Characterization and modeling of multi-conductor transmission line using Finite-difference Time-Domain method

A two-dimensional, 2D, finite-difference time-domain (FDTD) method is used to analyze two different models of multi-conductor transmission lines (MTL). The first model is a two-conductor MTL and the second is a threeconductor MTL. Apart from the MTL's, a three-dimensional, 3D, FDTD method is used to analyze a three-patch microstrip parasitic array. While the MTL analysis is entirely in time-domain, the microstrip parasitic array is a study of scattering parameter Sn in the frequency-domain. The results clearly indicate that FDTD is an efficient and accurate tool to model and analyze multiconductor transmission line as well as microstrip antennas and arrays.

Haja-asutusalueiden sähkönjakelujärjestelmien kehittäminen – erityisesti 1000 V jakelujännitteen käyttömahdollisuudet

Yhteiskunnan riippuvuus sähköstä on lisääntynyt voimakkaasti viime vuosikymmenien aikana. Sähkönjakelussa esiintyneet lyhyet ja pitkät keskeytykset ovat osoittaneet yhteiskunnan haavoittuvuuden ja yhteiskunta kestää entistä vähemmän sähkönjakelussa tapahtuvia häiriöitä. Keskeytyksistä aiheutuneiden haittojen arvostus on kasvanut ja tämä on luonut taloudelliset perusteet sähkön laatua parantaville investoinneille. Haja-asutusalueiden keskijänniteverkon johdot on rakennettu avojohtoina ja siten ne ovat alttiita sääolosuhteista johtuville myrsky- ja lumikuormavaurioille. Ilmastomuutoksen ennustetaan lisäävän tuulisuutta ja siten ongelmat sähkönjakelussa mahdollisesti lisääntyvät. Taajamissa käytetään enemmän kaapeleita ja johtolähdöt ovat lyhyitä, joten myrskyistä aiheutuvia keskeytyksiä on vähemmän kuin haja-asutusalueella. Olemassa olevat jakeluverkot ovat käytössä vielä vuosikymmeniä, joten uuden tekniikan kehittämisen rinnalla on kehitettävä myös olemassa olevaa jakeluverkkoa ja sen ylläpitoa. Ylläpidon tavoitteena on käyttövarmuuden parantamisen lisäksi huolehtia siitä, että jakeluverkkoihin sitoutunut omaisuus säilyttää arvonsa mahdollisimman hyvin pitoajan loppuun saakka. Jakeluverkkoihin investoitiin paljon 1950–70-luvuilla. Tältä ajalta on yhä käytössä puupylväitä, joiden ikääntymisen takia korvausinvestointien tarve kasvaa. Hyvänä puolena tässä on että käyttövarmuuden parantamiseksi olemassa olevaa jakeluverkkoa ei tarvitse uusia ennenaikaisesti. Tutkimuksessa päähuomio on haja-asutusalueiden 20 kV keskijänniteverkon kehittämisessä, sillä yli 90 % asiakkaiden kokemista keskeytyksistä johtuu keskijänniteverkon vioista. Erityisesti johtorakenteisiin ja johtojen sijoittamiseen on kiinnitettävä huomiota. Käyttövarmuuden lisäksi jakeluverkkojen kehittämistä ohjaavia tekijöitä ovat taloudellisuus, ympäristön huomioiminen, viranomaisvalvonta sekä asiakkaiden ja omistajien odotukset. Haja-asutusalueilla taloudelliset haasteet ovat suuret vakituisen väestön vähenemisen ja mahdollisesti sähköntarpeen pienenemisen takia. Taloudellisuus korostuu ja riskit kasvavat, kun tuottojen määrä supistuu tarvittaviin jakeluverkon investointeihin ja ylläpitokustannuksiin verrattuna. Ristiriitaa aiheuttaa se, että asiakkaat odottavat sähkönjakelulta parempaa luotettavuutta, mutta paremmasta sähkönlaadusta ei olla valmiita maksamaan juurikaan nykyistä enempää. Jakeluverkkojen kehittämistä voi hidastaa myös viranomaisvalvonta, jos tuottoja ei voida lisätä investointien lisätarpeiden suhteessa. Tutkimuksessa on analysoitu yleisellä tasolla kaapeloinnin lisäämistä, korkeiden pylväiden käyttämistä, leveitä johtokatuja, edullisten ja yksinkertaisten sähköasemien rakentamista haja-asutusalueille ja automaatioasemien lisäämistä keskijänniteverkon solmupisteisiin. Erityisesti tutkimuksessa on analysoitu uutena tekniikkana 1000 V jännitteen käyttömahdollisuutta jakeluverkkojen kehittämisessä. Sähköjohtojen siirtäminen teiden varsiin parantaa käyttövarmuutta, vaikka johdot rakennetaan samalla tekniikalla kuin olemassa olevat johdot. Hajaasutusalueille rakennettavilla sähköasemilla pitkät syöttöjohdot voidaan jakaa pienemmiksi syöttöalueiksi, jolloin keskeytyksistä aiheutuvat haitat koskettavat kerrallaan pienempää asiakasmäärää. Samaan tulokseen päästään oikein sijoitetuilla ja toteutetuilla automaatioasemilla. Tutkimuksen mukaan lupaavaksi tekniikaksi jakeluverkkojen kehittämisessä on osoittautumassa 1000 V jänniteportaan ottaminen 400 V pienjännitteen lisäksi. 1000 V verkoilla voidaan korvata häiriöherkkiä 20 kV keskijänniteverkon lyhyitä, alle viiden kilometrin pituisia haarajohtoja ja haarajohtojen jatkeita, missä siirrettävät tehot ovat pieniä. Uudessa jakelujärjestelmässä sähkö tuodaan 1000 V jännitteellä lähelle asiakasta, jossa jännite muunnetaan normaaliksi asiakkaille soveltuvaksi 400/230 V jännitteeksi. Edullisuus perustuu siihen, että rakentamisessa käytetään samoja pienjännitejohtoja kuin asiakkaille menevässä 400 V pienjänniteverkossa. 1000 V jakelutekniikassa sekä investointikustannukset että ylläpitokustannukset ovat pienemmät kuin perinteisessä 20 kV ilmajohtotekniikassa. 1000 V johdot säästävät maisemaa, sillä ne eivät tarvitse leveää johtokatua kuten 20 kV keskijännitejohdot. 1000 V verkkojen käyttö soveltuukin erityisesti vapaa-ajanasuntojen sähköistykseen herkissä ranta- ja järvimaisemissa. 1000 V verkot mahdollistavat kaapeliauraamisen lisäämisen ja näin voidaan vähentää ympäristöä haittaavien kyllästettyjen pylväiden käyttöä. 1000 V jakeluverkkojen osalta tutkimustyön tuloksia on sovellettu suomalaisessa Suur-Savon Sähkö Oy:ssä. Käytännön kokemuksia 1000 V jakelujärjestelmästä on useista kymmenistä kohteista. Tutkimustulokset osoittavat, ettei keskijänniteverkon maakaapelointi hajaasutusalueilla ole taloudellisesti kannattavaa nykyisillä keskeytyksistä aiheutuvilla haitta-arvoilla, mutta jos keskeytyskustannusten arvostus kasvaa, tulee kaapelointi kannattavaksi monissa paikoissa. Myös myrskyisyyden ja myrskyistä aiheutuvien jakelukeskeytysten lisääntyminen tekisi kaapeloinnista kannattavan. Tulevaisuudessa jakeluverkkojen rakentaminen on entistä monimuotoisempi tehtävä, jossa taloudellisuuden ja käyttövarmuuden lisäksi on huomioitava asiakkaat, omistajat, viranomaiset ja ympäristö. Tutkimusta jakelutekniikan kehittämiseksi tarvitaan edelleen. Tulevaisuuden osalta haja-asutusalueiden jakeluverkkojen kehittämiseen liittyy paljon epävarmuuksia. Hajautetun kiinteistökohtaisen sähköntuotannon lisääntyminen voi tehdä jakeluverkoista nykyistä tarpeettomampia, mutta esimerkiksi liikenteen sähköistyminen voi kasvattaa jakeluverkkojen merkitystä. Tästä syystä jakeluverkkojen rakentamisessa tarvitaan joustavuutta, jotta tarvittaessa voidaan helposti sopeutua erilaisiin kehityssuuntiin.

Assessment of the VoIP Transmission Quality over Digital Power Line Carrier Channels

This article is devoted to the research of VoIP transmission quality over Digital Power Line Carrier channels. Assessment of quality transmission is performed using E-model. Paper considers the possibility of joint using of Digital Power Line carrier equipment with different architecture in one network. As a result of the research, the rule for constructing of multi-segment Digital Power Line Carrier channels was formulated. This rule allows minimizing the transmission delay and saving frequency resources of high voltage Power Line Carrier range.

Distribution line models analysis for loss calculation within three-phase three-wire power flow algorithms

Three-phase three-wire power flow algorithms, as any tool for power systems analysis, require reliable impedances and models in order to obtain accurate results. Kron's reduction procedure, which embeds neutral wire influence into phase wires, has shown good results when three-phase three-wire power flow algorithms based on current summation method were used. However, Kron's reduction can harm reliabilities of some algorithms whose iterative processes need loss calculation (power summation method). In this work, three three-phase three-wire power flow algorithms based on power summation method, will be compared with a three-phase four-wire approach based on backward-forward technique and current summation. Two four-wire unbalanced medium-voltage distribution networks will be analyzed and results will be presented and discussed. © 2004 IEEE.

Fault-Location System for Multiterminal Transmission Lines

This research presents the development and implementation in a computational routine of algorithms for fault location in multiterminal transmission lines. These algorithms are part of a fault-location system, which is capable of correctly identifying the fault point based on voltage and current phasor quantities, calculated by using measurements of voltage and current signals from intelligent electronic devices, located on the transmission-line terminals. The algorithms have access to the electrical parameters of the transmission lines and to information about the transformers loading and their connection type. This paper also presents the development of phase component models for the power system elements used by the fault-location algorithms.

Transmission lines distance protection using artificial neural networks

This work presents the development and implementation of an artificial neural network based algorithm for transmission lines distance protection. This algorithm was developed to be used in any transmission line regardless of its configuration or voltage level. The described ANN-based algorithm does not need any topology adaptation or ANN parameters adjustment when applied to different electrical systems. This feature makes this solution unique since all ANN-based solutions presented until now were developed for particular transmission lines, which means that those solutions cannot be implemented in commercial relays. (c) 2011 Elsevier Ltd. All rights reserved.

Utilização de Cabos de alta Temperatura em linhas Aéreas em Média Tensão

A presente dissertação teve como objetivo fazer uma análise da viabilidade técnica da utilização dos condutores de alta temperatura nas linhas aéreas de MT, identificar vantagens, analisar inconvenientes, e estabelecer um comparativo a custos médios com as soluções convencionais. Foi efetuado o estudo de um caso real da EDP Distribuição que consistia na necessidade do aumento da capacidade de transporte de energia da linha aérea a 15 kV Espinho-Sanguedo. Neste foi ponderada a solução onde se poderia efetuar passagem de linha simples para linha dupla em alumínio-aço (AA) 160 mm2 ou a solução alternativa e inovadora de substituição dos condutores existentes por condutores de alta temperatura ACCC 182 mm2. Para isso foram efetuados cálculos e também criada uma ferramenta de apoio à decisão, para validação dos mesmos, com o intuito de mais tarde poder ser aplicada nas linhas aéreas em Média Tensão em todo o país e, sempre que necessário, se possa fazer um estudo de ponderação técnica de forma sistemática e estruturada. Neste trabalho estão identificadas as vantagens, foram relatados os inconvenientes, e estabeleceu-se um comparativo a custos médios da utilização de condutores de alta temperatura com as soluções convencionais. Antes de poder ser realizado um estudo do caso concreto da Linha aérea Espinho-Sanguedo foi necessário um aprofundamento do estado da arte no que diz respeito à comparação entre o cabo de alta temperatura ACCC e o cabo convencional ACSR, sendo este o mais utilizado nas linhas aéreas em MT. Os cabos de alta temperatura trouxeram inovações neste tema de transporte de energia, e como tal surgiu a necessidade de um estudo mais aprofundado da sua constituição, destacando o seu núcleo formado pelo compósito de fibra de carbono e fibra de vidro. Foi também analisado vantagens e desvantagens do cabo de alta temperatura e até mesmo situações onde a sua aplicação poderá ser vantajosa, de modo a tirar proveito das suas caraterísticas em que se destacam altas temperaturas de funcionamento e flechas reduzidas. Para elaborar um projeto de uma linha aérea em média tensão é necessário considerar a legislação em vigor, os aspetos ambientais e económicos, respeitando e garantindo as premissas do cálculo elétrico e mecânico. Economicamente este tipo de cabo (ACCC) é mais dispendioso do que os convencionais, no entanto o estudo realizado permitiu perceber que a sua implementação técnica é vantajosa em linhas aéreas de elevada capacidade de transporte de energia, sobretudo nos casos onde serão necessárias instalar linhas duplas ou linhas simples de seções elevadas. Devido às suas caraterísticas mecânicas, estes cabos permitem melhorar as linhas na sua dimensão, podendo diminuir o número de apoios a instalar, podendo diminuir a robustez dos apoios e permitir maior facilidade na montagem. Estas vantagens traduzem-se em menores impactos ambientais e permitem sobretudo reduzir os constrangimentos com os proprietários dos terrenos onde os apoios são implantados.

Dimensioning DC-voltage capacitor for a DC-distribution system and dynamic analysis

Technical analysis of Low Voltage Direct Current (LVDC) distribution systems shows that in LVDC transmission the customer voltage quality is higher. One of the problems in LVDC distribution networks that converters both ends of the DC line are required. Because of the converters produce not pure DC voltage, but some fluctuations as well, the huge electrolytic capacitors are required to reduce voltage distortions in the DC-side. This thesis master’s thesis is focused on calculating required DC-link capacitance for LVDC transmission and estimation of the influence of different parameters on the voltage quality. The goal is to investigate the methods of the DC-link capacitance estimation and location in the transmission line.

The influence of high cable penetration in distribution networks on earth fault currents and the operation of relay protection.

Recent Storms in Nordic countries were a reason of long power outages in huge territories. After these disasters distribution networks' operators faced with a problem how to provide adequate quality of supply in such situation. The decision of utilization cable lines rather than overhead lines were made, which brings new features to distribution networks. The main idea of this work is a complex analysis of medium voltage distribution networks with long cable lines. High value of cable’s specific capacitance and length of lines determine such problems as: high values of earth fault currents, excessive amount of reactive power flow from distribution to transmission network, possibility of a high voltage level at the receiving end of cable feeders. However the core tasks was to estimate functional ability of the earth fault protection and the possibility to utilize simplified formulas for operating setting calculations in this network. In order to provide justify solution or evaluation of mentioned above problems corresponding calculations were made and in order to analyze behavior of relay protection principles PSCAD model of the examined network have been created. Evaluation of the voltage rise in the end of a cable line have educed absence of a dangerous increase in a voltage level, while excessive value of reactive power can be a reason of final penalty according to the Finish regulations. It was proved and calculated that for this networks compensation of earth fault currents should be implemented. In PSCAD models of the electrical grid with isolated neutral, central compensation and hybrid compensation were created. For the network with hybrid compensation methodology which allows to select number and rated power of distributed arc suppression coils have been offered. Based on the obtained results from experiments it was determined that in order to guarantee selective and reliable operation of the relay protection should be utilized hybrid compensation with connection of high-ohmic resistor. Directional and admittance based relay protection were tested under these conditions and advantageous of the novel protection were revealed. However, for electrical grids with extensive cabling necessity of a complex approach to the relay protection were explained and illustrated. Thus, in order to organize reliable earth fault protection is recommended to utilize both intermittent and conventional relay protection with operational settings calculated by the use of simplified formulas.

Modelling of faults in low-voltage cables

Power line modelling has become an interesting research area in recent years as a result of advances in the power line distribution network system. Extensive knowledge about the power line cable characteristics can be implemented in a software algorithm in a modern broadband power-line communication modem. In this study, a novel approach for modelling power line cables (AMCMK) based on the broadband impedance spectroscopy (BIS) and transmission line matrix (TLM) techniques is recommended in characterizing a healthy cable and the various faults associated with low-voltage cables for both open and short circuit situation. Models for different cable conditions are developed and tuned, which include six models for both healthy and faulty cables situations. The models are on the basis of impedance response analysis of the cable. The resulting spectra from the simulations are also cross-correlated to determine the degree of similarities between the healthy cable spectra and their respective faulty spectra.

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developing the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. It s important to point out that, in spite of the loads being normally connected to the transformer s secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developping the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. Its important to point out that, in spite of the loads being normally connected to the transformers secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Modal transformation analyses for double three-phase transmission lines

Eigenvector and eigenvalue analyses are carried out for double three-phase transmission lines, studying the application of a constant and real phase-mode transformation matrix and the errors of this application to mode line models. Employing some line transposition types, exact results are obtained with a single real transformation matrix based on Clarke's matrix and line geometrical characteristics. It is shown that the proposed technique leads to insignificant errors when a nontransposed case is considered. For both cases, transposed and nontransposed, the access to the electrical values (voltage and current, for example) is provided through a simple matrix multiplication without convolution methods. Using this facility, an interesting model for transmission line analysis is obtained even though the nontransposed case errors are not eliminated. The main advantages of the model are related to the transformation matrix: single, real, frequency independent, and identical for voltage and current.

Analysis of the Electrical Characteristics of an Alternative Solution for the Brazilian-Amazon Transmission System

This article analyzes the electrical parameters of a 3-phase transmission line using a 280-m-high steel tower that has been proposed for the Amazon transmission system in Brazil. The height of the line conductors and the distance between them are intrinsically related to the longitudinal and transverse parameters of the line. Hence, an accurate study is carried out in order to show the electrical variations between a transmission line using the new technology and a conventional 3-phase 440-kV line, considering a wide range of frequencies and variable soil resistivity. First, a brief review of the fundamental theory of line parameters is presented. In addition, by using a digital line model, simulations are carried out in the time domain to analyze possible and critical over-voltage transients on the proposed line representation.

A constructive heuristic algorithm to Short Term Transmission Network Expansion Planning

In this paper a method for solving the Short Term Transmission Network Expansion Planning (STTNEP) problem is presented. The STTNEP is a very complex mixed integer nonlinear programming problem that presents a combinatorial explosion in the search space. In this work we present a constructive heuristic algorithm to find a solution of the STTNEP of excellent quality. In each step of the algorithm a sensitivity index is used to add a circuit (transmission line or transformer) to the system. This sensitivity index is obtained solving the STTNEP problem considering as a continuous variable the number of circuits to be added (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an interior points method that uses a combination of the multiple predictor corrector and multiple centrality corrections methods, both belonging to the family of higher order interior points method (HOIPM). Tests were carried out using a modified Carver system and the results presented show the good performance of both the constructive heuristic algorithm to solve the STTNEP problem and the HOIPM used in each step.