Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Electrical Engineering and Computer Science

First Advisor

Reinaldo Tonkoski


active power curtailment, adaptive dynamic programming, distributed generation, low voltage distribution network, renewable energy, solid state transformer


The modern voltage distribution systems consist of distributed generation (DG), like photovoltaics (PV) and wind. These resources are inexhaustible and environmentally friendly. The existing low voltage (LV) distribution networks are typically designed for unidirectional power flow. The integration of DG makes the LV distribution networks prone to difficulties related to voltage, frequency, and power quality. The main challenges in the integration of DG occur due to the intermittent nature of DG. The amount of DG compared with the total generation resource on a power system network is measured as penetration. The system undergoes through reverse power flow when there is a high penetration of DG and low loading conditions in the network. The reverse power flow in the network negatively affects the voltage profile of the LV distribution networks. Thus, voltage regulation is required in LV distribution networks for the integration of DG. Solid State Transformers (SSTs) are power electronic-based transformers that will be a vital component of the future smart grid. The future smart grid will have numerous DG which will require improved controllability to maintain proper coordination between stochastic DG and load. Among its various unique features, the reactive power compensating capabilities of SSTs can be explored in modern distribution systems for voltage regulation under high DG penetrations. SSTs are power electronic devices that show fast and non-linear dynamics which means the simulation models are often complicated and need small time steps for accurate solutions. This prevents real-time and long-term simulation of large distribution systems as the simulations become computationally prohibitive. This work designs a simplified equivalent model of an SST using simple current and voltage sources along with simple modeling equations. These simplified models can be used to perform long-term voltage regulation studies of distribution systems where traditional transformers are replaced with SSTs. Clean energy incentives and the continuous fall in the cost of PV installations have led to a steady growth in residential PV systems. One of the main consequences of higher PV penetration in LV distribution networks is the overvoltage problem. Active power curtailment (APC) of PV inverters has been previously used to curtail the output power of the inverters below its operating point to prevent such overvoltages. However, APC uses a constant droop-based approach to curtail the power, based on the difference between the measured voltage and a critical voltage level. In this thesis, APC is implemented with constant droop and other droop models in a typical LV distribution network in North America, with high PV penetration level. The simulation results show that the system undergoes excessive curtailment resulting in unnecessary energy loss. An adaptive droop-based approach using adaptive dynamic programming (ADP) is proposed as a possible solution to minimize the total energy loss in the system while keeping the system voltage under the critical operating limits. The energy loss due to curtailment decreased by 17.4% after implementing the adaptive-droop based approach using ADP.

Library of Congress Subject Headings

Low voltage systems.
Distributed generation of electric power.
Renewable energy sources.
Overvoltage -- Prevention.


Includes bibliographical references (63-67)



Number of Pages



South Dakota State University


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