Sizing the neutral wire cross-section and minimization of neutral currents using microgeneration in low voltage networks

Transcription

1 Sizing the neutral wire cross-section and minimization of neutral currents using microgeneration in low voltage networks André Braga Instituto Superior Técnico Av. Rovisco Pais, Lisbon, Portugal Abstract - This paper contributes to the sizing of neutral conductors and proposes new microgeneration features to reduce currents in the neutral conductor in low voltage distribution systems. The work proposes a relationship between the THD of the phase currents and the RMS value of the neutral current, allowing a correct sizing for the neutral conductor. In addition, a model is presented that improves the traditional microgeneration contribution, with respect to Power Quality, making it a part of the solution for some of the existing problems. This model is called Compensated Microgenerator and it has the aim of compensating the harmonics present locally in the respective phase, thus causing a reduction in the rms value of the neutral current. It is in this context that this work arises, i.e., it is a contribution to the sizing of neutral wires, in a low voltage grid, and by using microgeneration, reduces the current in the neutral wire. With the increase of nonlinear loads and the contribution of existing microgenerators to the degradation of PQ, the neutral wire (or conductor) is constantly in the presence of increasingly relevant harmonic currents. Thus, it is imperative to find a relationship between the THDi, the phase current and the neutral current. Figure 1 represents the multiplying factor, regarding the section of the conductors, in cables with 4 conductors, depending on the 3rd harmonic [IEC 30364/60364] [1], demonstrating the necessity of taking the harmonics into account, when sizing the conductor section. Keywords - Sizing the Neutral Conductor, Microgeneration, Harmonic Distortion, Power Quality, Low Voltage Grids. I. Introduction Nowadays, increasing investments have been made in new forms of decentralized production of energy at low voltage (LV), also known as microgeneration. However, these forms of small scale energy production contribute, although lightly, to the degradation of Power Quality (PQ). The increase in current Total Harmonic Distortion (THDi) injected into the grid is one of the major consequences. Additionally, the modern single-phase nonlinear loads absorb nonsinusoidal currents with harmonics multiple of three, which in turn, is reflected in an increased rms value of the neutral current, even in three-phase balanced systems. Figure 1 - Multiplying factor, regarding the section of the conductors, in cables with 4 conductors, depending on the 3rd harmonic [IEC 30364/60364] [1] The harmonic currents whose frequency is a multiple of three of the fundamental frequency add in the neutral wire. In a three-phase grid, the neutral current can assume a value three times the rms value of the phase if the phase currents are formed only by homopolar harmonics (multiple of three), also known as zero sequence harmonics [2]. 1

2 II. Low Voltage Grid To find the relationship between the neutral current and the phase current and its THDi, a three-phase low voltage network model is implemented using Matlab/Simulink SimPowerSystems Toolbox. The model contains the Medium/Low voltage transformer, the distribution cables and the electrical loads. The connection between the Medium Voltage and Low Voltage is performed by a transformer of 630kVA. The transformer (Figure 2) used in the simulations is ΔYN connected, where the secondary neutral is connected to the ground. In this work, it is considered a transformer with 10kV in the primary side and 400V in the secondary (phase-to-phase voltage) [3]. The loads have been divided into two main groups: linear and nonlinear. In the linear loads it is considered the purely resistive loads (Type R) and the inductive loads (Type RL). Nonlinear loads are represented by a single-phase rectifier (Figure 4). Figure 4 - Single-phase rectifier model Based on the single-phase rectifier power P and in the average value of the output voltage, it is possible to calculate the equivalent resistor (1) that represents the rectifier dc load. Figure 2 Equivalent scheme of the transformer The transformer parameters were calculated using the values of the open and short-circuit tests, provided in the catalog [3]. In the low-voltage grid, the power distribution uses usually overhead lines or underground cables. In this work, it was considered a grid in a residential park, and therefore, it is considered an underground distribution line. The distribution line models are designed using a modified π model, represented in Figure 3. Figure 3 Representation of the modified π model of the cable The cable used is the LSVAV 4x 9. The resistance, inductance and capacitance are calculated from the values given by the manufacturer [4]. (1) The input filter is calculated from a percentage α of the load value R, as shown in (2) (2) The capacitive filter has the function of 'flattening' the output voltage, guaranteeing a reduced ripple. = (3) III. Neutral Current & Harmonics In this section, the effects in the neutral current due to the THD of the phase current are demonstrated. For that, it is simulated a three-phase grid with the loads described previously. The losses on the line are considered, assuming that the transformer is at a distance of 100 meters from the respective loads. In a first scenario, it is considered that the total apparent power supplied by the grid is given by (4), which is equal for all phases, i.e., it is a balanced system. (4) 2

3 The active power required by the respective loads is shown in () { () In Table 1, it is shown the contribution, in percentage, of each type of load for various possible scenarios. It is considered a PF = 0.6 (power factor) for the load type RL. Table 1 Variation of the power demand, with respect to the type of loads presented Phase R Phase S Phase T NL R X NL R X NL R X Case Case Case Case Being a balanced system, it is assumed (6) and (7). (6) (7) Table 2 contains the neutral, phase currents and THDs of the cases presented in Table 1. Table 2 Phase currents and respective THDs [A] [A] Case Case Case Case From Table 2, one can interpret the relationship between the rms value of the neutral current and the THDi. As the power consumed by non-linear loads increases, so does the THD of the phase current, and therefore, confirming their contribution to the degradation of PQ. Being a balanced system, the rms value of the neutral current should be zero, however, due to the THDi, it can be higher than the phase currents. Figure 4 represents an interpolation (trend line) that relates the neutral current with the phase currents and their respective THDs. Figure Relation between the neutral current i n, the phase current i f and its respective harmonic distortion THDi f, in a balanced system The equation obtained by the interpolation is presented in (8) ( ) (8) Table 3 represents several cases of unbalanced systems. Table 3 Variation of the power demand, representing an unbalanced grid Phase R Phase S Phase T NL R X NL R X NL R X Case Case Case Case Table 4 - Currents and THDs of the respective phases, with respect to the cases presented in Table 3. Phase R Phase S Phase T Case Case Case Case

4 Generally, the grid is unbalanced. This happens because in most cases, the singlephase loads are not evenly distributed across the phases. However, the unbalanced grid is not an issue, when referring to the dimensioning of the neutral conductor. From Table 3, it can be seen that the neutral current is always inferior, or in the limit equal, to the phase with the highest power demand. In this way, it is not necessary to dimension the neutral conductor with a greater section. The issue of the dimensioning arises when speaking of a balanced grid. Even though it is a balanced grid, and as such, it should have a null neutral current, one can conclude, from Table 2, that for a certain value of THDi, the neutral current exceeds the phase current, thus justifying a greater section. In the current legislation, this problem is not considered. It is stated that "When the section of the neutral conductor is not inferior (or when it is equivalent) to the phase conductors, it is not necessary to provide overcurrent detection or cutting devices in the neutral conductor" []. Clearly, this legislation is inadequate. This does not contemplate the possibility of a greater neutral current, when compared to the phase current. This possibility can be verified in Table 2. Since this is a sizing, one must verify the worst case scenarios, i.e., cases in which one gets the maximum current. From this value, it is possible to dimension a correct section. In regard to the neutral conductor, object of the present study, it was verified that its highest value takes place in a balanced grid dominated by non linear loads. It is in this kind of situation that equation (8) adds value, enabling a reliable sizing. This method is applied to case 3, with the intent of clarifying its process. Being a balanced system, it is assumed (6) and (7). Thus, the neutral current is given by (9) ( ) (9) Using this method, it is possible to verify the worst operating condition, i.e., the maximum neutral current, which in this case, is presented in (9). Using this information, one can dimension correctly the section of the neutral conductor. It is presented Table, whose goal is, by comparing the values obtained by simulation and those calculated by equation (8), to demonstrate the reliability of the equation deduced. One can conclude, from equation (8), what is the value of the THDi that causes a neutral current higher than the phase current, in a balanced grid. From equation (10), one obtains (11). (10) ( ) (11) Solving equation (11), it is obtained (12) (12) Through the formula obtained (12), it is concluded that for balanced systems, the neutral current is higher than the phase current when the THDi f > 38.2, justifying a larger conductor section. Table Comparison between calculated neutral current and the one obtained by simulation Case Case Case Case

5 In short, one can confirm the validity of Equation (8). This has values that correspond to the neutral current with a maximum error of, in which the error is always lower than 1 A. In the following section, it is shown an introduction to Microgeneration with the intent of minimizing the neutral current in a Low Voltage grid. IV. Traditional Microgeneration Regardless of the type of Microgeneration (photovoltaic or wind), the connection between these and the low voltage grid is often made through a single-phase inverter and a filter that provides attenuation for high frequency harmonic currents. Therefore, in this section, it is presented a model of the single-phase inverter (Figure 6). Two types of filters are designed: a 1st-order (L) and a 3rdorder (LCL). These are then compared, with regard to the THDi. Figure 7 - Block diagram of the current control with a 1st order filter As already mentioned, it is considered a Proportional-Integral (PI) compensator, which ensures a 2nd order dynamic in a closed loop. This also ensures a zero static error, compensating with an acceptable rise time [6]. C(s) = (14) After making the current controller design, one obtains the result presented in Figure 8. In this figure, it is represented the waveform of the grid voltage and the current injected by the inverter in an ideal grid, with a 1st order filter L and a Proportional-Integral (PI) controller. Figure 6 Single-phase inverter A. 1 st Order Filter In this subsection, the inductive filter is designed. This is calculated through (13) [6]. = (13) In the connection between the grid and the inverter, the voltage is imposed by the grid, and therefore, the inverter is controlled through its current, in order to extract the maximum power from the microgenerator. A Proportional-Integral (PI) linear controller is used to control the output current i fase of the inverter. The process of energy conversion and the associated variations are not relevant to the scope of this study, thus, it was considered a reference current I ref, calculated based on the reference power of the microgenerator. The block diagram of the current controller of the inverter is represented in Figure 7. Figure 8 Grid voltage and current injected by the inverter with a 1 st order filter and a PI controller After a FFT analysis, it is verified that the THD present in the injected current is 2,63. B. 3 rd Order Filter Through this type of filter, it is possible to obtain a greater attenuation of the high frequency harmonics. However, the higher the order, the greater the complexity of the filter, plus it is more susceptible to problems caused by the distortion of the grid voltage [7]. Current control is accomplished in two ways: PI Controller and Polynomial control. In Figure 9 it is represented the connection between an inverter with LCL filter and the grid.

6 will equally cancel the zero present in the filter. In order to ensure a null static error response to a step, it is considered a pole at the origin. Figure 9 Connection between an inverter with LCL filter and the grid. In a first approach, it is considered a PI controller, in order to control the output current of the inverter. The block diagram is shown in Figure 10. = ( ) (1) It is introduced a 3rd pole (p fa ) in the compensator (16) with the goal of limiting the number of zeros, regarding the number of poles in the system. However, it is important that this has a frequency which is high enough, so that it does not interfere in the system dynamics. = ( ) (16) Figure 10 Control Block of the PI controller It is assumed that the voltage on the capacitor is approximately equal to the grid voltage. After designing the current controller, one obtains Figure 11. In this figure, it is represented the waveform of the grid voltage and the current injected by the inverter in an ideal grid, with a 3rd order filter LCL and a Proportional-Integral (PI) controller. Figure 12 represents the waveform of the grid voltage and the current injected by the inverter in an ideal grid, with a 3rd order filter LCL and a Polynomial current control. Figure 12 Grid voltage and current injected by the inverter with a 3rd order filter and a Polynomial control The THD present in the injected current is 0,11, which is the lowest value verified in the cases presented. Figure 11 Grid voltage and current injected by the inverter with a 3rd order filter and a PI controller The THD present in the injected current is 0,2. In a second approach, it is considered a Polynomial current control. In order to compensate the effects introduced by the LCL filter, it is assumed that the compensator C(s) (1) has three zeros (p 1, p 2 and p 3 ) equal to the poles introduced by the filter, and a pole (z) that V. Compensated Microgeneration Through the results presented in the previous section, one can conclude that the traditional Microgeneration contributes, although lightly, to the degradation of PQ, contributing to an increase in the rms value of the neutral current. However, in this section, it is proposed a microgenerator model that adds value to the microgeneration, contributing to the reduction of harmonic 6

7 currents injected by the consumer in a low-voltage network, increasing the PQ and therefore becoming a part of the solution to some of the existing problems. Thus, the goal is to inject the maximum power, supplied by the photovoltaic panel, and ensure that the current supplied by this, cancels the harmonics created by the nonlinear loads. In Figure 13, it is presented a schematic that represents the connection between the grid and the Compensated Microgenerator. nonlinear load that consumes an active power equal to 140W. Figure 1 represents the grid voltage, the load current and the current injected into the grid, respectively, for the 1 st scenario. Figure 13 Connection between the grid and the Compensated Microgenerator In this case, it is necessary, besides the already studied current control, a voltage control on the capacitor voltage U CF (Figure 14). Figure 1 1 st scenario The THD present in the current injected into the grid is 60,22. In Figure 16, it is presented the grid voltage and the current injected into the grid, respectively, for the 2 nd scenario. The current absorbed by the load is equal to the one shown in Figure 1. Figure 14 Voltage Control It is considered, for this voltage control, a PI compensator C v (s) (17), where K p represents the proportional gain and K i the integral gain. = + (17) In order to clarify the differences between the presented microgeneration models, two scenarios are simulated. In the first scenario, it is connected a Traditional microgenerator in parallel with a non linear load and the grid. The second scenario is identical to the first, however, instead of the Traditional Microgenerator, it is used a Compensated Microgenerator. The simulation is performed for a Figure 16 2 nd scenario The THD present in the current injected in the grid is 2,97. By inserting the Compensated Microgenerator, there is a significant decrease of the THDi, thus confirming its positive contribution to PQ. It will be shown in the next section that this contribution to the decrease of the THDi translates into a notable decrease in the rms value of the neutral current. 7

8 VI. Simulation In this section, three types of a three phase grid are simulated: Without Microgeneration, with a Traditional Microgenerator and with a Compensated Microgenerator. Table 6 represents various load scenarios. The purpose is to analyze the neutral conductor and its rms value for the various network types. In case 1 and case 2, it is considered a balanced grid. The analysis is focused on the rms values of the currents in each phase, which are identical since it is a balanced grid, and in the rms value of the neutral current. The analysis is also focused on the THDi of each phase. In case 3 and case 4, it is considered an unbalanced grid, and therefore, a different power is required in each phase. The simulation is performed under the same conditions presented in Section III. The power supplied by the Traditional Microgenerator and the Compensated Microgenerator is given by (18) and (19), respectively. (18) (19) Naturally, the Compensated Microgenerator needs a higher power to perform its functions effectively. It needs to compensate the harmonics, certifying that the current injected into the grid is a sinusoidal current. However, this function cannot compromise the power provided, ensuring at least a provided power equal to the one supplied by the Traditional Microgenerator. Figures 17 and 18 represent the THDi and the rms current values of the respective phases, corresponding to case 1 and case 2. The word Supplied and Injected presented in the upcoming Figures, represent the current supplied by the grid and the current injected into the grid, respectively. Figures 17 and 18 confirm the observations already made. A relevant difference can be seen between the rms values of the neutral currents. This is due to a higher contribution by nonlinear loads in case 2, causing, inevitably, a greater THDi, which will contribute to a higher neutral current. The Compensated Microgenerator makes a remarkable compensation of the harmonics caused by the nonlinear loads, guaranteeing practically a null neutral current. Furthermore, it injects roughly the same current injected by the Traditional Microgenerator in the grid. Table 6 Load scenarios Phase R Phase S Phase T NL R X NL R X NL R X Case Case Case Case Figure 17 THDi and rms value for case 1 8

9 Figure 18 THDi and rms value for case 2. Figure 19 THDi and rms value for case 3. It can be seen, from Figure 19, that the power required by the loads present in phase S, is smaller when compared with the remaining phases. Thus, in this phase, the power injected into the grid by both microgenerators is higher. The neutral current, in the case with Compensated Microgenerator, is higher than those observed in previous Figure 20 THDi and rms value for case 4. scenarios. This occurs because it is an unbalanced grid, and therefore, the RMS values of the phase currents are different, contributing to a greater neutral current. However, it remains always lower than the one observed in the case where there is no Microgeneration or when Traditional Microgeneration exists. 9

10 Figure 20 represents the case of a rural network, wherein all active loads are taking power from the same phase. In this case, where there is a total unbalance between phases, the neutral current is quite high, mainly due to the difference in the power between phases. The two types of Microgeneration inject the maximum power into the grid, for phase S and T, because in this case, the power required by the loads in phase S and T is practically zero. VII. Conclusions In this work, a relationship between the THD of the phase currents and the RMS value of the neutral current was obtained, allowing a correct sizing for the neutral conductor, and contributing to the design of the neutral conductor section in a threephase system with single-phase non linear loads. It was also proposed the concept of Compensated Microgeneration in order to mitigate the harmonics injected by nonlinear loads. Thus, it is possible to size the neutral conductor in a more reliable way. The neutral current depends directly on the THD present in the phases, assuming value zeros only in balanced systems with no harmonic currents. Through the formula obtained, it is concluded that for balanced systems, the neutral current is higher than the phase current when the THDi phase exceeds 38.2, justifying a conductor with a larger section. The section of the neutral conductor can be reduced using microgenerators able to mitigate harmonics injected by the consumer, thereby contributing to a low neutral current. The proposed Compensated Microgenerator confirmed its effectiveness and utility as a repairing solution of PQ, reducing the THDi values close to zero and contributing to a decrease in the neutral current, which is practically zero for a balanced grid, regardless of percentage of non-linear loads employed. With regard to the unbalanced grid, the harmonic mitigation is not sufficient to obtain a null neutral current, since in this case, the load differences between phases contributes to a greater neutral current, verifying, for this type of grid, a smaller decrease concerning the neutral current. However, for a balanced system, by inserting a Compensated Microgenerator in all phases, it was verified a neutral current 1 times lower, when compared to the case without Microgeneration. As the power consumed by nonlinear loads increases, so does the reduction of the neutral current. REFERENCES [1] Silva, José Fernando Alves, Sistemas de Alimentação Autónomos: Qualidade de Energia Elétrica, Instituo Superior Técnico, Lisboa. [2] IEEE TRANSACTIONS ON POWER DELIVERY, VOL 22, NO. 1, JANUARY [3] Catálogo de Transformadores a Óleo Herméticos, Transformadores de distribuição MT/BT. [4] S. Y. King, Underground Power Cables, June 200. [] MINISTÉRIO DA ECONOMIA E DA INOVAÇÃO, Portaria n.º 949-A/2006, Diário da República, 1.ª série, N.º 17, 11 de Setembro de [6] Silva, José Fernando Alves, Sistemas de Energia em Telecomunicações: Texto de apoio, Instituto Superior Técnico, 2008, Lisboa. [7] Shen, G; Xu, D.; Cao, L.; Zhu, X., An Improved Control Strategy for Grid-Connected Voltage Source Inverters With an LCL Filter, IEEE Trans. Power Electronics, vol. 23, no.4, pp ,