Solvable model for distribution networks on random graphs

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

Statistical mechanics of distribution networks

This thesis presents an analysis of the stability of complex distribution networks. We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks. We propose a model that describes a distribution process in a network. The model incorporates the currents between any connected hubs in the network, local constraints in the form of Kirchoff's law and a global optimizational criterion. The flow of currents in the system is driven by the consumption. We study two principal types of model: infinite and finite link capacity. The key properties are the distributions of currents in the system. We again use a statistical mechanics framework to describe the currents in the system in terms of macroscopic parameters. In order to obtain observable properties we apply the replica method. We are able to assess the criticality of the level of demand with respect to the available resources and the architecture of the network. Furthermore, the parts of the system, where critical currents may emerge, can be identified. This, in turn, provides us with the characteristic description of the spread of the overloading in the systems.

Identification of Microturbine Model for Long-term Dynamic Analysis of Distribution Networks

As one of the most successfully commercialized distributed energy resources, the long-term effects of microturbines (MTs) on the distribution network has not been fully investigated due to the complex thermo-fluid-mechanical energy conversion processes. This is further complicated by the fact that the parameter and internal data of MTs are not always available to the electric utility, due to different ownerships and confidentiality concerns. To address this issue, a general modeling approach for MTs is proposed in this paper, which allows for the long-term simulation of the distribution network with multiple MTs. First, the feasibility of deriving a simplified MT model for long-term dynamic analysis of the distribution network is discussed, based on the physical understanding of dynamic processes that occurred within MTs. Then a three-stage identification method is developed in order to obtain a piecewise MT model and predict electro-mechanical system behaviors with saturation. Next, assisted with the electric power flow calculation tool, a fast simulation methodology is proposed to evaluate the long-term impact of multiple MTs on the distribution network. Finally, the model is verified by using Capstone C30 microturbine experiments, and further applied to the dynamic simulation of a modified IEEE 37-node test feeder with promising results.

Integrated Optimal Power Flow for Distribution Networks in Local and Urban Scales

This paper develops an integrated optimal power flow (OPF) tool for distribution networks in two spatial scales. In the local scale, the distribution network, the natural gas network, and the heat system are coordinated as a microgrid. In the urban scale, the impact of natural gas network is considered as constraints for the distribution network operation. The proposed approach incorporates unbalance three-phase electrical systems, natural gas systems, and combined cooling, heating, and power systems. The interactions among the above three energy systems are described by energy hub model combined with components capacity constraints. In order to efficiently accommodate the nonlinear constraint optimization problem, particle swarm optimization algorithm is employed to set the control variables in the OPF problem. Numerical studies indicate that by using the OPF method, the distribution network can be economically operated. Also, the tie-line power can be effectively managed.

Assessing the contribution of microgrids to the reliability of distribution networks

The emergence of microgeneration has recently lead to the concept of microgrid, a network of LV consumers and producers able to export electric energy in some circumstances and also to work in an isolated way in emergency situations. Research on the organization of microgrids, control devices, functionalities and other technical aspects is presently being carried out, in order to establish a consistent technical framework to support the concept. The successful development of the microgrid concept implies the definition of a suitable regulation for its integration on distribution systems. In order to define such a regulation, the identification of costs and benefits that microgrids may bring is a crucial task. Actually, this is the basis for a discussion about the way global costs could be divided among the different agents that benefit from the development of microgrids. Among other aspects, the effect of microgrids on the reliability of the distribution network has been pointed out as an important advantage, due to the ability of isolated operation in emergency situations. This paper identifies the situations where the existence of a microgrid may reduce the interruption rate and duration and thus improve the reliability indices of the distribution network. The relevant expressions necessary to quantify the reliability are presented. An illustrative example is included, where the global influence of the microgrid in the reliability is commented.

Flexible Power Control of Photovoltaic Plants Connected to Distribution Networks

This paper presents a system to control the power injected by a photovoltaic (PV) plant on the receiving network. This control is intended to mitigate some of the negative impacts that these units may produce on such networks, while increasing the installed power of the plant. The controlled parameters are the maximum allowed value of injected active power and the corresponding power factor, whose setpoints values may be fixed or dynamic. The developed system allows a local and a remote control. The injected power and the corresponding power factor may be set by following a predetermined profile or by real time adjustments to fulfill specific operation constraints on the receiving network. The system acts by adjusting the control parameters on the PV inverters. The main goal of the system is, in the end, to control the PV plant, ensuring the accomplishment of technical constraints and, at the same time, maximizing the installed power of the PV plant, which may be an important issue concerning the economic performance of such plants

Rethinking genre studies through distribution analysis : issues in international horror movie circuits

The existence of any film genre depends on the effective operation of distribution networks. Contingencies of distribution play an important role in determining the content of individual texts and the characteristics of film genres; they enable new genres to emerge at the same time as they impose limits on generic change. This article sets out an alternative way of doing genre studies, based on an analysis of distributive circuits rather than film texts or generic categories. Our objective is to provide a conceptual framework that can account for the multiple ways in which distribution networks leave their traces on film texts and audience expectations, with specific reference to international horror networks, and to offer some preliminary suggestions as to how distribution analysis can be integrated into existing genre studies methodologies.

Directional earth fault relay operation in mutually coupled multiple circuit distribution lines

Many of the power utilities around the world experienced spurious tripping of directional earth fault relays in their mesh distribution networks due to induced circulating currents. This circulating current is zero sequence and induced in the healthy circuit due to the zero sequence current flow resulting from a ground fault of a parallel circuit. This paper quantitatively discusses the effects of mutual coupling on earth fault protection of distribution systems. An actual spurious tripping event is analyzed to support the theory and to present options for improved resilience to spurious tripping.

Protection of distributed generation interfaced networks

With the rapid increase in electrical energy demand, power generation in the form of distributed generation is becoming more important. However, the connections of distributed generators (DGs) to a distribution network or a microgrid can create several protection issues. The protection of these networks using protective devices based only on current is a challenging task due to the change in fault current levels and fault current direction. The isolation of a faulted segment from such networks will be difficult if converter interfaced DGs are connected as these DGs limit their output currents during the fault. Furthermore, if DG sources are intermittent, the current sensing protective relays are difficult to set since fault current changes with time depending on the availability of DG sources. The system restoration after a fault occurs is also a challenging protection issue in a converter interfaced DG connected distribution network or a microgrid. Usually, all the DGs will be disconnected immediately after a fault in the network. The safety of personnel and equipment of the distribution network, reclosing with DGs and arc extinction are the major reasons for these DG disconnections. In this thesis, an inverse time admittance (ITA) relay is proposed to protect a distribution network or a microgrid which has several converter interfaced DG connections. The ITA relay is capable of detecting faults and isolating a faulted segment from the network, allowing unfaulted segments to operate either in grid connected or islanded mode operations. The relay does not make the tripping decision based on only the fault current. It also uses the voltage at the relay location. Therefore, the ITA relay can be used effectively in a DG connected network in which fault current level is low or fault current level changes with time. Different case studies are considered to evaluate the performance of the ITA relays in comparison to some of the existing protection schemes. The relay performance is evaluated in different types of distribution networks: radial, the IEEE 34 node test feeder and a mesh network. The results are validated through PSCAD simulations and MATLAB calculations. Several experimental tests are carried out to validate the numerical results in a laboratory test feeder by implementing the ITA relay in LabVIEW. Furthermore, a novel control strategy based on fold back current control is proposed for a converter interfaced DG to overcome the problems associated with the system restoration. The control strategy enables the self extinction of arc if the fault is a temporary arc fault. This also helps in self system restoration if DG capacity is sufficient to supply the load. The coordination with reclosers without disconnecting the DGs from the network is discussed. This results in increased reliability in the network by reduction of customer outages.

Intelligent distribution planning and control incorporating microgrids

This paper proposes a comprehensive approach to the planning of distribution networks and the control of microgrids. Firstly, a Modified Discrete Particle Swarm Optimization (MDPSO) method is used to optimally plan a distribution system upgrade over a 20 year planning period. The optimization is conducted at different load levels according to the anticipated load duration curve and integrated over the system lifetime in order to minimize its total lifetime cost. Since the optimal solution contains Distributed Generators (DGs) to maximize reliability, the DG must be able to operate in islanded mode and this leads to the concept of microgrids. Thus the second part of the paper reviews some of the challenges of microgrid control in the presence of both inertial (rotating direct connected) and non-inertial (converter interfaced) DGs. More specifically enhanced control strategies based on frequency droop are proposed for DGs to improve the smooth synchronization and real power sharing minimizing transient oscillations in the microgrid. Simulation studies are presented to show the effectiveness of the control.

Multiple distribution static synchronous compensators for distribution feeder voltage support

The potential of multiple distribution static synchronous compensators (DSTATCOMs) to improve the voltage profile of radial distribution networks has been reported in the literature by few authors. However, the operation of multiple DSTATCOMs across a distribution feeder may introduce control interactions and/or voltage instability. This study proposes a control scheme that alleviates interactions among controllers and enhances proper reactive power sharing among DSTATCOMs. A generalised mathematical model is presented to analyse the interactions among any number of DSTATCOMs in the network. The criterion for controller design is developed by conducting eigenvalue analysis on this mathematical model. The proposed control scheme is tested in time domain on a sample radial distribution feeder installed with multiple DSTATCOMs and test results are presented.

Distribution feeder loads classification and decomposition

Load in distribution networks is normally measured at the 11kV supply points; little or no information is known about the type of customers and their contributions to the load. This paper proposes statistical methods to decompose an unknown distribution feeder load to its customer load sector/subsector profiles. The approach used in this paper should assist electricity suppliers in economic load management, strategic planning and future network reinforcements.

A hybrid simulation framework to assess the impact of renewable generators on a distribution network

With an increasing number of small-scale renewable generator installations, distribution network planners are faced with new technical challenges (intermittent load flows, network imbalances…). Then again, these decentralized generators (DGs) present opportunities regarding savings on network infrastructure if installed at strategic locations. How can we consider both of these aspects when building decision tools for planning future distribution networks? This paper presents a simulation framework which combines two modeling techniques: agent-based modeling (ABM) and particle swarm optimization (PSO). ABM is used to represent the different system units of the network accurately and dynamically, simulating over short time-periods. PSO is then used to find the most economical configuration of DGs over longer periods of time. The infrastructure of the framework is introduced, presenting the two modeling techniques and their integration. A case study of Townsville, Australia, is then used to illustrate the platform implementation and the outputs of a simulation.

A coordinated voltage control approach for coordination of OLTC, voltage regulator and DG to regulate voltage in a distribution feeder

Integration of small-scale electricity generators, known as Distributed Generation (DG), into the distribution networks has become increasingly popular at the present. This tendency together with the falling price of synchronous-type generator has potential to give the DG a better chance in participating in the voltage regulation process together with other devices already available in the system. The voltage control issue turns out to be a very challenging problem for the distribution engineers since existing control coordination schemes would need to be reconsidered to take into account the DG operation. In this paper, we propose a control coordination technique, which is able to utilize the ability of the DG as a voltage regulator, and at the same time minimizes interaction with other active devices, such as On-load Tap Changing Transformer (OLTC) and voltage regulator. The technique has been developed based on the concept of control zone, Line Drop Compensation (LDC), as well as the choice of controller's parameters. Simulations carried out on an Australian system show that the technique is suitable and flexible for any system with multiple regulating devices including DG.

Coordinated control of grid connected photovoltaic reactive power and battery energy storage systems to improve the voltage profile of a residential distribution feeder

Increasing penetration of photovoltaic (PV) as well as increasing peak load demand has resulted in poor voltage profile for some residential distribution networks. This paper proposes coordinated use of PV and Battery Energy Storage (BES) to address voltage rise and/or dip problems. The reactive capability of PV inverter combined with droop based BES system is evaluated for rural and urban scenarios (having different R/X ratios). Results show that reactive compensation from PV inverters alone is sufficient to maintain acceptable voltage profile in an urban scenario (low resistance feeder), whereas, coordinated PV and BES support is required for the rural scenario (high resistance feeder). Constant as well as variable droop based BES schemes are analyzed. The required BES sizing and associated cost to maintain the acceptable voltage profile under both schemes is presented. Uncertainties in PV generation and load are considered, with probabilistic estimation of PV generation and randomness in load modeled to characterize the effective utilization of BES. Actual PV generation data and distribution system network data is used to verify the efficacy of the proposed method.