IEEE 13-bus Test Feeder Research Articles

Distribution System Resilience Under Asynchronous Information Using Deep Reinforcement Learning

Resilience of a distribution system can be enhanced by efficient restoration of critical load following a major outage. Existing models include optimization approaches that consider available information without incorporating the inherent asynchrony of data arrival during execution of the restoration plan. Failure to consider the asynchronous nature of information arrival can lead to underutilization of critical resources. Moreover, analytical models become computationally inefficient for large scale systems. On the other hand, artificial intelligence (AI)-based tools have demonstrated efficient results for power system applications. In this paper, it is proposed a Reinforcement Learning (RL) model that learns how to efficiently restore a distribution system after a major outage. The proposed approach is based on a Monte Carlo Tree Search to expedite the training process. The proposed model strategy provides a robust decision-making tool for asynchronous and partial information scenarios. The results, validated with the IEEE 13-bus test feeder and IEEE 8500-node distribution test feeder, demonstrate the effectiveness and scalability of the proposed method.

A protection scheme for distribution utility grid with wind energy penetration

The impact of fault circumstances on distribution grid parameters in the presence of wind power generation is explored in this research. A protection algorithm (PA) is also proposed for detecting faulty events by using the proposed wind fault index, which is computed by analysing current signals using the Wigner distribution function and the Stockwell transform (ST). The sort of fault is determined by the number of faulty phases found. The zero sequence currents introduced to identify the ground’s involvement in a fault event are analysed to calculate a wind ground fault index. Single phase to the ground, double phase to the ground, double phase, three-phases, and three phases to the ground faults are all investigated fault events. It has been determined that PA outperforms discrete Wavelet Transform and ST-based approaches in terms of fault estimation time and noise effect. The study was conducted on the IEEE-13 bus test feeder, which was connected to wind power plants (WPPs).

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. To ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

On the Solution of the Optimal Power Flow for Three-Phase Radial Distribution Networks With Energy Storage

We study a multiperiod optimal power flow (OPF) problem in unbalanced three-phase radial distribution networks with batteries. To address this problem, we first take the resistance-line battery model that treats lossy batteries by adding resistive lines and virtual buses. Then, we derive a linearization for the power flow equations, called generalized three-phase simplified DistFlow, which accounts for shunt elements. Also, it is exact at a freely chosen point while having globally good performance. Using it, we extend the heuristic iterative OPF algorithm, CoDistFlow, to unbalanced three-phase networks. At convergence, three-phase CoDistFlow gives a solution that satisfies the exact nonlinear power-flow equations and the exact security constraints. To theoretically guarantee the convergence of three-phase CoDistFlow, we develop the forced convergent three-phase CoDistFlow. Moreover, we show how to adapt the three-phase CoDistFlow to solve a scenario-based OPF in the presence of uncertainties, whereas other existing OPF solution methods may not offer this possibility. Finally, we perform evaluations on the IEEE 123-bus test feeder and comparisons with Ipopt.

A Three-Layer Stochastic Energy Management Approach for Electric Bus Transit Centers With PV and Energy Storage Systems

Along with the increasing electric bus (EB) penetration, the impact of the extensive charging load on the distribution system has been aggravating. To mitigate such impact, energy storage systems (ESSs) and photovoltaic (PV) are usually installed in the EB transit centers (EBTCs). In this article, a three-layer stochastic energy management approach is proposed for EBTCs to reduce the operation cost while maintaining local voltage quality. In the first layer, a modified robust optimization over time (ROOT) approach is developed to obtain the charging/discharging margin with minimum EBTC operation cost. In the second layer, the voltage regulation impact on the local voltage quality is estimated through power flow analysis considering voltage fluctuation and line loss minimization. In the third layer, the charging/discharging strategy is optimized with dynamic programming based on a modified greedy algorithm. The performance of the proposed approach is evaluated in a case study based on the IEEE 123-bus test feeder and the real operation data obtained from St. Albert Transit in Alberta, Canada. The results indicate that the proposed approach can not only minimize the EBTC operation cost but also well maintain the local voltage quality, in comparison with existing energy management approaches.

Optimization of Economic Efficiency in Distribution Grids Using Distribution Locational Marginal Pricing

Distribution locational marginal pricing (DLMP) is an increasingly popular pricing signal that can be used to incentivize grid-friendly behavior of distributed energy resources (DER) to optimize economic efficiency in distribution grids. In this paper, a lossy direct-current optimal power flow (DCOPF) is utilized to obtain the iterative calculation framework for DLMPs. The two-stage algorithm iterates between the transmission system optimal power flow (OPF) and the distribution system OPF until no significant changes in DLMPs are observed. Real power losses are estimated using a static piecewise linear approximation technique. A sampling algorithm is proposed to minimize the possible convergence issues associated with the proposed mathematical model. DLMPs are calculated for the i) contemporary, ii) enhanced, and iii) meshed distribution grids using an IEEE 34-bus test feeder. The test transmission system is modeled using an IEEE 30-bus system. Finally, the calculated DLMPs in the enhanced grid are compared against three existing pricing mechanisms via three case studies to prove its validity and superiority, especially in congested systems with high penetration of price-responsive loads (PRLs).

Detection of Short-Term Voltage Disturbances and Harmonics Using μPMU-Based Variational Mode Extraction Method

Electric power quality (PQ) is one of the most critical factors effective on the reliability and energy efficiency of power systems. Power quality disturbances (PQDs), such as voltage sags and harmonics, can lead to power outages or interruption in service, and equipment damage, which is very expensive and time-consuming. Therefore, study, research, and investment are critical to evaluate and improve PQ. A wide-area monitoring system is required for PQDs detection to investigate the impact of these on the grid. In other words, the first step in detecting PQDs and taking corrective measures is PQ monitoring. This article has proposed using microphasor measurement units ( $\mu $ PMUs) for detecting short-term voltage PQ phenomena and harmonics at the system level. In other words, the $\mu $ PMU is used as a PQ monitor, and their optimal location is obtained according to the different PQ indices. The advantage of using $\mu $ PMU measurements is the continuous determination of system phasor information and the observation of dynamic network changes online. The accurate monitoring and detection of system PQ phenomena are implemented by network visibility and sending this information via the link created by $\mu $ PMUs. On the other hand, this article has investigated the efficiency of the variational mode extraction (VME) method in analyzing and extracting measured signals by $\mu $ PMUs and to detect PQDs. The proposed method is evaluated on the standard IEEE 13-bus distribution test feeder. The simulation results show the accuracy, correctitude, and speed of the proposed method compared with other methods proposed in other papers.

A blockchain based peer-to-peer trading framework integrating energy and carbon markets

Prosumers are active participants in future energy systems who produce and consume energy. However, the emerging role of prosumers brings challenges of tracing carbon emissions behaviours and formulating pricing scheme targeting on individual prosumption behaviours. This paper proposes a novel blockchain-based peer-to-peer trading framework to trade energy and carbon allowance. The bidding/selling prices of prosumers can directly incentivise the reshaping of prosumption behaviours to achieve regional energy balance and carbon emissions mitigation. A decentralised low carbon incentive mechanism is formulated targeting on specific prosumption behaviours. Case studies using the modified IEEE 37-bus test feeder show that the proposed trading framework can export 0.99 kWh of daily energy and save 1465.90 g daily carbon emissions, outperforming the existing centralised trading and aggregator-based trading.

Resilient Networked AC Microgrids Under Unbounded Cyber Attacks

This paper considers a cooperative and adversarial AC microgrid system consisting of cooperative leaders and inverters, as well as adversarial attackers. The attackers aim to destabilize the synchronization dynamics of the AC microgrid by first intercepting the communication channels, penetrating the local state feedback, and pretending to be a cooperative neighbor, and then initiating malicious attacks by launching unbounded injections. A fully distributed resilient control framework is offered for the secondary frequency regulation and voltage containment to ensure system stability and preserve bounded synchronization. In particular, a virtual resilient layer with hidden networks is developed to integrate with the original cyber-physical layer. The proposed resilient control framework is fully distributed without requiring any global information. A modified IEEE 34-bus test feeder benchmark system is emulated in a controller/hardware-in-the-loop environment, where the control objectives are met under different attack scenarios.

Optimal Volt/VAR control in distribution systems with prosumer DERs

This paper proposes an optimal Volt/VAR control method for distribution systems with proliferated prosumer distributed energy resources (P-DERs) with generation and consumption capabilities. The proposed method is developed based on a comprehensive mutual agreement between distribution system operator (DSO) and P-DERs to optimize the power loss and the cost of adjusting grid's voltage control assets by solving a multi-objective Volt/VAR control (MO-VVC) problem. In this paper, the proposed MO-VVC reduces the power loss by adjusting capacitor banks switches, tap position of on-load tap changer transformers, voltage regulators’ taps, and active and reactive power set-points of P-DERs. Three new sensitivity-based evolutionary algorithms are proposed to find the optimal solutions more accurately with reduced computational time. In addition, a payment system is proposed to calculate the financial benefits of participating parties. The performance of the proposed method is validated using the simulation results of the modified IEEE 34-bus test feeder with several P-DERs.

A security-based observability method for optimal PMU-sensor placement in WAMS

Optimal PMU placement (OPP) problem is one of the most important issues in wide area measurement systems (WAMS). Delivering the measured data to the control center is possible through communication infrastructure (CI) that is a part of the WAMS. However, to well estimate the state of the system, observability of the measurement system is necessary. In this paper, a security-based observability (SBO) method for the PMUs and related CI is proposed. A hybrid wireless sensor-based structure including energy harvesting sensor nodes (EHSNs) and plug-in powered sensor nodes (PPSNs) is utilized as the communication system. The contingency-constraint optimal PMU placement and related sensor-based CI is proposed and formulated. To increase the reliability of the CI, a reliability index for the wireless sensors is added as a constraint to the objective function which includes the total cost minimization subject to power system observability and communication constraints. The effect of zero-injection buses (ZIBs) and radial buses in the power system are also included in the model to get more practical results. A mixed-integer linear programming (MILP) is used for contingency constraint PMU placement and a binary-coded genetic algorithm (BCGA) is accordingly used for solving the examined communication optimization. The IEEE 13-bus and IEEE 37-bus test feeder systems are utilized to evaluate the effectiveness of the proposed method.

Detection and Mitigation of Data Manipulation Attacks in AC Microgrids

This paper presents a resilient control framework for distributed frequency and voltage control of AC microgrids under data manipulation attacks. In order for each distributed energy resource (DER) to detect any misbehavior on its neighboring DERs, an attack detection mechanism is first presented using a Kullback-Liebler (KL) divergence-based criterion. An attack mitigation technique is then proposed that utilizes the calculated KL divergence factors to determine trust values indicating the trustworthiness of the received information. Moreover, DERs continuously generate a self-belief factor and communicate it with their neighbors to inform them of the validity level of their own outgoing information. DERs incorporate their neighbors' self-belief and their own trust values in their control protocols to slow down and mitigate attacks. It is shown that the proposed cyber-secure control effectively distinguishes data manipulation attacks from legitimate events. The performance of proposed secure frequency and voltage control techniques is verified through the simulation of microgrid tests system implemented on IEEE 34-bus test feeder with six DERs.

Measurement Sensitivity and Estimation Error in Distribution System State Estimation using Augmented Complex Kalman Filter

Distribution state estimation (DSE) is an essential part of an active distribution network with high level of distributed energy resources. The challenges of accurate DSE with limited measurement data is a well-known problem. In practice, the operation and usability of DSE depend on not only the estimation accuracy but also the ability to predict error variance. This paper investigates the application of error covariance in DSE by using the augmented complex Kalman filter (ACKF). The Kalman filter method inherently provides state error covariance prediction. It can be utilized to accurately infer the error covariance of other parameters and provide a method to determine optimal measurement locations based on the sensitivity of error covariance to measurement noise covariance. This paper also proposes a generalized formulation of ACKF to allow scalar measurements to be incorporated into the complex-valued estimator. The proposed method is simulated by using modified IEEE 34-bus and IEEE 123-bus test feeders, and randomly generates the load data of complex-valued Wiener process. The ACKF method is compared with an equivalent formulation using the traditional weighted least squares (WLS) method and iterated extended Kalman filter (IEKF) method, which shows improved accuracy and computation performance.

Hierarchical planning of PEV charging facilities and DGs under transportation-power network couplings

The increasing penetration level of plug-in electric vehicles (PEVs), as well as distributed generators (DGs), imposes significant challenges on power system planning. This work presents a coordinated approach for the planning of PEV charging facilities and DGs, including both the locations and the capacities, with the consideration of the transportation - power network couplings. First, the PEV charging demand is characterized by a temporal-SoC (State of Charge) analysis, and the DG generation uncertainties are modeled by K-means clustering using historical data. The M/M/s/N queuing model is used to formulate the dynamics of charging stations and then obtain the optimal station capacity, including the number of chargers and waiting spaces. Furthermore, the placement of charging stations is optimized by the Floyd Algorithm to minimize the total distance to obtain charging service. Finally, the sitting and sizing of DGs are optimized over multiple objectives, including active power losses, reactive power losses, and voltage deviation. The solution is evaluated through a case study of the IEEE 53-bus test feeder coupled with a 25-node transportation network. It is shown that the proposed solution enables the active and reactive power losses as well as the voltage deviation to be reduced by 37.6%, 44.3%, and 33.6%, respectively, after the optimal integration of PEV charging stations and DGs. The scalability and effectiveness of the solution are further validated in an IEEE 123-bus test feeder coupled with the same transportation network, and the result confirms the effectiveness and scalability of the proposed solution.

Examination of the effect of the reactive power control of photovoltaic systems on electric power grids and the development of a voltage-regulation method that considers feeder impedance sensitivity

When relatively high-capacity renewable photovoltaic (PV) systems are connected to a grid, they can increase or decrease the voltage along feeders because of reverse power flow, even exceeding ± five percent of the rated voltage. Nowadays, grid-connected inverter-based PV systems that can control reactive power can alleviate such an increase or decrease in voltage by adjusting the reactive power, which is referred to as Volt/Var control and management. Therefore, the objective of this paper is to (a) perform case studies to analyze the steady-state response of a large distribution network (i.e., with more than 1000 buses) with high-capacity PV systems that can control Volt/Var (i.e., either producing or consuming reactive power) and (b) present a Volt/Var-control method for three-phase voltage regulation that uses the positive-sequence sensitivity impedance matrix with power-factor constraints. This method is verified in the IEEE 34-bus test feeder. Thus, the proposed methods can be used to regulate the voltage of a bus to which a PV system is connected if the system controls reactive power. These proposed methods can also be used for various impact studies for the operation or planning of distribution systems with such PV systems.

Data-Driven Sizing Planning of Renewable Distributed Generation in Distribution Networks With Optimality Guarantee

In this paper, we study the optimal sizing planning of renewable distributed generation (RDG) in distribution networks to minimize the long-term cost, including the investment cost, maintenance cost, and operating cost. In particular, the operating cost itself is optimized by solving an optimal power flow (OPF) problem at each time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> based on uncertain time-varying RDG output and load demand. As a result, the sizing planning problem is a bilevel stochastic programming problem, which is hard to solve. Instead of resorting to conventional meta-heuristic algorithms, this paper first proposes a novel data-driven approach based on the philosophy of online convex optimization to solve the problem with drastically lower complexity. As a key step to facilitate the algorithm, we derive a closed-form expression to iteratively update the sizing solution upon drawing each data sample. With sufficient data samples, the proposed algorithm guarantees to converge to the global optimal solution regardless of the underlying probabilistic distribution of RDG output and load demand. Numerical results on the IEEE 13-bus test feeder, the IEEE 33-bus test feeder, and the Southern California Edison (SCE) 56-bus feeder show that our data-driven method drastically outperforms the other methods in terms of both the solution optimality and computational complexity.

Two-Timescale Voltage Control in Distribution Grids Using Deep Reinforcement Learning

Modern distribution grids are currently being challenged by frequent and sizable voltage fluctuations, due mainly to the increasing deployment of electric vehicles and renewable generators. Existing approaches to maintaining bus voltage magnitudes within the desired region can cope with either traditional utility-owned devices (e.g., shunt capacitors), or contemporary smart inverters that come with distributed generation units (e.g., photovoltaic plants). The discrete on-off commitment of capacitor units is often configured on an hourly or daily basis, yet smart inverters can be controlled within milliseconds, thus challenging joint control of these two types of assets. In this context, a novel two-timescale voltage regulation scheme is developed for distribution grids by judiciously coupling data-driven with physics-based optimization. On a faster timescale, say every second, the optimal setpoints of smart inverters are obtained by minimizing instantaneous bus voltage deviations from their nominal values, based on either the exact alternating current power flow model or a linear approximant of it; whereas, on the slower timescale (e.g., every hour), shunt capacitors are configured to minimize the long-term discounted voltage deviations using a deep reinforcement learning algorithm. Extensive numerical tests on a real-world 47-bus distribution network as well as the IEEE 123-bus test feeder using real data corroborate the effectiveness of the novel scheme.

Two-Stage Distribution Circuit Design Framework for High Levels of Photovoltaic Generation

Present-day radial electric power distribution circuit faces multiple challenges due to the increased photovoltaic (PV) generation. This paper aims to examine and design modern distribution circuit topologies for accommodating high PV penetration, while addressing power quality concerns. The central hypothesis of the proposed design approach is that by decreasing the Thevenin impedance at the buses where PVs are connected, the impacts on feeder voltages due to PV generation become less pronounced thereby additional PV capacity can be integrated at the corresponding buses. A novel two-stage optimization framework is proposed. The first stage is a mixed-integer linear programing based formulation to design new optimal configuration for any given distribution circuit. The formulation allows the possibility that the circuit can be operated in either a radial or loop configuration. The second stage, a nonlinear programing based formulation, then finds PV hosting capacity for the identified optimal configuration. The proposed two-stage framework is evaluated for IEEE 123-bus test feeder. It is demonstrated that the PV hosting capacity of the feeder can be increased by 53% by optimally adding two new distribution lines with tie-switches.

PSO-based Siting and Sizing of Electric Vehicle Charging Stations

With the rapid growth of the number of electric vehicles, the optimization of charging network is imminent. In this paper, a screening method for the siting and sizing of electric vehicle charging station is developed to minimize the total cost including capital investment on stations, EV charging stations’ operation cost and maintenance cost. Driving distance of electric vehicles and service radius of stations are taken into account to pick out the optimal sites of EV charging stations. A mathematical model with electric physical constraints is designed to distribute appropriate capacities for each EV charging station to prevent the negative effects on the power grid and the PSO optimization algorithm is applied to obtain the optimal sizing parameters. Finally, the IEEE 123-bus test feeder case study is used to confirm the validity of the proposed method and increase the economic benefits.

A Discounted Stochastic Multiplayer Game Approach for Vehicle-to-Grid Voltage Regulation

Along with the diversification of electricity market, the voltage regulation (VR) service is opened up to various qualified providers to meet the enormous demand, among which, the electric vehicle (EV) aggregators (AGGs) can integrate the scattered EVs and play the role of VR sources with a high response speed and low cost. In order to coordinate the VR service providers to satisfy the total VR requirement, auction mechanisms are widely used to select VR sources to achieve better performance. Yet, it is challenging to optimize the strategy of each EV AGG in the auction process due to the stochastic EV mobility, various distribution network topology, and the competition mechanism. To address these challenges, we proposed a discounted stochastic multiplayer game (DSMG) approach to analyze the competition among EV AGGs. Due to the constraint of distribution network topology, the efficiency of the VR sources at different locations can be different. Thus, the impact of distribution network topology on the VR efficiency is investigated by DSO when evaluating the capacity of AGGs. The randomness of EV numbers is considered when predicting the AGGs’ available VR capacity so that the tendency for the AGGs to follow the optimal strategies can be modeled accurately. Accordingly, a linear power flow analysis approach and a battery pool model are developed to address the distribution network topology and EV mobility, respectively. Then, the DSMG approach is used in the VR auction process to optimize the AGGs’ strategies. The existence proof of the stationary Markov perfect equilibrium is presented, and the corresponding algorithms to obtain the equilibrium is proposed. The performance of the proposed DSMG approach is evaluated and compared with other approaches based on the IEEE 33-bus test feeder, IEEE 123-bus test feeder, and the real-world generation and load data from PVWatts Calculator and Market Analysis and Information System, respectively.