoints from selected seasonal historical operating scenarios for training local controls.Scenario selection determines the basis of the learned local schemes.
  • III. OPTIMIZED LOCAL CONTROL DESIGN: PV generation is estimated from historical expected injections and installed DG capacity because exact operational generation is unavailable without detailed monitoring.These uncertain estimates are used in the CC-OPF solution.
  • III. OPTIMIZED LOCAL CONTROL DESIGN: Season-specific or topology-specific local schemes can be changed to maintain behavior close to optimal throughout the year.The paper proposes changing schemes based on the season or distribution-network topology.

B. Derivation of DG local controls

DG active-power curtailment and reactive-power controls are represented by optimized piece-wise linear characteristic curves. An iterative constrained regression procedure refines breakpoints and slopes from optimal setpoints.

  • B. Derivation of DG local controls: The method derives individual DG curves for active-power curtailment and reactive-power control from CC-OPF active and reactive setpoints.The curves can contain arbitrarily many piece-wise linear segments and are optimized for each DG and network.
  • B. Derivation of DG local controls: Breakpoint locations and slope coefficients are optimized through iterative refinement combined with a constraint residual sum-of-squares problem.The procedure enforces monotonicity and slope constraints while fitting the piece-wise linear model.
  • B. Derivation of DG local controls: The algorithm returns complete local characteristic curves mapping voltage to active or reactive DG response after convergence and post-processing.The returned representation contains breakpoints and slope factors for each DG.
  • B. Derivation of DG local controls: The regression substitutes the nonlinear breakpoint-dependent term with a Taylor expansion around fixed breakpoints at each iteration.A parameter updates breakpoint locations toward the optimal values.

C. Local control of Battery Energy Storage Systems

Battery energy storage local controls use support-vector regression to approximate optimal active- and reactive-power setpoints from local operating features. Candidate kernels are compared using out-of-sample error to select the model.

  • C. Local control of Battery Energy Storage Systems: SVM regression balances flatness against deviations beyond an epsilon margin through the box constraint C.The method uses the margin and regularization parameters to control model fitting and overfitting.
  • C. Local control of Battery Energy Storage Systems: SVM regression approximates BESS active- and reactive-power setpoints using local voltage, load, and PV active-power features.The model is designed to mimic the CC-OPF response without requiring centralized real-time coordination.
  • C. Local control of Battery Energy Storage Systems: The BESS model tests linear, polynomial, and radial-basis-function kernels and retains the kernel with the lowest out-of-sample error.Kernel selection addresses potentially nonlinear relationships between local features and optimal setpoints.

D. Local control of Controllable Loads

The case study evaluates learned local controls for controllable loads and other DERs on an unbalanced European low-voltage grid. The learned load classifier achieves perfect accuracy on the reported data, while the broader monthly comparison shows local controls mitigate key network violations relative to industry practice.

  • D. Local control of Controllable Loads: The evaluation uses a typical European radial LV grid with uneven three-phase load and PV allocation to represent unbalanced operation.The case includes PV units, a BESS, and a flexible load connected at specified nodes and phases.
  • D. Local control of Controllable Loads: The one-month comparison contrasts German grid-code control, perfect-communication OPF control, and the proposed learned local controls.The study uses 7200 summer training samples and evaluates the methods during a separate monthly test period.
  • D. Local control of Controllable Loads: PV units near the substation show capacitive reactive-power behavior, whereas units near the feeder end use inductive behavior at lower voltages.The reported curves reflect loss optimization near the substation and overvoltage management near the feeder end.
  • D. Local control of Controllable Loads: The controllable-load classifier achieves 100% overall accuracy because its training data are perfectly linearly separable.Its three classes represent load decrease, no shifting, and load increase.
  • D. Local control of Controllable Loads: The classifier increases load above 0.3 p.u. PV injection, while reducing or not shifting load during low-PV periods to preserve daily demand.The decision boundaries use local voltage magnitude and PV injection as features.

B. Results

The proposed local control mitigates voltage, thermal-loading, and balancing problems while satisfactorily mimicking OPF-based control without communication. It also outperforms current local regulations in the demonstrated network.

  • Method 2 mitigates overvoltages and overloads to grid-code-acceptable values, improves balancing, and mimics OPF-based control without communication.The method has only small balancing violations during 5 hours of the month, described as acceptable by grid codes.
  • The proposed local control is more conservative than OPF-based control because the PV unit absorbs less reactive power across most voltage levels.
  • Method 0 produces frequent overvoltages, whereas the OPF-based approach and proposed local control satisfy voltage security constraints.
  • The methodology targets secure and optimized operation in challenging distribution networks without the monitoring and communication infrastructure required by centralized control.
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