# Transient Stability Performance of Power Systems with High Share of Wind Generators Equipped with Power-Angle Modulation Controllers or Fast Local Voltage Controllers

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## Abstract

**:**

## 1. Introduction

## 2. Modelling Aspects of the Case Study

^{TM}PowerFactory

^{®}version 2018 SP1, by using a processor Intel

^{®}Core™ i7-8650 CPU with 2.11 GHz.

#### 2.1. Wind Generator Type IV with Current Control

^{TM}PowerFactory

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_{max}) that the grid side converter can handle is assumed to be 1.1 pu, in line with a theoretical expected overloading capacity for a wind generator type IV [11,12].

_{w-PAM}and a time constant T

_{w-PAM}). As explained in [5], unlike the similar approach with power system stabilizers applied in synchronous generators, the phase compensators (i.e., lead-lag filters) are not part of the PAM controller. This compensation is obviated due to the assumption of a small phase lag between the active current reference and the active power output of the grid side converter of the wind generator type IV [5]. The input of the PAM controller attached to a wind generator type IV is the rotor angle deviation between the slack synchronous generator of the system and the synchronous generator that is electrically close to the wind generator. Interested readers can find a detailed description of the working and design principles of the PAM controller in [5].

#### 2.2. Wind Generator Type IV with Fast Local Voltage Control

_{w-FLVC}and a time constant T

_{w-FLCV}).

_{w-FLVC}and a time constant T

_{w-FLCV}) is used here as well to perform such fast reaction.

#### 2.3. Synthetic Model of the GB System

## 3. Controller Tuning Based on Parametric Sensitivity

_{r}formula, typically used to find the unique permutations, or combinations, of n objects taking r items at a time.

_{w}= 60 and a time constant values T

_{w}= 0.01 s can be considered for all washout filters used in the PAM controller added on the wind generator models with current control. By contrast, gain values K

_{w-FLVC}= 0.03 and time constant values of T

_{w-FLVC}= 0.01 s can be considered for all washout filters used by the wind generator models with FLVC.

## 4. Controller Tuning Based on Optimization

#### 4.1. Formulation of the Optimization Problem

_{1}and t

_{2}are the initial and end time of the time window (i.e., time of fault occurrence and end simulation time) defined to compute the angle difference between any pair of synchronous generators of the system. The difference takes into account the deviation w.r.t. the steady-state angular value (i.e., computed in the initialization, $\Delta {\delta}_{\mathrm{ss}-i}$) of $\Delta \delta $.

**x**, shown in (6), comprises the parameters of all PAM controllers attached to the WGs that support the transient stability of the system, cf. (7).

_{w-PAM}and T

_{w-PAM}are the gain and time constant of each washout filter, respectively. N

_{WG}is the number of active PAM controllers. The minimum and maximum bounds (x

_{min}, and x

_{max}) of K

_{w-PAM}and T

_{w-PAM}were defined based on the reference values shown in [15]. For the synthetic model of the GB system with 75% share from wind power generation, there are eight WGs equipped with PAM. The locations of these WGs are highlighted in Figure 4 with red points, and they correspond with the zones 3, 5, 10, 13, 15, 16, 19, and 20 shown in Figure 4. Therefore, the solution vector

**x**has 16 optimization variables (eight WGs, each one with two optimization variables, i.e., K

_{w-PAM}and T

_{w-PAM}).

^{TM}PowerFactory

^{®}version 2018 SP1). The solution of the problem is done by using a heuristic optimization algorithm. In existing literature of heuristic optimization, there are several types of algorithms that could be used for this purpose. Among these algorithms, the mean-variance mapping optimization algorithm is selected (MVMO) due to its outstanding performance in solving different types of computational expensive optimization problems [16], including several applications to optimization problems in the field of power systems [4,17]. The optimal tuning of MVMO and a comparison of its performance (to solve the optimal tuning of PAM) against the performance of other competitive algorithms is being investigated and will be presented in a future publication. The basic notions of MVMO and its use to tackle the optimal tuning of PAM are concisely presented in the next sub-section.

#### 4.2. Solution of the Optimization Based on MVMO Algorithm

**x**based on the fitness/objective function value associated with the previously evaluated solution vectors. Interested readers can find a detailed description of the general working principle of MVMO in [16]. In this paper, the emphasis in on the overview of the procedure based on MVMO to tackle the optimal tuning of PAM, which is illustrated in Figure 10.

**x**. Each random value follows a uniform probabilistic distribution function, which is defined between the minimum (min) and maximum (max) bounds of the corresponding optimization variable. The initial solution vector

**x**is normalized, i.e., each random value is transformed from the original min-max scale into the range 0–1. The normalized solution vector is fed into the block of fitness evaluation, which has two internal functions: one function is used to de-normalize elements of the solution vector (i.e., K

_{w-PAM_i}and T

_{w-PAM_i}), whereas the other function is used substitute the values of K

_{w-PAM_i}and T

_{w-PAM_i}in the dynamic model of each WG with PAM, and to run the RMS time domain simulations needed to evaluate (3) and (4). A static penalty scheme is used to penalize the objective function value by adding a high value (e.g., 1 × 10

^{6}) when (4) is not satisfied. The penalized objective function value constitutes the so-called fitness value.

_{w-PAM_i}and T

_{w-PAM_i}) of the first ranked solution are kept in the new solution vector, whereas the remaining values are generated by using the so-called mapping function [16]. The amount of elements and their indexes (positions) within the new solution vector that are generated via the mapping function are selected based on a quadratic function (evaluated as a function of the number of maximum function evaluations, and computed between the half of all the total number of optimization variables and only one optimization variable) and a random-sequential strategy, respectively [16]. The iteration loop and the whole MVMO algorithm stops when a maximum number of fitness evaluations is done. Given the computationally expensive nature of the problem of optimal tuning of PAM, it was selected to have a maximum of 50 fitness evaluations, which is the same number of calculations of margin performed by parametric sensitivity in in Section 3 (cf. Table 1 and Table 2), and it is also in line with the number of function evaluations that are usually selected as stop criteria in different competitions on computationally expensive optimization problems [16]. The initialization, fitness evaluation, and iterative loop of MVMO are performed in Python™ 3.8, whereas the RMS simulations needed for fitness evaluation are done in DIgSILENT

^{TM}PowerFactory

^{®}version 2018 SP1.

#### 4.3. Optimization Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

WG | Wind Generator |

SG | Synchronous Generator |

PAM | Power-Angle Modulation |

PCC | Point of Common Coupling |

FRT | Fault ride-through |

MVMO | Mean-variance mapping optimization |

FLVC | Fast local voltage control |

GB | Great Britain |

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**Figure 1.**Structure of the model wind generator type IV with current control: (

**a**) core functions based on the IEC 61400-27-1 international standard; (

**b**) addition of the power–angle modulation (PAM) controller for modification of the active current reference (i

_{dref}) [5].

**Figure 2.**Reactive power–voltage control channel of a wind generator type IV with fast local voltage control (FLVC) [7].

**Figure 3.**Active power control loop of a wind generator type IV with FLVC [7].

**Figure 4.**Geographical spread of conventional power plants with only synchronous generators (points with blue color); only wind power plants (points with green color) and zones with combined power production (points with red color), in the synthetic model of the Great Britain system. The location of the generator that serves as a reference for relative rotor angle position is indicated with the black arrow [5].

**Figure 6.**Dynamic response of rotor angles of the Scottish area for a three-phase fault at Line 6–9. Wind generators with current control and PAM vs. Wind Generators with FLVC.

**Figure 7.**Dynamic response of rotor angles of the east area for a three-phase fault at Line 6–9. Wind generators with current control and PAM vs. Wind Generators with FLVC.

**Figure 8.**Dynamic response of rotor angles of the west area for a three-phase fault at Line 6–9. Wind generators with current control and PAM vs. Wind Generators with FLVC.

**Figure 9.**Dynamic response of rotor angles of the North area for a three-phase fault at Line 6–9. Wind generators with current control and PAM vs. Wind Generators with FLVC.

**Figure 10.**Solution of optimal tuning of PAM based on mean-variance mapping optimization (MVMO) [16].

**Figure 11.**Dynamic response of rotor angles of the Scottish area when PAM controllers of the wind generators (WGs) are tuned based on parametric sensitivity or via optimization by using the MVMO algorithm.

K_{w-PAM} (pu) | T_{w}_{-PAM} = 0.01 s | T_{w}_{-PAM} = 0.1 s | T_{w}_{-PAM} = 0.5 s | T_{w}_{-PAM} = 1 s | T_{w}_{-PAM} = 2 s |
---|---|---|---|---|---|

5 | 113.573924 | 110.993499 | 106.889155 | 106.82208 | 109.983239 |

10 | 114.194974 | 110.533619 | 106.49231 | 106.549299 | 109.138616 |

15 | 114.33812 | 110.401192 | 106.874311 | 106.77717 | 107.551964 |

20 | 114.46991 | 110.8884 | 107.795573 | 107.658466 | 107.040612 |

30 | 114.47489 | 111.32369 | 107.782444 | 108.517307 | 106.607745 |

40 | 114.60601 | 111.33531 | 107.972349 | 108.555885 | 106.040406 |

50 | 114.555886 | 110.48688 | 107.86319 | 108.535094 | 106.362925 |

60 | 114.644445 | 108.825084 | 107.82782 | 108.679708 | 105.885481 |

70 | 114.596488 | 107.124135 | 107.462067 | 108.7965 | 105.865487 |

80 | 114.561704 | 106.133411 | 107.47635 | 108.743309 | 105.960977 |

K_{w-FLVC} (pu) | T_{w-FLVC} = 0.01 s | T_{w-FLVC} = 0.1 s | T_{w-FLVC} = 0.5 s | T_{w-FLVC} = 1 s | T_{w-FLVC} = 2 s |
---|---|---|---|---|---|

0.01 | 116.764009 | 116.740816 | 116.732117 | 116.726369 | 116.768093 |

0.03 | 116.710271 | 116.69212 | 116.682921 | 116.68814 | 116.700344 |

0.06 | 116.705135 | 116.63646 | 116.528762 | 116.51443 | 116.495143 |

0.09 | 116.673304 | 116.549523 | 116.160469 | 116.079402 | 116.088324 |

0.12 | 116.632554 | 109.881039 | 105.5759 | 106.079699 | 113.508529 |

0.15 | 116.656753 | 83.722557 | 100.674551 | 83.588175 | 98.72954 |

0.2 | 111.403347 | 76.145396 | 72.293358 | 71.37069 | 71.656834 |

0.25 | 61.237631 | 75.672211 | 73.583924 | 71.742324 | 71.298735 |

1 | 54.433136 | 63.914148 | 53.563227 | 51.301188 | 63.508494 |

Parameters | Value |
---|---|

Archive Size | 5 |

Initial Scaling Factor | 1 |

Final Scaling Factor | 30 |

Initial Number of Mutated Variables | 8 |

Final Number of Mutated Variables | 1 |

Min.–Max. bounds of washout gain (K_{w-PAM_i}) | 1–100 pu |

Min.–Max. bounds of washout time constant (K_{w-PAM_i}) | 0.003–0.005 s |

WG with PAM | K_{w-PAM_i} (pu) | K_{w-PAM_i} (s) |
---|---|---|

WG3 | 19.67341 | 0.01911 |

WG5 | 29.47981 | 0.01426 |

WG10 | 49.28106 | 0.01001 |

WG13 | 36.92419 | 0.01790 |

WG15 | 52.57345 | 0.01397 |

WG16 | 26.81379 | 0.00884 |

WG19 | 69.33790 | 0.00874 |

WG20 | 13.28935 | 0.00936 |

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## Share and Cite

**MDPI and ACS Style**

Perilla, A.; Papadakis, S.; Rueda Torres, J.L.; van der Meijden, M.; Palensky, P.; Gonzalez-Longatt, F.
Transient Stability Performance of Power Systems with High Share of Wind Generators Equipped with Power-Angle Modulation Controllers or Fast Local Voltage Controllers. *Energies* **2020**, *13*, 4205.
https://doi.org/10.3390/en13164205

**AMA Style**

Perilla A, Papadakis S, Rueda Torres JL, van der Meijden M, Palensky P, Gonzalez-Longatt F.
Transient Stability Performance of Power Systems with High Share of Wind Generators Equipped with Power-Angle Modulation Controllers or Fast Local Voltage Controllers. *Energies*. 2020; 13(16):4205.
https://doi.org/10.3390/en13164205

**Chicago/Turabian Style**

Perilla, Arcadio, Stelios Papadakis, Jose Luis Rueda Torres, Mart van der Meijden, Peter Palensky, and Francisco Gonzalez-Longatt.
2020. "Transient Stability Performance of Power Systems with High Share of Wind Generators Equipped with Power-Angle Modulation Controllers or Fast Local Voltage Controllers" *Energies* 13, no. 16: 4205.
https://doi.org/10.3390/en13164205