# Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines

^{*}

## Abstract

**:**

## 1. Introduction

_{var}) controller [19] is applied.

## 2. Case Study

_{E}

_{30}in Figure 1. In this case study, the residual load, which either has to be covered by the 5M, or by power import from the external grid, is called P

_{C}(see Figure 1).

_{C}, P

_{E}

_{30}, wind speed, grid frequency, f

_{grid}, and the ambient temperature were measured on 05 April 2017, which was a day with changing and eventually quite good wind conditions and a typical load profile for the campus. The measurements of P

_{C}, P

_{E}

_{30}, wind speed, and the ambient temperature are already published [5]; hence, they are not reproduced here.

_{grid}, is essential [22]. Therefore, Figure 2 shows f

_{grid}, the calculated ROCOF and the frequency spectrum of f

_{grid}and the ROCOF as measured on 5 April 2017.

## 3. WT Simulation Model

#### 3.1. Power Controller

#### 3.2. Continuous Feed-In Management Control

_{TR}) and too high voltage, V

_{C}, in the campus grid (see Figure 1). Consequently, FIM becomes necessary in situations of high wind speeds, and/or very low local consumption in the campus grid. The FIM controller, which is shown in Figure 6 addresses the thermal loading of the transformer as well as V

_{C}[5].

#### 3.3. Continuous Inertial Response Control

_{var}) controller has numerous advantages [19]. The main motivation for this controller is that WTs can continuously contribute to the inertia in the power system, without running the risk that drastic negative ROCOFs lead to disconnections of the WT. In principle, a WT with the H

_{var}controller behaves like a synchronous generator. However, unlike a synchronous generator, the rotational speed of a WT is not constant. In an AC-connected synchronous generator, the rotor speed varies with f

_{grid}. Since in most power systems f

_{grid}varies only in a very narrow band, the rotational speed of AC connected synchronous generators can be considered almost constant. In a WT, however, the rotational speed is not determined by f

_{grid}, but by the wind speed. Hence, it can vary in a wide range. Therefore, the H

_{var}controller varies the inertia constant, which is emulated by the WT, according to the current rotational speed, see Figure 5. At rated speed, the variable inertia constant is equal to the value demanded by the grid operator (H

_{dem}).

_{var}controller defines an inertia constant for every prevailing rotational speed [9]:

_{var}controller: Since the inertia contribution drops to zero when the rotational speed is as low as the cut-in speed, the WT never disconnects from drastic negative ROCOFs. At low wind speeds (i.e., also low rotational speed and low power), a single WT provides little inertia. However, this seeming disadvantage is not a problem for the grid: in such a situation, the prevailing load is either supplied by a larger number of WTs (which in total supply sufficient inertia) or by other generators, which can also supply the needed inertia. Equation (2) and Equation (3) reveal that the contributed inertia is scaled with the current speed and therefore also with current power infeed of the WT. Hence, if low wind speed allows one WT to produce only little power, then the overall load in the grid has to be covered by a larger number of WTs. This automatically distributes the generation of H

_{dem}over all WTs that are equipped with an H

_{var}controller. In total the grid is supplied with the inertia that the grid operator demands.

#### 3.4. Combined Control Circuit

_{var}controller interact with the 5M WT via the power setpoint, P

_{dem}. Figure 6 illustrates that the continuous FIM controller responds to the transformer temperature, ϑ

_{TR}, and the voltage in the campus grid, V

_{C}. The H

_{var}controller generates the H

_{var}from the demanded inertia constant, H

_{dem}, and the generator speed. The inertial response power setpoint, P

_{SI_varH}, is a result of the ROCOF, f

_{grid}and the current H

_{var}, see Equation (4) [19].

_{dem}has no impact on the rotational speed reference of the WT. Hence, even with P

_{dem}< 1 pu, the speed of the WT reaches rated speed if the wind speed suffices [21]. This characteristic is beneficial for continuous inertia provision, as it allows the WT to produce H

_{dem}for a maximum duration.

_{dem}, they could, potentially, also interfere with each other. However, Figure 6 shows that they are decoupled from each other by the different controllers. Due to the long thermal time constant of the transformer, the temperature controller lets P

_{max_TR}respond only very slowly. P

_{max_TR_volt}has an instantaneous effect on P

_{max_TR_lim}. This variable only serves as setpoint for the P

_{dem}controller, which is tuned to fit the vibratory behaviour of the WT. P

_{SI_varH}, however, acts instantaneously on P

_{dem}. With this configuration, inertia contribution is clearly prioritized over FIM. Even if P

_{SI_varH}leads to V

_{C}violating any limits, this can only impact on the power output of the WT via the dynamics of the P

_{dem}controller. This prioritization is justified, as power from inertia contribution oscillates around zero. Hence, it has no lasting impact on the transformer temperature. However, if inertial power is essential for maintaining angular stability, violations of voltage limits are of subordinate importance. This is discussed further in the section on frequency domain analysis.

_{var}controller was initially published with a functionality to mitigate potentially harmful excitations on the mechanical structure of the WT [19]. This functionality is deliberately omitted here to be able to assess the maximum inertial response capabilities. At the same time, it is the goal of this paper to reveal the maximum negative impact of inertial response on the WT. Hence, the worst case scenario is considered here.

_{var}controller inherently distributed the inertial power generation among any participating generators. Even in a wind farm, where wake effects lead to grossly differing operating points of neighbouring WTs, the H

_{var}controller assures that the inertia contribution of individual WTs is adapted to their instantaneous capabilities.

## 4. Frequency Domain Analysis

#### 4.1. Transfer Function of WT

_{gen}, is independent of the rotational speed. This assumption is only valid in the case of small signal perturbation. Hence, in the following, the response of the rotational speed to power variations is assessed.

_{var}controller, see Figure 5. Full load, on the other hand, is also less interesting as this operating point is only seldomly met when the grid connection capabilities demand FIM. In addition, inertial response can draw extra power from the wind when the WT is in full load operation; hence, the impact on the speed is not decisive for the power.

_{DT}(s), can be combined with the transfer function of the power control loop to form the transfer function from P_ref to speed_gen, G

_{WT}(s). For this purpose, G

_{P_cntrl_OL}(s) in Equation 1 has to be turned into the transfer function of the closed power control loop. Linearization around the operating point speed_gen = 1.138 pu allows setting up the block diagram of G

_{WT}(s), as shown in Figure 9.

#### 4.2. Transfer Function of Transformer

#### 4.3. Transfer Function of P_{dem} Controller

_{dem}controller is a PI controller with a proportional gain of three and an integral gain of nine. The P

_{dem}controller is the separator between FIM and inertia contribution; i.e., if inertial power leads to instantaneous violation of V

_{C}, the P

_{dem}controller prevents this having an instantaneous effect on the combined power setpoint, and hence, also the inertia contribution. Equation (12) shows the transfer function of the P

_{dem}controller.

#### 4.4. Comparison of Frequency Responses

_{C}, responds to not only the active power P

_{C}and the power from the 5M, P

_{5M}, but mainly to the local reactive power consumption/production, Q

_{C}(see Figure 1). The importance of Q

_{C}is shown by the ratio between reactance and resistance in the grid connection transformer, which is X/R = 3.84 [5].

_{WT}(s) (red amplitude response) of the P

_{dem}controller, G

_{PI_P_dem}(s), (green amplitude response) and of the transformer, G

_{TR}(s), (blue amplitude response); as well as the frequency spectra of ROCOF (green line), P

_{C}(magenta dotted line) and Q

_{C}(cyan dotted line).

_{TR}(s)) responds strongly to very low frequencies only. The generator speed of the WT, however, responds to power setpoint (P

_{ref}) changes strongest in the range from 1 Hz to 3 Hz (G

_{WT}(s)).

_{C}). Both active and reactive power variations decline with increasing frequency. Hence, also the extent to which FIM has to respond to V

_{C}declines with increasing frequency. In contrast to this, the magnitude of the ROCOF increases with frequency.

_{dem}controller decouples FIM very well from inertial power. Comparing the green lines in Figure 10 reveals that the response to ROCOF happens in a frequency range where the P

_{dem}controller exhibits very small gain. Hence, if inertial power leads to excessive V

_{C}FIM cannot respond to that, i.e., it cannot dampen the inertial power as the P

_{dem}controller prevents this.

## 5. Simulations and Discussion of Results

_{var}controller that it potentially leads to drastic power variations in the affected WT whenever the wind speed is high [19]. Hence, both continuous FIM and inertial response with the H

_{var}controller are most dominant in upper part load. The inertial response can potentially worsen the overloading of the grid. Due to the decoupling from the wind both controllers add to the mechanical loads in the WT at the same time.

_{var}controller allow it to. Figure 11 shows the simulated scenario for continuous FIM operation with enabled (blue) and disabled (red) continuous inertia contribution. The blue curve is hardly visible, as there is only little effect of inertial response on FIM operation.

#### 5.1. Effect of Generator–Converter Time Constant on Continuous FIM

_{max_TR_lim}whenever the voltage is too high (P

_{max_TR_volt}in Figure 6), which demands a de-loading of the generator by lowering the generator torque.

#### 5.2. Effect of Variable H Controller on the WT

_{var}controller has on the WT shall be discussed here.

_{dem}values are tested. Generally, the H

_{var}controller causes little impact on the WT, which is already visible from the fact that the two curves in Figure 11 hardly differ. Since the continental European grid frequency only rarely exhibits large ROCOFs, H

_{dem}is set to 12 s to achieve high power setpoint changes due to inertial response. This way, also the circumstances in smaller, i.e., more agile grids can be emulated. The analysis of all WT signals reveals that the acceleration of the generator and of the tower in lateral direction are affected most. Hence, these are the only signals considered here. However, Figure 14 and Figure 15 show that even H

_{dem}= 12 s has hardly any effect on the generator acceleration and on the lateral tower acceleration, respectively. It has to be mentioned, that the grid frequency recorded on 5 April 2017 is representative of a normal day in continental Europe. Although it did not contain any extreme events, it is still challenging in terms of inertial response, as the grid frequency appears to vary with extreme ROCOFs due to electromagnetic illusions.

_{var}controller where H

_{dem}was set to 6 s. The f

_{grid}time series were artificially generated to contain severe frequency events. With these time series the performance of the WT and the resulting loads were assessed at different wind speeds. The fatigue load analysis revealed that even with regularly occurring severe events in f

_{grid}the H

_{var}controller consumes only very little lifetime of the WT [9]. Also, as one consequence of the findings of this project, the demanded inertia constant is set to H

_{dem}= 12 s here.

#### 5.3. Effect of Continuous FIM and Inertia Provision on the Grid

_{grid}control), either oversized feeders or conservative power truncation is inevitable.

_{grid}, and the ROCOF, see Equation (13).

_{inertia}. Instead, the frequency converter has to be controlled such that the WT exhibits inertial behaviour, i.e., it produces synthetic inertia. Hence, H

_{dem}, or in case the H

_{var}controller is applied, H

_{var}is decisive for the inertial power, see Equation (14).

_{inertia}. In addition, it has to be pointed out that the mean value of P

_{inertia}is zero in normal power system operation (only if there is a persistent deviation of f

_{grid}from its rated value the mean value of P

_{inertia}≠ 0). This is further shown in Figure 16 and Figure 17. Hence, P

_{inertia}cannot interfere with the transformer temperature and it can only temporarily interfere with V

_{C}.

_{inertia}. When considering certain durations, such as the 24 h of the 5 April 2017, the energy exchange between grid and WT, which results from inertia contribution, can be derived according to Equation (15).

_{dem}of the H

_{var}controller in the 5M is set to 6 s and to 12 s. The resulting P

_{inertia}are compared with the P

_{inertia}of an AC connected synchronous generator with a fixed inertia constant H

_{fixed}= 6 s. Figure 16 shows these three different P

_{inertia}for the 24 h of 5 April 2017. Comparing Figure 16 with Figure 11 reveals that the inertia contribution of the 5M depends on the prevailing power operating point. Integrating P

_{inertia}according to Equation (15) leads to the inertial energies, E

_{inertia}, which are listed in Table 1. In Table 1 E

_{inertia}is not only given for the whole day, but also for the first half and for the second half of the day.

_{dem}is set to 12 s, the inertia contribution in the afternoon of 5 April 2017 is even 23% greater than that of the synchronous generator. It has to be kept in mind that in the scenario simulated here, the 5M is burdened with continuous FIM. Hence, it operates only intermittently and only for short durations at rated power and rated speed. Each time the speed drops the inertia contribution drops as well, see Figure 5. Without FIM the inertia contribution could increase even further in the afternoon.

_{dem}leads to a doubling of E

_{inertia}. This proves that inertia contribution has virtually no impact on the rotational speed and on the aerodynamic performance of the WT.

_{SI_varH}in Figure 6, as it is not possible to extract P

_{inertia}from P

_{5M}. There are several factors that make such a comparison impossible: P

_{inertia}is camouflaged in P

_{5M}by the turbulent wind and the motion of the mechanical components of the WT, namely the generator rotor, the blades in-plane and out-of-plane, as well as the motion of the tower in longitudinal and in lateral direction. The power reference for the frequency converter (in the model this variable is called P_setpoint, see Figure 3) is derived from the measured rotational speed of the generator. The driving power that is instantaneously available for the WT is determined by the wind speed and the aforementioned motions of mechanical components, as these interfere with the ambient wind speed, leading to a perceived wind speed. Therefore, P

_{inertia}can be magnified or weakened in single occasions. Considering longer durations, these effects are assumed to level out. However, very rapid P

_{inertia}variations cannot be realized by the generator–converter unit with its time constant (T_PT1_geno_substi = 25 ms). It has to be kept in mind, however, that the response of the AC-connected synchronous generator (in Table 1) is derived with Equation (14). The limited dynamic response of a synchronous generator is not taken into account here either.

_{SI_varH}, and the power that the 5M feeds into the grid, P

_{gen}. To show a drastic example Figure 17 shows the response to the peak in ROCOF at 11:14 (compare Figure 2), which is assumed to be an electromagnetic illusion. Figure 17 reveals that P

_{gen}follows P

_{SI_varH}quite well (note that the ranges of the two y-axes in Figure 17 are identical). The difference in magnitude of the excursion in P

_{SI_varH}and in P

_{gen}is caused by the damping effects of the power controller and the generator–converter unit. Hence, the comparison in Table 1 is deemed valid.

_{var}controller and H

_{dem}= 12 s; both with continuous FIM.

## 6. Conclusions

_{var}controller. By doing so, the grid reliably maintains controllability of the frequency. The WTs, on the other hand, suffer neither undue wear, nor noticeable loss of energy yield.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Setup of the case study of Flensburg campus supplemented by a 5 MW WT (5M) with connection to the external grid.

**Figure 5.**Variable inertia constant, H

_{var}, for the demanded rated inertia constants H

_{dem}= 6 s and H

_{dem}= 12 s. Constant inertia constant H = 6 s.

**Figure 10.**Bode plots of the transfer functions G

_{WT}(s), G

_{PI_P_dem}(s) and G

_{TR}(s) (top) in comparison to the frequency spectra of the different excitations: ROCOF, P

_{C}and Q

_{C}(bottom).

**Figure 11.**WT power (top) generator speed (middle) and pitch angle (bottom) of 5M for the case of continuous FIM operation (red curves) and for the case of continuous FIM with inertial response (blue curves in the background).

**Figure 12.**Generator acceleration (top) and frequency distribution of generator acceleration (bottom) of 5M in continuous FIM operation for two different generator-converter time constants.

**Figure 13.**Lateral tower top acceleration (top) and frequency distribution of lateral tower top acceleration (bottom) of 5M in continuous FIM operation for two different generator–converter time constants.

**Figure 14.**Generator acceleration (top) and frequency distribution of generator acceleration (bottom) of 5M when performing continuous FIM, with and without continuous inertia provision.

**Figure 15.**Lateral tower top acceleration (top) and frequency distribution of lateral tower top acceleration (bottom) of 5M when performing continuous FIM, with and without continuous inertia provision.

**Figure 16.**P

_{inertia}from an AC connected synchronous generator with H = 6 s (blue), P

_{inertia}from the 5M with H

_{var}controller and H

_{dem}= 6 s (red) and H

_{dem}= 12 s (green). The bottom diagram is a zoom-in view of the top diagram.

**Figure 17.**The inertial response power setpoint, P

_{SI_var}, (red) and the generator power, P

_{gen}, from the 5M. P

_{gen}is shown for the case of FIM only (green) and FIM with inertial response (blue).

**Table 1.**E

_{inertia}from an AC connected synchronous generator with H = 6 s, E

_{inertia}from the 5M with H

_{var}controller and H

_{dem}= 6 s and H

_{dem}= 12 s.

5 April 2017 00:00–24:00 | 5 April 2017 00:00–12:00 | 5 April 2017 12:00–24:00 | |
---|---|---|---|

H_{fixed} = 6 s | 88.2029 kWh | 41.5384 kWh | 46.6645 kWh |

H_{var} from H_{dem} = 6 s | 33.0589 kWh | 4.3307 kWh | 28.7283 kWh |

H_{var} from H_{dem} = 12 s | 66.1327 kWh | 8.6603 kWh | 57.4724 kWh |

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**MDPI and ACS Style**

Jauch, C.; Gloe, A.
Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines. *Energies* **2019**, *12*, 3013.
https://doi.org/10.3390/en12153013

**AMA Style**

Jauch C, Gloe A.
Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines. *Energies*. 2019; 12(15):3013.
https://doi.org/10.3390/en12153013

**Chicago/Turabian Style**

Jauch, Clemens, and Arne Gloe.
2019. "Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines" *Energies* 12, no. 15: 3013.
https://doi.org/10.3390/en12153013