# A Comprehensive Review of Power System Stabilizers

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## Abstract

**:**

## 1. Introduction

## 2. Classic Solutions for PSSs

## 3. Artificial-Intelligence-Based PSSs

## 4. Modern Control Systems in PSs

## 5. PSSs in Networks with Renewable Sources

## 6. Use of New Optimization Methods for Tuning PSSs

## 7. Discussion and Problems

## 8. Conclusions

- Performing transient analyses only for the simplest systems and network systems (e.g., for the SKIB system) without verifying the results in a more complex system;
- Basing only on standard parameters of mathematical models of PS elements without referring to the problems of estimating reliable parameters of these models;
- Narrow conclusions only in the context of the research carried out without reference to technical problems occurring in real systems;
- Presentation of only a narrow part of the obtained results;
- Omitting technically important problems in scientific research, including interactions between different waveforms occurring in a real system;
- Presentation of unusual behaviors of a system that, without any additional explanation, may be considered factual errors.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Power System (Test System) | Number of Papers | References | ||
---|---|---|---|---|

In General | In Chapters | |||

SMIB (single-machine infinity bus) | 79 | Ch. 2 | 10 | [14,20,21,29,30,31,32,33,34,38] |

Ch. 3 | 21 | [51,55,56,57,58,60,61,64,65,66,67,68,69,70,71,72,73,78,80,81,83] | ||

Ch. 4 | 23 | [7,80,84,86,88,89,91,92,93,96,98,99,102,103,104,105,106,118,122,125,126,127,129,130] | ||

Ch. 5 | 3 | [135,139,142] | ||

Ch. 6 | 22 | [133,150,151,152,156,163,164,166,168,173,175,179,182,183,184,185,186,187,188,189,190,191] | ||

4M2A (two-area four-machine) power system | 58 | Ch. 2 | 6 | [13,16,18,19,23,49] |

Ch. 3 | 14 | [52,53,54,56,57,59,63,74,75,76,78,80,81,82] | ||

Ch. 4 | 16 | [87,88,94,95,97,101,106,107,109,110,114,115,116,125,131,132] | ||

Ch. 5 | 3 | [133,138,139] | ||

Ch. 6 | 19 | [133,150,153,155,170,171,176,177,189,190,195,196,197,198,199,200,201,202,203] | ||

New England 10 (10-machine, 39-bus power system) | 26 | Ch. 2 | 2 | [10,40] |

Ch. 3 | 2 | [82,83] | ||

Ch. 4 | 5 | [85,107,108,113,116] | ||

Ch. 5 | 1 | [133] | ||

Ch. 6 | 16 | [133,157,158,161,162,169,174,176,178,199,201,202,204,205,206,209] | ||

New England 16 (16-machine, 68-bus power system) | 8 | Ch. 3 | 1 | [79] |

Ch. 4 | 3 | [111,112,124] | ||

Ch. 5 | 1 | [137] | ||

Ch. 6 | 3 | [159,172,203] | ||

WSCC (three-machine power system) | 23 | Ch. 2 | 3 | [17,35,36] |

Ch. 3 | 2 | [79,83] | ||

Ch. 4 | 6 | [85,117,120,121,123,128] | ||

Ch. 5 | 3 | [134,141,147] | ||

Ch. 6 | 9 | [151,158,160,161,167,191,192,193,194] | ||

NORDIC (20-machine multivoltage power system) | 2 | Ch. 2 | 2 | [9,42] |

IEEE 14 (5-machine power system) | 5 | Ch. 2 | 3 | [10,26,28] |

Ch. 5 | 2 | [141,147] | ||

Other | 32 | Ch. 2 | 10 | [12,13,15,24,25,27,37,40,41,49] |

Ch. 3 | 4 | [53,58,62,77] | ||

Ch. 4 | 6 | [87,90,95,104,119,124] | ||

Ch. 5 | 5 | [136,143,144,145,146] | ||

Ch. 6 | 7 | [154,165,200,206,207,208,209] |

**Table A2.**Types of stabilizers used (division according to [50]).

PSS | Number of Papers | References | ||
---|---|---|---|---|

In General | In Chapters | |||

PSS1A (lead-lag PSS) | 70 | Ch. 2 | 19 | [13,14,15,16,18,19,20,21,22,25,26,28,31,33,35,36,40,44,49] |

Ch. 4 | 9 | [108,120,121,124,126,128,129,130,131] | ||

Ch. 6 | 42 | [133,150,151,152,155,156,159,160,161,162,163,164,166,167,168,169,170,171,172,174,176,177,182,184,188,189,190,191,192,193,194,195,196,197,198,200,201,202,203,204,205,206] | ||

PSS2A | 8 | Ch. 2 | 5 | [21,24,29,34,41] |

Ch. 6 | 3 | [154,165,180] | ||

PSS2B | 3 | Ch. 2 | 2 | [26,43] |

Ch. 6 | 1 | [199] | ||

PSS3B | 5 | Ch. 2 | 3 | [27,30,37] |

Ch. 6 | 2 | [175,207] | ||

PSS4B/PSS4C | 12 | Ch. 2 | 5 | [19,23,26,40,49] |

Ch. 4 | 5 | [93,95,100,104,106] | ||

Ch. 6 | 2 | [158,209] | ||

PID-PSS | 11 | Ch. 2 | 1 | [20] |

Ch. 3 | 6 | [54,59,60,61,62,63] | ||

Ch. 4 | 1 | [84] | ||

Ch. 6 | 3 | [149,153,183] | ||

Other | 17 | Ch. 2 | 3 | [17,38,39] |

Ch. 4 | 10 | [86,92,97,98,99,101,103,105,115,125] | ||

Ch. 6 | 4 | [157,185,186,208] |

Tools | Number of Papers | References | ||
---|---|---|---|---|

In General | In Chapters | |||

Matlab | 66 | Ch. 2 | 9 | [14,15,16,18,20,22,30,32,36] |

Ch. 3 | 22 | [51,52,53,55,56,57,59,60,61,63,64,65,66,68,69,71,74,75,76,78,79,80,83] | ||

Ch. 4 | 13 | [80,85,90,91,96,105,106,110,116,118,122,128,129] | ||

Ch. 5 | 5 | [133,138,139,144,148] | ||

Ch. 6 | 17 | [153,155,156,157,165,166,168,170,174,182,184,187,188,189,193,196,204] | ||

DigSILENT PowerFactory | 1 | Ch. 2 | 1 | [39] |

ETAP | 2 | Ch. 2 | 1 | [40] |

Ch. 5 | 1 | [147] | ||

PSCAD | Ch. 2 | 1 | [27] | |

Power World Simulator | 1 | Ch. 2 | 1 | [35] |

PSASP7 | 1 | Ch. 2 | 1 | [29] |

PSS-E | 4 | Ch. 2 | 2 | [25,46] |

Ch. 6 | 2 | [190,207] | ||

Scilab | 1 | Ch. 2 | 1 | [31] |

NEPLAN | 1 | Ch. 3 | 1 | [55] |

MiPower | 1 | Ch. 5 | 1 | [141] |

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**Figure 2.**Graphical interpretation of an incorrect comparison of solutions based on only one criterion (A, B—original solutions; ΔX—vector of change in the properties of solution A transforming it into a new solution A’).

**Table 1.**Detailed comments on selected papers analyzed in Section 2.

Detailed Comments | Paper |
---|---|

A paper on general issues related to PS stability. PSs with different, complex structures of power network were analyzed. Particular attention was paid to the problems of PS management (its control) resulting from current changes in the power network. Only 52 items were referred to in the literature list, but the paper should be treated as a literature review in the analyzed topic. The authors, through a critical analysis of the existing solutions, presented a possible transition path from the current, hierarchical control system (PS) to a new structure that, according to the authors, supports the decarbonization of electricity generation. | [8] |

In this paper, the authors presented the problems occurring in PSs related to the relatively high power generation by photovoltaic (PV) sources and proposed solutions that could help reduce these problems. | [9] |

This paper presents the current problem regarding the increase in the number of electricity sources characterized by stochastic changes in the generated power, which result in stochastic changes in frequency in PSs. The authors proposed new methods of PS modeling, taking into account distributed generation with stochastic properties. | [10] |

This paper describes the problems related to PSSs installed in an Indian PS. The authors presented many interesting technical problems. | [11] |

In this paper, the authors proposed the use of properly tuned (e.g., optimized by simultaneous tuning of many stabilizers) classic PSSs to damp inter-area oscillations as an alternative to expensive FACTS systems. | [13] |

This paper, through a thorough analysis of the hydraulic-mechanical part of a generator drive system, presents a justification for the need to take into account turbine model in electromechanical tests of transients, as well as in the optimization of PSS parameters and voltage regulators (AVRs). However, the authors in their research unfortunately used a simplified generator and network model (SMIB), which might lead to a lack of reliability of the obtained results. | [14] |

The authors presented a solution to the problem of limiting the allowable gain in a PSS main circuit resulting from the provisions of the “guide for setting test of power system stabilizer” of China. By modifying the structure of a PSS, improvement in the damping of inter-area oscillations was achieved. | [15] |

In this paper, an interesting modification of the structure of a lead-lag single-entry power system stabilizer improving its properties was presented. | [16] |

The paper concerns research related to the first nuclear power plant in Egypt (El-Dabaa). The authors, apart from specifying the stabilizer for the actual generating unit, presented the parameters of a mathematical model of this unit. | [17] |

The authors presented research leading to the elimination of low-frequency swings in PSs. The influence of several PSSs installed in Spanish power plants on the damping of inter-area swings (0.15 Hz) occurring in the European system was analyzed. The appendix to the paper provides the parameters of the mathematical models used. | [24] |

In this paper, an analysis of the event (disturbance) that took place in Canada on 22 May 2018 is presented. This event caused power oscillations in a PS. The PSS-E program from Siemens was used for the simulation tests. | [25] |

In this paper, research on the Iraqi Super Grid is presented. Unfortunately, despite being a case study, only the results for a 14-machine test system (South-East Australian) were included. | [26] |

The authors of this paper used Power System Computer-Aided Design software (PSCAD) to carry out simulation tests. The Tehri Hydropower Plant (HPP) and Koteshwar HPP high-power hydropower plants in India, part of the Tehri Hydro Power Complex with an installed capacity of 2400 MW, were investigated. | [27] |

This paper concerns a technical problem that occurs in real control systems, i.e., the influence of the PSS dead zone on the operation of a stabilizer and the principles of design of this dead zone. | [28] |

The authors, using research on transient states in PSs, presented an interesting alternative to Matlab, i.e., the SCILAB program. | [31] |

The paper presents, among others, measurements made at the Power System Stability Laboratory of TU Sofia. The authors presented a lot of results of simulation tests obtained with the use of ready-made models from the Matlab toolbox. | [32] |

The authors presented measurements and analyses of the operation of a power plant in Inner Mongolia (China) under the load of two generators at 70% and 30% of the rated power. | [34] |

Using stability studies, the authors presented the possibilities of the Power World Simulator program for the investigation of transients in PSs. | [35] |

In this paper, an analysis of the influence of excitation systems on electromechanical transients is presented. Two types of excitation systems, DC1A and ST1A [50], were tested. | [36] |

This paper presents a two-input, “single-band” stabilizer of the PSS3B type rarely described in the literature. According to the author, the paper aimed to fill the gap in the PSS3B’s ability to provide good phase compensation for a wide frequency range. Two PS models, three- and two- machine ones, were analyzed. The summary presented conclusions and technical recommendations, e.g., regarding the advantages and disadvantages of the PSS3B stabilizer, including the possibility of damping torsional oscillations. | [37] |

Using DigSILENT Power Factory software, the authors presented the risks associated with increase in PS power generation by wind turbines. | [39] |

Using the ETAP program, the authors presented the problem of transients occurring in a PS with connected generating units, including wind, photovoltaic, and Diesel engine. | [40] |

The authors present studies on the actual fragment of the large PS (Yunnan - China Southern) containing HVDC links. The analyzed PS fragment contains as many as 7 HVDC links. The paper presents a solution to the described problems. | [41] |

**Table 2.**Detailed comments on selected papers analyzed in Section 3.

Detailed Comments | Paper |
---|---|

The introduction to this paper contains a very extensive literature review containing 42 items. | [54] |

One of the goals of the tuning described in the paper was to minimize the overshoot and maximize the undershoot of the angular speed deviation. In this context, it seems that there was lack of in-depth analysis of the impact of such a criterion on the generator terminal voltage waveforms. | [55] |

When examining the transients in a SMIB system, the authors assumed, among others, an unusual disturbance in the form of a load power change of 0.2 p.u. | [64] |

The authors emphasized the practical importance of classic PSSs (i.e., not based on artificial intelligence) resulting from their simpler structure and ease of tuning. | [78] |

It is worth comparing these two selected papers due to the very similar, partially repeated investigations. One paper [68] is from the conference taking place on 30 April–3 May 2017 (date added to IEEE Xplore: 15 June 2017), while the other paper [67] is from the conference on 21–24 May 2017 (date added to IEEE Xplore: 7 August 2017). | [67,68] |

In Section 2 of this paper, the concept of modeling uncertainty used in creating the model was introduced. To identify the system, a test signal introduced as a reference value to the generator excitation system was used. The signal was a square wave with a relatively large amplitude of ±0.2 p.u. | [76] |

The authors of this paper presented research in which PS electromechanical transients caused, among others, by asymmetrical short circuits, i.e., single-phase fault-to-ground, were analyzed. Nevertheless, the applied mathematical model did not take into account asymmetric states and did not assume subtransient symmetry (Xd” for all three machines was different than Xq”—a more extensive description of the model used is presented in [47] from the reference list of this paper). | [77] |

The paper provides a broad review of the literature on various ways of stabilizing PSs. | [79] |

In the introduction to this paper, the authors presented a list of selected failures caused by power swings in PSs. | [83] |

**Table 3.**Detailed comments on selected papers analyzed in Section 4.

Detailed Comments | Paper |
---|---|

In the introduction to this paper, an extensive literature review was carried out in which as many as 49 items were analyzed. In the research, a step change in the reference voltage from 0.9 to 0.8 p.u was used as the cause of the transient. When analyzing the recorded waveforms during laboratory tests, a typical phenomenon could be noticed: improvement in the generator power waveform caused by the operation of PSS deteriorated the voltage waveform (Figure 5, page 220). | [7] |

This paper presents a PSS based on the use of artificial intelligence methods as a stabilizer for a static synchronous series compensator (SSSC). This is a good example illustrating the fact that the use of a PSS in a PS is no longer reserved only for the excitation systems of synchronous generators. Such a situation has been forced by changes in PS structure and, in particular, the connection of renewable sources that adversely affect the stability of a system. | [80] |

This paper presents comparative studies of the effectiveness of the operation of many different types of PSSs working in SMIBs. | [84] |

In this paper, a stabilizer using Park real-time transformation was proposed. The obtained results were experimentally verified using a synchronous generator with an apparent power of 83 kVA. | [86] |

In this paper, a specific problem observed in a real PS is presented. “In April 2016, when an asynchronous connection test was performed to connect the Yunnan power grid to China Southern Power Grid (main grid), a ultra-low-frequency oscillations arose in the Yunnan power grid with an oscillation frequency of 0.05 Hz and amplitude of 0.1 Hz.” (page 1) The authors modeled this case and proposed a solution to the problem. | [87] |

In simulation studies, the authors analyzed changes untypical for real systems causing the transient state in a PS, namely a large step change of 30% in field voltage and a step change in mechanical power of up to 10 p.u. for a duration of 10 ms (page 5059). | [88] |

This paper contains an extensive theoretical introduction. The authors referred to only 20 items; however, the issues under consideration were described in detail. | [91] |

In the simulation studies presented in this paper, the authors used a 10% step change in mechanical torque as the cause of a transient state in a PS. It is also worth noting that, in the tested PS, in the steady state (before and after the disturbance), the terminal voltage had a large value of 1.172 p.u. (Figure 4b, page 714). The authors included only two sentences in the conclusion. | [92] |

Using the example of this paper, it is worth asking the following question: why is a “broadband” PSS (which is for damping electromechanical swings in a wide frequency range) such as a PSS4B tested in a single-machine system (SMIB)? In real PSs, power swings are usually associated with the simultaneous influence of many generating units. | [93] |

This paper presents research on two PSs. In the first part, the authors used a popular 4M2A system. The second part describes a large system—the North China System—consisting of 547 generating units and 8647 lines. It is a pity that the authors presented so few research results and did not show selected waveforms for the large PS. | [95] |

This paper presents research on a “multi-band” system stabilizer (MBPSS) with a different structure than the PSS4B known from the literature. An MBPSS is for simultaneously damping electromechanical swings of many frequencies. It is worth paying attention to the extensive literature review, which included as many as 52 items. | [104] |

In the PS analyzed by the authors, in the steady state (after introducing the disturbance) there was a power imbalance, which was evidenced by a non-zero deviation in the angular speed of the rotors of synchronous generators. It should be emphasized that, in real systems, such an imbalance is corrected by appropriate control systems. | [106] |

In a 4M2A system, the influence of load characteristics on PS operation was analyzed. Two equivalent induction motors constituting dynamic loads were used as the load. It is worth emphasizing that, in a real PS, the loads are of different character. The differences in the character of loads were considered later in the paper, additionally treating loads as a source of uncertainty, which is a relatively rare but deliberate approach in the investigation of PS stability. | [107] |

In the introduction, a comparative analysis of various solutions with energy storage improving the operation of PSs in transient states was made (Table 1, page 3). A solution based on distributed measurements was proposed. | [119] |

As one of the issues considered in this paper, the rarely discussed problem of optimizing the location of PSS installation is presented. This problem was solved on the basis of an analysis of participation factors of rotor speed. Based on the results, it was observed (which is already known from the literature) that the appropriate allocation of a PSS improved the damping of transient waveforms in a PS. | [131] |

**Table 4.**Detailed comments on selected papers analyzed in Section 5.

Detailed Comments | Paper |
---|---|

This paper contains a comparison of optimization algorithms, including the collective decision optimization (CDO) algorithm, the grasshopper optimization algorithm (GOA), and the salp swarm slgorithm (SSA), used for the optimization of power system stabilizers in a network with installed photovoltaic sources. | [134] |

In this paper, a one-input lead-lag stabilizer with only one phase compensation element was analyzed. | [135] |

In this paper, it was proved that the regulation of renewable sources (in particular, wind farms), despite a reduction in the power generated in the source, was beneficial because the lack of such regulation had many more dangerous consequences, including the possibility of a failure in a PS and the related financial consequences. | [138] |

In this paper, the problem of the uncertainty of parameters of a PS mathematical model was taken into account. The paper described the tests at a hydroelectric power plant in Brazil (a power plant with 23 generating units with apparent power of 350 MVA each). In the conclusion, the authors stated that the safe application of adaptive control techniques in real, large power plants is a challenge, as opposed to research based only on simplified computational models. The reason was that real systems have many nonlinearities and uncertainties of parameters that may not be taken into account in simplified calculation models. The authors of the publication showed improvement in the waveforms in simulation tests by applying a new regulation technique. However, the improvement in the waveforms for the real object was not significant. It should be emphasized that such a situation is natural. | [142] |

The authors analyzed an actual PS associated with the hydroelectric dam and power plant in Aswan, Egypt. Unfortunately, in the paper, there was a lack of measurement verification of the analyzed case. | [143] |

The authors used ready-made mathematical models of PS elements available in Matlab Toolbox. It should be emphasized that the authors analyzed symmetrical and asymmetrical short circuits (single- and two-phase to ground) without specifying in the content of the paper whether the mathematical model used allowed for modeling the phenomena occurring in asymmetrical transient states. The authors analyzed the reactive power waveforms during transient states, as well as asymmetrical ones, i.e., with distorted waveforms (Figure 7, page 5040). However, the paper did not refer to the applied power theory according to which the authors determined the reactive power waveforms in the tested system. | [144] |

The paper contains investigations of a PS with photovoltaic sources and energy storage in steady and transient states. The conclusion to the paper consisted of only 62 words. They were very laconic and obvious. | [145] |

The authors investigated transients in PSs with fractional-order control systems. These studies concerned, among others, the system response to a step change in the voltage reference value, including a surprisingly large change from 0 to 1 p.u. (Figure 2b, page 4). | [146] |

This paper contains practical postulates, e.g., concerning an assessment of critical short-circuit times and stability margin in the study of power microgrids. In the paper, an analysis method that allowed studying the stability and influence of PSSs on microgrids was proposed. | [148] |

**Table 5.**Detailed comments on selected papers analyzed in Section 6.

Detailed Comments | Paper |
---|---|

In this paper, three different optimization algorithms for PSS parameters were compared. The results were compared with a “classic” PSS (as the authors called it). Unfortunately, the conclusions concerned only the analyzed algorithms and did not refer to technical problems in real systems. | [153] |

In the introduction to this paper, the authors analyzed the content of as many as 48 literature items. | [152] |

As a disturbance in the steady state, the authors used, among others, a step change in the driving torque. | [156,185,189] |

The reference stabilizer in this research was the “classic” PSS. Unfortunately, the system with the reference stabilizer was unstable. Therefore, it was difficult to assess the solution presented in the paper. | [166] |

In these papers, the authors provide a broad review of the literature. | [170,183] |

The literature review in the introduction to this paper contained 36 items. | [171] |

The paper is one of the few that analyzed the problem of determining the place of PSS installation. The analysis was based on the study of eigenvalues of the PS model state matrix. | [174] |

In the introduction, the authors presented a review of 22 literature items. A two-input stabilizer, one input signal of which was a hard-to-measure drive torque signal, was investigated. | [175] |

Only the eigenvalues of the state matrix of the investigated PS were analyzed in this paper. Despite the lack of analysis of the waveforms in the test system (without linearization), the following was stated in the conclusions: “The results indicated that the system remained stable, with high damping margin, even in different loading scenarios, demonstrating the robustness of the parameterization obtained.” (page 772) | [178] |

This review paper contained extensive descriptions of the analyzed problem. It deserves attention despite the fact that it does not apply directly to PSS tuning (except for one literature item regarding the coordinated design of a PSS and an SVC to maximize damping). However, the paper is an example of reliable literature research on optimization algorithms. | [181] |

The authors presented a method of PSS parameter optimization based on the analysis of the position of the system state matrix eigenvalues on a complex plane. A slight improvement compared to the “classic” solution was obtained. This fact should not come as a surprise, as the actual system was analyzed in the paper. Unfortunately, the authors presented only the instantaneous power waveforms, and in this case, the generator stator voltage waveforms would also be extremely interesting. There was also a lack of research into the effectiveness of the proposed solution with regard to a larger PS. | [187] |

This paper presents an interesting, practical tool for PSS tuning. | [190] |

In the introduction, the authors reviewed only four literature items. | [192] |

This paper deals with the interesting issue of situational awareness, i.e., the knowledge of the current and future PS state. | [198] |

This paper presents an analysis of rotor angular speed after a short circuit lasting 80 ms, with the time of observation of the waveforms assumed to be as high as 100 s, during which the speed oscillated. | [199] |

This paper presents an interesting method of designing a PSS for complex PSs. The method was based on the SMIB model. | [201] |

Wavelet transform was used in this research on PS stability. As part of the introduction, the authors presented a description of the issues contained in 33 papers. | [203] |

This paper includes a very extensive introduction with an analysis of various tuning methods. The content of the paper presents an extended description of selected algorithms. The authors presented a comparison of six different tuning methods and performed a convergence analysis. | [209] |

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## Share and Cite

**MDPI and ACS Style**

Nocoń, A.; Paszek, S.
A Comprehensive Review of Power System Stabilizers. *Energies* **2023**, *16*, 1945.
https://doi.org/10.3390/en16041945

**AMA Style**

Nocoń A, Paszek S.
A Comprehensive Review of Power System Stabilizers. *Energies*. 2023; 16(4):1945.
https://doi.org/10.3390/en16041945

**Chicago/Turabian Style**

Nocoń, Adrian, and Stefan Paszek.
2023. "A Comprehensive Review of Power System Stabilizers" *Energies* 16, no. 4: 1945.
https://doi.org/10.3390/en16041945