Relative to the total short-circuit current, the average contribution of solar PV plants is slightly less—as expressed by the SCC PV ratios. In similar fashion, the solar PV plants have a limited say in the transient stability at this bus due to the small short-circuit contribution by the solar PV plants. In the analysis, certain variables which influence the transient stability e.
From the analysis it was shown that solar PV plants play an important role in one of the variables affecting transient stability i. Such an example was presented when evaluating the bus at GTB. In this studied case, the solar PV plants affected the transient stability notably. Additionally, for higher SCC PV ratios as case 4, it was shown that the transient stability was affected the most for this case when removing the dynamic behavior of the solar PV plants as the SCC PV ratio was the highest.
For these cases it was shown that the low contribution to the total short-circuit current by the solar PV plants led to them having little to no influence on the transient stability. Electricity , 1 79 Looking into the future, power system networks shall continue to phase out synchronous generators and add renewable energy sources such as solar PV plants.
Consequently, the short-circuit current in the various regions shall decline as synchronous generators provide significantly more short-circuit current compared to renewable energy sources.
This overall decline in short-circuit current and increase of short-circuit current contribution by solar PV plants shall progress a lot of areas towards higher SCC PV ratios and thus solar PV plants and other RES shall have a continuingly increasing influence on the transient stability. The remarks above state the impact which solar PV plants have on the transient stability.
It is also important to highlight when significant decrease in transient stability is witnessed. If the total short-circuit current at a faulted bus is highly contributed by synchronous generation units, then for certain situations in which synchronous generation units are put out of service, the short-circuit current at such a bus might decrease significantly henceforth potentially leading to harmful effects for the transient stability. Also, if a fault occurs at a bus near a synchronous generation unit which contains a low short-circuit current, transient stability problems might arise when such a synchronous generation unit is operating at a high operating point close to its active power limit and under-excited.
Improving Transient Stability In this section, methods to improve transient stability shall be proposed. To illustrate this point, GTB shall be evaluated connections at this bus are shown in Figure 11 and the operating point of the synchronous generator nearby will be varied. To examine the impact of operating point of the synchronous generator on the transient stability, case 2 has been used.
The different operating points and the respective critical clearing times are provided in Table Table Operating points of synchronous generator at bus For these operating points only the reactive power output of the synchronous generator has been varied, while the active power output is close to its limit. These operating points yield the lowest critical clearing times because the rotor angle is at a higher operating point yielding less margin for transient stability.
In these cases, it is due to the high amount of active power being generated relative to the Pmax of the generator. Additionally, it is also seen that the critical clearing time for operating point 3 is the worst. Thus, the synchronous generator is at its most critical when a combination of high amount of active power generation and an under-excited generator is present. On the other hand, it is seen that the active power generation is not as high compared to operating points 1 till 3 and hence the critical clearing time is not as low.
Concludingly, it is illustrated that the transient stability is highly dependent on the operating point of the synchronous generator. Furthermore, the operating point of the generator has the most significant effect on the transient stability when the active power generation is close to its limits and the generator is under-excited.
Consequently, for critical areas where synchronous generators are in danger of losing synchronism, limitations can be set on the synchronous generators near such relevant areas regarding the active power production and reactive power output to improve the transient stability.
Addition of reactive compensation device: As shown in the analysis, the short-circuit current at the faulted bus has a significant say in the transient stability. To illustrate this phenomenon, case 2 at the bus of EBKA is looked at without and with the addition of a reactive compensation device. The reactive compensation device has been added to the high voltage bus, in this case bus EBKA. The added reactive compensation device has a rating of MVA.
The critical clearing time of these two cases is shown in Table CCT with and without synchronous condenser. This is due to the added short-circuit current contribution of the added device. Conclusively, it was shown that by adding a reactive compensation device such as a synchronous condenser or STATCOM, the total short-circuit current at the faulted bus increases hence improving the transient stability. Additionally, such devices also contribute to the voltage support. To demonstrate this point, bus GTB and case 2 has been looked at.
A modification has been made by decreasing the reactance of the line between the synchronous generator at bus and the faulted bus GTB. The initial and modified reactance and the obtained critical clearing times for the two cases is provided in Table Modified reactance and CCT of studied cases.
This can be explained by looking at the power flow transfer equation shown in Equations 10 and This alternative is very costly and does not provide any direct benefits other than an improved robustness and transfer capacity of added line.
This alternative offers redundancy and the ability to spread the transfer over two lines. Conclusions This paper proposes a method for obtaining a standard parameter set for representing large-scale and aggregated solar PV plants to address the research gap concerned with a lack of accepted parameters sets for representation of solar PV plants. The parameters of the models which align with the grid connection requirements were determined by the specified requirements—such important parameters are the reactive current gain and the reactive current injection deadband.
Parameters which are manufacturer dependent were assigned values of existing solar PV plants in the Dutch grid. Furthermore, certain parameters did not have influence on the dynamic behavior of the PV system, these were assigned by typical values.
Finally, for the remaining parameters, a parametric sensitivity study and literature research were combined to assign these values. It is worth noting that the parameter sensitivity analysis can be done in a more intricate manner, by way of optimization-based tuning; such a method can be carried out as an extension of this research. The analysis of the transient stability was conducted in such a manner as to isolate the behavior of the short-circuit current on the transient stability.
This was achieved by evaluating a certain bus and setting the synchronous generator near that bus to a fixed operating point across all cases. Additionally, the voltage of this generator bus was brought within a range of 0. These changes have been made to solely evaluate the impact of short-circuit current at the faulted bus on the transient stability.
The analysis concluded that the impact of solar PV plants at a bus near a synchronous generator on the transient stability is predominantly determined by the SCC PV ratio equation defined. This relationship defined the amount of short-circuit contribution by the solar PV plants relative to the total short-circuit current at the faulted bus. As this ratio became higher, the solar PV plants started to have a bigger impact on the transient stability. As solar PV plants are being added to power systems and synchronous generation units are being decommissioned, more areas will tend towards high SCC PV ratios hence the impact of the solar PV plants on the transient stability will only increase.
Moreover, proposed methods to improve the transient stability are limiting the operating region of critical synchronous generators, increasing the short-circuit current at a certain bus or region by adding a synchronous condenser or STATCOM and decreasing the reactance between the critical synchronous generator and the faulted bus. Author Contributions: Conceptualization, N. All authors have read and agreed to the published version of the manuscript. Electricity , 1 82 Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest. Table A1. Parameter Description Unit Value Tfltr Voltage or reactive power measurement filter time constant s 0. Table A4. Parameter Description Unit Value Trv voltage measurement transducer time constant s 0.
Qin, D. NASA Team. Global Surface Temperature. Butler, C. Climate change, health and existential risks to civilization: A comprehensive review — Public Health , 15, Ruyssenaars, P. Akpan, U. The contribution of energy consumption to climate change: A feasible policy direction. Energy Econ. Policy , 2, 21— United Nations. Paris Agreement. Eguia, P. Use of generic dynamic models for photovoltaic plants.
Energy Power Qual. Yamashita, K. Lammert, G. International industry practice on modelling and dynamic performance of inverter based generation in power system studies. Electricity , 1 85 Breithaupt, T. Deliverable D1. Boemer, J. Oh, S. Transient impact analysis of high renewable energy sources penetration according to the future korean power grid scenario. Sustainability , 10, Mohamed, S.
Investigation on the impact of high-penetration of PV generation on transient stability. Thesis, University of Kassel, Kassel, Germany, Pourbeik, P. Generic dynamic models for modeling wind power plants and other renewable technologies in large-scale power system studies.
IEEE Trans. Energy Convers. Modeling and validation of photovoltaic plants using generic dynamic models. Machlev, R. Verification of utility-scale solar photovoltaic plant models for dynamic studies of transmission networks. Energies , 13, Gas Turbines Power. September ; 9 : Blisks suffer from flutter, a self-sustained vibration caused by aerodynamic coupled forces. This instability could cause serious damage to the blades and the machine. Flutter stability is usually analyzed based on the eigenvalue method in the aspect of the linear structural dynamic system, which transforms a dynamics stability analysis into a point of equilibrium in an infinite time scale.
However, in reality, most of the blisk vibrations arise on a finite time horizon. The transient vibration amplification may cause serious damage. This paper proposes a transient flutter stability analysis method in a finite time for structural mistuned blisk based on the energy growth method.
First, two common blisk models coupled aerodynamic force with different complexity are built and are all expressed in the state space representation. A novel energy growth method is then employed to analyze the transient stability and to find the maximum energy growth of the models. The optimal initial condition which leads to the maximum energy growth is obtained.
A new flutter stability criterion is developed to consider the transient stability based on the energy growth method and the infinite time stability based on the eigenvalue method. The new transient stability method is verified by two numerical studies.
It is found that the structural mistuned blisk model which is traditionally predicted stable still has a transient instability in a finite time due to the non-normal property of the dynamic state matrix. Sign In or Create an Account.
Sign In. Advanced Search. Skip Nav Destination Article Navigation. The tripping of a loaded generator or the abrupt dropping of a large load may also cause in- stability [4]. The effect of short circuit faults , the most severe type of disturbance to which a power systems is subjected, must be determined in nearly all stability studies. During a fault, electrical power from near by generators is reduced drastically, while power from remote generators is scarcely affected.
In some cases, the system may be stable even with a sustained fault where as other systems will be stable only if the fault is cleared with sufficient rapidity. Whether the system is stable on occurrence of a fault depends not only on the system itself but also on the type of fault, location of fault, rapidity of clearing and method of clearing , i.
The transient stability limit is almost always lower than the steady state limit, but unlike the latter, it may exhibit different values depending on the nature, location and magnitude of disturbances [5]. Modern power systems have many interconnected generating stations, each with several generators and many loads. The machines located at anyone point in a system normally act in unison. It is, therefore, common practice in stability studies to consider all the machines at one point as one large machine.
Also machines which are not separated by lines of high reactance are lumped together and considered as one equivalent machine. Thus a multimachine system can often be reduced to an equivalent few machine system.
If synchronism is lost, the machines of each group stay together although they go out of step with other groups. Qualitative behavior of machines in an actual system is usually that of a two machine system.
Because of its simplicity, the two machine system is extremely useful in describing the general concept of power system stability and the influence of various factors on stability. It will be seen that a two machine system can be regarded as a single machine system connected to infinite system. Stability study of a multimachine system must necessarily be carried out on a digital computer. Multi-Machine Stability Modern power systems are interconnected and operate close to their transient and steady state stability limits.
In large interconnected systems, it is common to find a natural response of a group of closely coupled machines oscillating against other groups of machines. These oscillations have a frequency range of 0. The lowest frequency mode involves all generators of the system. This oscillation groups the system into two parts - with generators in one part oscillating against those of the other part.
The higher frequency modes are usually localized with small groups oscillating against each other. Unfortunately, the inter-area oscillation can be initiated by a small disturbance in any part of the system.
These small frequency oscillations fall under the category of dynamic stability and are analyzed in linear domain through the liberalization of the entire interconnected systems model. Inter-area oscillations manifest wherever the power system is heavily interconnected.
The oscillations, unless damped, can lead to grid failure and total system collapse. Multimachine equations can be written similar to the one-machine system connected to the infinite bus.
This representation neglects the effect of saliency and assumes constant flux linkages. A group of coherent machines is represented by one equivalent machine. Vi is the terminal voltage of the ith generator Pi and Qi are the generator real and reactive powers. To include voltages behind transient reactances, m buses are added to the n-bus power system network. To simplify the analysis, all nodes other than the generator internal nodes are eliminated using the Kron reduction formula.
To eliminate the load buses, the bus admittance matrix is portioned such that the n buses to be removed are represented in the upper n rows. Since no current enters or leaves the load buses, currents in the n rows are zero.
The classical transient stability study is based on the application of a three- phase fault. This is simulated by removing the kth row and column from the prefault bus admittance matrix.
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