A Multi-Port Approach to Solve Distribution Networks with Meshes and PV Nodes

A new methodology based on the backward/forward (b/f) technique for the load flow solution in distribution systems is here proposed. The methodology takes efficiently into account the fixed voltage nodes and uses a reduced bus impedance matrix. In this way, it is possible to attain, for the unknowns at the PV nodes, the same values that are attainable solving the network with the methods adopted for transmission systems. With the same methodology it is possible to take into account also the meshes. If the network contains only meshes, the relevant model is linear and it is the one including the compensation currents. The presence of PV nodes introduces non linearity in the model and an iter…

Evolving non-dominated solutions in multiobjective service restoration for automated distribution networks

Abstract The problem here dealt with is that of Service Restoration (SR) in automated distribution networks. In such networks, configuration and compensation level as well as loads insertion status can be remotely controlled. The considered SR problem should be handled using Multiobjective Optimization, MO, techniques since its solution requires a compromise between different criteria. In the adopted formulation, these criteria are the supply of the highest number of loads and the minimum power losses. The Authors propose a new MO approach, the Non-dominated Sorting Fuzzy Evolution Strategy, NS_FES, which uses part of the Non-dominated Sorting Genetic Algorithm, NSGA, proposed by K. Deb. Th…

Load modelling influence on voltage stability assessment in distribution systems. Part I: Stability index and critical power for a single-line system

The single-line equivalent model is commonly used for voltage stability studies in both distribution and transmission systems. Referring to a single-line system, in the companion paper [1] the authors presented the theoretical aspects of voltage stability related to the load characteristics. In particular, expressions of the stability index for constant power, constant impedance and constant current loads, singularly and in all the possible combinations have been obtained. This index indicates how far the load node is from its voltage collapse point, allowing the maximum load power beyond which voltage collapse takes place to be evaluated. In this paper a simple method to evaluate the param…

A new formulation of the optimal compensation and reconfiguration problem including minimum load nodes unavailability for automated distribution networks

This paper deals with a new formulation of the optimal operation of electrical distribution networks problem in regular working state. In the new deregulated energy market providing reliable and economical service to customers is a primary task. The multiobjective formulation of the reconfiguration and compensation problem used in this paper considers as a primary object also the minimisation of the load nodes unavailability (UA) expressed in probabilistic terms. Therefore, the objectives to be attained through the optimisation strategy are: minimal power losses operation, minimum UA of the load nodes, load balancing among the HV/MV transformers, and voltage profile regularisation. The appl…

A model for reactive power tracing by addition of fictitious nodal injections

Abstract This paper proposes an efficient solution to the problem of reactive power flow tracing in electrical transmission networks. For such systems, the tracing techniques used for active power flows cannot be used straightforwardly, due to reactive power variations induced by the line reactances, these variations often being comparable to the powers delivered to the loads. In other words, as is well known, in transmission systems the reactive flows are strongly influenced by the inductive and capacitive effects of the network, making the tracing of power flow and allocation of losses more critical. In this paper, after discussing some methodological aspects, an approach based on the use…

Some improvements in solving radial distributions networks through the backward/forward method

In the electrical radial distribution networks analysis, the backward/forward method shows good features in terms of robustness, independence from load nature, small use of hardware resources and limited calculation time. In the present paper, some procedures to improve the b/f method with the aim of reducing the calculation time are presented. The adopted procedures regard the choice of the initial values of the nodes voltages and the way in which the convergence criterion is applied. The results of some tests carried out on some electrical test systems here reported have shown the efficiency of the proposed methodology in terms of calculation time reduction, especially when solving heavil…

An Efficient Procedure for Solving Radial Distribution Networks through the Backward/Forward Method

In the paper, after having presented the general backward/forward methodology for radial systems analysis, a new b/f procedure showing some interesting features that improve its performance in terms of convergence speed and calculation effort is presented. The features that fundamentally are responsible for such improvements concern the main steps of the b/f procedure. The starting voltage profile solution is different from the flat profile and is suitably modified. In the backward phase and starting from the second iteration, the branch currents variations due to the loads changes are evaluated; the latter variations are calculated on the basis of the difference of nodal voltages at the be…

An improved method for determining voltage collapse proximity of radial distribution networks

The two-bus equivalent model is commonly used for voltage stability studies in both distribution and transmission systems. The paper presents a simple method to evaluate, for each bus, the parameters which define the equivalent circuit of a radial distribution network. In particular, a straightforward way for determining the Thévenin equivalent impedance behind a load node is proposed, which allows to better identify the maximum loading point beyond which the voltage collapse takes place in the network. Simulation results show that the proposed method is significantly more accurate than other existing methods on evaluating the critical power at a particular node (i.e. the weak node of the n…

Influence of losses partition criteria on power flow tracing

The paper proposes a methodology for tracing active power flow which also considers power losses partition. It requires the partition of the active power losses in each line over different flow components. Then, the differences arising from the selection of different criteria for the allocation of the mutual terms (deriving from the non-linearity of losses) are investigated. Power flows tracing and losses allocation at each generator (or load) must be carried out simultaneously; therefore, a suitable order is required for the analysis of nodes and lines in a network. A procedure for the direct evaluation of all the components of the power flows and of the losses in the lines assigned to the…

Influence of ANN parameters on the performance of a refined procedure to solve the load-flow problem

In recent years, interest in the application of Artificial Neural Networks (ANN) to electrical power systems has grown rapidly. In particular the use of ANN in the solution of the load-flow problem in wide electrical networks is an interesting research topic, because it constitutes a good alternative to the classical numerical algorithms. In this paper a refined solution strategy based on statistical methods, on a particular Grouping Genetic Algorithm (GGA) and on Progressive Learning Network (PLN) is presented. Tests on the solution of load-flow equations of the standard IEEE 118 bus network confirm the good potential of this approach; in particular the search for optimal values of the PLN…

A new backward/forward method for solving radial distribution networks with PV nodes

Abstract In this paper, a new backward/forward (b/f) methodology for the analysis of distribution systems with constant power loads is presented. In the proposed method, at each iteration, the loads are considered as constant impedances; in the backward sweep all the network variables (bus voltages and branch currents) are evaluated considering a scaling factor which is determined at the end of the backward phase. Indeed the forward sweep is eliminated and the node voltages calculation does not demand the sequentiality needed in the b/f methodology. The developed method, although deriving conceptually from the b/f methodology, presents only the backward phase in which all the network variab…

Multiobjective service restoration in distribution networks using an evolutionary approach and fuzzy sets

Abstract In this article, the service restoration (SR) problem in electrical distribution networks is dealt with using an evolutionary strategy (ES) with a fuzzy definition of the conflicting objectives. The normal operation status allows the remote control of tie-switches, of capacitor banks and load connection. When a permanent fault occurs, the same remote control actions can be performed with the aim of restoring the service in the concerned areas. The status of these remotely controllable elements is the boolean optimisation variables for the SR problem. Besides this, here the SR problem is dealt with in a multiple objectives (MO) formulation. Indeed, the power losses’ term is consider…

Technical and Economical Aspects on Integrated PV-UPS Systems

This paper shows a technical-economical analysis of a novel Uninterruptible Power Systems (UPS) configuration, in which the backup batteries would be replaced by a photovoltaic (PV) system. Many interesting technical and economical issues concerning the proposed configuration are discussed against the traditional UPS and backup batteries solution. Moreover the technical solutions concerning the proposed integrated system realized using a double conversion UPS are motivated. Finally the operating costs of the proposed integrated PV-UPS system and the classical system with UPS and batteries with different sizes, and as the back-up time varies, are also compared and interesting results have be…

Voltage collapse proximity indicators for radial distribution networks

Based on the single-line equivalent system of a radial distribution network, two simple methods to evaluate two efficient voltage collapse proximity indicators are presented and discussed. The two methods differ on the determination of the parameters which define the equivalent system from which the indicators are derived. Both methods can be conveniently used jointly for on-line applications to assess the state of a distribution system from the viewpoint of voltage stability; the first to monitoring the stability margin of the whole system loading, the second to sharpen the stability analysis at the critical node when the system operating point is in the vicinity of the loadability limit. …

Load Flow Solution of radial distribution networks with ZI loads

In this paper, a methodology to solve radial distribution networks, with constant current and/or impedance loads, is proposed. The techniques currently available to solve such systems are based either on iterative methods or on the bus impedance matrix. The method developed is the extension of a technique that is valid to solve networks made of impedances with one supply point. The methodology can be applied to directly and rapidly solve large distribution systems in which the loads are modeled as constant current/impedance. It is also able to solve meshed systems having voltage-dependent loads, inside an iterative backward/forward method.

Backward solution of PV nodes in radial distribution networks

In this paper an iterative backward methodology to solve radial distribution networks with fixed voltage (PV) nodes and with constant power loads or mixed loads (with at least one component with constant power) is proposed. The method developed, although deriving conceptually from the backward/forward (b/f) methodology, presents only the backward phase in which all the network variables are evaluated. In themethods developed up until nowfor the solution of such systems, PV nodes are taken into account at the end of each iteration by evaluating, based on the known quantities of the network, the unknowns associated with PV nodes. In the methodology developed here the unknowns relevant to PV n…

Constrained Robust MultiObjective Optimization for Reactive Design in Distribution Systems

This paper presents a new formulation including robustness of solution of constrained multiobjective design or reactive power compensation. The algorithm used for optimization is the NSGA-II (Non dominated Sorting Genetic Algorithm II) with a special crowded comparison operator for constraints handling. The need for including the issue of robustness of solutions derives from the simple observation that loads are uncertain in distribution systems and their estimation is often affected by errors. In design problems it is desirable to consider the loads with a certain range of variation. In this paper the NSGA-II algorithm is applied to efficiently solve the issue and the solutions attained co…

A Compensation Based Method to Model PV Nodes in Backward/Forward Distribution Network Analysis

PurposeThis paper proposes to identify a new model of the fixed voltage nodes (PV nodes) for medium voltage distribution systems analysis. The model is used within backward/forward (b/f) analysis method applied to solve radial and weakly meshed systems.Design/methodology/approachThe model is based on the compensation currents method for multi‐port systems which has been extensively used, within b/f analysis methods, to take into account the presence of meshes and PV nodes.FindingsTest results prove the approach to be more efficient and precise than previous methodologies and put into evidence the good performance of the proposed model in terms of speed and convergence properties.Research li…

A heuristic approach for optimal operation of grid connected source-battery-load systems

In the paper an optimal management procedure for a system composed of a renewable energy source, storage batteries and a load, permanently connected to a distribution network, is presented. The issue follows two objectives: a) maximum economic benefit for the system, and b) minimum energy exchange with the network. The operation cost of storage facilities, as well as the technical and economic constraints on power exchanges between the system and the network and the technical constraints about charging and discharging cycles of the batteries are considered. The effectiveness of the management procedure is numerically tested and the results are presented.

Load modelling influence on voltage stability assessment in distribution systems. Part II: Extension to a complex radial system and applications

The single-line equivalent model is commonly used for voltage stability studies in both distribution and transmission systems. Referring to a single-line system, in the companion paper [1] the authors presented the theoretical aspects of voltage stability related to the load characteristics. In particular, expressions of the stability index for constant power, constant impedance and constant current loads, singularly and in all the possible combinations have been obtained. This index indicates how far the load node is from its voltage collapse point, allowing the maximum load power beyond which voltage collapse takes place to be evaluated. In this paper a simple method to evaluate the param…

Fast solution of radial distribution networks with automated compensation and reconfiguration

Abstract Optimal operation of radial distribution networks with automated compensation and reconfiguration requires the solution of a combinatorial optimisation problem, since the variables are the on/off status of capacitor banks and the open/close status of tie-switches. The solution approaches recently proposed use iterative algorithms such as genetic algorithms, simulated annealing and tabu search, for which the network needs to be solved in different configurations and at different compensation levels. The aim of this evaluation is that of attributing a quality index to each solution so that all the solutions can be suitably ordered. In an automated network, any configuration can be ob…

Decoupled solution of radial and weakly meshed distribution networks through a backward method

A methodology for the analysis of radial or weakly meshed distribution systems supplying voltage dependent loads is developed. The solution process is iterative and, at each step, the loads are simulated by means of impedances. The network is divided into two sub-networks which must be solved separately and sequentially; in the first, named RP-net, only the lines resistances and the loads shunt equivalent resistances are considered; in the second, named XQ-net, only the lines reactances and the shunt equivalent reactances are taken into account. After a brief presentation of the b/f method, which is currently the most commonly used technique to solve distribution networks, the proposed meth…

Transient stability analysis for symmetrical and unsymmetrical faults in mixed three-phase and six-phase power systems

Abstract The aim of this paper is to analyse the transient stability of a three-phase power system with six-phase lines interconnected by three-phase to six-phase transformers. For these mixed power systems a transient stability analysis is performed under all main types of disturbances (short-circuits, generator and load rejection, line outages), particularly in the case of faults at six-phase buses. A generalized procedure to evaluate transient stability is explained in detail. It is based on the symmetrical components method, which allows one to consider also unsymmetrical faults both at three-phase and six-phase buses. For every possible unsymmetrical short-circuit an equivalent fault a…

A Package for the Analysis of Automated MV Distribution Networks

A fuzzy-logic based evolutionary multiobjective approach for automated distribution networks management

In this paper, a methodology to treat constrained scheduling problems based on the repeated application of a fuzzy-logic-based multiobjective algorithm is presented. The application domain is that of automated distribution systems management. In particular, the problem of voltage regulation and power loses minimization is here considered. The classical formulation of the problem of optimal control of shunt capacitor banks and under load tap changers, ULTC, located at high voltage/medium voltage (HV/MV) substations has been coupled with the optimal control of tie-switches and capacitor banks on the feeders of a large radially operated meshed distribution system with the aim of attaining mini…

Minimum Losses Reconfiguration of MV Distribution Networks through Local Control of Tie Switches

This paper deals with the problem of optimal reconfiguration of radial distribution networks for minimum loss operation. The proposed control strategy of the open-closed status of the tie-switches is distributed, since every MV/LV node is provided with local controllers having some measured entities as input. It also does not prevent the system from the future implementation of centralized control; instead it may represent the first step toward a complete automation of the distribution system. The proposed strategy is indeed organized in hierarchic levels, the highest of which may be in the future a central control. After introducing the general problem of networks reconfiguration, a review…

Voltage Regulation and Power Losses Minimization in Automated Distribution Networks by an Evolutionary Multiobjective Approach

In this paper, the problem of voltage regulation and power losses minimization for automated distribution systems is dealt with. The classical formulation of the problem of optimal control of shunt capacitor banks and Under Load Tap Changers located at HV/MV substations has been coupled with the optimal control of tie-switches and capacitor banks on the feeders of a large radially operated meshed distribution system with the aim of attaining minimum power losses and the flattening of the voltage profile. The considered formulation requires the optimization of two different objectives; therefore the use of adequate multiobjective heuristic optimization methods is needed. The heuristic strate…

Multiobjective design of distributed reactive power production in a deregulated electric market

Abstract Reactive flows compensation optimal design for losses reduction in MV automated distribution systems is a problem deeply studied in literature. In this paper, the design problem is formulated considering the new deregulated energy market. These new operational conditions allow the MV grid operator to consider the generation of reactive energy also as a service that can be sold to the transmission system above. In this case, the transmission system would be helped in all the working conditions in which a strong modulation of the reactive flow through the HV/MV node is required. Then, for the MV grid operator, the compensation system optimal design problem is therefore that of the se…

A Simple Method to Assess Loadability of Radial Distribution Networks

This paper proposes a simple method to asses loadability in radial distribution systems. The relevant problem of voltage stability has been dealt with in past times with reference to higher voltage systems for generation and transmission. In more recent papers, the problem has been considered also at distribution level, since the new electrical energy market requirements and the increasing loadings are now more and more influencing these systems. The proposed method is based on a static approach and proceeds by first evaluating the stability indices and then the different loadability factors (related to real, reactive and apparent power). These calculations are carried out by identifying, s…

Service restoration in compensated distribution networks using a hybrid genetic algorithm

In this paper a genetic algorithm (GA) based approach to the service restoration (SR) problem in automated distribution networks is presented. Normal operation within the network comprises both automatic reconfiguration and compensation so as to reduce power losses, allow load balancing and improve the voltage profile. In the restorative state, the reconfiguration is performed together with compensation, taking mainly into account the load supply requirement and secondarily, the losses reduction requirement. After a general discussion on the restoration problem together with a short review of recent papers on the topic, a solution strategy is proposed. Then, a short account about classical …

A backward sweep method for power flow solution in distribution networks

Abstract A methodology for the analysis of radial or weakly meshed distribution systems supplying voltage dependent loads is here developed. The solution process is iterative and, at each step, loads are simulated by means of impedances. Therefore, at each iteration, it is necessary to solve a network made up only of impedances; for this kind of network, all the voltages and currents can be expressed as linear functions of a single unknown current (in radial systems) or of two unknown currents for each independent mesh (for meshed systems). The methodology has been called “backward” since the unique equation, in case of radial network, and the linear system of equations, in case of meshed n…

Feasible Domain-Driven Genetic Operators for Distribution Systems Optimal Reconfiguration

In this paper, the problem of minimum losses reconfiguration in weakly meshed medium voltage (MV) distribution systems is dealt with. The presence of meshes can either be a cause of the presence of particular loads, favoured customer (FC) nodes, requiring a double supply path or of distributed generation (DG) nodes, that cannot work in islanded mode. The problem has been brought back to the more general problem of radial networks reconfiguration with the major aim of minimising power losses subject to constraints on voltage drops at load nodes and current in branches as well as on the partition of power generated among supply nodes in the network. The problem is non-linear and combinatorial…