Analytical Methods of Voltage Stability in Renewable Dominated Power Systems: A Review
Abstract
:
1. Introduction
 Investigate the analysis and verification of voltage stability studies based on different renewable energy generation types;
 Classify and compare voltage stability analysis methods based on different microgrid operation modes and types of DGs; and
 Evaluate voltage stability techniques and conduct a simulation verification to demonstrate the most suitable simulation platform with different microgrid settings.
2. Voltage Stability Methods of Analysis
2.1. Static Voltage Analysis Techniques
2.1.1. Continuation Load Flow Method Using P–V and V–Q Curves
2.1.2. Modal Analysis of the Jacobian Matrix Based on V–Q Sensitivity
2.1.3. Singular Value Decomposition Using NetworkLoad Admittance Ratio
2.1.4. Transfer Capability Evaluation Using Static Analysis Methods
2.2. Dynamic Voltage Analysis Techniques
2.2.1. Small Signal Analysis Method
2.2.2. Large Signal Analysis Method
3. Voltage Stability Analysis Indices
3.1. VSI Classification
3.2. Voltage Stability Indices Review
3.2.1. JacobianMatrixBased VSIs
3.2.2. SystemVariableBased VSIs
4. Verification Case Studies for the Voltage Stability Analysis
4.1. Analysis and Verification Case Studies with Integrated PV Generation Only
4.2. Analysis and Verification Case Studies with Integrated Wind Generation Only
4.3. Analysis and Verification Cases with Hybrid Distributed Generation
 When a sampling method uses the standard error of the mean (SEM), the fitting probability ratio may be negative, while sampling methods using CMEM have greater effectiveness and accuracy;
 The computational speed of the method based on CMEM is significantly higher than that of the Monte Carlo method, resulting in a time saving of 99.95%;
 The higher the penetration rate of renewable energy, the greater the load margin fluctuation, leading to a more unstable system;
 As the correlation degree of external weather factors, such as the wind speed and solar irradiation rate, increases, the mean value of the load margin is almost unchanged, but the fluctuation degree increases.
4.4. Examples of Simulation Validation under Different Scenarios
 Basic load condition;
 Different load models;
 The model works under the critical state.
 A twonode power system model with a 90degree initial voltage angle for a flat start;
 A 1900 MW pure active load connected at the receiving end of the power system.
 Bus 8–9 outage;
 G3 outage;
 Bus 12 load increment.
5. Conclusions
 Systematic development of dynamic voltage stability analysis methods: Although several dynamic methods to evaluate the voltage profile of a system are available, additional work needs to be performed to improve their accuracy and efficacy levels.
 Online realtime techniques for assessing the state of the system’s voltage and the threshold of instability: It can be anticipated that power systems can be further optimized in an efficient and timely manner if the voltage collapse is detected at an early stage.
 Coping with increasing asynchronous generation from renewables: The increasing complexity of the network due to the higher level of renewable penetration may lead to more stability issues. Increasing the integration of DGs may exponentially increase the risk of large disturbance instability. Therefore, it may become important to coordinate the expanding asynchronous power supplies with the current synchronous generation.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Ref  VSI/Method  Analytical
Foundation 
Index Type  Equation  Stability Threshold 
[78]  Jacobian matrix singular point  Static  ,  
[79]  index  Load flow equation  Static  
[75]  TVAI  Approximated step function  Dynamic  
[73]  VSI  Twobus equivalent circuit  Static  
[80]  VSI  Twobus equivalent circuit  Static  
[60]  Energy function  Static  
[43]  Load flow Jacobian matrix  Static  Ranges from 0 to 1
(Stability limit point to no load) 

[81]  Saddlenode and finite induced bifurcation  Static  Ranges from 0.25 to 0
(No load to collapse point) 

[82]  Sensitivity matrix  Linearized load flow equation  Static  If the sensitivity measure is positive, the system is stable; if not, the system is unstable.  
[83]  GSA  Optimal load flow and probabilistic model  Static  
[84]  IB index  Traditional IB index  Dynamic  If the load impedance is located inside the circle with a radius , the system is unstable.  
[85]  MSV(Minimum Singular Value)  Singular point of Jacobian matrix  Dynamic  ΔΣ is the change in singular value due to the uncertainty of wind power.
MSV is used to assess whether the added wind turbine generator has a positive or negative effect on the voltage stability of the power system. 

[86]  V–Q modal analysis,
V–Q curve analysis 
V–Q modal analysis, V–Q curve analysis  Static  For modal analysis: A positive value means the system is stable. A negative value means the system is unstable.
For the V–Q curve, the reactive power margin can show the voltage collapse margin. 

[87]  P–V Curve theory  Static  This essay uses the combined method to conduct the voltage stability analysis for the P–V curve; the active power margin can show the voltage collapse margin. For VSI, the larger the voltage stability index, the more stable the system.  
[88]  Monte Carlo based voltage stability analysis  Eigenvalue, reactive power margin, real and reactive power loss
Monte Carlo simulation 
Static  For the modal analysis: A positive value means the system is stable. A negative value means the system is unstable.
For the V–Q curve, the reactive power margin can show the voltage collapse margin. 

[89]  LILO  Integralintegral estimate theory, LIOS properties  Dynamic  The system outputs satisfy the equation  
[90]  VPS  P–V and V–Q curve  Static  The active power margin can show the margin of voltage collapse  
[74]  Line stability index  Static  , the system is stable
, the system is stable FVSI is close to 1, and the system is close to instability. 

[91]  Voltage Stability Condition  Steadystate load properties, Lyapunov stability theory  Static  Assuming that for any branch (i,j), the power system is at a QV regular operating point, if the following condition is satisfied:  
[92]  P–V and V–Q curve  P–V and V–Q curve  Static  The active power margin can show the margin of voltage collapse.  
[5]  PV analysis  Continuation load flow algorithm  Static  The active power margin can show the margin of voltage collapse.  
[93]  PV analysis  Continuation load flow algorithm  Static  The active power margin can show the margin of voltage collapse.  
[94]  Softwarebased Simulation method  Software function  Static  N/A  Compare the system voltage plots with the voltage sag or UCAP between simulation software packages. 
[95]  VSI  Optimal load flow  Static  
[96]  Simulation Softwarebased method  Modal Analysis  Static  N/A  Determined using the General Algebraic Modeling System (GAMS) optimization software and analyzed with the CONOPT4 solver. 
[97]  P–V and V–Q curve  P–V and V–Q curve  Static  The active power margin can show the margin of voltage collapse.  
[98]  P–V curve  Static  
[54]  Topological model  Static  The number of intersection points between the unit circle and the function’s curve can show stability.
The presence of zero intersection points indicates instability, and the presence of two intersection points indicates stability. The presence of one intersection point indicates a stable margin. 

[34]  VSI  Timesynchronized measurements  Dynamic  The system is stable if the VSI is 1. The system is unstable if the VSI is 0.  
[70]  Jacobian matrix singular point, PDF  Static  The formulation can measure the loading margin. 
Operation Mode  Type of DG(s)  References 
GridConnected  PV  [43,78,88,90,97,98] 
Wind  [5,54,74,84,85,89,94,96]  
PV, Wind  [70,79,80,83,92]  
PV, Hydro  [75]  
PV, Wind, Hydro  [86]  
Islanded  PV  [60] 
Wind  [81]  
PV, Wind  [34,82] 
Voltage Stability Index  Formulation  Calculation Runtime (Units) 
Index 2003  0.8171  
Index 2014  0.8172  
Novel Index  0.7997 
Voltage Stability Analysis Method  Simulation Result 
Lindex method  This method requires the least amount of calculation and has a good level of consistency with most other methods. 
Modal analysis  The method is most suitable for determining the strongest and weakest buses in the system. 
V–Q sensitivity analysis  This scheme has difficulty distinguishing different stability modes in the system and may be misleading when applied to large systems with multiple regions. 
Power flow based methods  Too many system parameters are considered in the calculation, and the accuracy is relatively low. 
Dynamic voltage stability analysis  Cannot accurately calculate the stability margin for each bus. Overlapped timedomain actions in the interconnected networks may exist, leading to the wrong analysis result. 
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Liang, X.; Chai, H.; Ravishankar, J. Analytical Methods of Voltage Stability in Renewable Dominated Power Systems: A Review. Electricity 2022, 3, 75107. https://doi.org/10.3390/electricity3010006
Liang X, Chai H, Ravishankar J. Analytical Methods of Voltage Stability in Renewable Dominated Power Systems: A Review. Electricity. 2022; 3(1):75107. https://doi.org/10.3390/electricity3010006
Chicago/Turabian Style
Liang, Xinyu, Hua Chai, and Jayashri Ravishankar. 2022. “Analytical Methods of Voltage Stability in Renewable Dominated Power Systems: A Review” Electricity 3, no. 1: 75107. https://doi.org/10.3390/electricity3010006