Neutral to Earth oltage Reduction Methods in ThreePhase Four Wire Distribution Systems G. Ahmadi and S.M. Shahrtash ran University of Science and Technology (UST) gahmadi@ieee.org Center of Excellence for Power System Automation and Operation associated to UST shahrtash@iust.ac.ir ABSTRACT Neutral to earth voltage can vary significantly depending on the load unbalance. Here, an analysis of neutral to earth voltage in multigrounded threephase fourwire distribution system is presented that considers load unbalance and the effect of explicitly represented neutral wire. A multiphase load flow algorithm is developed based on bacward/forward sweep to examine the effects of various factors on the neutral to earth voltage (NE), including unsymmetrical system configuration and load unbalance. The magnitude of NE is investigated under various conditions on the number of grounding rods per feeder lengths and the grounding rods resistance. The algorithm and the associated models are tested on EEE 1 bus system. Keywords Neutral to Earth oltage, threephase fourwire systems, fivewire line model, multigrounded neutral. clearly visualized. The proposed methodology for evaluation of NE is applied on EEE 1 bus distribution networ.. MODELNG OF RADAL DSTRBUTON NETWORKS The presented method in this paper for radial distribution system analysis is an improved method of one introduced in []. n this approach, the distribution feeder is modeled by a fivewire model to reveal the profile of neutral to earth voltages. n the proposed method, along with the usage of five wire model for multigrounded distribution feeders, the parameters of this model are derived according to Carson s relations. Moreover, the self and mutual impedance of ground equivalent wire are assigned according to []. A multigrounded distribution feeder may be divided to segments. Fig. 1 illustrates a three phase feeder with two segments. 1. NTRODUCTON Generally, distribution networs are operated in an unbalanced configuration and also service to consumers. This fact causes current flowing through neutral conductor and voltage dropping on neutral wire. The unbalance load and excessive current in neutral wire is one of the issues in threephase fourwire distribution systems that causes voltage drop through neutral wire and maes tribulations for costumers. The existence of NE maes unbalance in three phase voltages for three phase customers and reduction of phase to neutral voltage for single phase customers. Thus, its evaluation and reduction have many interests for operators. n this paper, the effects of load balancing, threephasing of singlephase loads and power factor correction on NE have been analyzed in threephase fourwire distribution systems. n addition, the results of various conditions on the number of grounding rods per feeder lengths and the grounding rods resistance on magnitude of NE have been studied. n order to perform NE analysis, an appropriate load flow algorithm [1] and the associated power system modeling technique is advanced for NE profile calculation on various conditions. The load flow method is based on bacward/forward sweep method which is capable of fivewire simulation (three phase, multigrounded neutral wire and ground equivalent wire) and neutral voltage calculation. Since the neutral wire is explicitly represented in the utilized power flow technique, neutral currents are calculated directly. Thus, NE can be computed by using the neutral wire current. n this way, the impact of different parameters on NE can be Fig. 1. A three phase multigrounded feeder The number of segments depends on the times that the neutral is connected to the ground. Then, in order to reduce the size of the load flow problem, the junction nodes of grounding resistance should be eliminated. The Kron reduction can be applied to simplify the above circuit with multiple segments to one segment for each feeder. The resulting equivalent circuit is shown in Fig... POWER FLOW ALGORTHM The proposed bacward/forward sweep algorithm to solve the radial system can be divided into two parts: 1) bacward current sweep and ) forward voltage sweep. Bacward Current Sweep: For a radial feeder, the branch current can be calculated by summing the injection currents from the receiving bus toward the sending bus of the feeder. The general equation can be expressed as: 1
the source node voltage, with taing the initial voltage of neutral wire and ground equivalent wire as zero, i.e. ia ib ic in ig ( ) a = a. ref. ref ref a = e jπ () Fig.. The equivalent circuit of a multigrounded feeder la lb lc ln lg = ja jb jc ( jn ) ( ) jg + m Ω j where the relation is derived for th iteration and; abcn [ l ] is current flows on line section l, [ j ] is current injections at bus j, j is set of line sections connected downstream to bus j. Forward oltage Sweep: For a radial distribution system if branch currents were calculated, the bus voltages can be found from the sending bus toward the receiving bus of the feeder. The general equation can be expressed as: Δ = ia ib = ic in ig aa ab ac an ag ab bb bc bn bg ac bc cc cn cg ja jb jc jn jg an bn cn nn ng ag bg cg ng nn ma mb mc mn mg ( h) la where, as in (1), the relation is derived for th iteration and; [ i ] is the voltage of bus i, is the branch impedance from bus i to bus j. [ ] lb lc ln lg (1) () n [], the resulting branch current vector is explained and its formation procedure is presented. Thus, it can be written: [ A ] [ ] = () where [ A ] is the coefficient vector of currents for the branch between bus i and j. The next step is to calculate the bus voltage variations with respect to the current injection vector, which can be calculated by combining () and the forward voltage sweep and expressed as: [( ) ] = [ HA][ ] s (5) where s is the source node voltage, and is the bus voltage vector. [ HA ] is the relationship matrix between bus voltage vector and current injection vector, that the formation procedure is explained in [].. TEST SYSTEM SMULATON n this paper, the EEE 1 bus test distribution system [5] is made less complex [] for modeling and simulating as shown in Fig., and the effects of load conditions and system parameters variations on NE have been studied. Fig.. Test distribution system The power flow calculation is started with initial voltages for three phases at all nodes. t is necessary to assume that the initial voltage for all nodes at fundamental frequency is equal to 15
5. RESULTS Results obtained by performing the proposed power flow method on EEE example system are shown in next steps. 5.1. Effect of load balancing on NE To examine the effect of load balancing on NE, first load index is introduced as a + b + that means c vector sum of three phase currents at each bus and downstream. Then, to analyze the effect of load balancing on neutral voltage, load on bus (Fig. ) is made unbalance by shift of percent of load from phaseb to phasec. Then, 1 percent of the phase B load is increased, while the same value is decreased in phase C. The mentioned index values for buses,, and their downstream which are calculated at these conditions, are shown in Table 1. As seen, the effect of this is descending severely at middle branch of networ (related to bus, Fig. ), but it has less effect on other branches (related to buses and ). Table 1Effect of load on main branches current % % 1%.%,5.51.5.55.5,,7,...17.15,.11.11.1.15 Ground and neutral wire current is decreased with decrease at middle branch (refer to Table 1). Consequently, ground and neutral wire voltages are decreased at buses,, 7 and (Figs and 5). 5.. Three phasing of single phase load As previously mentioned, three phasing of single phase load is a method of NE reduction. n the case that the NE is increased by single phase load, this method can be used for NE reduction. Figs and 7 present the result of three phasing of load at bus. Due to load of networ, three phase currents are different and voltage drops are not equal in phases A, B and C and it causes voltage on load node. Therefore, despite the load balancing in bus, voltage maes unequal current flowing through three phase load and accordingly, neutral current and voltage are raised. Generally, three phasing method decreases NE on related bus. Nevertheless, it may increase NE on other buses, as shown in Figs and 7. n(volt) g(volt) n(volt) 1 1 1 1 7 5 1 1 5 7 Fig.. Effect of load balancing of bus on n 1 5 7 Fig. 5. Effect of load balancing of bus on g 1 5 7 % % 1% % % % 1% % Single phase Three phase Fig.. n variation for three phasing of single phase load on bus 1
g(volt) 7 5 1 Fig. 7. n variation for three phasing of single phase load on bus 5.. Power factor correction n this section, the effect of power factor correction is investigated on neutral and ground voltage. As it is mentioned, all of the bus voltages (excluding bus ) are unbalanced by unsymmetrical and unbalanced system. n the test system, there is a three phase balanced load on bus and a voltage drop on phaseb more than other phases. n simulations, power factor of load of bus in phasea and phaseb is increased from.7 to.5 lag and the resultant neutral and ground equivalent wire voltages are illustrated in Figs and. As it is seen, voltage and consequently neutral and ground voltage are decreased as power factor of phaseb is increased. On the contrary, voltage is raised while power factor of phasea is improved and neutral and ground voltage is magnified. 5.. ariation of grounding rod s resistance R g n this step, the effect of R g variations on the NE is examined with three Rg quantities:, 1 and 5. Figs. 1 and 11 show the neutral and ground voltage. Neutral voltage is sensitive to the change in R g. The higher R g causes higher neutral voltages, as expected. n Fig.1, it can be seen that n is increased as R g is increased; because the current through the ground equivalent wire is decreased with R g enlargement. Subsequently, the current flow through the neutral wire is increased. Therefore, the voltage drop in neutral wire is increased. Besides, Fig. 11 presents that as g decreases, R g increases due to the decrease in the current flowing through the ground. 5.5. Number of grounding rods per length unit Single phase Three phase 1 1 5 7 n this part, the resistance of rods is taen as 1 ohms. The results of three simulations are shown in Figs. 1 and 1. t can be seen, when the number of R g increases, or in other words when the connection of neutral wire to ground becomes better; generally, there is a trend of decreasing in n. The variation of n depends on the resistance of grounding rods, where the larger R g s cause smaller variation in n (not shown). n(volt) g(volt) n(volt) 7 5 1 7 5 1 7 5 1 1 5 7 Fig.. n variation for cos correction 1 5 7 Fig.. g variation for cos correction Rg= Rg=1 Rg=5 1 5 7 Fig. 1. n variation for various R g cosb=.5 cos=.7 cosa=.5 cosb=.5 cos=.7 cosa=.5 17
n(volt) g(volt) 1 1 1 1 1 7 5 1 1 5 7 Fig. 11. g variation for various R g 1 5 7 Rg= Rg=1 Rg=5 times/m times/m 1 times/m magnitude of NE is investigated under various conditions on the number of grounding rods per feeder lengths and the grounding rods resistance and the results are given. n addition for NE calculation, a power flow method for radial distribution system is presented, which is an improvement in the method of []. n this improvement the distribution feeder is modeled by a five wire model to reveal the profile of neutral to earth voltages. 7. REFERENCE [1]. G. Ahmadi, S.M. Shahrtash, Neutral to Earth oltage Analysis in Harmonic Polluted Distribution Networs with MultiGrounded Neutrals, World Academy of Science, Engineering and Technology, ol. 7, Dubai,, pp. 5. [].. H. Teng, C.Y. Chang, Bacward/Forward SweepBased Harmonic Analysis Method for Distribution Systems, EEE Transactions on Power Delivery, 7, pp. 15 17. []. R. M. Ciric, A. P. Feltrin, L. F. Ochoa, Power Flow in FourWire Distribution Networs General Approach, EEE Transactions on Power System,, pp.11. [].. jiang, Elevated NeutraltoEarth oltage in Distribution Systems ncluding Harmonics A Dissertation Presented to the Graduate School of Clemson University,. [5]., Radial Distribution Test Feeders, Distribution System Analysis Subcommittee Report, EEE Power Engineering Society, 1, pp.1. [].. H. Teng, A Direct Approach for Distribution System Load Flow Solutions, EEE Transactions on Power Delivery,, pp.7. Fig. 1. n variation for various numbers of rods per length unit g(volt) 1 1 1 1 1 5 7 times/m times/m 1 times/m Fig. 1. g variation for various numbers of rods per length unit. CONCLUSON n this paper, effects of load balancing on neutral voltage have been studied. And, it has been shown that load balancing at one bus not also can decrease the neutral wire voltage at other buses but also can increase them in unbalance and unsymmetrical distribution systems. Moreover, it has been shown that threephasing of singlephase loads in one bus for decreasing the neutral wire voltage can boost the neutral wire voltage at other ones. Furthermore, load factor correction can decrease NE as well as it can increase it too. Also the 1