Model of DFIG reactive limit in improved IB index

Different types of stability and voltage stability

The behavior of power system stability changes dynamically and all dynamic systems are based on complicated mathematical equations. From an economical viewpoint, a power system cannot be stable for any perturbations. When a perturbation appears, power system variables such as bus voltages, and machine rotor speeds, active and reactive power will change greatly. These variations activate all governors and voltage regulators to restore a power system to the equilibrium point. Even some elements may be disconnected from network to preserve the main system from cascading instability (Kundur et al., 2004). Power system stability can be categorized in several forms based on: 1) main variables of the power system; 2) extent of the perturbations; 3) time scales of simulation. Figure 1.1 shows the main types of the power system stability (Canizares, 2002). Long-term voltage stability includes slow dynamic elements such as OLTC, OXL, and some controlled loads. The time scale of this voltage stability is until several minutes. Different forms of instability may change from one form to another in the power system dynamically. To realize the instability forms, it needs to be familiar with dynamic operation behavior of power systems (Kundur et al., 2004). Long-term voltage stability can be divided into large-disturbance and smalldisturbance voltage stability.

The small-disturbance voltage stability problem can be modeled with linearized power system equations with acceptable error. But it cannot disregard nonlinear behavior of some elements such as OLTC. Increasing the active and reactive power in the inductive elements has a major effect on voltage reduction. Over excitation and under excitation limits of generators or synchronous compensators may intensify this process of voltage reduction when a fault causes and also when the reactive power is not sufficient. In addition, transferring the reactive power for long distance is improper. It has a negative effect on active and reactive power losses and it increases the risk of voltage collapse (Taylor, Balu et Maratukulam, 1994). When the short-term dynamics have diminished, the long-term dynamics (slow dynamics) will remaines and it should be considered. Long-term (LT) voltage instability is classified into three types of instability (Canizares, 2002; Cutsem et Vournas, 1998). LT1 is loss of equilibrium. This instability is the most common instability procedures; load restoration and OLTCs affect on this instability. LT2 is a lack of attraction towards a stable equilibrium. For instance, first LT1 occurs and then corrective actions are performed with a delay. Therefore, there is not enough time to restore the operating point. LT3 is a slow growth of the voltage oscillation. This instability is less common; one example can be produced by the cascaded load restoration or incorrectly tuned OLTCs.

Effect of OLTCs on voltage stability

The OLTCs have an important role on voltage stability and they may trigger the instability process. The tap ratio can be changed via manual or automatic procedure. Some OLTCs operate accompany with an automatic voltage regulator (AVR) in power systems, so this action worsen the procedure of voltage instability. The behavior of OLTC equipped with AVR can be presented by two models (discrete or continuous). OLTCs generally operate after a pre-specified delay, and then the tap ratio keeps constant the load side voltage (Weedy et al., 2012). There are some ways to control the voltage stability by OLTCs which is known as corrective actions. These corrective actions used to control the restoration schemes after a contingency which have negative impacts on voltage stability problem. These are classified into groups below (Vournas et Karystianos, 2004): 1) Tap blocking behavior of an OLTC. One of the easiest methods is the tap blocking of an OLTC which ends to the continuation of the voltage instability. It has some disadvantages such as decreasing the voltage level in both the transmission and distribution system and producing the negative effect on other load restoration processes. Also, it is hard to prevent unnecessary tap blocking and it has a problem in finding which tap needs to be blocked. 2) Specific tap or voltage switching of an OLTC.

This method avoids the continuation of voltage reduction from a specific value. It can be limited by a specific tap ratio or a reference value of the voltage. These values can obtain from the highest probability of contingency or the operator experiences. 3) Tap reversing behavior of an OLTC. This way operates to control the voltage level in both the distribution and transmission sides. An OLTC wants to keep the voltage magnitude at an acceptable level. It causes to prevent the voltage collapse. The tap reversing behavior avoids the voltage reduction and operates more profitable than other corrective actions. Tap reversing behavior of an OLTC provides enough time for a system to employ other corrective actions. There are some methods to optimize an OLTC setting such as the gradient projection method which is based on maximizing the stability margin (Polak, 1971; Vournas et Karystianos, 2002). In (El-Sadek et al., 1999), a case study is analyzed as a Thevenin’s equivalent system which E is an equivalent Thevenin’s emf and ? is the load node voltage. Then a ?? ?? criterion (El-Sadek et al., 1997) is introduced as an analytical factor to evaluate the behavior of OLTCs. Note that tap ratio does not change the maximum active and reactive power of a load. Furthermore, finding the critical OLTCs can help to improve the voltage stability problem. In (Thukaram et Parthasarathy, 1996; Thukaram et al., 2004), the linear programming method has been applied to solve two objective functions which are the minimization of the voltage deviations from desired values and the minimization of the sum square of L-indices. Thus, these methods can show the critical OLTCs which may lead to the voltage instability under the peak load conditions.

Effect of load models on voltage stability

Some elements can intensify the effects of load on voltage stability, such as OLTCs, voltage regulators, thermostats and motor slip adjustments. Restored loads consume more and more reactive power which it cuts down the voltage magnitudes. Moreover, different types of load models have impacts on the voltage stability problem (Lee et Lee, 1993; Pal, 1992; Zeng, Berizzi et Marannino, 1997). It is beneficial for the electricity industry to develop dynamic load models instead of conventional load models. Note that only dynamic systems have the unstable behavior (Hatipoglu, 2014). (Pal, 1992) proposes an accurate load model with a constant MVA characteristic. The dynamic behavior of this model is indicated by a firstorder delay term. (Chowdhury et Taylor, 2000) compares between two methods of stability evaluation (QV curve obtained from the conventional PF approach and the dynamic simulation). This paper evaluates three worst outages which are stable in the dynamic simulation, but they are unstable by the PF approach and there is no operating point in the QV curve. Thus, the results of the PF approach are not reliable. Well-known curves such as PV and QV curves cannot consider the dynamic load characteristics, because they are not time-dependent. In (Lian et al., 2010), the authors propose a method to consider the dynamic load characteristics. It first converts a power system into an equivalent two-node system and then an approximated method is used to model the dynamic load with a polynomial form. Figure 1.7 represents that different types of load models have distinct operating points. It shows that constant impedance (Z), constant current (I) and constant power (P) load models have significant impacts on the voltage stability problem due to different intersections in the PV curve. (Regulski, 2012) investigates a voltage stability evaluation in different load characteristics. When a contingency occurs, some loads act quickly and reach to new operating points, while others act with delay. In the case of a constant power load, an operating point may be vanished; when it passes maximum active power limit. Thus, consideration of fixed value for the load model creates many errors in the voltage stability results.

Table des matières

INTRODUCTION
CHAPTER 1 LITERATURE REVIEW
1.1 Basic principles of voltage stability
1.1.1 Different types of stability and voltage stability
1.1.2 Operating points and zones
1.1.3 Voltage stability evaluation methods
1.1.4 QSS time-domain simulation
1.2 Evaluation of main effects on voltage stability
1.2.1 Effect of reactive power limits on voltage stability
1.2.2 Effect of OLTCs on voltage stability
1.2.3 Effect of load models on voltage stability
1.3 Methods of solving reactive power dispatch problem
1.4 Analysis of main voltage stability indices
1.4.1 Evaluation of loading margin as global index
1.4.2 Indices based on singular value method
1.4.3 Line voltage stability indices (LVSIs)
1.4.4 Indices based on L-Index
1.5 Different types of VSC-OPF approach
1.5.1 Power transfer constraint
1.5.2 Loading margin constraint
1.5.3 Singular value constraint
1.5.4 L-Index constraint
1.5.5 LVSI constraint
1.6 Stochastic Optimal Power Flow (SOPF)
1.6.1 Demand Response (DR) in SOPF
1.6.2 Energy Storage Systems (ESSs) in SOPF
1.7 Conclusion
CHAPTER 2 A NOVEL APPROACH TO DYNAMIC VOLTAGE STABILITY ANALYSIS FOR DFIG WIND PARK INTEGRATION
2.1 Introduction
2.2 Background
2.2.1 Impedance matching theory and its application
2.2.2 DFIG capability curve limits
2.2.3 VSC-OPF model
2.3 Proposed impedance-Based index
2.3.1 Model of DFIG reactive limit in improved IB index
2.3.2 OLTC model in improved IB index
2.4 Proposed VSC-OPF method
2.5 Simulation result and discussion
2.5.1 Voltage stability monitoring
2.5.1.1 Modified WECC test system
2.5.1.2 Modified IEEE 39-bus system
2.5.2 VSC-OPF
2.5.2.1 IEEE 39-bus system
2.5.2.2 IEEE 57-bus system
2.5.2.3 Polish 2746-bus system
2.6 Conclusion
CHAPTER 3 MULTI-OBJECTIVE STOCHASTIC OPTIMAL POWER FLOW CONSIDERING VOLTAGE STABILITY AND DEMAND RESPONSE WITH SIGNIFICANT WIND PENETRATION
3.1 Introduction
3.2 Multi-objective SOPF formulation and constraints
3.3 Operating points and zones
3.4 Fuzzification of multi-objective SOPF
3.5 Line voltage stability index (LVSI)
3.6 Simulation result and discussion
3.6.1 Voltage stability monitoring of LVSIs
3.6.1.1 Modified WECC test system
3.6.1.2 IEEE 39-bus system
3.6.2 Multi-objective SOPF
3.7 Conclusion
CHAPTER 4 FREQUENCY AND VOLTAGE CONSTRAINED STOCHASTIC OPTIMAL POWER FLOW CONSIDERING WIND POWER AND DEMAND RESPONSE RESOURCES
4.1 Introduction
4.2 Background review
4.2.1 System frequency response model
4.2.2 Frequency restoration scheme
4.2.2.1 Level one (frequency below 59.2 )
4.2.2.2 Level two (frequency between 59.2 and 59.5 )
4.2.2.3 Level three (frequency between 59.5 and 59.7 )
4.2.3 EL-Index calculation
4.3 Proposed frequency and voltage constrained SOPF
4.4 Numerical analysis
4.4.1.1 Maximum single contingency
4.4.1.2 Double contingency
4.5 Conclusion
CONCLUSION
APPENDIX I IMPEDANCE MATCHING THEORY
APPENDIX II INPUT DATA FOR SOPF APPROACH
APPENDIX III IEEE RTS 96-BUS SYSTEM
APPENDIX IV IEEE 39-BUS SYSTEM
APPENDIX V IEEE 57-BUS SYSTEM
LIST OF REFERENCES

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