CC BY
76Electronic Journal «Technical Acoustics» http://www .ejta.org
2005, 38 A. Kazemi, A. R. Entezary
Department of Electrical Engineering, Iran University of Science and Technology Iran, Tehran
Voltage stability assessment by dynamic PV curve and time domain simulations with developed STATCOM model
Received 01.08.2005, published 13.12.2005
In this paper voltage stability is evaluated by both dynamic PV curve and time domain simulations with a developed and detailed model of STATCOM. Also effect of load with different power factors in voltage stability assessment is studied. The results presented in this paper show that STATCOM can greatly improve the voltage stability and maximum loading capacity of power systems, especially in lower power factors. It is also shown that the margin of stability can be easily and effectively evaluated by PV curves because they cover a wide range of system operating conditions. Also it is illustrated that reactive power has more effects on voltage stability rather than real power.
INTRODUCTION
Power system stability means the ability of the system to move from one steady-state operating equilibrium to another following a disturbance without losing synchronism. Different types of stabilities have been introduced yet, among them steady-state stability involves slow or gradual changes in the operating condition, such as incremental changes in load or generation. In other words farther the operating point from the instability point, more is reliability and stability of power system. With increasing system loading and open transmission access pressures, power systems are more vulnerable to voltage instability as shown by a number of major incidents throughout the world [1]. Therefore voltage stability is increasingly becoming a limiting factor in planning and operation of many power systems. In addition, increased demand for electric power requires increasing transmission capabilities. However financial, environmental and other relating factors, are constrain which should be notified in the construction of new transmission lines [2]. Electric utilities are forced to operate the system in ways which make maximum use of existing transmission facility [3]. Therefore, the stability and reliability margin of the system is decreased. Margin of the voltage stability is one of the other limits that decrease the loading of the system. As some parameters in the system change, due to parallel flexible AC transmission system (FACTS) devices on voltage stability of particular system load, the voltage magnitude slowly declines. System operators usually control the voltage collapse at some buses by increasing reactive generation, capacitor switching and/or tap changing. As some devices reach their limits, the ability of controlling the voltage is lost; furthermore, at a certain loading of the system, one type of instability occur which called voltage collapse. This phenomenon is characterized by a
sharp and fast decrease in voltage magnitude. This fact illustrated by PV curves in later sections.
The recently developed Flexible AC Transmission system (FACTS) technology provides a way to relieve the stability problem imposed by increasing load demand [4]. FACTS controller provides very fast and reliable control over the three main transmission parameters,
i.e., voltage magnitude, phase angle and line impedance. For this reason control of FACTS devices has received a lot of attention in power system stability enhancement. In [5] the authors have used standard voltage collapse analysis tools to study the effect in the maximum load margin of the location of a given static var compensator (SVC); an approximate model is used for computations. F. D. Galiana et al. [6] proposed a method to evaluate the impact of FACTS on steady-state behaviors of the power systems through the concept of generalized security regions and a scalar measure showing the stability status of those areas.
This paper focuses on such FACTS controller for voltage support as a dynamic reactive power (var) source, namely the static compensator (STATCOM). The static compensator (STATCOM) is the modern version of the well-established reactive power compensator. Various experimental systems are already in service. Most of them use the multipulse converters topology. Alternatively, multilevel converters can be used, thus eliminating the complex transformer array needed to suppress harmonics. Reactive compensation of transmission lines increases the quality of transmitted power and consequently reduces the margin separating the normal operating point to collapse.
The main role of a STATCOM is to provide voltage support at critical points of a transmission system. The behavior of a STATCOM is very similar to that of a synchronous compensator. If the voltage generated by the STATCOM is less than the voltage of the system busbar to which it is connected, the STATCOM will act as an inductive load, drawing reactive power from the supply system. Conversely, a STATCOM will act as a shunt capacitor, generating Mvar into the supply system, when its generated voltage is higher than the system voltage. This normally comprises a reactive current controller at the converter level and a line voltage controller at the transmission system level. In general, the reactive current injected by a STATCOM is proportional to the voltage difference between the STATCOM and the line. Therefore, adjusting the converter voltage can control the reactive current. In general the design and the performance of the internal control systems of a STATCOM depend on how its output voltage is controlled. Depending on the switching pattern employed, converters can be classified as either directly or indirectly controlled. In
[7], two internal nonlinear control strategies based on the feedback linearization technique for cascaded multilevel STATCOM are presented. The strategies depend on the control capability of the converter output voltage and are suitable for line frequency-switched converters. The first strategy considers a STATCOM where the voltage is set independently of the dc link voltage. Fast reactive power control within sub cycle time response is achieved. The second strategy is constrained to a voltage whose amplitude remains proportional to the dc link voltage. Despite this limitation, the proposed strategy allows full stabilization of the STATCOM dynamics and relatively fast control for most STATCOM applications.
Typically, time-domain simulations are employed to analyze the performance of power systems containing both conventional equipment and FACTS controllers for voltage/var
support. This approach, however, usually requires a large number of study cases at different system operating conditions and contingencies to evaluate the relationship between system and control parameters and voltage stability [8]. In this work, performance of STATCOM under the loads with different power factors from 0.6 to 1.0 is studied. The application of PV curves also provides a means to evaluate the voltage stability of a power system for various conditions and contingencies [9, 10]. Evaluations of voltage stability for an AC/DC hybrid system and for a system with FACTS controllers were reported in [11, 12]. Validity of voltage stability with FACTS controllers depends on accuracy of the controller.
In this paper, power system performance is evaluated considering STATCOM applications for voltage/var support. Both PV curves and time-domain simulations are carried out and compared to verify the agreement between two study methods. The basic concept of STATCOM and their working principle is discussed in section 1. In addition, an index value “Voltage Stability Proximity Index” is applied. It is shown in section 2 that this index value is an effective means to evaluate the impacts of the system and control parameters on voltage stability. In section 3, the results of simulation on test system is presented and discussed. Finally, section 4 summarizes the main points and results of this paper.
1. STATCOM MODELING
A six pulse STATCOM with a detailed controller used for voltage stability study. Figures 1-3 schematically displays the performance of the internal control systems of a STATCOM. Voltage control loop is implemented by generation of angle order based on voltage error in first block. Measured voltage and reactive power are as input for this part of controller. These signals are compared with their references. The output of PI controller is the angle order; it represents the required shift between system voltage and voltage generated by STATCOM; the shift determines the direction and amount of real power flow (Fig. 1). Angle order is applied for generation of firing pulses.
Pulse width modulation (PWM) is an extension of simple concept of harmonic control. Gate turn off (GTO) thyristors are repetitively turned on and blocked, during each half cycle. The sequential switching instants are selected in a co-ordinated manner, to satisfy simultaneous requirements, i.e. to develop the desired fundamental voltage. PWM control consists of two parts. In first part, which is in figure 2, voltages of three phases are inputs of the controller. In this part, generation of triangular waveforms is synchronized with system ac voltage. Two sets of signals (reference and triangular ones) are needed; one set for turning on and second one (a negation of first set of signals) for turning off. “Trgon” (triangular on) and “Trgoff’ (triangular off) signals are produced in this part of the controller.
Phase locked loops (PLL) with all ac/dc converters take an important role in providing a reference phase signal synchronized with the ac system. This reference signal is used as a basic carrier wave for deriving valve-firing instants are calculated using the PLL output as the base signal and adding the desired valve firings [13, 14]. Typically, the desired firings are calculated in the main control circuit achieving regulation of some output system variables. In both parts of PWM control, the PLL block is used.
Figure 1. STATCOM phase control, where “Angle Order” is the phase shift between the
controller ac voltage and its bus voltage
a)
b)
Figure 2. PWM control:
a) Part 1: generation of triangular waveforms synchronized with system ac voltage;
b) Part 2: generation of reference waveforms synchronized with system ac voltage
and shifted by the angle order
In the second part of PWM control, generation of reference waveforms is synchronized with system ac voltage and shifted by the angle order. Three phase voltages and angle order that produced in voltage control loop are used as input of the block (Fig. 2). Finally outputs of two parts of PWM are applied for generation of firing pulses. Firing pulses are generated using comparison of reference signals to triangular signals. Two signals are being sent to each switch, the first one tells to turn on or off, the second one determines an exact moment of switching and is used by interpolation procedure which allows for switching between time steps.
2. DEFINITION OF “VOLTAGE STABILITY PROXIMITY INDEX”
A power system is an electrical network containing components such as generators, transmission lines, loads and voltage controllers. A simplified theory of line stability index derived by Moghavvemi et al. [14] from the stability analysis for each line of the system is used for the prediction of static voltage collapse. The same concept is utilized and extended for the proposed power margin calculation. The power system can be modeled as shown in Fig. 3.
Figure 3. A single line of power system model ZSAO is the line impedance, Zris the corresponding load impedance, </)=tan-1(Qr/Pr)
It is sufficient to consider only a typical scenario where only the modulus of the load impedance is varied while (f> remains constant. This assumption does not reduce accuracy but will simplify the problem at hand. In practice, constant power factor load is also maintained. With the increase of demand in load, Zr decreases and current increases. This leads to a voltage drop at the receiving end:
1 = ' 2* 2, (1) (ZS cosO + Zr cos^) + (ZS sinO + Zr sin^)
V = ZI = _VS_________ (2)
r ' ZS .¡1+(z^7zS)^+2(z^7zS)C0s(^-i) ■ ()
Therefore the power at the receiving end is described as Pr = VrI cos^, which can be written as
Pr =------------------------------------^-Z, (3)
r 1 + (Zr /Zs)2 + 2(Zr /Zs)cos(0-«>) Z, v ' '
The maximum real power that can be transferred to the receiving end can be obtained using the boundary condition dPr / dZr = 0, where Zr / Zs = 1.
Substituting Zr / Zs = 1 in equation (3), the maximum transferable power is derived as
VS cos^
r(max) ZS 4 2O-$y (4)
S 4cos --------—
2
Based on these maximum permissible quantities, the following Voltage Stability Proximity Index is used:
Pr cmax) Maximum real power that can be transferred
VSPI = r(x) =----------------------- -------------------------------. (5)
Pr Real power transferred to the receiving end
3. SIMULATION RESULTS
For the system shown in figure 4, two cases are simulated by two methods (i.e. time domain and PV curve).
Figure 4. A single line of study system
A. Time Domain Simulation Results
Time domain simulation results were performed for a three terminal line outage for both the system with the STATCOM and without STATCOM.
Three phase to ground fault is simulated at bus N2. This fault occurs at 1.5 seconds and lasts for 0.75 seconds. The time domain simulation results for these two cases are shown in figures 5 and 6. In controlled case, STATCOM maintain voltage almost equal to 1.0 p.u. (reference voltage) but as shown in figure 7, voltage at bus 2 decreases dramatically from 0.83 p.u. to 0.59 p.u.
Figure 8 shows reactive power transferred between STATCOM and the power system. After fault occurring at 1.5 s, this reactive power increases from 100 MVAr (steady state) to 370 MVAr (for short time) then 300 MVAr during fault. Reactive power increases for voltage maintaining that leads to better voltage stability and reliability. Figure 9 shows active power transmitted between power system and STATCOM.
Figure 5.
Voltage at bus N2 without STATCOM
Figure 6.
Voltage at bus N2 with STATCOM
Main : Graphs
■ V_pu
1.00-
0.80- (
0.60-
0.40-
0.20 -
0.00-
0.00 0.50 1.00 1.50 2.00 2.50
►
Figure 7.
Reactive power between STATCOM and power system
Figure В.
Active power between STATCOM and power system
Figure 9.
Relationship between angle order of STATCOM and real power
B. Dynamic PV Curve Simulation Results
Dynamic PV curve simulations were performed for the same power system shown in figure 4. At the beginning of this PV curve simulation, the loads at bus N2 and N3 were set to 0, then loads were gradually increased keeping the same load power factor. This work is performed for different load power factors from 0.7 to 1.0. Figures 10-12 represent PV curves for power factor 0.8, 0.9 and 1.0 for both the system with the STATCOM and without STATCOM. The curves 1 and 2 represent the cases “with STATCOM” and “without STATCOM”, respectively. As real power reach its limits, the ability of controlling the voltage is lost; furthermore, at a certain loading of the system, one type of instability occurs which will be called voltage collapse. This phenomenon is characterized by a sharp and fast decrease in voltage magnitude.
P.F.=1.0
P
Figure 10.
PV curves with P.F. = 1.0 for two different states:
1) without STATCOM 2) with STATCOM
P.F.=0.90
P
Figure 11.
PV curves with P.F. = 0.9 for two different states:
1)without STATCOM
2)with STATCOM
P.F.=0.80
V
Figure 12.
PV curves with P.F. = 0.8 for two different states: 1) without STATCOM
2) with STATCOM
For more explanation, PV curves both without STATCOM and with STATCOM are shown in figure13 and 14 respectively. In this figures PV curves are plotted for power factors
0.7, 0.8, 0.9 and 1.0. In controlled case, an overlap between curves take places, that means greater effects are at lower power factors. We should say to those operating points behind the curve noise are impractical, because in these points the voltage of system decreases dramatically and subsequently voltage collapse occurred. As it is seen, Voltage Stability Proximity Index (VSPI) is affected by various load power factor. In figure 15 calculated Voltage Stability Proximity Index improvement after STATCOM insertion to power system is shown for different power factors.
Figure 13.
PV curves without STATCOM for different power factors
Figure 14.
PV curves with STATCOM for different power factors
Figure 15.
Voltage Stability Proximity Index (VSPI) improvement after STATCOM insertion
P.F.=0.8 P.F.=0.9 P.F.=0.95 P.F.=1.0
200 P
C. Discussion on Simulation Results
Some basic observations based on these figures are as follows:
1. In time domain simulation, it was observed significant voltage decrease after faults that means voltage collapse in the base case without the STATCOM but was avoided with the STATCOM in-services, STATCOM can greatly improve the voltage stability of power system.
2. Reactive power in figure 10, represents STATCOM, in steady state, transmit reactive power to system due to the load is inductive (P.F. =0.9 lag). In case of capacitive load, STATCOM absorbs reactive power from system.
3. We can deduce from figure 10 and 11 that reactive power has more effects on voltage stability rather than real power.
4. The peak (i.e. noise point) of PV curves for the case “with STATCOM” is very larger than for the “base case”.
5. On the stable operating side (i.e. upper side) of the PV curve with STATCOM in services, the voltage is relatively flat at 1.0 p.u. with respect to load active power. This represents the effect of STATCOM operation for voltage regulation.
6. In less power factor (i.e. 0.7) effect of STATCOM on increasing maximum real power which can be transferred, become significantly greater than higher power factors, therefore STATCOM can play a vital role in voltage stability and reliability of power system.
7. PV curves are much more illustrative because they cover a wide range of system operating conditions, whereas the time domain simulation are for only one operating point.
4. CONCLUSION
In this paper, PV curve and time domain simulations were applied to evaluate voltage stability of a power system with a STATCOM which includes a detailed control model. Also effect of load with different power factor in voltage stability assessment is studied. STATCOM exhibits the fact that insertion of this device in power system can increase line power and loading capability of the network as well as enhancing the system voltage stability, especially, in lower power factors. It should be noted that PV curves provide much more information on the relationship between system control parameters and voltage stability, because they cover a wide range of system operating conditions. Also from time domain simulation we can deduce that reactive power has more effects on voltage stability rather than real power.
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