COMPARISON OF PERFORMANCE OF SYNCHRONIZATION ALGORITHMS FOR GRID CONNECTED POWER ELECTRONICS CONVERTERS ACCORDING TO PROPOSED EVALUATION QUALITY CRITERIA

. In this paper a comparison of synchronization methods for power electronics converters is presented. Proposed evaluation criteria are based on Transmission System Operators requirements, as well as on criteria parameters based on requirements for design, computation and operation under normal/distorted conditions. Additionally a classification of various kinds of synchronization algorithms is discussed with a brief description of the role of power electronics in the modern power systems. All of the tested algorithms were subjected to appropriate tests validating the quality criteria for each of them. The tests were performed in terms of simulations. The investigation results are summarized in the table, which can serve as a basic selection guide.


Introduction
Modern industry is becoming more and more dependent on the correct operation of power converters. Power electronics is becoming one of the most important elements of today's reality. Many of converters applications are being considered as critical for plant production process. The power electronics technology allows the systems and the electric machines (motors and generators) to run efficiently and sustainably. Lack of this solution would make the electric motors run at full speed, and the renewable sources such as solar and wind power, wave energy, fuel cells could not be fed into the power grid. Modern, sustainable energy systems introduce the concept of "Smart grids", where the flow of the energy can be controlled in a sustainable way.
For grid connected power electronic converters basic information are frequency and angle of the utility network. For proper and safe operation phase angle of current or voltage of the fundamental component at the point of common coupling of a system or converter with the grid should be recognized "online" in a real time manner. If this condition is fulfilled the control of the flow of energy between the converter and the network can be achieved. Thus, the most efficient working mode of converters can be utilized.
It is worth noting that such performance mode of power electronics converters (maximum sync = ability to provide maximum efficiency) it is desirable from the point of view of the Transmission System Operators [7]. This due to the fact that having perfectly synchronized elements of the systems increases the stability margin of the system. Usually, various TSO's have different synchronization requirements. The set of such rules is stated in so-called grid codes. Grid codes are technical interconnection requirements for power networks.
Depending on the country, point of connection, grid condition, energy sources connected, load distribution, different requirements may occur. To show how the very definition of synchronization can be recognized, a quote from the polish TSO (PSE Operator) is presented: the synchronization is an "operation concerning the connection of the generating unit with the power system of connection of different power systems after their frequencies, phase and voltages are equalized to reduce the disparity of the vectors of connected voltages to a value close to zero" [8].

Proposed evaluation criteria
The selection and evaluation of the effectiveness of the synchronization algorithm is difficult. The choice should be relevant to the TSO requirements and depend on application type. As described in [1], there are currently no criteria for the selection of synchronization algorithm for power converters. Another important issue is the possibility of comparing the performance of different synchronization algorithms. In the absence of such standards, the choice of the appropriate method is very limited. This shows that the need for a selection guide is straightforward. In order to create a reference guide for choosing a suitable synchronization algorithm define quality criteria are needed. A set of such evaluation criteria is presented on Figure 1.
The proposed solution is based on so called "three-legged stool model" [2], which is suitably modified according to the needs. The three legs are determined as follows: synchronization criteria leg, computation criteria leg and design criteria leg. The evaluation criteria determining the algorithm design phase consists of the following elements: application, noise immunity, single phase utilization, algorithms protection modes, required additional features (signal filtering etc.), methods of realization (analog, digital) and proposed in [1] THD level of a sinus of estimated phase angle.
Looking at the performance of the method, a very important aspect to take into account the computation criteria. This is due to the fact, that respectively established constraints can make our algorithm fast "enough" with cheaper solution. Criteria in this subgroup are determined by total number of signals and variables, number of addition/subtractions and multiplications/scaling operations, transient response, state variable/integrations, computational load and order of signals processed in a cascade.
But the most important part of those rules, basically the core, is the synchronization criteria set. The group consists of following criteria: phase angle jump overshoot level, phase angle settling time, phase frequency jump overshoot, phase frequency settling time, frequency adaptive operation, frequency estimation accuracy, method bandwidth and high frequency characteristics. Going throughout the whole quality criteria selection set, one has to take into account two possible circumstances. Assessment of different synchronization algorithms should be carried out under normal conditions and during grid distortions.

Types of synchronization algorithms
In the literature there are many examples of different synchronization algorithms types. Number of methods used for synchronization is extremely high. Proper selection of the algorithm, taking into account the application, resistance to distortions, implantation method, usually is quite difficult. This was mainly due to the lack of proper classification of the synchronization methods. One of the first classifications of those algorithms is proposed in [1] and can be seen in Figure 2. It is based on the reference frame in which the algorithm is operating. Fig. 2. Proposed classification method for synchronization algorithms [1] Having in mind that power electronics converters cover a wide range of different kinds of applications and functions, a more detailed classification is proposed in [3], and the basic scheme of this classification can be seen in Figure 3.  [3] For the purpose of the quality criteria evaluation several synchronization algorithms have been chosen. The following synchronization algorithms have been tested:  Alpha beta filtering method [3]

Methods evaluation
The selected methods are evaluated according to the proposed quality criteria. It has to be noted that only the operation in nominal (stable) conditions is considered. Only in the case of the frequency estimation accuracy and the THD calculation of a sinus of the estimated phase angle the evaluated synchronization algorithms were subjected to disturbed grid conditions. Figure 4 presents examined system structure. Simulated part is enveloped in gray rectangle. The other parts could be either sources of energy or loads, but for the grid-side converter (and synchronization algorithms) it does not matter.    The fastest response is coming from SRF-PLL, which is achieving the settling time at 10 ms. The DDSRF-PLL has the settles at 350 ms and the DSOGIQSG-PLL, with the DSOGIQSG-PLL with the positive sequence cancelation have the settling time of 250 ms value. An example of the operation under distorted conditions during voltage disturbance for SRF-PLL can be seen in Figure 6.
It can be easily observed that during normal operation the algorithm can accurately determine the grid angle. However, in the case of grid voltage disturbance the estimation is not working well. As a result undulation in the angle signal appears.
It can be easily observed that during normal operation the algorithm can accurately determine the grid angle. However, in the case of grid voltage disturbance the estimation is not working well. As a result undulation in the angle signal appears. Figure 7 presents the example algorithms operation during 15% THD grid distortion. The DDSRF-PLL, DSOGIQSG-PLL and the DSOGIQSGPSC-PLL synchronization algorithms settle down after 200 ms. The estimation error in their case is around ±1. This performance is acceptable. The SRF-PLL estimates the frequency with an error of ±10%. The estimated signal is oscillating form 45 Hz to 50 Hz.
One of the proposed design criteria is the THD of sinus of an estimated phase angle. During normal operation all of the methods having the level of the THD below 1%. However, the appearance of any kinds of disturbances (for example harmonics), results in different performance for the algorithms. For testing the of the methods performance 15% THD distortion is applied to the grid voltage. Each of the methods achieves different result.
Namely the DSOGIQSGPSC-PLL is achieving 0.1% THD of the sinus of the estimated grid angle, the DSOGIQSG-PLL has 0.5%, the DDSRF-PLL has 0.2%, SRF-PLL hast the 1.5% THD level and the αβ-filtering method with SVCO have 15% THD level. Table 1 present the performance of the selected algorithm in terms of synchronization criteria.  Table 2 presents the performance of the selected algorithms in terms of computation criteria. As it can be observed the more complex synchronization algorithm (order of signal processed, total number of mathematical operationscaling, addition, multiplications) the better performance it can achieve. This also applies to the possibility of working under different disturbances, as it was presented before. On the other hand with the more complex synchronization structure higher computational load is needed, the transient response can be longer. But overall performance, the frequency estimation accuracy, frequency adaptive operation possibility are higher. But overall performance, the frequency estimation accuracy, frequency adaptive operation possibility are higher. But overall performance, the frequency estimation accuracy, frequency adaptive operation possibility are higher.

Conclusions
This paper presents the evaluation of selected synchronization algorithms based on the proposed evaluation criteria. Choosing the appropriate synchronization method should be based on the determination of the application, power grid stiffness (with the emphasis on the power/voltage quality), possible ways of implementation. For helping in decision making, each of the selected methods were subjected to different types of tests. All of the results were collected in tablets, as well as presented in the article.