Improving and warning the static stability limit of complex power grid tie-line based on WAMS

In order to solve the technical problems of traditional power system classic formulas that are difficult to explain the static stability limit changes of power grid interconnection lines, as well as the difficulties in improving and warning the static stability limit power of interconnection lines, this paper provides a method for improving and warning the static stability limit of power grid interconnection lines. Firstly, based on the electrical quantities measured by the wide-area measurement system (WAMS) of the power grid, the equivalent reactance of the power grid interconnection lines, and the equivalent impedance from the high voltage side and medium voltage side of the three coil transformers on both sides of the interconnection line are determined. Secondly, under pre-set operation mode and constraint conditions, the configuration quantity and capacity of the dynamic reactive power sources on the medium voltage side of the three coil transformers on both sides of the interconnection line are determined. Finally, based on the determined configuration and pre-set operation mode of the dynamic reactive power sources on the medium voltage side of the three coil transformers on both sides of the interconnection line, the historical electrical quantities measured by WAMS. The static stability limit and static stability margin of the interconnection line are calculated, and warnings are provided.


Introduction
China vigorously promotes the development of ultra-high voltage AC/DC, achieves large-scale and optimized resource allocation, and leverages the advantages of ultra-high voltage AC/DC with large capacity and long-distance transmission [1][2].In 2009, the Changzhi Nanyang Jingmen UHV AC test demonstration project was officially put into operation, forming an interconnected synchronous power system consisting of 12 provincial (municipal) level power grids in North China and Central China.In 2011, the expansion project of the ultra-high voltage AC test demonstration project was officially put into operation, further improving the transportation capacity of the North China Central China interconnection line.According to the guidelines for power system security and stability, static stability analysis is required for large power transmission lines, cross-regional or provincial interconnection lines, and weak sections in the network.The static stability limit of the transmission section plays an important role in power system operators grasping the power transmission capacity of the transmission section [3].
With the rapid development of the power system, the transmission section power of existing power grid line channels is becoming higher and closer to its static stability limit.After the system is impacted by faults, it may cause more severe synchronous oscillation or even more severe asynchronous oscillation in two interconnected power systems, seriously affecting the safe and stable operation of the power system.In addition, for complex power systems connected to large regions, there are too many factors, even thousands, that affect the static stability limit of the interconnection channel.It is difficult to explain the variation law of the static stability limit of the interconnection channel based on classic formulas of the power system.The improvement of the static stability power limit of the interconnection channel has fallen into a bottleneck.The static stability of communication channels has become one of the focuses of widespread attention both domestically and internationally [4].
At present, research has proposed some methods to calculate static stability limits, such as the collapse point method [5][6] and the optimal power flow method (OPF) [7][8][9][10].However, these methods are applicable to a set of deterministic loads and power generation.They cannot accurately estimate SVSL when there is uncertainty in the system caused by intermittent power sources (such as wind and solar energy), measurement errors, prediction errors, rounding, truncation errors, etc. Due to these uncertainties, the stable capacity of the power system may undergo significant changes, affecting the safety of the system.
In order to solve the technical problems of traditional power system classic formulas that are difficult to explain the static stability limit changes of power grid interconnection lines, as well as the difficulties in improving and warning the static stability limit power of interconnection lines, this paper provides a method for improving and warning the static stability limit of power grid interconnection lines.Firstly, based on the electrical quantities measured by the wide-area measurement system (WAMS) of the power grid, the equivalent reactance of the power grid interconnection lines, and the equivalent impedance from the high voltage side and medium voltage side of the three coil transformers on both sides of the interconnection line are determined.Based on this, under pre-set operation mode and constraint conditions, the configuration quantity and capacity of the dynamic reactive power sources on the medium voltage side of the three coil transformers on both sides of the interconnection line are determined.Finally, based on the determined configuration and pre-set operation mode of the dynamic reactive power sources on the medium voltage side of the three coil transformers on both sides of the interconnection line, the historical electrical quantities are measured by WAMS.The static stability limit and static stability margin of the interconnection line are calculated, and warnings are provided.

Basic introduction and engineering application of static stability limit for interconnection lines between large regional power grids
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The problem of determining the static stability limit of interconnection lines in complex power systems
The active power P and reactive power Q of the interconnection line in a simple power system are: Both the analysis based on PMU data of the power grid and the simulation of complex power grids using software such as PSASP and PSD-BPA indicate that due to the complexity of actual interconnected systems, the stability limits of interconnection lines are difficult to determine, further leading to difficulty in capturing sensitivity factors.Therefore, it is urgent to propose a calculation method for the static stability limit and sensitivity factor of large-scale interconnected power grids.

The operating characteristic formula considering the equivalent model of three winding interconnected transformer
The voltage, current, and active power of the four measurement nodes shown in Figure 1 should have a sampling accuracy greater than 100 Hz to ensure the effectiveness of one cycle sampling value.Therefore, the sampling accuracy of PMU in this article is assumed to be at or above 100 Hz.At present, the interconnection lines between regional power grids in China are generally ultra-high voltage interconnection lines, with a voltage level higher than the voltage level within the region.Therefore, three winding transformers are configured at both ends of the interconnection line for voltage transformation.Due to the fact that the PMU can configure three winding transformers on three sides, the voltage, current, active power, and reactive power on the three sides of transformers can be considered as known conditions under online operation and simulation conditions.

XL
The operating characteristic equations considering the equivalent model of three winding transformers can be expressed as Equations ( 2) -( 7), as follows: Power supply side: ( ) Power receive side: According to actual measurement and experience, all impedance angles in Figure 1 are less than 90 degrees.Therefore, in the direction from U a to U b , without the injection of other reactive power sources, the voltage vector modulus will show a gradually decreasing trend.
According to the above equation, it can be seen that the stability limit of the interconnection line considering the three coil transformers depends on the voltage modes of Ta U  , Tb U  , a U  , b U  , and their relative angles.X .Through PMU measurement, the voltage vector and current vector at both ends are known quantities (1 cycle value), and the analytical solution values within one cycle can be obtained according to Equation (8). ,2 Based on N ( 1, 2,3,... ,..

N n N 
) scans per day (N is manually set based on experience), the analytical solution for i-th measurement can be expressed as: Similarly, the impedance parameters of the B-side transformer can be obtained.

Evaluation of impedance parameters for interconnection line
For line L, if the voltage vector and current vector at both ends are known through PMU measurement, the analytical equation within one cycle can be obtained according to Equation (12): , sin According to Equation (10), although an analytical solution can be obtained for L X , the calculation results of L X obtained from different PMU sampling values are not the same due to various complex factors in power grid operation.When the number of samples taken by the PMU device in a day is N, the analytical solution of L X for any i-th measurement can be expressed as L,i X .
For all results, it is assumed that the estimated result of L X is X , and the probability is denoted as L, ( ) i Psb X .Then Equation ( 11) is used as the estimated value for simulation.

Method for configuring the number and capacity of dynamic reactive power sources on the medium voltage side of interconnecting transformers
Based on Equation ( 2), the configuration parameters and quantity of dynamic reactive power sources on the medium-voltage side of the connecting transformer at the sending and receiving ends are determined through simulation calculations.
Under a given typical operating mode, constraint conditions are set.(1) Upper and lower limits of capacity on the medium voltage side of side A; (2) Upper and lower limits of capacity on the medium voltage side of side B; (3) Other safety and stability conditions of the power system.
The "large power loss fault" in step 1 of the figure refers to a typical large power loss fault that may cause the tie line to exceed its static stability limit, which is manually selected based on experience in the receiving end AC system.In general, this fault is set as a bipolar blocking of a large-power DC line.
The priority value H for installing one side of step 2 in the figure is calculated as follows: ,2 ,2   corresponding to the moment when the power reaches its peak during a transient process.
If H is greater than 0, it indicates that the voltage on side b is the main limiting factor when reaching the limit static stability value under the given mode.Otherwise, it indicates that the voltage on the side a is the main limiting factor when reaching the limit static stability value under the given mode.
The overall process of the method is shown in Figure 2.

Perform transient stability calculations for specified largepower loss faults
Has the capacity on side A reached the upper limit?
Has the capacity on side B reached the upper limit?

Calculate the priority value H case1 case2
Increase capacity and perform stability calculations Does the power of the interconnection line meet the demand?
Increase the transmission power of the interconnection line and perform stable calculations

Calculation method for static stability limit and static stability margin of the interconnection line
In a quasi-real-time warning environment, the missing power of large power loss faults (such as DC bipolar blocking) is generally a fixed planned value, and the load change is also basically a fixed value.Namely, it is assumed that 1: the missing power of the fault is given; 2. The fixed load of the two interconnected AC systems is known; 3. The corresponding time for setting the voltage of the camera and generator excitation system is known.

Static stability limit and static stability margin of the interconnection line
The minimum values of Equations ( 14) and ( 16) are taken as the static stability limit of the quasireal-time interconnection line, as shown in Equation (17

Quasi-real-time static stability margin
In the field of power system production, the power control limit control P for the interconnection line will be set every half year for specific operating modes.Assuming Mg is the quasi-real-time static stability margin, and then Mg is dynamically updated according to Equation ( 18

Example validation
Taking a cross-regional ultra-high voltage line C as an example, C is the main power transmission channel for the North China and Central China power grids, with an initial power of 5000 MW.It is assumed that a bipolar blocking fault occurs on a DC line of the Central China Power Grid at 1 s, resulting in the loss of active power of 8000 MW.The static stability limit of line C after the fault occurs is analyzed.
Based on the method proposed in this paper, the static stability limit of tie line C under initial conditions is obtained to be 8100 MW.The accuracy of this result is verified through simulation calculations.As shown in Figure 3, after the fault, the actual static stability limit of connecting line C is about 8100 MW.According to the calculation method in this paper, adding a reactive power compensation device of 600 MVar to the Central China Power Grid can increase the static stability limit of line C to 8900 MW.As shown in Figure 4, after adding a reactive power compensation device of 600 MVar, the maximum transmission power of line C after the fault is about 8500 MW, and the system has not experienced power oscillation, thus verifying the accuracy of the method proposed in this paper.

Conclusions
This paper proposes a method for improving and warning the static stability limit of power grid interconnection lines.After verification by numerical examples, the proposed method can accurately obtain the static stability limit power of the interconnection line and provide reasonable suggestions for reactive power compensation devices.By using the strategy proposed in this paper to install reactive power compensation devices, the static stability limit of the interconnection line can be significantly improved.
The research results can be applied to the static stability analysis and early warning work of large power grids, improving the safety and stability level of power grids.

Figure 1 .
Figure 1.Electrical schematic diagram of the interconnection line considering the model of three winding transformer

3 .
Evaluation method for impedance parameters of interconnection line and three winding transformers based on WAMS measured data 3.1.Evaluation of impedance parameters for three winding transformers Assuming obtained through short-circuit tests, and then the estimated measurement quantities are 1

Figure 3 .
Figure 3. Static stability limit of line C under initial conditions

Figure 4 .
Figure 4. Static stability limit of line C after adding reactive power compensation device Method 1 (quasi-real-time, which means predicting the operation mode after Tpre time, where Tpre is the leading time and can generally be taken as 1 hour or 0.5 hour). ).