INTRODUCTION
Background
The electric power system encompasses generation, transmission, and distribution, continually evolving to meet rising demand in a cost-effective, efficient, and reliable way for both utilities and customers This has transformed the electric power grid into a complex and highly invested industry, driven by ongoing technological advancements Innovations such as SCADA, Energy Management Systems (EMS), Distribution System Management (DMS), Smart Grid technology, and Distribution Automation (DA) have emerged, enhancing the functionality and efficiency of the power grid.
Smart Grid
The smart grid concept emerged from the establishment of Independent System Operators (ISOs) and Regional Transmission Organizations (RTOs), as recommended by the Federal Energy Regulatory Commission (FERC) These entities aim to enhance the electrical grid's intelligence to meet the demands of the 21st century The U.S Department of Energy (DOE) articulates a comprehensive vision for the Smart Grid, emphasizing its importance in modern energy management.
1 Intelligent Automation– having sensors to sense overload conditions and rerouting power and avoiding outage conditions; automatic isolation of faulted areas with minimum disruption of power
2 Smooth Integration of Distributed Generation (DG) – integration of any fuel source including solar and wind as easily and transparently as coal and natural gas; also other technologies like energy storage
3 Sophisticated Demand Response Capabilities – supporting real-time communication between the consumer and utility so consumers can alter their energy consumption based on individual inclinations, like price and/or environmental concerns
4 Quality-centric – capable of delivering the power which is free of sags, spikes, disturbances and interruptions
5 Robust – highly resistant to cyber-attack and natural disasters as it becomes more decentralized
The implementation of Smart Grid technology offers significant advantages for the country, including a reduction in cascading outages and decreased reliance on foreign fuel sources A key goal of the Smart Grid initiative is to facilitate the seamless integration of distributed generation (DG) and innovative storage technologies into the existing grid These small-scale power generation systems, situated near the point of use, enhance cost efficiency, improve reliability, and contribute to lower emissions.
Distributed generation
The rise of smart grid technology has prompted utilities to integrate distributed generation (DG) into their existing infrastructure, offering significant technological and environmental advantages DG helps meet local consumer demand, reduces power losses, and mitigates the need for expanding transmission and distribution systems While traditional power sources were once the norm, renewable energy sources like wind power, solar photovoltaic, fuel cells, and micro-turbines have emerged as viable solutions to address increasing consumer demand, volatile fossil fuel prices, and environmental concerns Electromechanical DG can connect directly to the power grid, while other types require inverter-based systems for integration.
While integrating distributed generators (DGs) into the grid offers numerous benefits, it also presents several challenges This integration transforms the conventional unidirectional power flow of a radial distribution network into a two-way flow, complicating the operation of traditional relays and protection devices that lack directional capabilities Additionally, the connection of DGs through power electronic devices can negatively impact power quality, potentially leading to current and voltage waveform distortions and the introduction of harmonics.
Solar energy stands out as the most abundantly available renewable energy source, with photovoltaic (PV) generators experiencing rapid growth in the distributed generation (DG) market, projected at an annual increase of 25-35% This growth can be attributed to advancements in power electronics and storage devices, which are crucial for large-scale PV installations Additionally, PV generators are promoted to address environmental challenges such as the greenhouse effect and air pollution, while also alleviating thermal overloads and minimizing losses in distribution systems The flexibility of solar technology allows it to adapt to various power demands, with energy produced by PV systems reducing the apparent load and surplus energy being fed into the grid However, a significant drawback is that the intermittent nature of solar generation can disrupt the voltage profile of distribution systems, particularly when installed close to the load side.
Voltage Control
The simplest voltage control methods in a distribution system use local measurements for maintaining the voltage profile and data transfer between the distribution nodes is not required
Coordinated voltage control methods involve data transfer between distribution nodes, utilizing comprehensive information from the entire distribution network to determine control actions Various centralized voltage control strategies have been developed for distribution systems, each differing in effectiveness, complexity, communication requirements, and cost efficiency Examples of coordinated voltage management include Centralized Distribution Management System (DMS) control and the coordination of components such as On Load Tap Changers (OLTC), voltage regulators, distributed generators (DGs), and switched capacitors Figure 1 illustrates the various elements used in distribution systems for effective voltage control.
Figure 1 Voltage Control in Distribution System
A tap changer is an essential device used in power transformers to regulate output voltage to desired levels by adjusting the turn ratios in the transformer windings This technology provides flexible control, ensuring that voltage supply remains within specified limits Tap changers can be classified as either on-load or off-load, with on-load tap changers allowing for seamless current transfer between voltage taps without interrupting the supply Additionally, tap changers can be customized to meet specific application requirements, making them a vital component in voltage management systems.
A voltage regulator is an essential device that ensures a stable voltage level in electric power distribution systems Installed at substations or along distribution lines, it guarantees that all customers receive consistent voltage, regardless of their power consumption Typically, voltage regulators can adjust the voltage by up to 10%, either increasing or decreasing it as needed.
Shunt capacitor banks (SCBs) are primarily utilized for capacitive reactive compensation and power factor correction Their growing popularity stems from their affordability, ease of installation, and versatility in deployment across various network locations Additionally, installing SCBs enhances load voltage, improves voltage regulation, reduces energy losses, and leads to cost savings by deferring investments in the transmission system.
Cyber Attack in Power System
The rise of technological innovations and the growing need for dependable energy have driven the evolution of smart grids These advanced systems aim to enhance the existing power grid's generation, transmission, and distribution capabilities, accommodating distributed generation, renewable energy sources, electric vehicles, and effective demand-side power management.
The modern distribution system is set to integrate advanced technologies like phasor measurement units (PMUs), wide area measurement systems, substation automation, and advanced metering infrastructures (AMI) to achieve its goals However, this technological advancement increases the dependence on cyber resources, making them vulnerable to potential attacks Over the past decade, the power grid has faced numerous cyber-related incidents, raising concerns about security vulnerabilities and their significant impact on critical power grid infrastructure The cyber-physical structure of the power grid is illustrated in Figure 2.
Figure 2 Power Grid Cyber-Physical Infrastructure [13]
The different types of attacks that can affect the normal operation of a power distribution system as described in [14] are:-
1) Denial of Cooperative Operation (DoS): In this attack, the communication channels are jammed by flooding them with junk packets which can result in loss of important data and might affect the automated control operations
2) Desynchronization attacks: In this attack, the control algorithms of automated operation which are time dependent are attacked
3) Data Injection Attacks: In this attack, false operational data such as status or control information are send that can significantly affect the operations of a power grid This type of attack requires thorough knowledge of the communication protocol
Problem Statement
This thesis aims to create a reliable voltage controller utilizing multiple linear regressions to optimize voltage profiles in distribution systems with connected distributed generators (DG) The regression employs the least squares method, leveraging data from precise simulations of the distribution network Key independent variables include the active power output of DG, total load, and var injection from the capacitor bank, while the dependent variable focuses on the per unit voltage at buses experiencing violations The effectiveness of the proposed controller is validated through simulations on the IEEE 13 bus distribution system and the American Electric Power System feeder, modeled in OpenDSS.
This thesis presents a model for two types of cyber-attacks in power distribution networks: data integrity attacks on the voltage control loop and load redistribution attacks, alongside addressing inconsistencies in electrical design parameters To detect these cyber-attacks, a regression-based distributed detection algorithm utilizing local detection agents is developed for distribution systems integrated with distributed generation (DG) The proposed algorithm identifies a selection of buses to serve as elected buses, from which linear regression-based local agents are created The cyber-attacks and detection methodologies are implemented in the AEP feeder, modeled using OpenDSS.
This thesis demonstrates the effectiveness of the proposed voltage controller strategy in mitigating data integrity attacks on the voltage control loop, addressing load redistribution attacks, and resolving inconsistencies in electrical design parameters within a power distribution network, specifically modeled in the AEP Distribution feeder.
This article examines the impact of inconsistencies in electrical design parameters on line loss calculations for overhead lines in AEP feeders without distributed generation (DG) Specifically, it focuses on line reactance as the key parameter influencing these inconsistencies, which are modeled using OpenDSS software.
A few assumptions made in this thesis work are listed below,
• Voltage regulators are turned off in both IEEE 13 bus distribution system and AEP feeder for all the proposed strategies
• Data sets for the independent variables and dependent variables for the regression are taken from the exact simulation of the distribution system in OpenDSS.
Approach
The sections to follow will develop voltage controller model, cyber-attacks and distributed cyber- attack detection technique The key aspects of this research are highlighted in subsections below
The integration of distributed generation (DG) into a distribution system, along with varying load conditions, significantly influences the voltage profile Therefore, it is essential to consider these factors when formulating a strategy for effective voltage regulation in distribution systems.
• Exact models of the distribution systems are modeled in OpenDSS for the analysis
In Minitab, multiple linear regression analysis is conducted using per unit voltage at violating buses as the dependent variables, while the independent variables include the active power output of distributed generation (DG), total load, and reactive power injection from the capacitor bank.
• Data sets for the dependent and independent variables are generated from OpenDSS using random network and loading conditions
• Optimum var settings for capacitor banks are calculated in Matlab using the regression models of per unit voltage of violating buses
A novel agent-based detection technique utilizing linear regression has been developed to identify cyber-attacks in distribution systems This method is effective for various attack types, including data integrity attacks on voltage control loops and load redistribution attacks, as long as the system's topology remains unchanged.
• Exact models of the distribution systems are modeled in OpenDSS for the analysis
• Cyber-attacks are modeled in OpenDSS in the exact model itself
• A distributed algorithm using local agents based on linear regression is developed for the detection of the cyber-attacks The linear regression analyses in done in Minitab software
• The detection technique is tested for different cases of cyber-attacks in AEP feeder
1.7.3 Electrical Design Parameters Inconsistency effect on Losses Calculation
This article discusses the impact of inconsistencies in electrical design parameters, specifically focusing on line reactance, on the calculation of line losses in overhead lines within AEP feeders without distributed generation (DG) The analysis is conducted using OpenDSS to model these inconsistencies, highlighting their significance in understanding line loss behavior.
• The AEP feeder 1 is studied thoroughly and all the different conductor type lines are identified
• The different types of geometries used for all the different types of lines are identified in the AEP feeder 1
The losses for both 2-conductor and 4-conductor lines have been calculated, taking into account all identified geometries, including their original configurations.
• The effect of different types of geometries on different types of lines is analyzed.
Outline
The outline of the remaining chapters is given in this section
Chapter 2 is a comprehensive literature review on voltage control in distribution system using voltage regulators, OLTC, capacitor banks, DGs or a combination of any of these A literature review on the different cyber-attacks in power system is also discussed in details
Chapter 3 is about mathematical formulation of multiple linear regression technique, modeling of the inconsistencies in the electric design parameters, data integrity attack on voltage control loop and load redistribution attack in a distribution system The voltage controller strategy and cyber- attack detection technique is also formulated
Chapter 4 gives a comprehensive description of the software packages used in this study The advantages presented by the software to the pertinent applications are also discussed
Chapter 5 presents the test systems, simulations for voltage control strategy and associated regression models and the cyber-attack detection technique and the associated regression models The effect of the cyber-attacks on voltage control in a distribution system is also presented Finally, chapter 6 lists conclusion of this study and provides scope for future work
LITERATURE REVIEW
Voltage Control in distribution system
In today's distribution systems, various strategies can be employed by Distribution Management Systems (DMS) or Distribution Automation (DA) to address voltage instability Key methods include regulator control through adjustable tap settings and capacitor control for supplying or absorbing reactive power (Kvar) The primary objectives of capacitor control are to minimize losses from reactive load currents, lower kVA demand, decrease customer energy consumption, enhance voltage profiles, and ultimately boost revenue.
Extensive research has focused on capacitor control methods, both offline and online, to regulate voltage profiles in distribution systems Traditional strategies, including timers, voltage controls, and voltage with time bias, have been analyzed for their benefits and limitations Additionally, advancements in capacitor control technologies, such as Fisher Pierce Current Control, Beckwith Electric Co Inc., and RTE Combinational Capacitor Control, have been explored Furthermore, a comprehensive search methodology has been proposed to identify optimal set points for capacitor bank switching.
A proposed control strategy aims to optimize voltage and reactive power management at distribution substations and feeder levels by minimizing the weighted sum of squared set point values for key variables This study focuses on controlling voltage, reactive power, and feeder losses to enhance overall system efficiency.
Reference [17] presents a two-stage algorithm for the optimal placement, replacement, and control of capacitors in distribution systems, utilizing a Genetic Algorithm to identify high-quality solution neighborhoods, followed by a second stage aimed at enhancing these solutions Similarly, Reference [19] addresses the challenges of determining the optimal location, type, and size of capacitors in a radial distribution system, factoring in voltage constraints and load variations, and formulates the problem as a mixed integer linear programming issue.
Reference [22] discusses a novel approach for capacitor placement and real-time control in unbalanced distribution systems, detailing the problem formulation, solution methodology, and mathematical validation The process is divided into two main subproblems: determining the optimal placement of capacitors and implementing real-time control strategies Utilizing quadratic integer programming, the study identifies the optimal number, location, and size of capacitors for installation Numerical studies supporting these findings are presented in reference [23].
The use of step-up voltage regulators effectively maintains voltage profiles at each customer's meter in accordance with ANSI standards These regulators function as tap-changing autotransformers Additionally, dynamic control of local regulating devices in distribution substations and feeders is essential, as highlighted in recent studies, to adapt to changing system conditions rather than relying solely on local measurements.
The problem of minimizing the real power losses and enhancing the voltage profile in a distribution system is solved using a reconfiguration methodology built on a new adaptive imperialist competitive algorithm in [21]
Distributed capacitor control methodologies for voltage profile regulation in distribution systems involve segmenting the network into distinct control zones according to the reactive power areas of each manageable shunt capacitor This approach aims to identify the optimal setting point for each zone, as illustrated in Figure 3, which depicts the division of areas based on reactive power domains.
Reference [26] presents an effective voltage and var control strategy utilizing solid state transformers (SST) for voltage regulation and var compensation, aiming to reduce overall system power loss while ensuring the voltage profile remains within acceptable limits in a distribution system Additionally, an optimal capacitor control algorithm is developed in [27], incorporating various types of distributed generation (DG) and their distinct mathematical models to achieve the best set point for performance enhancement.
Figure 3 Divided Areas based on Reactive Power Domains [24]
Both offline and online capacitor bank control modes have their drawbacks Offline control operates on a fixed schedule that may not align with actual loading conditions, lacking a feedback mechanism to adjust for real-time system demands, potentially leading to inefficiencies Conversely, online control necessitates continuous monitoring of the power factor or other relevant metrics through microprocessor-based relays, which can be costly and complex due to fluctuating loading conditions and intermittent distributed generation (DG) integration Additionally, inconsistencies in electrical design parameters or cyber-attack scenarios can render capacitor control impractical, complicating the calculation of necessary var injections.
Cyber Attacks in Power Systems
The rise of distributed generation (DG) has increased the necessity for demand-side management and control of industrial and residential loads through demand response, prompting electric utilities to implement Distribution Management Systems (DMS) These systems leverage advanced communication technologies, sensors, and automation to facilitate real-time adjustments to fluctuating loads, generation, and system disturbances DMS primarily enhance reliability and service quality while maintaining acceptable frequency and
Advanced systems in power infrastructures introduce new vulnerabilities, particularly within smart grid automated control systems, wide area measurement, and supervisory control and data acquisition systems Research has identified various types of attacks, including deception attacks and denial of service (DOS) attacks targeting networked control systems Deception attacks compromise the integrity of control packets by manipulating sensor and actuator behavior As illustrated in Figure 4, cyber-attacks can occur at multiple points within a control system, with A1 and A3 representing data integrity attacks, A5 indicating a physical system attack, and A2 and A4 targeting the communication links between the physical system and the controller.
Figure 4 Cyber-Attack on Control System [29]
False Data Injection Attacks (FDIA) pose significant threats to static estimators in SCADA systems, as detailed in references [30-34] In these attacks, adversaries manipulate sensor readings to distort the smart grid's decision-making processes Research in [30] illustrates that even with incomplete knowledge of power grid parameters, such as circuit breaker and voltage regulator positions, attackers can still evade detection by state estimators Furthermore, [32] reveals that if attackers have full knowledge of network conditions, existing bad data detection techniques are ineffective Reference [31] introduces a novel analytical approach for assessing the vulnerability of state estimation in the presence of FDIA within electric grid SCADA systems Additionally, [34] discusses deception attacks using outdated or perturbed grid models, highlighting that both linear and non-linear state estimators are susceptible The findings indicate that the more accurate information an attacker possesses, the greater the threat level of the deception attack, as illustrated in Figure 5, which depicts a schematic of such an attack on a power grid's state estimator.
Figure 5 Deception Attack on State Estimator in a Power Grid [34]
Load redistribution (LR) attacks represent a subclass of the False Data Injection Attacks (FDIA) recently examined in studies [35-37] Specifically, reference [35] models an LR attack targeting smart meters within a smart grid, where the load is altered at various buses while keeping the overall load unchanged The implications of such attacks on security constrained economic dispatch (SCED) have been analyzed, revealing that LR attacks can effectively circumvent inadequate detection mechanisms if the network conditions are understood.
An LR attack can effectively bypass existing bad data detection techniques, even when network information is incomplete, as demonstrated in Reference [36] The article also provides a quantitative analysis of the potential damage these LR attacks pose to the operations and security of power systems.
[37] and the prevention measures are also provided
Data integrity cyber-attacks significantly impact the SCADA-controlled voltage control loop within transmission systems, particularly targeting the voltage control provided by FACT devices A sensitivity analysis technique is utilized to identify which devices to attack to influence specific buses Additionally, the effects of cyber-attacks on the automatic generation control loop are also discussed, highlighting the vulnerabilities within these critical infrastructure systems Figure 6 illustrates the schematic of a SCADA-controlled voltage loop in a transmission system.
Figure 6 SCADA Controlled Voltage Loop in a Transmission System [44]
As cyber threats to automated control systems and state estimators in smart grids continue to evolve, it is crucial to enhance defensive mechanisms There are two primary strategies for safeguarding power grid control applications: first, developing robust control algorithms capable of detecting or withstanding malicious data alterations; and second, ensuring the protection of sensor measurements and other critical data from manipulation.
Numerous studies have focused on detecting cyber-attacks on state estimators within SCADA systems One method highlighted in reference [38] utilizes both active and reactive power measurements to accurately identify the attacked transmission lines Reference [39] introduces a strategy that safeguards specific sensor measurements by validating them to detect potential attacks Additionally, reference [40] presents a fully distributed approach for identifying cyber-physical attacks in power networks, where the network is segmented into distinct areas, each monitored by a local control center, and employs a detection filter based on a sparse residual filter in descriptor form.
Figure 7 Detection of Cyber-Attack with Local Agents for each Area [40]
References [41-42] address the challenge of physically protecting a subset of Phasor Measurement Units (PMUs) to mitigate cyber-attacks Reference [41] employs graph algorithms to determine the minimum number of PMUs that require physical protection to effectively neutralize such threats Meanwhile, Reference [42] tackles the issue of selecting small subsets of measurements that can be fortified to ensure the entire system's immunity against data injection attacks Due to the complexity arising from the extensive size of the electrical grid, a fast greedy algorithm is utilized for the strategic placement of secured PMUs.
MATHEMATICAL MODEL AND FORMULATION
Theory of Multiple Linear Regression (MLR) [48]
Multiple linear regression (MLR) is a statistical technique that models the linear relationship between a dependent variable, such as load, voltage per unit, or transmission loss function, and one or more independent variables that influence it This regression model represents the dependent variable as a linear function of the predictor variables along with an error term, allowing for a comprehensive analysis of how various factors impact the outcome.
Where, 𝑌 is the dependent variable, 𝑋 1 , 𝑋 2 ,…., 𝑋 𝑘 are the predictor variables, 𝑏 1 , 𝑏 2 ,…., 𝑏 𝑘 are regression parameters with respect to 𝑋 1 , 𝑋 2 ,…., 𝑋 𝑘 , and 𝑒 is the error term
Let each of the 𝑘 predictor variables, 𝑋 1 , 𝑋 2 ,…., 𝑋 𝑘 , have 𝑛 levels The system of 𝑛 equations can be represented in matrix notation as follows:
The matrix 𝐗 holds data on the predictor variable levels corresponding to the observations, while the vector 𝐛 encompasses all regression coefficients Typically, the average difference between the actual value of 𝑌 and the predicted value 𝑌̂ approaches zero.
20 can be assumed that the error term in equation (2) has an average value of 0 The error term can therefore be omitted in calculating parameters
The regression model is derived by estimating the coefficients (b) using the least squares method, which minimizes the sum of the squared differences between the observed and predicted values The resulting estimated coefficients are essential for accurate predictions in the model.
𝑏̂ = (𝑋 ′ 𝑋) −1 𝑋 ′ 𝑌 (3) The multiple linear regression model also referred as fitted model can now be estimated as:
The observations, 𝑌 𝑖 , may be different from the fitted values 𝑌̂ 𝑖 obtained from this model The difference between these two values is the residual, 𝑟̂ 𝑖 The vector of residuals, 𝐫̂, is obtained as:
The regression equation is estimated such that the total sum-of-squares can be partitioned into components due to regression and residuals:
The explanatory power of the regression is explained by its 𝑅 2 value, calculated from the sums- of-squares terms as
The residual mean square (MSE) is the sample estimate of the variance of the regression residuals
The 𝑅² value and the Mean Squared Error (𝑀𝑆𝐸) are key metrics for assessing the goodness of fit in regression analysis A 𝑅² value approaching 1 indicates a strong relationship between predictor variables and the dependent variable, while a smaller 𝑀𝑆𝐸 value signifies a better fit of the regression model to the data.
Modeling attacks and anomalies
There are two attacks considered here the data integrity and LR attack as well as inconsistencies in electrical design parameters This section models both the attacks and parameter inconsistencies
3.2.1 Inconsistencies in electrical design parameters
A distribution system model has many parameters which define it completely like line resistance
(R), line reactance (X), line geometry, conductor type, regulators type, etc Any incorrect or uninformed parameter will lead to model errors and hence risk of operation of the entire system
Here inconsistencies are modeled as statistical variations with probabilities such as for example a variation δX in a distribution line L with reactance X
This attack necessitates a deep understanding of communication protocols to transmit deceptive or harmful status and control signals A study highlights a data integrity attack targeting the control signals for voltage management in FACTs devices and substation controllers Additionally, a similar attack on the voltage control loop within a distribution system is examined, where the attacker acquired knowledge about several key capacitors.
In control systems, the actual signal from the control center is denoted as u(t), while [u min (t), u max (t)] represents the range of possible control signals A "Min attack" occurs when u(t) is set to u min (t) during a specific duration τ, whereas a "Max attack" is characterized by u(t) being equal to u max (t) This min-max attack is unobservable, as discussed in [29], and its impact is particularly significant in regions close to the point of effect.
This article discusses a specific type of false data injection attack, where load variations occur at different buses without changing the total load It is posited that only load bus power injection and line power flow measurements are vulnerable, as comprehensive physical protection of all meters is impractical Previous research has shown that such load redistribution attacks are undetectable by current bad data detection methods in state estimators However, larger load changes may be identified through short-term load forecasting For an attack to remain undetectable, it must adhere to the condition that the load multiplier τ is less than 0.5 times the true load value, with the total load remaining constant Consequently, this study assumes that the magnitude of the attack on load measurements does not exceed τ = 50% of the actual load.
To execute undetectable load redistribution (LR) attacks, it is crucial that the overall system loading remains constant, expressed as ∑ 𝐿 + △ 𝐿 = L Additionally, the load variation at each node must stay within acceptable limits, which can be ensured by maintaining τ, the load multiplier, below 0.5 L.
Distributed Cyber Attack Detection Method
In a power system characterized by a set of buses denoted as 𝜆, there exists a subset L comprising buses with known demand, a subset S containing buses equipped with solar generating units, and a bus C that houses a capacitor unit The voltage at any bus j within the set J, which includes buses numbered from 1 to 𝜆, is represented by the vector 𝑉𝑝𝑢 𝑗, where each vector consists of k-dimensional real values reflecting various network conditions To analyze this system, a k-means clustering approach, as outlined in equation (10), is utilized.
Cluster set S = { 𝑆 1 , 𝑆 2 ,… , 𝑆 𝑡 } are assigned to datapoints where 𝑆 𝑖 is the set of observations {
An agent 𝐴 𝑗 from a cluster 𝑆 𝑗 is min 𝑖 ∑ 𝑘 𝑖=1 |(𝑉𝑝𝑢 𝑗 − 𝑉𝑝𝑢 à𝑖 )| ⩝ 𝑗 = 𝑎, 𝑏, … , ℎ (11)
From a highly correlated set of agents 𝐴 𝑖 and 𝐴 𝑗 an agent pair is created where 𝐴 𝑗 𝜖 𝑆 𝑗 ∩ 𝐴 𝑖 𝜖 𝑆 𝑖
= ϕ and 𝑆 𝑖 𝑎𝑛𝑑 𝑆 𝑗 ⊂ S Consider the behavior of agent 𝐴 𝑖 on 𝑉𝑝𝑢 𝑗 as a regressive model given by eq (12)
The calculation of the coefficients 𝑏 𝑖 result in eq (13)
The statistical relationships among the selected agent pairs are illustrated in Figure 3 In a distribution network experiencing a cyber-attack, the bus voltages of the chosen pairs are compared to the corresponding bus voltages obtained from the same network If the voltage variation surpasses a specified threshold, the agent identifies a cyber-attack event A consensus from at least two agent pairs leads to a definitive conclusion regarding the occurrence of a cyber-attack.
Proposed Voltage Controller Methodology
In a power system characterized by a set of buses denoted as 𝜆, there exists a subset of buses L with known demand and another subset S that houses solar generating units, along with a bus C containing a capacitor unit The total real power demand across the buses in set L is represented as 𝑑, while the real power generated at bus S is indicated by p Additionally, the total kVars injected by the capacitor at bus C is denoted as Kvar The voltage per unit at any bus 𝑗 within the set 𝜆 is also a critical parameter to consider in this system.
In this study, the total system loading, real power output from the connected distributed generation (DG), and reactive power from the capacitor related to node voltage j are identified as predictor variables The dependent variable is the per unit voltage (Vpu) at any bus j that exceeds the established voltage limits.
A statistical model of dependent variable, with defined predictor variables is given by eq (14)
A calculation of coefficients of 𝑏 𝑖 yields eq (15) for Vpu of a bus j which is further used for voltage control
Statistical models are created for buses in the distribution system that are at risk of voltage violations After obtaining these models using Minitab software, a statistical reactive power model algorithm is developed to calculate the necessary kVars to ensure that the voltage levels at the violated buses remain within acceptable limits.
The Kvar calculation model in Matlab utilizes statistical models from equation (15) along with the necessary voltage at the violated bus to estimate the kVars needed to rectify voltage violations at that bus, as illustrated in Figure 8.
The kVars estimated from this algorithm remain unaffected by data injection attacks until there is a change in network topology, as the statistical models derived from validated datasets of both dependent and predictor variables ensure accuracy and reliability.
Figure 8 A Statistical Reactive Power Model Algorithm
SIMULATION TOOLS AND SOFTWARE
Open Distribution System Simulator (OpenDSS)
The Open Distribution System Simulator (OpenDSS) is a comprehensive open-source tool designed for simulating electric utility distribution systems, developed by the Electric Power Research Institute It facilitates steady-state analysis, integration of distributed generation, and time series power flow, and includes various test cases for IEEE benchmark test feeders ranging from 4 to 8500 nodes OpenDSS offers two implementations: a standalone executable platform that allows users to create and solve circuits using direct script codes, and a COM server DLL that enables integration with third-party analysis programs such as MATLAB, VBA, C#, and Python, providing flexibility and ease of use for electrical engineers and researchers.
27 execute custom solution modes and features of the simulator.The DSS is designed in such a way so that it can to be effortlessly altered to meet future needs
The OpenDSS program can be used for the following applications [45]:
• General Multi-phase AC Circuit Analysis
• Analysis of Distributed Generation Interconnections
• Annual Load and Generation Simulations
• Risk-based Distribution Planning Studies
• Neutral-to-earth Voltage Simulations
• Distribution Feeder Simulation with AMI Data
• Analysis of Unusual Transformer Configurations
OpenDSS configuration is shown in figure 9 [46] which show the three different ways by which the DSS engine can be initiated
• OpenDSS scripts – Using direct scripting codes to define the circuit and solve it
• COM interface – Driving it externally from any third party analysis program
• User Written DLL – Writing suitable DLL which can be linked with the engine
Some of the special features of OpenDSS used in this work are listed below
4.1.1 Extensive Range of Solution Modes
OpenDSS offers various solution applications for power flow analysis in distribution systems, treating the substation as an infinite energy source It employs two primary methods: iterative and direct power flow methods In the iterative approach, loads and distributed generators are modeled as injection sources, utilizing algorithms such as normal current injection and Newton current injection to solve the power flow problem Conversely, the direct method incorporates loads and generators into the system admittance matrix as admittances, allowing for direct resolution without iterations.
DSS effectively addresses both meshed and radial systems with equal efficiency It features a snapshot power flow mode that provides a single power flow solution based on the current load Additionally, it offers daily, yearly, and duty cycle power flow modes for simulating various time periods Users can choose between a user-specified load shape or a default load shape provided by the engine for these simulations.
After conducting power flow analysis, essential data such as losses, voltages, and currents for the feeder system are obtained Energy meters provide kW and kVar loss information for each time instant across all zones and loads This thesis utilizes OpenDSS to perform a three-phase unbalanced distribution power flow analysis for the AEP feeder Additionally, a photovoltaic (PV) unit and a capacitor bank are integrated into the model to facilitate voltage control calculations, enabling accurate power flow assessments.
The OpenDSS COM interface is a powerful feature that enables users to execute custom solution modes from external platforms, allowing for analyses that go beyond the capabilities of direct script codes Users can integrate third-party programs such as MS Office via VBA, MATLAB, Python, and C#, enhancing their analytical capabilities Additionally, the COM interface supports complex loop structures like for, if, and if-then-else, which are not possible with direct DSS scripts Furthermore, users can retrieve most results from the DSS engine through this interface, making it a versatile tool for advanced simulations.
This interface facilitates the integration of OpenDSS with MATLAB, enabling the calculation of necessary kVars from capacitor banks under varying network conditions and line losses It specifically addresses different geometries within distribution networks, which is essential for the analysis conducted in our thesis.
Minitab
Minitab is a comprehensive statistics software developed in 1972 at Pennsylvania State University by Barbara F Ryan, Thomas A Ryan, Jr., and Brian L Joiner This powerful tool supports various regression analyses, including linear, non-linear, and orthogonal regression Additionally, Minitab excels in creating time series plots, developing ANOVA tables, conducting correlation analysis, and cascading graphs, making it a versatile choice for statistical analysis.
In our thesis, we utilize Minitab for conducting regression analysis on both voltage controller models and cyber-attack detection models, ensuring precise results presentation.
SIMULATION AND RESULTS
AEP Test Circuit
Previous research has modeled the AEP system and analyzed the effects of photovoltaic (PV) penetration The AEP feeder I, depicted in Figure 12, consists of a radial system with 395 buses, supplied by a 12.47 KV medium voltage substation, represented as a voltage source behind impedance This distribution system features two main circuits along with laterals and distributed loads, which comprise a combination of residential and industrial demands, resulting in a total load on the system.
2.27 MVA (2.042 MW and 1.00 MVAR) and the active power losses represent 1.52 % of the total system load The load buses in this system are modeled as PQ loads Three voltage regulators (two 3-phases and one single phase) employed in this feeder are turned off A 3-phase solar power generating unit is added at bus 43_west and a 1-phase capacitor is added at bus 131_west.3
Figure 12 AEP Feeder 1 Network Diagram
5.2.1 MLR based Statistical Voltage Controller
An unbalanced three-phase power flow (UTDPF) analysis is conducted to assess the voltage profile of the distribution system The active power output from renewable generators is adjusted based on their daily generation curve, followed by a recalculation of bus voltages This process identifies sections of the network where voltage violations occur most frequently under varying conditions, highlighting optimal locations for capacitor installation Additionally, the analysis considers variations in active power generation across four buses.
The voltage violations are most prevalent at 164_west, 146_west, 143_west, and 132_west, which are treated as dependent variables in this analysis The predictor variables include kVars from the capacitors, the active power output of photovoltaic systems, and total loading, as detailed in Table 3 The accuracy of the models is evaluated using the coefficient of determination (R²) and mean squared error (MSE), along with a plot of residuals against data points.
Table 3 demonstrates that the R² values are nearly one and the MSE values approach zero for all models, indicating an excellent fit and confirming that the predictor variables account for almost 100% of the variations in the dependent variable Additionally, Figure 13 presents the normal probability plot of the residuals for the regression models, further illustrating the overall goodness of fit across all models.
Table 3 Regression Models for Voltage in p.u for Buses 164_west, 146_west, 143_west and 132_west
Vpu at node 164_WEST Vpu at node 143_WEST
Vpu at node 146_WEST Vpu at node 132_WEST
Figure 13 Normal Probability Plots for the Regression Models for Buses 164_west, 146_west, 143_west and 132_west
The reactive power outputs from the regressive model (Model 2) for a typical 24-hour load curve, peaking at 1.42 KW, are illustrated in Figure 14 These reactive power requirements are then compared to those derived from traditional capacitor control implemented in OpenDSS (Model).
1) and as seen in figure 14
Figure 14 Controller validation for the Kvar calculation models for buses 164_west, 146_west, 143_west and 132_west
Model 1 Model 2 Model 1 Model 2 Model 1 Model 2 Model 1 Model 2
Kvar (164_WEST) Kvar (143_WEST) Kvar (146_WEST) Kvar (132_WEST)
Hours Load PV Power Output
This section evaluates the MLR controller's robustness against model inconsistencies and cyber-attacks The controller's performance is analyzed as the reactance increases from 1.79 pu to 3.79 pu A deception attack is simulated by altering the reactive power injection control signal of the capacitor at 131_west, increasing it from 150 kVar to 300 kVar (a 50% rise) Additionally, an LR attack is executed by adjusting the load value at 644_7231501-1 from 75 kW to 150 kW, while simultaneously decreasing the load at 382_7231503-1 from 22.5 kW to 147.5 kW It is important to note that these events are not simulated at the same time.
Line Geometry (an example to show the effect of inconsistency of electrical design parameters)
AEP feeder 1 experiences line losses primarily due to its overhead lines, which consist of three types with varying geometries: 2-conductor, 3-conductor, and 4-conductor The 2-conductor and 4-conductor lines contribute significantly to these losses, with 17 and 14 distinct line geometries, respectively This analysis assumes a unity load and does not incorporate any distributed generation (DG) into the system.
Figures 15 and 16 illustrate the maximum losses for both 2-conductor and 4-conductor lines The white-dotted bars represent line losses with the original geometry, while the other bars reflect losses calculated using alternative geometries Notably, line losses vary significantly depending on the geometry employed for the same line This inconsistency in electrical design parameters can lead to serious issues when applying these results to distribution system problems.
Figure 15 Losses in Four Maximum Losses giving Lines with Each Type of Line Geometry for 2-Conductor Type Line
Figure 16 Losses in Four Maximum Losses giving Lines with Each Type of Line Geometry for 4-Conductor Type Line
Figure 17 Controller Testing for the Voltage Controllers against Electrical Design Parameter Inconsistencies, Deception Attack and LR Attack
The predictor variables for a 24-hour period were analyzed under various capacitor control models, including conventional control (Model 1), MLR base voltage controller (Model 2), and models with inconsistencies and attacks (Models 3, 4, and 5) The results, illustrated in Figure 17 alongside the load and solar generation output from Figure 14, reveal that Models 3, 4, and 5 exhibit significant voltage deviations compared to the stable performance of Models 1 and 2 While Models 1 and 2 effectively maintain voltage within permissible limits, the other models struggle during specific hours, potentially disrupting system operations.
5.2.3 Cyber Attack Distributed Detection Method
The study presents solutions for unbalanced three-phase distribution power flow in the AEP distribution system across 25 different network conditions, with voltage data for all system buses calculated using OpenDSS As outlined in section 3.3, four distinct clusters are formed, as illustrated in figure 18, leading to the identification of six agent pairs The k-means clustering method applied in Matlab results in four clusters, as increasing the number of clusters diminishes their separation while reducing the number of clusters leads to fewer agents The silhouette plot in figure 18 reveals that the first, third, and fourth clusters exhibit high silhouette values above 0.8, indicating good separation from neighboring clusters In contrast, the second cluster is characterized by numerous points with low and even negative silhouette values, suggesting poor separation.
Table 4 presents the MLR models developed for the agent pairs, demonstrating a strong correlation coefficient exceeding 0.98 and a mean squared error (MSE) near zero, indicating an excellent fit Additionally, these agent pairs are categorized into distinct cluster sets Figure 19 illustrates the normal probability plot of the residuals from the statistical models used for attack detection, further confirming the models' goodness of fit.
Table 5 presents the total number of buses, centroid values, and the two selected buses for each cluster based on the lowest sum of absolute values From the entire network, six elected pairs have been identified A linear regression analysis was conducted on these selected pairs using Minitab software to determine six local agents.
Figure 18 Cluster Division for AEP Feeder 1 Network
Table 4 Statistical Models for Attack Detection
Table 5 Total Number of Buses and the Centroid Value
Figure 9 Normal Probability Plots for the Regression Models of the Agents
The cyber-attack distributed detection method is tested against deception attack and LR attack on the AEP Feeder 1 with different attack scenarios constructed in OpenDSS
Scenario 2: Increase in var injection of capacitor at 131_west from 150 kVar to 300 kVar (50%) Scenario 3: Decrease in var injection of capacitor at 131_west from 150 kVar to 75 kVar (50%) Scenario 4: Increase in var injection of capacitor at 131_west from 150 kVar to 180 kVar (20%)
Scenario 2: Increase in load 644_7231501-1 from 75 kW to150 kW and decrease in load
Scenario 3: Increase in load 25_7231504-1 from 160 kW to 270 kW and decrease in load
Scenario 4: Decrease in load 331_7231503-1 from 115 kW to 60 kW and increase in load
Figures 20 and 21 illustrate the local decisions made by each agent, alongside the final decisions for the scenarios involving deception and load redistribution attacks In these figures, green blocks signify a "no cyber-attack" decision, while red blocks indicate a "cyber-attack" decision from the agents The results demonstrate that the proposed detection method accurately identifies both types of attacks across all scenarios Specifically, in the case of the deception attack, most agents successfully detect the attack due to significant changes in voltage levels caused by capacitor var injection Conversely, for the load redistribution attack, fewer agents detect the attack, as the modifications to individual loads are relatively minor compared to the overall load of the system in AEP Feeder 1.
Figure 20 Decision Table for Deception Attack
Figure 21 Decision Table for LR Attack
CONCLUSION AND FUTURE WORK
Conclusion
This thesis introduces an innovative multiple linear regression method for controlling bus voltages in distribution systems that incorporate renewable energy sources It presents a statistical distributed detection technique utilizing local decision-making agents, which has been validated through practical application The methods are demonstrated on a real-world distribution system feeder, specifically the AEP system Feeder 1, modeled in OpenDSS, with regression analyses conducted using Minitab software The findings and conclusions from both approaches are summarized in this section.
This thesis presents a robust voltage controller utilizing multiple linear regressions to effectively maintain the voltage profile in a distribution system integrated with distributed generators (DG) The proposed controller is validated through simulations on the IEEE 13 bus distribution system and the American Electric Power System feeder, modeled in OpenDSS.
The developed voltage control strategy relies on precise initial network simulations, eliminating the need for further calculations unless the network topology changes This method demonstrates effectiveness even amidst inconsistencies in electrical design parameters, data integrity attacks, and LR attacks, making it a strong alternative to traditional capacitor controllers.
6.1.2 Distributed cyber-attack detection technique
A regression-based distributed detection algorithm utilizing local detection agents has been created to identify cyber-attacks in distribution systems integrated with distributed generation (DG) This algorithm selects specific buses in the system to serve as elected bus pairs, from which linear regression-based local agents are developed The cyber-attack detection techniques have been validated using the AEP feeder model in OpenDSS.
The developed technique for cyber-attack detection utilizes precise network simulations at the outset, requiring no additional calculations unless the network topology changes By selecting buses that are sparsely distributed along the feeder and exhibit strong correlations, the method successfully identifies all attack scenarios with high accuracy.
Future Work
Voltage control and cyber-attack detection in modern smart grids rely on real-time data communication and the validation of variables impacting the distribution system Additionally, the dynamic topology of the distribution system must be accurately modeled and quickly updated to ensure effective and precise assessment.
In our study, we incorporate variations in the tap settings of voltage regulators into regression analysis for developing statistical models focused on voltage control and cyber-attack detection To enhance real-world applicability, these models should allow for updates at specified intervals or upon detecting changes in the distribution system's topology Additionally, increasing the number of selected buses can enhance the total agents within the distribution system, thereby improving the accuracy of cyber-attack detection.
1 “Smart Grid: An Introduction”, Program Concept paper, U.S Department of Energy,
2 Rabinowitz M., “Power Systems of the Future”, IEEE Power Engineering Review, 2000
3 Chen C., Zhu Y., Xu Y., “Distributed generation and Demand Side Management”, Proceedings of the 2010 China International Conference on Electricity Distribution, 13-
4 Guan F H., Zhao D M., Zhang X., Shan B.T., Liu Z., “Research on distributed generation technologies and its impacts on power system”, Proceedings of the International Conference on Sustainable Power Generation and Supply, 6-7 Apr 2009, pp 1-6
5 Driesen J., Belmans R., “Distributed generation: challenges and possible solutions”, Proceedings of the IEEE Power Engineering Society General Meeting, 2006, pp 1-8
6 Chowdhury B H., Sawab A.W., “Evaluating the value of distributed photovoltaic generations in radial distribution systems” IEEE Transactions on Energy Conversion, vol
7 Fitzer J., Dillon W E., “Impact of Residential Photovoltaic Power Systems on the Distribution Feeder,” IEEE Power Engineering Society Winter Meeting, 1986
8 McMillan R., “Siemens: Stuxnet worm hit industrial systems,” COMPUTERWorld, 14 Sept 2010
9 Cherry S., Langner R., “How Stuxnet Is Rewriting the Cyberterrorism Playbook”, IEEE Spectrum, 13 Oct 2010
10 U.S.-Canada Power System Outage Task Force, “Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations”, April 2004 Online: https://reports.energy.gov/BlackoutFinal-Web.pdf
11 Annual report 2011, The Repository for Industrial Security Incidents (RISI), Online: http://www.securityincidents.net/index.php/products/indepth/risi_annual_report/
12 2011 Report on control system cyber security incidents, online: http://community.controlglobal.com/content/risi-cyber-incident-report-2011-calendar- year-out-risicybersecurity-
13 Sridhar S., Hahn A., Govindarasu M., “Cyber-Physical System Security for the Electric Power Grid”, Proceedings of the IEEE, vol 100, no 1, Jan 2012, pp 210-224
14 Goetz E., Shenoi S., “Critical Infrastructure Protection,” Springer Nov 2009
15 Coughlan B.W., Lubkeman D.L., Sutton J., “Improved control of capacitor bank switching to minimize distribution systems losses”, Proceedings of the 22 nd Annual North American Power Symposium, 15-16 Oct 1990, pp 336-345
16 Bunch J.B., Miller R.D., Wheeler J.E., “Distribution system integrated voltage and reactive power control”, IEEE Transactions on Power Apparatus and Systems, vol PAS-
17 Miu K.N., Hsiao-Dong C., Darling G., “Capacitor placement, replacement and control in large scale distribution systems by a GA based 2 stage algorithm”, IEEE Transactions on Power Systems, vol 12, no 3, Aug 1997, pp 1160-1166
18 Kersting W.H., “Distribution feeder voltage regulation control”, IEEE Transactions on Industry Applications, vol 46, no 2, Mar.-Apr 2010, pp 620-626
19 Baran M.E., Wu F.F., “Optimal capacitor placement on radial distribution systems”, IEEE Transactions on Power Delivery, vol 4, no 1, Jan 1989, pp 725-734
20 Borozan V., Baran M.E., Novosel D., “Integrated Volt/var control in distribution systems”, IEEE Power Engineering Society Winter Meeting, 2001, pp 1485-1490
21 Mirhoseini S H., Hosseini S.M., Ghanbari M., Ahamadi M., “A new improved adaptive imperialist competitive algorithm to solve the reconfiguration problem of distribution systems for loss reduction and voltage profile improvement”, International Journal of Electrical Power & Energy Systems, vol 55, Feb 2014, pp.128-143
22 Jin-Cheng W., Hsiao-Dong C., Miu K.N., Darling G., “Capacitor placement and real time control in large scale unbalanced distribution systems: loss reduction formula, problem formulation, solution methodology and mathematical justification”, Proceedings of IEEE Transmission and Distribution Conference, 15-20 Sept 1996, pp 236-241
23 Jin-Cheng W., Hsiao-Dong C., Miu K.N., Darling G., “Capacitor placement and real time control in large-scale unbalanced distribution systems: numerical studies”, IEEE Transactions on Power Delivery, vol 12, no 2, Apr 1997, pp 959-964
24 Klienberg M., Miu K.N., “A study of distributed capacitor control of electric power distribution systems”, North American Power Symposium, 4-6 Aug.2011, pp 1-6
25 Klienberg M., Miu K.N., Segal N., Lehmann H., Figura T.R., “A partitioning method for distributed capacitor control of electric power distribution systems”, IEEE Transactions on Power Systems, vol 29, no 2, Mar 2014, pp 637-644
26 Shen Z., Wang Z., Baran M.E., “Optimal volt/var control strategy for distribution system with multiple voltage regulating devices”, IEEE PES Transmission and Distribution Conference and Exposition, 7-10 May 2012, pp 1-7
27 Jen-Hao T., Chia-Yen C., Chi-Fa C., Yi-Hwa L., “Optimal capacitor control for unbalanced distribution systems with distributed generations”, IEEE International Conference on Sustainable Energy Technologies, 24-27 Nov 2008, pp 755-760
28 Amin S., Cardenas A., Sastry S., “Safe and secure networked control systems under denial-of-service attacks,” in Hybrid Systems: Computation and Control, vol 5469, Apr
29 Huangc Y.-L., Cárdenasa A A., Aminb S., Linc Z.-S., Tsaic H.-Y., Sastrya S.,
“Understanding the physical and economic consequences of attacks on control systems,” International Journal of Critical Infrastructure Protection, vol.2, no 3, Oct 2009, pp 72-
30 Rahman M.A., Mohsenian-Rad H., “False Data Injection Attacks with Incomplete
Information against Smart Power Grids”, IEEE Global Communications Conference, 3-7 Dec 2012, pp 3153-3158
31 Hug G., Giampapa J.A., “Vulnerability Assessment of AC State Estimation With Respect to False Data Injection Cyber-Attacks”, International Journal of Critical Infrastructure Protection, vol 2, no 3, Oct 2009, pp 72-83
32 Liu Y., Ning P., Reiter M.K., “False data injection attacks against state estimation in electric power grids,” Proceedings of 16 th ACM conference on Computer and communication security, Oct 2010, pp 21-32
33 Dan G and Sandberg H., “Stealth attacks and protection schemes for state estimators in power systems,” Proceedings of 1 st IEEE International Conference Smart Grid
34 Teixeira A., Amin S., Sandberg H., Johansson K.H., Sastry S.S., “Cyber security analysis of state estimators in electric power systems,” Proceedings of 49 th IEEE Conference on Decision Control, 2010, pp.5991–5998
35 Yuan Y., Li Z., Ren K., “Modeling Load Redistribution Attacks in Power Systems,” IEEE Transactions on Smart Grid, vol 2, no 2, June 2011, pp 382-390
36 Liu X and Li Z., “Local Load Redistribution Attacks in Power Systems With Incomplete Network Information,” IEEE Transactions on Smart Grid, vol 5, no 4, July 2014, pp 1665-1676
37 Yuan Y., Li Z., Ren K., “Quantitative Analysis of Load Redistribution Attacks in Power Systems,” IEEE Transactions on Parallel and Distributed Systems, vol 23, no 9, Sept
38 Sou K.C., Sandberg H., Johansson K.H., “Detection and Identification of Data Attacks in Power System,” American Control Conference, 27-29 June 2012, pp 3651-3656
39 Bobba R.B., Rogers K.M., Wang Q., Khurana H., Nahrstedt K., Overbye T.J., “Detecting False Data Injection Attacks on DC State Estimation”, 1 st Workshop on Secure Control Systems, Apr 2010
40 Dorfler F., Pasqualetti F., Bullo F., “Distributed Detection of Cyber-Physical Attacks in Power Networks: A Waveform Relaxation Approach,” 49 th Annual Allerton Conference on Communication, Control, and Computing, 28-30 Sept 2011, pp 1486-1491
41 Giani A., Bitary E., Garciay M., McQueenz M., Khargonekarx P., Poolla K., “Smart Grid Data Integrity Attacks: Characterizations and Countermeasures,” IEEE International Conference on Smart Grid Communications, 17-20 Oct 2011, pp 232-237
42 Kim T.T., Poor H.V., “Strategic Protection against Data Injection Attacks on Power Grids,” IEEE Transactions on Smart Grid, vol 2, no 2, June 2011, pp 326-333
43 Sridhar S., Manimaran G., “Data integrity attacks and their impacts on SCADA control system,” IEEE Power and Energy Society General Meeting, July 2010, pp 1 –6
44 Sridhar S., Manimaran G., “Data integrity attack and its impacts on voltage control loop in power grid,” IEEE Power and Energy Society General Meeting, July 2011, pp 1 –6
45 OpenDSS Manual, Electric Power Research Institute, Jul 2010 Available: http://sourceforge.net/projects/electricdss
46 http://www.smartgrid.epri.com/doc/OpenDSS Level 1 Training.pdf
47 Ramachandran V., Solanki J., Solanki S.K., “Steady state analysis of high penetration PV on utility distribution feeder,” IEEE PES Transmission and Distribution Conference and Exposition, May 2012, pp 1 –6
48 Yan X., Su X G., “Linear Regression Analysis: Theory and Computing”
West Virginia University Electronic Problem/ProjectlResearch Report
I certify that I have obtained written permission from the copyright owners of any third-party materials included in my thesis, dissertation, project report, or other research documents, allowing for distribution as outlined upon submission.
I grant West Virginia University and its agents a non-exclusive license to archive and make accessible my document in various media formats, while I retain ownership rights and copyright as outlined in the WVU copyright policy Additionally, I maintain the right to utilize any part of this document in future works, including articles or books.
The document has been reviewed and approved by the students' advisory committee The undersigned acknowledge their agreement to the terms outlined above and confirm that this Signature Form supersedes all prior Signature Forms.
Non-wVU Email Account Vivelft'rr L) r, 57 @qrys^il'co,
- thgDls problem/ProjecUResearch Report tohph vl"> ate