Document Type

Dissertation - Open Access

Award Date

2026

Degree Name

Doctor of Philosophy (PhD)

Department / School

Electrical Engineering and Computer Science

First Advisor

Xiaojun Xian

Abstract

The transition toward power systems with higher levels of inverter-based generation requires operating models that account for the dynamic support available from distribution-connected resources. Although inverter-based DERs can provide fast reactive-power support through functions such as Volt–VAR control, conventional optimal power flow models generally represent these resources as static power injections. In addition, transmission-level dispatch commonly represents the downstream distribution system as an aggregated load and does not explicitly consider the voltage at the point of common coupling. Consequently, an OPF solution may satisfy the transmission-bus voltage constraints while producing an operating point at which the downstream DERs do not have sufficient dynamic reactive-current capability to maintain or recover acceptable PCC voltages following a disturbance. The primary objective of this dissertation is to develop a time-coupled optimal power flow framework that incorporates DER Volt–VAR dynamic constraints so that transmission-level dispatch is coordinated with the voltage-dependent dynamic response of distribution-connected DERs. The first part of this dissertation reviews existing methods for integrating dynamic constraints into steady-state power system optimization models. The review covers conventional power system optimization, dynamic and security-constrained optimal power  flow, frequency and voltage dynamics, voltage-collapse mechanisms, and numerical methods for solving dynamic optimization problems. Existing formulations primarily emphasize synchronous-generator, rotor-angle, and frequency dynamics, while the voltage-dependent response of distribution-connected DERs is less frequently represented. The review identifies the need for computationally manageable formulations that directly incorporate DER voltage dynamics and coordinate the response of inverter-based resources with transmission-level dispatch. A centralized hybrid voltage-control framework is subsequently developed for an active distribution network. The proposed method coordinates discrete and continuous voltage-control resources, including on-load tap changers, capacitor banks, distributed generation, battery energy storage systems, and demand response. Recursive least-squares sensitivity estimation and a recursive matrix update are applied to reduce the computational requirements associated with repeated voltage-sensitivity calculations. The framework is evaluated using a modified IEEE 34-bus distribution system under small and large disturbances. The results show that the controller maintains the network voltages within the prescribed range of 0.95–1.05 pu under small disturbances, with an average computational time of approximately 1.2 s per control iteration. For large rapid disturbances caused by load variations of up to three times their nominal values, the controller restores the network voltages within a maximum response time of approximately 6 s while coordinating the available control devices and satisfying their operating constraints. Because the available output of solar-based DERs depends on local irradiance conditions, this dissertation also develops a spatiotemporal downscaling framework for producing localized day-ahead solar irradiance forecasts from coarse-resolution data. A nearest-neighbor random forest model is developed and compared with a nearest-neighbor Gaussian process model. The methods incorporate temporal observations, meteorological variables, and irradiance measurements from neighboring sites to capture spatial and temporal relationships. Their performance is evaluated using sites in Texas and further examined through a case study in Puerto Rico. The nearest-neighbor random forest generally provides higher forecasting accuracy and lower computational requirements. In the Texas study, the random forest model achieves an average validation accuracy of approximately 90.61% and requires approximately 2.5 times less computation than the Gaussian-process model. The results demonstrate the ability of the downscaling models to provide localized renewable-resource information for DER planning and power system operational studies. The next part of the dissertation develops a computationally efficient data-driven method for modeling aggregate DER Volt–VAR dynamics. Detailed electromagnetic transient representations can reproduce inverter and controller behavior but require extensive system information and significant computational effort. To reduce this burden, discrete voltage and current measurements are transformed into smooth and continuously differentiable functions using B-spline basis functions and functional data analysis. The derivatives obtained from the fitted functions are used to estimate low-order ordinary differential equations through linear least-squares regression for different Volt–VAR operating regions. The resulting equations provide an interpretable representation of the relationship between PCC voltage and aggregate DER current. The proposed model is compared with a conventional system-identification benchmark during training and validation. The first-order B-spline-based model achieves an accuracy of 98.78%, compared with 99.03% for the system-identification model, while reducing the modeling time from 254.07 s to 52.16 s. The computational advantage increases for higher-order models, demonstrating that the proposed method can represent aggregate DER dynamics accurately without the nonlinear parameter-estimation burden of conventional system identification. The identified DER dynamic equations are then discretized using the backward Euler method and incorporated into a time-coupled alternating-current optimal power flow formulation. The initial formulation is demonstrated using a simplified two-bus system. The optimization jointly determines the generator dispatch, PCC voltage trajectory, and DER reactive-current response while enforcing the network power-balance equations, generator operating limits, DER current capability, voltage-recovery requirements, and discretized dynamic equations over the optimization horizon. The results show that PCC voltage recovery is directly affected by the available DER reactive-current capability. Increasing the DER current limit improves the achievable voltage recovery, while insufficient dynamic current capability prevents the voltage from reaching the prescribed range. The optimized voltage and current trajectories are implemented in MATLAB/Simulink, where the time-domain results confirm the dynamic behavior obtained from the optimization. Finally, the proposed DER dynamic-constrained OPF is extended to a modified IEEE 9-bus transmission network with three DER-connected PCCs. Equivalent distribution paths and PCC buses are added to allow the transmission-level optimization to account for downstream voltage drops and the dynamic reactive-current capabilities of multiple DER aggregations. The formulation includes voltage-dependent DER dynamic constraints, deadband screening, feasibility management, contingency-constrained voltage recovery, and iterative consistency between the optimized PCC voltages and the selected dynamic operating regions. Results obtained without the DER dynamic constraints show that the transmission-bus voltages can satisfy their limits while the downstream PCC voltages remain below the acceptable range. Under this dispatch, the DERs provide reactive-current support but cannot fully recover the PCC voltages following an undervoltage contingency because the initial transmission-level setpoints do not provide sufficient voltage margin. When the PCC representation and DER dynamic constraints are incorporated into the OPF, the generators are dispatched at voltage setpoints that are compatible with the available DER support. The resulting increase in transmission-bus voltage, together with the coordinated reactive-current response of the DERs, restores the PCC voltages to their prescribed operating range. Time-domain validation confirms that the DERs increase reactive-current injection following undervoltage contingencies and absorb reactive current following overvoltage contingencies. In the overvoltage cases, the DER response reduces and settles the PCC voltages at approximately 1.02 pu. The proposed nine-bus time-coupled optimization is completed in 183.97 s on a local desktop computer and produces only a marginal increase in the objective value. The generator active-power setpoints, which represent the primary component of the power-dispatch cost, show no significant increase after the DER dynamic constraints are incorporated. These findings demonstrate that explicitly coordinating transmission-level generator dispatch with the dynamic Volt–VAR capability of downstream DERs improves PCC voltage recovery and stability with negligible impact on the primary cost of power dispatch.

Publisher

South Dakota State University

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Rights Statement

In Copyright