# A Methodology for Provision of Frequency Stability in Operation Planning of Low Inertia Power Systems

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## Abstract

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## 1. Introduction

#### 1.1. Motivation

#### 1.2. Overview of Available Countermeasures for Supporting Low Inertia

#### 1.3. Paper Contribution

## 2. Background

#### 2.1. Classic Inertia

_{sys}), which is dependent on the inertia constants (H

_{i}) of all synchronous generators in the system and system rated power (S

_{sys}).

_{n}—nominal frequency.

#### 2.2. Synthetic Inertia

## 3. Synthetic Inertia Aimed for Large Disturbances and RoCoF Limitation

#### 3.1. Derivation of the Method

_{max}to the required value, RoCoF

_{lim}, entails delivering power corresponding to the difference between the two RoCoF values,

_{lim}is the system security setting as explained in Section 1 of this paper, here assumed to be ±1 Hz/s. RoCoF

_{max}is the worst-case scenario RoCoF calculated in the operation planning phase. Equation (8), therefore, provides a description of how much power on average needs to be delivered in order to reach the required RoCoF. The proposed SI method answers the question how to do it and is explained below.

_{lim}, a formula expressing the amount of energy $\Delta E$

_{1s}needed to be supplied in time t in order to change RoCoF by RoCoF

_{diff}is obtained:

_{500ms}is presented in Figure 2. The main premise is that the controller will act only in a short timeframe, which corresponds to the inertial response of the system. In this case, according to Equation (5), the input signal to this controller will be in a form of a linear decrease (or rise, depending on power imbalance sign); therefore, in order to transform it to a constant signal, a derivative function is used. Then, a stabilising low-pass filter and main filter are used to shape the response of the synthetic inertia to a step change in a desired manner.

_{SI}(s) the main control objective can be met:

#### 3.2. Tuning of Synthetic Inertia Controller

_{sys}= 4 s was assumed in this case. The grey area corresponds to primary frequency control response range, which should deploy its full reserves within several to fifteen seconds. However, for considerable load imbalances this reaction might be too slow, and the frequency might drop to a level where under-frequency protection might be triggered, thus additional support has to be introduced in order to retain RoCoF above the required level. This support can be offered by synthetic inertia in a much faster regime, during the inertial response period marked as the red area.

_{SI}should be selected in such a way that most of the time response of G

_{SI}(s) passes before time τ, as depicted in Figure 3b. This guarantees that the inertial response will not overlap with the FFR response too much. Calculation of the main gain K

_{SI}is possible based on Equations (10) and (13). It should be noted, however, that the proposed controller is an open-loop controller, and by definition, its output depends on the magnitude of the input. The magnitude of the input, which is Δf, initially depends on the size of the disturbance but shortly after is influenced by instantaneous power delivered by the SI (which is the controller’s output). Thus, the required energy E

_{500ms}can be delivered only if RoCoF is equal to RoCoFlim, which can happen only if E

_{τ}is equal to E

_{500ms}. In practice, it is impossible to keep this equilibrium during the dynamic process, thus small deviations should be expected.

#### 3.3. Synthetic Inertia Concept Verification Based on Simple Theoretical Model of a Power System

_{max}for this ΔP is equal to 1.92 Hz/s, whereas the goal is to limit the RoCoF to RoCoF

_{lim}= 1.0 Hz/s. According to Equation (10), this task entails delivering additional energy E

_{1s}from BESS equal to 56.2 MWs within the time of contribution of synthetic inertia, which in this case, is assumed to be one second. As a rule of thumb, the controller measurement time constant, T

_{m}, is selected to be equal to 20 ms. An inherent feature of the controller described by Equation (12) with T

_{m}= 0.02 s is that after time τ = T

_{SI}, it will deliver 61% of total energy, and after time τ = 2 T

_{SI}, 86% of energy, which is a direct consequence of Equation (13). By using this relationship, the main time constant T

_{SI}can be adjusted to satisfy the requirement of the speed of response of the SI controller. Finally, based on Equations (13) and (14), gain K

_{SI}can be calculated to match the required amount of energy $\Delta {E}_{\tau}$ and, in this example, is equal to 61.49 MWs/Hz.

## 4. System Operation Planning Methodology with Focus on RoCoF

- For each time step of the forecast the algorithm starts with static evaluation of the grid’s state through a load flow. In this stage equivalent, system inertia is calculated according to Equation (2), and based on Equation (3), maximum and minimum RoCoF are calculated for load and generation tripping, respectively. ΔP in this equation is the largest possible active power imbalance found in the load flow data.
- In the second stage, dynamic evaluation is performed. This step might be considered optional for Scenario 1 but is a must for Scenario 2, if wind generation or other devices operating in the power system are equipped with synthetic inertia. The purpose is to accurately determine RoCoF through dynamic simulation of a power system model that encompasses dynamic responses of relevant elements to frequency changes.
- Step three is a simple check—if the resulting value of RoCoF is within the predefined range, the algorithm moves to another time step, as the system is able to withstand the largest possible outage in given grid operation conditions. If not, Step 4 is executed.
- Step four consists in determining necessary additional inertia to keep RoCoF in the assumed range, i.e., between RoCoF
_{min}for generation trip and RoCoF_{max}for load trip. The methodology is demonstrated using BESS, which are used for SI service due to their excellent controllability but support from other devices is also possible. Then, based on Equations (10) and (13), controller parameters are calculated. In fact, controller’s time constants do not have to be updated often. They could even be hardcoded in the SI controllers based on average inertia level in the power system and response time of fast frequency control of the frequency-governing devices. On the other hand, the overall SI gain needs to be calculated for every time step, as it influences the contribution level of SI. - In Step five, the SI is distributed among selected assets by assigning a weighting factor to each device so that the sum of weighting factors is equal to 1, and final dynamic simulation is performed to confirm the calculations. It has to be noted that more than one BESS or other device can take part in SI service. Calculated energy ΔE
_{τ}can be distributed among available units arbitrarily by the TSO, e.g., by engaging units being furthest from their respective limits, or by typical market mechanisms, such as merit order or long-term contracts, etc.

_{sys}(red thick line). Note the reduced value of E

_{sys}at night indicating temporary tripping of generators due to low demand night period. Expected worst-case scenario RoCoF can also be noticed (red line) and should it exceed the threshold level necessary actions could be taken, as described in Step 4. Right-hand side plot of Figure 7 is constructed for a scenario in which a part of synchronous generation is superseded by wind generation, whose total power output is marked with green line. Calculated system inertia is, thus, lower and resulting RoCoF is lower. In this scenario, generation is also switched off during the night because of wind generation supplying low system demand. Note that there are many intervals for which RoCoF is below the threshold of −1 Hz/s, thus synthetic inertia is introduced.

_{500ms}, is calculated, and the gain of the SI controller is changed accordingly, based on Equation (13). Figure 8 shows the result of SI activation in BESS for the scenario with synchronous and wind generation for the operation planning period depicted in Figure 7. RoCoF values for the system operating without SI are presented in the top row. Plots in the middle row show quantities associated with BESS and SI: maximum power reached during the transient (grey curve), energy output in the first 500 ms (ΔE

_{τ}, light purple curve) and total energy output during the transient (dark purple curve). The bottom plots show minimum and maximum RoCoF values for the scenario with SI active. None of the cases with RoCoF below −1 Hz/s or above 1 Hz/s are observed, which implies that the proposed synthetic inertia controller and deployment methodology can be an effective tool to address issues associated with too low inertia.

_{SI}, which is changed to achieve the required level of SI. Plots in the top row show power contribution from SI delivered by BESS. Since it is a multimachine system, the responses are more oscillatory than in the theoretical case shown in Figure 3, but the general characteristics of the inertial response are preserved. Note that after the rapid injection of active power has decayed the sign of active power changes to negative, as it is indirectly dependent on the second derivative of frequency (see Figure 2 for control block diagram). This issue is further explained in the subsequent section. Nevertheless, the SI controller improves the frequency decline phase of the frequency regulation process by increasing RoCoF to a permissible level.

## 5. Validation of the Synthetic Inertia Concept in Real-Time Simulation Environment

#### 5.1. Real-Time Simulation Environment

#### 5.2. Battery Energy Storage System Model

#### 5.3. Synthetic Inertia Controller in RTDS

_{SI}> 0 when f < f

_{n}or P

_{SI}< 0 when f > f

_{n}.

_{SI}

_{ref}). The last row of plots shows that irrespective of PLL settings, the power converter of BESS is unable to deliver active power requested by SI due to too high-voltage distortion. This is however, out of scope of this paper. Nevertheless, application of the slower PLL is sufficient for frequency measuring purpose.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A. Frequency response stages as described in [29].

**Figure 2.**Proposed structure of the synthetic inertia controller and visualization of the idealized control signals (above).

**Figure 3.**(

**a**) Response to generation trip (0.2 pu) of 1. purely inertial system (dash–dot line), 2. inertial system with power-frequency load characteristics, 3. as in 2 with simplified steam turbine with governor added, 4. as in 2 with simplified gas turbine with governor added; (

**b**) shape of time response of G

_{SI}(s).

**Figure 4.**Single line diagram of the modified 14-bus IEEE system with BESS added to bus 12; the BESS model is a generic current injection model with WECC BESS Control System for RMS simulation [33] (

**left**) and equivalent block diagram for this model in a lumped form (

**right**).

**Figure 5.**Response to generation trip of 1. purely inertial system (grey line); 2. inertial system with synthetic inertia (SI support exhibiting linear decline of frequency in the first 0.5 s (red line); 3. same as no. 2 but with governor action (dashed line).

**Figure 7.**Generation and consumption data (forecast) for the planning timeframe; plots represent data processed in Step 1 of the proposed methodology.

**Figure 8.**Effect of SI activation on rate of change of frequency (RoCoF) for the 24 h planning period for generation tripping (left) and load tripping (right): RoCoF for the scenario with synchronous and wind generation (top), BESS power and energy output (middle), RoCoF for the same scenario with SI activated.

**Figure 9.**Reponses to generation trip of the system equipped with SI (blue) and without SI (grey) for four different instants during the planning period.

**Figure 10.**The diagram of BESS with batteries, neutral point clamped (NPC) converter with firing controller, filter and transformer.

**Figure 11.**Synthetic inertia control diagram for BESS; the output of the controller can be either signal P_SI: normal operation of SI or blocked blocking criteria are met.

**Figure 12.**Comparison of responses to 40 MW trip: with no synthetic inertia support (blue), with SI support without blocking logic (black) and with SI with blocking logic (green).

**Figure 13.**Comparison of SI controller response to three-phase short-circuit (left column) and singe-phase short-circuit (right column) for fast (k

_{p}= 5, T

_{i}= 0.01 s) and slow (k

_{p}= 1, T

_{i}= 0.15 s) PLL settings.

Gen 1 | Gen 2 | Gen 3 | Gen 6 | Gen 8 | |
---|---|---|---|---|---|

Type | Synchronous | Synchronous | Synchronous | Wind | Wind |

Rating [MVA]/Load [MW] | 200/50 | 220/30 | 160/117 | 72/49 | 100/77 |

H [s] | 3.2 | 4.0 | 2.0 | 0 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Kosmecki, M.; Rink, R.; Wakszyńska, A.; Ciavarella, R.; Di Somma, M.; Papadimitriou, C.N.; Efthymiou, V.; Graditi, G.
A Methodology for Provision of Frequency Stability in Operation Planning of Low Inertia Power Systems. *Energies* **2021**, *14*, 737.
https://doi.org/10.3390/en14030737

**AMA Style**

Kosmecki M, Rink R, Wakszyńska A, Ciavarella R, Di Somma M, Papadimitriou CN, Efthymiou V, Graditi G.
A Methodology for Provision of Frequency Stability in Operation Planning of Low Inertia Power Systems. *Energies*. 2021; 14(3):737.
https://doi.org/10.3390/en14030737

**Chicago/Turabian Style**

Kosmecki, Michał, Robert Rink, Anna Wakszyńska, Roberto Ciavarella, Marialaura Di Somma, Christina N. Papadimitriou, Venizelos Efthymiou, and Giorgio Graditi.
2021. "A Methodology for Provision of Frequency Stability in Operation Planning of Low Inertia Power Systems" *Energies* 14, no. 3: 737.
https://doi.org/10.3390/en14030737