Uncertainty Of Distributed Generation Research Articles

Optimal Configuration of Hybrid AC/DC Distribution Network Considering the Temporal Power Flow Complementarity on Lines

To mitigate the voltage violation and overloading caused by the integration of Distributed Generation (DG) and Electric Vehicle Charging (EVC) loads, a feasible solution is to convert some AC medium voltage distribution lines to DC ones and formulate an AC/DC hybrid distribution network, based on which flexible power shifting between lines can be achieved. However, the complementarity of power flows amongst AC/DC lines is hardly described and embedded in existing configuration optimization methods in which only the average loading or the variations of loading for a certain period is considered. Solution space will be geometrically increased if operation scenarios are fully simulated for configuration caused by the strong uncertainties of DGs and EVC loads. This paper proposes an analytic quantifiable method to describe the power complementarity between AC/DC lines. The Gaussian mixture model is used to depict the temporal correlation and uncertainties. The complementarity is calculated by the conditional probability of multi-dimensional joint probability density function of AC/DC hybrid lines. Accordingly, an optimal configuration method of hybrid AC/DC distribution network is proposed considering the complementarity of power flows on AC/DC lines, in which the size and location of Voltage Source Converters (VSCs) are optimized. Simulations studies are performed to verify the proposed method.

Robust optimization of the active distribution network involving risk assessment

Inherent dynamic constraints of distributed generations (DGs) and the correlation between injected variables bring great challenges to distribution network operation. In order to improve the degree of coupling and interconnection coordination between different energy devices, improve the ability of the distribution network to cope with the uncertainty of DGs, achieve low-carbon operation, and improve the environmental friendliness of distribution network operation, this article proposes a robust optimization approach involving risk assessment. The semi-invariant method and scene clustering are used to deal with the uncertainty of DGs and load, thus formulating a robust optimization model for distribution network distribution based on risk indices. To address the time-varying constraints of energy storage systems (ESSs) and gas turbines, a two-stage box-based decomposition model is established. Dynamic constraints are included in the first stage to constrain the operating state and operating domain of the unit and ESSs. In the second stage, the multi-timescale optimization problem is transformed into multiple single-timescale optimization problems, which are solved by the column and constraint generation (C&CG) algorithm to improve the solution efficiency. The feasibility of the comprehensive optimization model based on dynamic reconfiguration and distributed robust optimization (DRO) is demonstrated with the PG&E 69 bus system.

Optimization of decentralized control strategies of distributed resources under cyber failures in flexible distribution network

The flexible multi-state switch (FMSS) can realize the optimal control of the distribution network under normal and faulty situations. The dependence of distribution network on cyber system becomes heavier as distributed resources such as FMSS and distributed generations (DGs) integrated to the network. To reduce the operational risks under cyber failure scenarios, this paper proposes an optimization model to enable decentralized control strategies of distributed resources under cyber failures. First, the model of flexible cyber-physical distribution system is established and the coordinated control strategies of distributed resources under different operation statuses are analyzed. Then, the adaptive fuzzy-C means method and fault tree method based on consistency of failure consequences are used to cope with the uncertainties of DGs and cyber failures, respectively. On this basis, a bi-level optimization model of the decentralized control strategies of distribution resources is established to minimize the voltage deviation and load shedding. Second order cone method and heuristic algorithm are adopted for solving the optimization problem. Finally, the proposed control strategy is validated by case studies. This study is an effective operation strategy for distributed resources in flexible distribution network.© 2017 Elsevier Inc. All rights reserved.

Three-Phase Unbalanced Distribution Network Dynamic Reconfiguration: A Distributionally Robust Approach

The active distribution network has witnessed an increasing penetration of distributed generation (DG) while the stochasticity and variability arising from DGs also impose significant challenges on system operation. To mightily accommodate the uncertainty of DG, we introduce a distributionally robust chance-constrained dynamic reconfiguration approach for a three-phase unbalanced distribution network. The proposed framework optimizes the switching cost and the expected power supply cost from upstream grid, and stipulates that the chance constraints hold under the worst-case distribution within a novel ambiguity set, which incorporates the Wasserstein distance and the first-order moment. Then we develop tractable and scalable solution methods to tackle the expected objective function and chance constraints. As a result, the proposed model is reduced to a mixed-integer linear programming problem that can readily be implemented. Numerical experiments are carried out on the IEEE 34-bus and 123-bus test systems to demonstrate the effectiveness and efficiency of the suggested approach.

Dynamic Topology Awareness in Active Distribution Networks Under DG Uncertainties Using GMM-PSEs and KL Divergence

The frequent switching operations and triggering events of automation devices are poorly documented in distribution management systems, leading to challenging work regarding the timely detection of system state changes. Additionally, the limited measurements in distribution networks and the randomness of plug-and-play devices make obtaining real-time observations of system states difficult. Furthermore, distributed generation (DG) output uncertainties exacerbate the situation. Thus, we propose a dynamic topology awareness (DTA) approach to make judgments regarding operational states and identify all possible topology changes (including normal operations, islanding and outages) in the absence of real-time DG measurements. The method consists of two steps. The first step applies parallel Gaussian mixture model-based probabilistic state estimators (GMM-PSEs) of subareas and extended subareas to calculate the probability distributions of border bus voltages with full consideration of DG uncertainties. The second step utilizes the Kullback-Leibler (KL) divergence measure to evaluate the difference between the two probability distributions estimated by subareas and extended subareas, thereby obtaining an indicator (average KL divergence) for identifying possible topologies. The effectiveness of the proposed method is examined on the IEEE 33-bus and IEEE 123-bus test cases. It is computationally efficient and accurate when identifying all possible topologies under limited measurements and DG uncertainties.

Optimal stochastic scenario-based allocation of smart grids’ renewable and non-renewable distributed generation units and protective devices

The smart grid reliability is dramatically affected due to system uncertainties. Although much efforts have been devoted to developing the Monte Carlo simulation (MCS)-based or analytical methods for reliability-based optimal allocation distributed generation (DGs) and protective devices (PDs), there is a research gap about developing the probabilistic scenario-based optimization methods. This paper proposes a novel stochastic scenario-based reliability evaluation method for optimal allocation of smart grids’ PDs and DGs. The scenario reduction is applied using the k-means algorithm and modified system state, including the clusters of renewable-based DGs. The malfunction of PDs is concerned, which is one of the most important contributions of the introduced method. The introduced clustering-based reliability evaluation method is applied to IEEE 33-bus test system. Test results infer that around 10% inaccuracy occurs in deterministic approaches without considering uncertainties of DGs and PDs. Obtained test results also imply that the impacts of renewable DGs’ uncertainties are more considerable than eventual malfunctions of PDs. The MCS-based methods are used to verify the precision of the introduced method. Moreover, by comparing the introduced method with other available analytical methods, it is shown that the obtained results are 1.2% more precise than current analytical ones.

Optimal V2G Method Considering Uncertainty of Distributed Generation and Load

The penetration of electric vehicles (EV) has brought many benefits to the active distribution network due to their unique advantages. But, EV also has negative impacts on the distribution network for their uncertainty. Moreover, the integration of distributed generation (DG) and the uncertainty of load demand also increase the negative impacts of EV on the distribution network. In this paper, optimal vehicle-to-gird (V2G) method considering uncertainty of distributed generation (DG) and load was proposed to reduce the negative impacts by minimizing the load peak-valley difference and maximizing the user economic benefits. To reduce the uncertainty of DG, we combined particle swarm optimization (PSO) and backpropagation neural network to create a prediction model to predict the output of DG. And Time-of-use (TOU) is used to optimize the load curve. Finally, the optimal charging and discharging time in a day can be obtained by improved particle swarm optimization algorithm (IPSO). The proposed method is verified by numerical analysis, which highlights that the proposed V2G scheduling can significantly improve distribution network stability and user economic benefits.

Multi-Period Active Distribution Network Planning Using Multi-Stage Stochastic Programming and Nested Decomposition by SDDIP

This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method.

A lattice method for jump-diffusion process applied to transmission expansion investments under demand and distributed generation uncertainties

Strategic decision making for rare events is considered to be an arduous course of actions as their impacts cannot accurately be modeled. Transmission of electrical power is a major challenge in this day and age due to the prevalent of rare events. Decision makers of generation units, distribution utilities, and transmission networks do not often cooperate, which creates severe uncertainties for all players. Growth of demand for electricity and installation or removal of distributed generation (DG), considered to be a rare event, are among uncertainties encountered by transmission network owners. Expansion decisions for transmission lines should be strategically executed because installations of DGs may create a stranded cost for transmission owners. In this study, we propose a real options framework that quantifies the values of transmission investments under demand and DG uncertainties to guide decision makers of transmission companies regarding how to adapt their expansions decisions. We model demand uncertainty as a geometric Brownian motion process and DG uncertainty as a Poisson arrival process. We devise a computationally-efficient lattice diagram to discretize both processes in a single grid, which can also be employed to model other types of rare events in various sectors. The proposed framework is demonstrated on a realistic transmission network. Numerical study shows that our proposed lattice model is computationally superior over existing diagrams. As for managerial insights, it shows that depending on the locations of DG installations, DG penetration may not reduce the value of a transmission network. If the center at which a DG is installed has a large-capacity local generator, the installation may not undervalue the transmission network.

Data‐driven distributionally robust joint planning of distributed energy resources in active distribution network

With the increasing penetration of distributed energy resources (DERs) in the active distribution network (ADN), how to enable joint planning of DERs under the uncertainty of distributed generations (DGs) has become a challenging problem. This study establishes a two-stage joint planning model considering doubly-fed induction generator, photovoltaics (PVs) with the ancillary services of PV inverter, distributed energy storage systems and different types of controllable loads in the ADN. To address the uncertainties of DGs, a two-stage data-driven distributionally robust planning model is constructed. The proposed model is solved in a `master and sub-problem' framework by column-and-constraint generation algorithm, where the master problem is to minimise the total cost and find the optimal planning decision under the worst probability distributions, and the sub-problem is to find the worst probability distribution of given uncertain scenarios. Besides, the original mixed-integer non-linear planning problem is converted into a mixed-integer second-order cone programming problem through second-order cone relaxation, Big-M and piecewise linearisation method. The numerical results based on 33-bus system verify the effectiveness of the proposed model.

Reactive Power Optimization of a Distribution System Based on Scene Matching and Deep Belief Network

With a large number of distributed generators (DGs) and electrical vehicles (EVs) integrated into the power distribution system, the complexity of distribution system operation is increased, which arises to higher requirements for online reactive power optimization. This paper proposes two methods for online reactive power optimization, a scene-matching method based on Random Matrix (RM) features and a deep learning method based on Deep Belief Network (DBN). Firstly, utilizing the operation and ambient Big Data (BD) of the distribution system, we construct the high-dimension Random Matrices and extract 57 state features for the subsequent scene-matching and DBN training. Secondly, the feature-based scene-matching method is proposed. Furtherly, to effectively deal with the uncertainty of DGs and to avoid the performance deterioration of the scene-matching method under a new unknown scene, the DBN-based model is constructed and trained, with the former features as the inputs and the conventional reactive power control solutions as the outputs. This DBN model can learn the nonlinear complicated relationship between the system features and the reactive power control solutions. Finally, the comprehensive case studies have been conducted on the modified IEEE-37 nodes active distribution system, and the performances of the proposed two methods are compared with the conventional method. The results show that the DBN-based method possesses the better performance than the others, and it can reduce the network losses and node voltage deviations obviously, even under the new unknown and unmatched scenes. It does not depend on the distribution system model and parameters anymore and can provide online decision-making more quickly. The discussions of the two methods under different DG penetrations and the historical data volume were given, verifying the adaptability, robustness and generalization ability of the DBN-based method.

Equivalent modeling of active distribution network considering the spatial uncertainty of renewable energy resources

Modeling the uncertainties of active distribution networks (ADNs) is essential to dispatch process. Existing techniques focus on the uncertainty of the forecasting errors of distributed generation (DG) caused by changing weather conditions. This paper proposes an equivalent modeling approach for ADNs considering the spatial uncertainty of DG, which is caused by the dispersed locations of distributed renewable energy resources. The boundary injections of this model are composed of deterministic and uncertain components. The deterministic component is calculated based on the fitted power characteristics, while the uncertain component is described using a probability distribution. Model parameters of both components are estimated using an enhanced reinforcement learning algorithm to track the time-varying equivalent loads and DG. Simulation results demonstrate that the equivalent ADN model can accurately represent the aggregated feature of the ADN considering the spatial uncertainty caused by distributed renewable energy resources.

Energy Storage Scheduling in Distribution Systems Considering Wind and Photovoltaic Generation Uncertainties

Flexible distributed energy resources, such as energy storage systems (ESSs), are increasingly considered as means for mitigating challenges introduced by the integration of stochastic, variable distributed generation (DG). The optimal operation of a distribution system with ESS can be formulated as a multi-period optimal power flow (MPOPF) problem which involves scheduling of the charging/discharging of the ESS over an extended planning horizon, e.g., for day-ahead operational planning. Although such problems have been the subject of many works in recent years, these works very rarely consider uncertainties in DG, and almost never explicitly consider uncertainties beyond the current operational planning horizon. This article presents a framework of methods and models for accounting for uncertainties due to distributed wind and solar photovoltaic power generation beyond the planning horizon in an AC MPOPF model for distribution systems with ESS. The expected future value of energy stored at the end of the planning horizon is determined as a function of the stochastic DG resource variables and is explicitly included in the objective function. Results for a case study based on a real distribution system in Norway demonstrate the effectiveness of an operational strategy for ESS scheduling accounting for DG uncertainties. The case study compares the application of the framework to wind and solar power generation. Thus, this work also gives insight into how different approaches are appropriate for modeling DG uncertainty for these two forms of variable DG, due to their inherent differences in terms of variability and stochasticity.

Probabilistic Assessment of Hosting Capacity in Radial Distribution Systems

High penetration of distributed generation (DG) is mainly constrained by voltage-related issues. Due to the uncertainties associated with type, size, and location of DGs, it is difficult to quantify their integration limits in distribution networks, i.e., hosting capacity (HC). To address this issue, this paper proposes a probabilistic-based framework to determine the maximum integration limits of DGs considering the voltage rise and voltage deviation constraints. Such framework requires the use of the HC model, which can be formulated as a nonlinear optimization problem. Adding the voltage deviation constraint in the HC problem makes the model unsolvable. We address this issue by proposing a two-step algorithm to linearize the HC model. Then, using the linearized model, a probabilistic framework is proposed for considering the load variability and DGs uncertainties. To validate the efficacy and accuracy of the proposed framework, we identify the HC of a balanced and an unbalanced distribution networks and compare our results with those obtained from comprehensive power flow method and the traditional conservative planning. Finally, using the proposed framework, the impact of voltage deviation constraint, load growth, DG type and network structure on the HC are comprehensively studied using different DG technologies (i.e., Photovoltaics and wind).

Maximum Uncertainty Boundary of Volatile Distributed Generation in Active Distribution Network

The increasing integration of distributed generation introduces severe challenges to the secure operation of active distribution networks (ADNs) due to volatile power injections. One way to ensure ADN operation security is to evaluate acceptable boundaries of distributed generation uncertainties, namely maximum uncertainty boundary (MUB). In this paper, a novel set-based method is proposed to formulate the MUBs of distributed generation and the operation constraints of ADNs as security sets of polytopes. The advantages of the proposed set-based model lie not only in the simplified modeling with extremely high computational efficiency, but also in the potentials to take control instructions into account. The MUBs with operation scheduling (MUB-OS) and with available operation region (MUB-AOR) are further established as security sets of polytopes solvable by the toolbox of computational geometry. This paper proves the theorems that enable the transformation of MUBs from security sets into computational geometry-based descriptions, and then develops the corresponding algorithms on MUB, MUB-OS, and MUB-AOR. A novel evaluation framework is proposed to comprehensively assess the performance of the estimated MUB. The effectiveness and efficiency of the proposed methodology are comprehensively verified on a 3-node system and a modified IEEE 33-node system.

An affine arithmetic-based multi-objective optimization method for energy storage systems operating in active distribution networks with uncertainties

Considering uncertain power outputs of distributed generations (DGs) and load fluctuations, energy storage system (ESS) represents a valuable asset to provide support for the smooth operation of active distribution networks. This paper proposes an affine arithmetic-based multi-objective optimization method for the optimal operation of ESSs in active distribution networks with uncertainties. Affine arithmetic is applied to the optimization model for handling uncertainties of DGs and loads. Two objectives are formulated with affine parameters including the minimization of total active power losses and the minimization of system voltage deviations. The affine arithmetic-based forward-backward sweep power flow is first improved by the proposed pruning strategy of noisy symbols. Then, the affine arithmetic-based non-dominated sorting genetic algorithm II (AA-NSGAII) is used to solve the multi-objective optimization problem for ESSs operation under uncertain environment. Furthermore, three types of indices with respect to convergence, diversity, and uncertainty are defined for performance analysis. Numerical studies on a modified IEEE 33-bus system with embedded DGs and ESSs show the effectiveness and superiority of the proposed method. The optimization results demonstrate that the obtained Pareto front has better convergence and lower conservativeness in comparison to the interval arithmetic-based NSGA-II. A multi-period case considering seasonality of DGs and loads is further simulated to show the applicability in real applications.

Uncertain flow calculations of a distribution network containing DG based on blind number theory

A large number of distributed generations (DG) integrated into a distribution network challenge the planning for traditional power systems making traditional deterministic power flow calculations not applicable. Based on the interval and credibility of the blind number theory, this study is about the uncertainty of DG and the correlation between DGs. The interval models for wind power and solar power are established based on the characteristics of the wind power generator output and the photovoltaic cell output. The improved analytic hierarchy process is applied to determine the credibility of the intervals. The blind number theory and Cholesky decomposition are applied to study the correlation between wind speed and light intensity. According to the result of the power flow calculation with uncertainty, the voltage operational quality index is proposed to measure the impact of the DG. Through a modified IEEE 33-bus system, the feasibility and effectiveness of the blind number model for the DG and the necessity of considering the correlation between wind speed and light intensity are verified.

Risk Assessment for Distribution Systems Using an Improved PEM-Based Method Considering Wind and Photovoltaic Power Distribution

The intermittency and variability of permeated distributed generators (DGs) could cause many critical security and economy risks to distribution systems. This paper applied a certain mathematical distribution to imitate the output variability and uncertainty of DGs. Then, four risk indices—EENS (expected energy not supplied), PLC (probability of load curtailment), EFLC (expected frequency of load curtailment), and SI (severity index)—were established to reflect the system risk level of the distribution system. For the certain mathematical distribution of the DGs’ output power, an improved PEM (point estimate method)-based method was proposed to calculate these four system risk indices. In this improved PEM-based method, an enumeration method was used to list the states of distribution systems, and an improved PEM was developed to deal with the uncertainties of DGs, and the value of load curtailment in distribution systems was calculated by an optimal power flow algorithm. Finally, the effectiveness and advantages of this proposed PEM-based method for distribution system assessment were verified by testing a modified IEEE 30-bus system. Simulation results have shown that this proposed PEM-based method has a high computational accuracy and highly reduced computational costs compared with other risk assessment methods and is very effective for risk assessments.

Distribution system planning incorporating distributed generation and cyber system vulnerability

An optimisation model for distribution network expansion is proposed to acquire the optimal economical scheme by planning the installation of distributed generations (DGs) as well as the investment on newly constructed lines. The scenario-based method is employed to deal with the uncertainties of DGs including wind generation and photovoltaic units together with energy storage devices. Especially, the model highlights the cyber security requirements as additional constrains by means of introducing a risk index to evaluate the vulnerability of cyber system, and the payoff of cyber system failure is estimated by the load losses after the load shedding operations for the sake of system security and reliability. An improved genetic algorithm is applied to solve the aforementioned optimisation model. Finally, case studies are carried out on the 16-bus system with typical substation automation architecture to verify the effectiveness of the proposed model and method.

Optimal operation of distribution networks with presence of distributed generations and battery energy storage systems considering uncertainties and risk analysis

This paper presents a probabilistic framework for the operation of distribution networks considering distributed generations (DGs) and battery energy storage systems. This framework considers the uncertainty of electricity prices and output power of DGs. To account for uncertainties, the probability distribution function is used, which generates scenarios by Monte Carlo Simulation at each hour. The aim of this paper is to calculate the distribution of daily profit and risk analysis. Value at Risk (VaR) is used as risk measure, and sensitivity of VaR with respect to changes in standard deviation is assessed. Numerical examples for two case studies are presented to illustrate the impact of uncertainty of DGs and prices on the profit and risk.