2010 IEEE International Conference on Power and Energy (PECon2010), Nov 29 - Dec 1, 2010, Kuala Lumpur, Malaysia
Impact of Static Load on Voltage Stability of an Unbalanced Distribution System Sugunesan Gunalan
Agileswari K. Ramasamy
Renuga Verayiah
Electronics & Comm. Dept. Universiti Tenaga Nasional Selangor, Malaysia Email:
[email protected]
Electronics & Comm. Dept. Universiti Tenaga Nasional Selangor, Malaysia Email:
[email protected]
Electrical Power Dept. Universiti Tenaga Nasional Selangor, Malaysia Email:
[email protected]
Abstract—Static load which is known for three different characteristics i.e. constant power, constant current and constant impedance shows a different voltage profile because both of their real power and reactive power vary differently as the voltage varies except for constant power. This paper will analyze the impact of each load characteristic individually and also as combination on voltage stability of an IEEE 34 Bus Distribution System by increasing the load demand, and also transient analysis i.e. creating a single phase-to-ground fault i.e. on phase a and balanced three phase fault. The most suitable load to study the voltage stability is also proposed. It was found that, with constant power loads, the reactive power demand increases significantly when load real power and reactive power increases by 25%. Constant current loads and combination loads, on the other hand, the reactive power demand increases but only slightly and the demand is even lesser when with constant impedance loads. However, as the load real power and reactive power increases by 50%, constant power loads causes voltage collapse whilst constant current loads and combination loads turn out to be the next in the order followed by constant impedance loads. In transient analysis, during the single phase fault, with combination loads, phase b voltage increases drastically but only small increment observed in phase c voltage. During the three phase fault, phase b voltage is slightly higher than phase c voltage followed by phase a voltage. As comparison to combination loads, constant power loads causes lesser three phase voltages. After the fault was cleared, a smooth voltage waveform obtained in the period of retaining back to the same pre-fault voltage, however, distortions in the voltage recovering waveform seen when dynamic load included in the system. Constant power load is found to be the suitable load to study the voltage stability. Keywords—Static load; Voltage stability; IEEE 34 Bus Distribution System; Demand; Transient; Fault; Dynamic load
I.
INTRODUCTION
Distribution system is one of the most complex systems in power system domain. Distribution systems are generally unbalanced. It is served by substation which is radial or weakly meshed either in balanced or unbalanced [1]. Balanced distribution system consists of three-phase laterals with the loads being equally distributed among the three phases. Unbalanced distribution system, on the other hand, is a mixture of three-phase, two-phase and single-phase laterals. The loading of distribution feeder is also unbalanced as they are large number of unequal single-phase loads. An additional unbalanced is introduced
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as non-equilateral conductor spacing of three-phase overhead and underground line segment [2]. Radial distribution system is one of the power systems that may suffer from voltage instability. This is due to the high power losses as the resistance to reactance ratio is high [3]. Voltage instability is due to inability of power system to maintain steady-state voltage at all buses following a disturbance, increased in load demand or change in operating condition given initial operating condition [4]. The main factor that causes voltage instability is inability of distribution system to meet the reactive power demand [5]. Load stability also known as voltage stability as they are main driving force into voltage instability [6]. Hence, analyzing the load can determine the voltage stability of a distribution system. Load models can be classified into static (“snap-shot” with respect to time) and dynamic (time varying). Static models are based on the steady-state method representation in power flow networks. Static load models represent load as a function of voltage magnitude. Dynamic models involve an alternating solution sequence between a timedomain solution of the differential equations describing electromechanical behavior and a steady-state power flow solution based on the method of phasors [7]. Static load also known as voltage dependent load can be modeled either by exponential or as polynomial model. Both models express the characteristics of the load at any instant of time as algebraic functions of the bus voltage magnitude and frequency at any instant. This load can be further divided into different load characteristics i.e. constant power, constant current and constant impedance. These loads can be individually modeled by specifying the exponent value as will be described in the next section. An alternative model to represent these types of load characteristics would be polynomial model. This model is also known as “ZIP model” as it is composed of constant impedance (Z), constant current (I) and constant power (P) components [8]. Constant power load such as electric motors or regulated power supplies, the real and reactive power are always constant as the voltage changes. When the voltage decreases, amount of current drawing increases which increases the voltage drop. Constant impedance load such as incandescent lighting or resistive water heaters, the impedance is always constant as the voltage changes and the power varies with the square of the voltage magni-
tude. When the voltage decreases, the current draw also drops hence the voltage drop decreases. In constant current load, the current is constant as the voltage changes and the power varies directly with the voltage magnitude. As the voltage decreases, the current draw stays constant so the voltage drop also does not change [9]. Despite that, constant current load represent aggregate behaviour of a mixture of constant impedance and constant power loads and 50/50 mixture of constant power and constant impedance loads looks very much as this load [10]. Many papers have been published on static voltage stability of using different types of load characteristics. However, most of the research has focused on system such as balanced IEEE Test System and simple power system. Besides that, the transient analysis of using different load characteristics also has been discussed in many papers but most of them are with balanced system. Some papers have discussed the behaviour of constant impedance load and compare with induction motor. However, no works have been published of analyzing this unbalanced distribution system by varying the load demand, and also transient analysis with different types of load characteristics to study the voltage stability of this distribution system. Therefore, this paper aims to investigate the each load characteristic on voltage stability of an IEEE 34 Bus Distribution System individually, i.e. constant power, constant current and constant impedance and also as combination. An increment of load real power and reactive power by a factor of 1.25 (125%) will be analyzed to study the reactive power demand. Also, increment of load real power and reactive power by a factor of 1.5 (150%) will be analyzed to study the stability of the distribution system. Based on analysis, the suitable load to study the voltage stability of distribution system will be proposed. In addition to that, transient analysis of the system with combination loads and also constant power loads will be done to study the effect of voltage on each phase before, during and after the single phase-to-ground fault and balanced three phase fault. A comparison study of static load and then with the inclusion of induction motor in the distribution system will also be done to study the voltage recovery after the fault has been cleared. The distribution system is modeled using DIgSILENT software and simulation results obtained for each load characteristics and combination loads are systematically explained. II.
d) Shunt capacitors e) Unbalanced loading with both “spot” and “distributed” loads. Distributed loads are assumed to be connected at the center of the line segment Loads are consisting of combination of different load characteristics i.e. constant power, constant current and constant impedance loads. A. Static Load Modeling Loads are modeled as active and reactive power connected at the bus and centre of the line section. Static loads or the voltage dependency of loads have been represented by the exponential model as described below: (1) (2) where P and Q are active power and reactive power of the load respectively in the considered bus when the voltage magnitude is V. The subscript 0 indicates initial operating conditions. The exponents “a” and “b” can be 0, 1, or 2, to represent constant power, constant current, or constant impedance characteristics, respectively [8]. An alternative model to represent the voltage dependency of loads is known as “polynomial model” or “ZIP model” as shown below. _
_
_
_
_
_
(4)
Coefficients ap to cp and aq to cq are the parameters and general load model in the DIgSILENT introduces the coefficient value for each term where the sum of the coefficients of the equation is equal to one. Therefore, a small modification was done to this model to obtain the exponential model as described above. One of the coefficient values was set such that equal to one while the rest of coefficients set to zero and by specifying the respective exponents (e_aP/e_bP/e_cP and e_aQ/e_bQ/e_cQ) with 0,1 or 2 the inherent load behavior can be modeled [12]. III.
DISTRIBUTION SYSTEM AND LOAD MODELING
(3)
CASE STUDIES
Three buses were chosen for analysis i.e. bus 816, 832 and 842. Bus 816 is located near to voltage regulator whereas bus 832 and 842 are located within the load concentrated zone. For the purpose of analysis, voltage regulators were removed from the system so that the impact of different load characteristics can be seen and analyzed easily. The distribution system was analyzed for four different cases. Case 1 represents during normal operating condition i.e. without increment of load real power and reactive power. Case 2 represents an increment of load real power and reactive power by a factor of 1.25 (125%). Case 3 represents an increment of load real pow-
A single line diagram of the distribution network, as shown in Fig.1 in Appendix, is used to study and analyze the impact of the static load on voltage stability. The test system shown is actual radial system located in Arizona. The system’s nominal voltage is 24.9 kV. It is characterized by [11]: a) Very long and lightly loaded b) Two in-line regulators required to maintain a good voltage profile c) An in-line transformer reducing the voltage to 4.16 kV for a short section of the feeder
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er and reactive power by a factor of 1.50 (150%). In each case, the system was analyzed with each load characteristic individually i.e. model all the loads as constant power, constant current and constant impedance and also modeled the loads with combination of these load characteristics (base case). Case 4 represents transient analysis of the system with combination loads and also constant power loads. A. Case 1 (Normal operating condition) The impact of each load characteristic and also as combination on voltage during normal operating condition i.e. without increment of load real power and reactive power is shown from Fig.2 to 4.
Figure 2.Voltage vs. Bus (Phase a)
Figure 3.Voltage vs. Bus (Phase b)
high real power and reactive power losses. This increases the voltage drop. Constant impedance load, as a result of decreases in voltage, the load power also decreases as it is directly proportional to the square of voltage. This causes the current draw to drop, resulting the reactive power demand also to drop as well. Hence, the voltage drop is also found to be lesser. Constant current load, on the other hand, also causes the load power to decrease due to decreased in voltage. However, as its power is directly proportional to the voltage, it causes the current draw to be constant and that causes the reactive power demand also to be constant, resulting the voltage drop to be constant. In addition to that, similar phase b voltages obtained when the loads are modeled as constant current or as combination. However, there is a small difference in phase a and phase c voltages which can be seen in Fig. 2 and 4 where the voltages are happened to be slightly lower when modeled as constant current than by combination. As combination loads are consist of three different types of load characteristics, and constant current load which is also known for a mixture of constant power and constant impedance loads resulting in similar voltage profile as what can be seen from the Figs. above. During the simulation the loading of distribution transformer was also observed. The transformer loading is the same i.e. 51% when the loads are modeled as constant current or as combination. This is because as only one load is connected to the distribution transformer and a similar load is also connected in the base case resulting to the same loading percentage. On the other hand, the loading decreases to 44% when the loads are modeled as constant impedance. However, the loading increases to 65% when modeled as constant power. This proves that the amount of current and reactive power drawing by constant power load is higher and increases when the voltage decreases as compared to other load characteristics and also by combination. It is also proven that the behaviour of constant current load is a mixture of constant power and constant impedance loads as can be seen from the loading of distribution transformer where it was found to be in between constant power and constant impedance loads. B. Case 2 (Increment of load real power and reactive power by 25%) When the load real power and reactive power increases by a factor of 1.25 (125%), the voltage drop seems to be greater. The voltage profile patterns are similar as in case 1 where the voltages turn out to be lowest when the loads are modeled as constant power and highest when modeled as constant impedance. The voltages are found to be the same when the loads are modeled as constant current or as combination except in phase a and phase c where constant current results in slightly lower voltages as can be seen in Fig. 5 and 7. Simulation results also showed that the increment of load real power and reactive power increases the distribution transformer loading. The increment of distribution
Figure 4.Voltage vs. Bus (Phase c)
It was observed that, among the three buses, bus 832 and 842 has a lower voltage compared to bus 816. This is due to the fact that both buses are located in load concentration zone. Among these loads, more voltage drop can be observed when the loads are modeled as constant power whereas lesser voltage drop can be observed when modeled as constant impedance in all the three phases and buses. This is because constant power load is invariant to voltage which means it maintains a constant power draw from the system despite the changes in voltage. As a result of decreases in voltage, the current drawing increases and this will demand for reactive power, however, transfer or flowing of reactive power will cause
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transformer loading is same i.e. 13% when the loads are modeled as constant current or as combination and 8% when modeled as constant impedance. On the other hand, an overloading of distribution transformer was observed when modeled as constant power i.e. 101%. This shows, with constant current loads and combination loads, the reactive power demand increases slightly and it is even lesser when with constant impedance loads. However, with constant power loads, the reactive power demand increases significantly. This causes the voltage drop to increase more as compared to previous case.
Figure 5.Voltage vs. Bus (Phase a)
Figure 6.Voltage vs. Bus (Phase b)
Figure 7.Voltage vs. Bus (Phase c)
The study presented in this case clearly showed that the most critical load to the system is when it is modeled as constant power. It is also known, from the analysis, this load has the highest tendency to cause voltage collapse when the load demand increases. C. Case 3 (Increment of load real power and reactive power by 50%) Further increment of load real power and reactive power causes severe voltage drop and higher current drawing and reactive power demand. Inability of distribution system to meet reactive power demand will result in voltage instability or voltage collapse as what happens in this case where the power flow does not convergence when the system loads are modeled as constant power. The inability of the power flow convergence shows the
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system becomes unstable which means voltage collapse occurs. However, the power flow converges when some loads after bus 832 were removed from the system. This confirms that load causes voltage instability or voltage collapse. Other load characteristics and also combination loads show slightly higher voltage drop and the voltage profile pattern among them, as usual, maintained as in previous cases. D. Case 4 (Transient Analysis) Single phase-to-ground fault i.e. on phase a and balanced three phase fault were chosen to analyze this unbalanced system. The unbalanced system becomes very unbalance when unbalanced fault occur compared to balanced fault. This results in big differences on each phase voltage. Therefore, these two faults were analyzed by observing the pre-fault, during the fault and post-fault voltages. Faults were created along the line from bus 852 to bus 832 and fault resistance of 40 ohms was chosen as it is a standard value used by many electric cooperatives [13]. For the purpose of analysis, bus 832 was chosen and time-domain simulation was used so as can capture the pre-fault, during the fault and post-fault voltages. Two different cases were analyzed i.e. model the loads as combination and also as constant power. The respective graph during single phase fault is shown in Fig. 8 and 9. The pre-fault phase b voltage is slightly higher than phase c voltage when the loads are modeled as constant power whereas in the base case it is found to be the other way round. When single phase fault occurs at t=1 second, it was found that phase b voltage rises drastically i.e. more than 1.05 pu whereas phase c voltage increases only slightly with the voltage within the limit. The phase a voltage, on the other hand, does not drop to zero but to a lower value i.e. 0.35 pu due to the fault resistance which causes existence of voltage across the phase a and the ground. On the other hand, the phase a, phase b and phase c voltages are found lesser than in base case when the loads are modeled as constant power. During the three phase fault, as shown in Fig. 10 and 11, phase b voltage is slightly higher than phase c voltage followed by phase a voltage. These phase voltages are found to be lesser than 0.435 pu. The only difference, when the loads modeled as constant power, is that the voltage is slightly lower in each phase compared to base case. The reasons of phase b voltage to be higher than phase c voltage during these faults are due to the unbalanced loading and untransposed lines. Besides that, the reactive power injection from both shunt capacitors located on bus 844 and bus 848 is slightly higher in phase b than phase c. After the three phase fault is cleared at t=1.16 seconds, as shown in Fig. 12, a smooth voltage waveform can be observed in the period of retaining back to the same pre-fault voltage. This is because of fixed coefficient characteristic of the static load. To verify the result, 180kW/4.16kV delta-connected induction motor was added at bus 888 in the base case. A balanced three phase fault was used. It was observed, in
Fig. 13, the voltage waveform tends to have some distortions before it achieves to the steady-state condition. This is due to the dynamics of motor. Therefore, it is sufficient enough to study the impact of static load on voltage stability in steady-state mode for transient analysis. However, if a dynamic load is included in the system, time-domain simulation is required.
Figure 12.Voltage vs. Time (Combination loads)
Figure 8.Voltage vs. Time (Combination loads)
Figure 13.Voltage vs. Time (With Induction motor)
IV. CONCLUSION This paper investigated the impact of different types of load characteristics i.e. constant power, constant current constant impedance individually and also as combination on voltage stability of an unbalanced distribution system for various cases. It was found that constant power loads demanding more reactive power as the load real power and reactive power increases by 25%. Constant current loads and combination loads, on the other hand, the reactive power demand increases but only slightly and the demand is even lesser when with constant impedance loads. However, with constant power loads, voltage collapse occurs when the load real power and reactive power increases by 50%. Constant current loads and combination loads, on the other hand, are considered to be the next in the order of causing voltage instability or voltage collapse followed by constant impedance loads. When single phase-to-ground fault occurs i.e. on phase a on the line from bus 852 to bus 832, the phase b voltage and phase c voltage increases but the increment in phase b voltage is more drastic as compared to phase c voltage. However, when three phase fault occurs, phase b voltage is slightly higher than phase c voltage followed by phase a voltage. The results obtained for three phase fault and single phase fault with constant power loads are similar to that of combination loads except that the voltages are slightly lesser. It was also known that, a system with static loads, a smooth voltage waveform can be observed during the period of retaining back to the same pre-fault voltage. Therefore, steady-state analysis can be used only if static load is used in the distribution system. However, with induction motor or any rotating machines in the system, time-domain simulation will give a better insight to
Figure 9.Voltage vs. Time (Constant power loads)
Figure 10.Voltage vs. Time (Combination loads)
Figure 11.Voltage vs. Time (Constant power loads)
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the voltage recovery after the fault is cleared due to its dynamics which cannot be seen in steady-state analysis. Hence, among the different load characteristics, constant power load is the most suitable load to study the voltage stability of a distribution system as this load can cause worst case scenario in terms of voltage drop as compared to other load characteristics and also combination loads. This is because of its real power and reactive power is independent to the voltage which causes the load to be very much dependent on reactive power. REFERENCES [1] [2] [3]
[4]
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Selvan, M.P. and Swarup, K.S., “Unbalanced Distribution System Short Circuit Analysis- An Object-Oriented Approach”, IEEE Region 10 Conference, pp. 1-6, November 2008. William H.Kersting, “Distribution System Modeling and Analysis,” New York: CRC Press LLC, 2002, pp. 5. Nasser G.A. Hemdan and Michael Kurrat, “Distributed Generation Location and Capacity Effect on Voltage Stability of Distribution Networks”, Annual IEEE Conference, pp. 1-5, February 2008. Claudia Reis, Antonio Andrade and F.P. Maciel, “Voltage Stability Analysis of Electrical Power System”, International IEEE Conference on Power Engineering, Energy and Electrical Drives, pp. 244-248, March 2009. Raj Kumar Jaganathan and Tapan Kumar Saha, “Voltage Stability Analysis of Grid connected Embedded Generators”, Australasian Universities Power Engineering Conference, pp. 1-6, September 2004. M. H. Haque and U. M. R. Pothula, “Evaluation of Dynamic Voltage Stability of a Power System”, IEEE Conference on Power System Technology, pp. 1139-1143, November 2004. Leonard L. Grigsby, “The Electric Power Engineering Handbook,” New York: CRC Press LLC, 2001, pp.6-2. P. Kundur, Power System Stability and Control, New York: McGaraw-Hill, Inc., 1994, pp.272-273. Tom A.Short, Electric Power Distribution Handbook, New York: CRC Press LLC, 2004, pp.241-242. H. Lee Willis, Power Distribution Planning Reference Book, 2nd ed., New York: Marcel Dekker, Inc., 2004, pp.50-51. W. H. Kersting, "Radial Distribution Test Feeders”, IEEE Power Engineering Society Winter Meeting, vol.2, pp. 908 – 912, 2001. DIgSILENT PowerFactory Version 14.0, "PowerFactory Manual," 2009. W.H. Kersting and W.H.Philips, “Distribution System Short Circuit Analysis”, Energy Conversion Engineering Conference, pp. 310-315, August 1990.
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Figure 1. Single line diagram of IEEE 34 Bus Distribution System
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