# Methodology for Tuning MTDC Supervisory and Frequency-Response Control Systems at Terminal Level under Over-Frequency Events

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## Abstract

**:**

## 1. Introduction

_{DC}) set points cannot be fixed directly in each terminal. This disadvantage is solved by centralised control. However, in a pure centralised control scheme, disturbances in the AC side can provoke the master terminal to lose its control capability and, consequently, the shutdown of the entire DC grid [6].

_{DC}droop functions in the slave terminal of a centralised control structure [7,8,9,10,11]. In [7], a hybrid centralised DC voltage control based on a master–slave architecture and complemented with P-V

_{DC}droop functions in the slave terminal is proposed, in contrast to [8,9,10,11], for a multi-terminal HVDC. The present paper is a continuation of the work presented in [7] by investigating the effects of including grid code compliance frequency requirements in the control scheme, in contrast to [8,9,10,11,12,13] where no grid code is considered. Besides, a proportional resonant current control is used in the HVDC converters, instead of operating the entire control schemes in the most common dq coordinates [8,9,10].

## 2. Frequency Response According to United Kingdom (UK) National Grid Code Requirements

_{FSM}, for the sake of simplicity. This will define one aspect of the strategies proposed by the developed methodology.

## 3. Multi-Terminal Direct Current (MTDC) Grid Topology and Control Systems

#### 3.1. MTDC Grid Supervisory Control System

_{WF,1}and P

_{WF,2}, by means of a proportional constant k

_{PRO}, as Equation (1) shows.

#### 3.2. Control Systems at Terminal Level

#### 3.2.1. Onshore Terminals

_{DC}Q scheme. By following this scheme, the DC voltage is controlled by means of i

_{d,ref}(Figure 2a) and includes a f

_{grid}V

_{DC}slope characteristic where the LFSM/FSM frequency-response function is implemented by means of the k

_{FSM}parameter. Besides and according to the V

_{DC}Q scheme, the reactive power is controlled by means of i

_{q,ref}, where a V

_{AC}Q

_{AC}slope droop function is included to contribute to AC voltage stability of the AC grid (Figure 2b).

_{grid}P

_{AC}characteristic where the k

_{FSM}frequency-response function is implemented to comply with the frequency requirements specified in the UK national grid code, as in the master terminal. The slave terminal also contributes to DC voltage stability by means of a droop V

_{DC}P

_{AC}characteristic with dead band around the DC voltage reference. For this purpose, it follows a PQ scheme where the control of reactive power is the same as in the onshore master terminal (Figure 2b). The difference with the master terminal is found at the generation of the i

_{d,ref}, where active power magnitudes are operated instead of DC voltage variables, as shown in Figure 3.

_{FSM}= k

_{LFSM}, and for the sake of simplicity k

_{FSM}is used from now on.

#### 3.2.2. Offshore Terminals

_{DC}f

_{grid}characteristic is added, which allows to modify the wind farm grid frequency, taking advantage of the capability of the wind generators to change their generation against frequency variations.

_{meas,WF,eq}and P

_{meas,WF,eq}, are measured to calculated the active and reactive power references of the aggregated wind generator, P

_{ref,WF,eq}and Q

_{ref,WF,eq}.

_{WF}, which is aimed at attenuating oscillations provoked by the phase-locked loop (PLL).

_{ref,WF,eq}.

_{ref,WF,eq}. Since the offshore wind farms follow a fixed power factor control, the reactive power reference is obtained from the measured active power and the chosen power factor.

_{α,ref,WF,eq}and i

_{β,ref,WF,eq}, are calculated by using the previously calculated, P

_{ref,WF,eq}and Q

_{ref,WF,eq}magnitudes, jointly with the voltage vector, also in αβ frame, measured at the output of the aggregated wind farm generator, $\overline{{v}_{\alpha \beta ,WF,eq}}$. According to the operation shown in Figure 4, the current references in the αβ frame are transformed into dq frame by means of the Park transform, considering the angle measured by the PLL, θ

_{WF,eq}.

_{d,ref,WF,eq}and i

_{q,ref,WF,eq}, and the θ

_{WF,eq}angle.

## 4. Open-Loop Frequency Response of the MTDC Grid

_{DC}(p.u.)) are shown as a final proof of compliance with the frequency response. Different settling times have been obtained to reach set points of 10 s and 30 s as well as holding times of 20 s to maintain the frequency at a constant value at several stages of the sequence. The simulation results show that the proposed control structure is compliant with the grid code requirements.

## 5. Onshore Alternating Current (AC) Grid Model to Emulate Frequency Response

_{0}, which will be a generation trip for under-frequency events and a load trip for over-frequency events.

_{0}is the active power mismatch, H

_{i}, and S

_{i}the inertia constant and the apparent power of the individual generators making up the system, S

_{T}the total capacity in the system and H

_{eq}the equivalent inertia of the system. The computation of frequency deviation in the steady-state value in a power system with several generators is also straightforward by applying Equation (3).

_{droop,i}is the droop constant of the individual generators making up the system, D

_{t}, the damping constant in the system, and R

_{droop,eq}the equivalent droop constant in the system.

_{r}, ω

_{n}, ζ, and θ

_{1}can be calculated based on [16] and considering a first-order system. K

_{eq}and T

_{eq}are respectively the gain and time constant of the first-order governor in Gen 1 and t

_{min}is calculated with Equation (5):

## 6. Novel Methodology to Tune MTDC Supervisory and Frequency-Response Control Functions at Terminal Level in Over-Frequency Events

_{FSM}value, even the order type of the frequency signal may be reduced from 2nd order to 1st order.

_{DC,ref,slave}). The values tested for P

_{DC,ref,slave}have been selected according to four equal shares of the maximum capacity of the slave terminal.

_{FSM}). The values that k

_{FSM}adopts are chosen among those recommended by the UK national grid code [19,20] (3–5%), and even trying greater values such as 7.5% to check for further improvements.

_{DC,ref,slave}and k

_{FSM}are clarified.

_{DC,ref,slave}or the k

_{FSM}values can also transform the 2nd order nature of the frequency excursion into a 1st order nature.

_{DC,ref,slave}or the k

_{FSM}values can be readjusted and reductions of the frequency peak at PCC can be checked. For this purpose, a threshold value for frequency can be selected and the established limit for the LFSM band, i.e., 50.4 Hz, is proposed. In this way, this limit bounds the frequency signal out of the LFSM compulsory band, and therefore, the risk of instability is reduced.

## 7. Application Case of the Methodology to the Considered MTDC + Onshore AC Grid

#### 7.1. Impact of Tuning Strategies on the Reduction of the Frequency Peak

_{FSM}= 5% (strategy 2) can be observed with respect to the original system without frequency-response function, i.e., k

_{FSM}= 0% (strategy 1). Both tuning strategies are parameterised according to different P

_{DC,ref,slave}values, in order to further reduce the peak value in a more moderate manner than with the change of k

_{FSM}, so that the lowest P

_{DC,ref,slave}value yields to the greatest peak frequency reduction.

_{FSM}= 0% to first-order type with k

_{FSM}= 5%. An intermediate value of k

_{FSM}= 3% has been also simulated and this presents a second-order type, but for the sake of clarity it has been removed from Figure 9a. The k

_{FSM}= 5% is the limit value up to which the frequency curve is a second-order type. For larger values, such as k

_{FSM}= 7.5%, the first order type curve is still maintained and further greater reductions in the frequency peak are shown, as depicted in Figure 9b.

_{DC,ref,slave}and k

_{FSM}variables contribute to this peak reduction slightly and more considerably, respectively, being k

_{FSM}even capable of changing the polynomial order type of the frequency signal and P

_{DC,ref,slave}values able to slightly modify the final peak value derived from k

_{FSM}variation.

_{DC,ref,slave}values. The greatest improvements in frequency peak are observed for strategy 3 with k

_{FSM}= 7.5% and P

_{DC,ref,slave}= 0.25, reaching 50.39 Hz, and the worst case is observed for strategy 1 with P

_{DC,ref,slave}= 1, reaching 50.66 Hz, as seen in Figure 10.

_{FSM}value, one can distinguish that for 0, 5 and 7.5%, the greatest P

_{DC,ref,slave}value leads to the largest frequency peak value. Therefore, those strategies which employ high P

_{DC,ref,slave}set points lead to worst case scenarios for a given k

_{FSM}. This can be especially observed in frequency peak reduction provided by strategy 1, which presents the greatest improvements made by P

_{DC,ref,slave}values from all the selected cases, as the target variables are reduced more drastically when P

_{DC,ref,slave}is decreased from 1 to 0.25.

_{DC,ref,slave}set point value, greater reductions in frequency peaks are obtained as far as k

_{FSM}is increased. Moreover, several P

_{DC,ref,slave}values achieve in strategy 3 frequency peak values lower than 50.4 Hz, namely, P

_{DC,ref,slave}= 0.25 and P

_{DC,ref,slave}= 0.5. These combinations ensure that the complete frequency signal is out of the LFSM compulsory zone, where mandatory extra frequency response should be added if frequency values greater than 50.4 Hz are maintained.

_{FSM}and P

_{DC,ref,slave}values correspond to a case where an optional FSM ancillary service would be contracted. When the frequency-response function is contracted with the electrical utility as an ancillary service, several considerations must be addressed. In [29], a typical frequency response for a synchronous area under frequency disturbances for effective primary control is shown. In [29], the response is exemplified with an under-frequency event where the transient behaviour is characterised by oscillations and a time response from 15 s to 30 s. Therefore, it is important to test these reductions for a certain variation of the synchronous generator parameters. Among tuning strategies, strategy 2 (k

_{FSM}= 5%) is chosen due to its intermediate reduction of the frequency peak and being k

_{FSM}= 5% a limit value for the first-order behaviour of the frequency curve at PCC.

#### 7.2. Guidance for Tuning k_{FSM} and P_{DC,ref,slave} when Different MTDC Control Structure and Synchronous Generator Characteristics Are Considered

_{FSM}and P

_{DC,ref,slave}, when the control structure of the MTDC grid is varied, i.e., instead of master–slave, a distributed control scheme, or the onshore AC grid characteristics are modified.

_{DC,ref,slave}, implies a moderate tuning of the frequency-response function, k

_{FSM}= 5%, of onshore terminals.

_{FSM}for the LFSM mode has to be at least 2% per each 0.1 Hz. In principle, for those frequency ranges that belong to the LFSM band there would be no problem since, k

_{FSM}= 7.5% exceeds this recommended minimum slope of 2% per each 0.1 Hz. However, for those frequency values belonging to the FSM band, the recommended k

_{FSM}value lays between 3% and 5% per each 0.1 Hz, as reported in [20]. By contrast, these boundaries for k

_{FSM}within the FSM band are neither justified in the grid code [19] nor in the guidance note for DC converter stations [20].

_{FSM}= 7.5% could imply a bit aggressive control, considering that the FSM frequency range is narrower than the LFSM range. Moreover, although not considered in this paper, k

_{FSM}can also present an opposite sign, as it should also consider under-frequency values with respect to 50 Hz. However, this could be more critical for a more complex distributed frequency control structure with a specifically located centre of inertia; nevertheless, the present paper considers a hierarchical master–slave structure. Therefore, more moderate values of k

_{FSM}are recommended for distributed control structures than in master–slave structures, while P

_{DC,ref,slave}can be varied for the entire range, as it conducts to lower peak reductions or just peak amendment.

_{FSM}value is recommended and thus strategy 2 of Table 1 has been chosen. Therefore, strategy 2 is selected to be evaluated against a variation of the Gen 1 synchronous generator characteristics, such as the total inertia, H

_{eq}, and the damping, D

_{t}, according to Equations (2)–(4). Strategy 2 is tested against a variation of H

_{eq}, adopting the values of 1.5 s, 2 s and 6 s, and the impact on the frequency peak is shown in Figure 11a.

_{eq}= 6 s conducts to the slowest set of curves as well as the greatest reductions (50.32 Hz with P

_{DC,ref,slave}= 0.25), while H

_{eq}= 1.5 s conducts to the fastest profiles and smaller reductions of the peak (50.49 Hz with P

_{DC,ref,slave}= 1).

_{DC,ref,slave}values also contribute to the decrease of the peak values, as far as they are reduced. The H

_{eq}= 6 s value yields to frequency values out of the compulsory LFSM zone since the peak values are lower than 50.4 Hz. This strategy would ensure that the complete frequency signal is out of the LFSM compulsory zone, where mandatory extra frequency response should be added if frequency values greater than 50.4 Hz are maintained.

_{eq}values close to 6 s, it may be sufficient to tune P

_{DC,ref,slave}values to smooth the peak and ensure the frequency signal outside the LFSM range. In contrast, for H

_{eq}values close to 1.5–2 s, the curves are transiently inside of the LFSM zone, but getting out of this area thanks to the frequency-response function. Therefore, for large H

_{eq}values, a smaller k

_{FSM}value than 5% could also provoke reductions in the peak, while P

_{DC,ref, slave}is kept to a minimum. For lower H

_{eq}values, a substantially greater k

_{FSM}value would be needed, in order to achieve greater peak reductions.

_{t}, the complete model has been tested when D

_{t}adopts the values of 0, 1.25 and 2.5, which would lead to a system without and with damping, respectively. In Figure 12a, the effect of these variations on the frequency behaviour is shown, and in Figure 12b, the peak values are compared.

_{t}= 0, with the greatest peak values, and another with D

_{t}= 2.5, leading to peak reductions. Apart from this, the decrease of the P

_{DC,ref,slave}values contribute to the peak reduction. With D

_{t}= 2.5, the frequency peak is outside the LFSM compulsory area when the P

_{DC,ref,slave}value equals to 0.25.

_{t}value, a greater k

_{FSM}value than 5% has a great influence in achieving peak reductions in a more efficient way than P

_{DC,ref, slave}. However, for greater D

_{t}values, just by maintaining a low P

_{DC,ref, slave}value, the peak reduction is easily obtained, without the need for increasing the k

_{FSM}slope.

_{DC,ref,slave}and k

_{FSM}values, the peak of the frequency signal can be further reduced in a slight and a more considerable manner with the proper combination of k

_{FSM}and P

_{DC,ref,slave}values, respectively. Additionally, the complete frequency curve can be fully bounded outside the LFSM area, reducing the risk of the system to instability. This also is applicable when a certain variation of the onshore grid synchronous generator characteristics is simulated.

## 8. Conclusions

_{DC,ref,slave}, and the slope of the frequency-response functions in outer loop control schemes of onshore terminals, k

_{FSM}.

- First, the combination of a coordinated frequency control structure with a centralised master–slave scheme to operate a MTDC grid implemented to ensure the proper share the distribution of power set points, while at the same time, comply with the considered grid code.
- The comparison between control responses with and without this k
_{FSM}frequency-response function shows the benefit of having it implemented, i.e., the reduction of transient frequency oscillation amplitude. - The strategies which use P
_{DC,ref,slave}= 1 are less preferable than those with P_{DC,ref,slave}< 1, but can also achieve great frequency peak and slope reductions if an adequate k_{FSM}is tuned. - The DC power reference for the slave terminal plays an important role in smoothing the frequency peak value but the role of k
_{FSM}at terminal level has a larger influence in reducing the frequency peak value. - For a given DC power reference at the slave terminal, a higher k
_{FSM}, e.g., 5%, is advised over lower values, and this guarantees the stability of the system at each moment and presents first order behaviour; or even 7.5%, as it bounds the frequency signal out of the LFSM compulsory area for certain P_{DC,ref,slave}values. - For a given k
_{FSM}value, it is advisable to have the lowest P_{DC,ref,slave}value at the slave terminal, as 0.25 was demonstrated to be the set point which most reduces the frequency peak. - Besides, guidance is given on how to select the k
_{FSM}value, if the control structure of the MTDC grid is changed. If, for example a distributed control structure was considered, more moderate values for k_{FSM}are recommended. - Additionally, a sensitivity analysis is performed to give guidance on how to tune P
_{DC,ref,slave}and k_{FSM}, considering variations in the equivalent inertia H_{eq}and the damping, D_{t}. According to these deviations, the frequency peak values may vary, and thus the strategies have to be redefined if their derived peak reduction is not sufficient. Therefore, for large H_{eq}values, a smaller k_{FSM}value than 5% could also provoke reductions in the peak, while P_{DC,ref, slave}is kept to a minimum. For lower H_{eq}values, a substantially greater k_{FSM}value would be needed, in order to achieve greater peak reductions. Furthermore, for a null D_{t}value, a greater k_{FSM}value than 5% has a great influence in achieving peak reductions in a more efficient way than P_{DC,ref, slave}. However, for greater D_{t}values, just by maintaining a low P_{DC,ref, slave}value, the peak reduction is easily obtained, without the need for increasing the k_{FSM}slope.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Name | Value |
---|---|

Apparent nominal power | 1800 MVA |

Nominal AC voltage | 400 kV |

Power factor | 0.8 |

Inertia constant (2H_{eq}) | 4 s |

Synchronous reactances (x_{d} = x_{q}) | 2 p.u. |

Stator resistance | 0 p.u. |

Stator reactance | 0.1 p.u. |

Rotor mutual reactances (x_{rld} = x_{rlq}) | 0 p.u. |

Transient time constants (T_{d}′ = T_{q}′) | 6 s |

Transient reactances (x_{d}′ = x_{q}′) | 0.25 s |

Sub-transient time constants (T_{d}″ = T_{q}″) | 0.018 s |

Sub-transient reactances (x_{d}″ = x_{q}″) | 0.16 s |

Filter delay time (T_{b}) | 10 s |

Filter derivative time constant (T_{a}) | 2 s |

Governor gain constant (K_{eq}) | 100 p.u. |

Exciter time constant (T_{e}) | 0.5 s |

Turbine power coefficient (A_{t}) | 1 p.u. |

Frictional losses (D_{t}) | 0 p.u. |

Controller droop (R_{droop}) | 0.01 p.u. |

Governor time constant (T_{eq}) | 5 s |

Name | Value |
---|---|

Proportional constant-reactive power control (K_{q}) | 0.4 p.u. |

Time constant-reactive power control (T_{q}) | 0.01 s |

Filter time constant–DC voltage (T_{rVDC}) | 0.01 s |

Filter time constant–reactive power (T_{rq}) | 0.02 s |

Filter time constant–AC voltage (T_{rq}) | 0.02 s |

Dead band droop AC voltage | 0.005 p.u. |

AC voltage setpoint (V_{AC,ref}) | 1 p.u. |

Proportional constant–DC voltage control (K_{v}) | 15 p.u. |

Time constant–DC voltage control (T_{v}) | 0.05 s |

Integral constant–proportional resonant control (K_{i}) | 5000 |

Proportional constant–proportional-resonant control (K_{p}) | 1.5 |

Resonant angular frequency–proportional resonant control (ω) | 314.159 |

Name | Value |
---|---|

Reactive power control constant (K_{q}) | 0.4 p.u. |

Filter time constant–reactive power control (T_{rq}) | 0.02 s |

Filter time constant–DC voltage (T_{rudc}) | 0.01 s |

Filter time constant–active power (T_{rp}) | 0.02 s |

Filter time constant–AC voltage (T_{ruac}) | 0.02 s |

AC voltage setpoint (V_{AC,ref}) | 1 p.u. |

Active power control constant (K_{p}) | 0.5 p.u. |

Time constant–active power control (T_{p}) | 0.02 s |

DC voltage setpoint (V_{DC,ref}) | 1 p.u. |

Name | Value |
---|---|

Proportional constant–AC voltage control (K_{AC}) | 1 |

Time constant–AC voltage control (T_{AC}) | 0.01 s |

Filter time constant–DC voltage (T_{rVDC}) | 0.01 s |

Filter time constant–AC voltage control (T_{rAC}) | 0.005 s |

DC voltage dead band | 0.03 s |

DC voltage setpoint (V_{DC,ref}) | 1 p.u. |

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**Figure 2.**Onshore master terminal control V

_{DC}Q scheme. Generation of: (

**a**) i

_{d,ref}and (

**b**) i

_{q,ref}.

**Figure 9.**Frequency peak values for different strategies (k

_{FSM}) and P

_{DC,ref,slave}values: (

**a**) strategies 1 and 2 and (

**b**) strategy 3.

**Figure 10.**Comparison of frequency peak values among curves in Figure 9.

**Figure 11.**Sensitivity analysis for the variation of H

_{eq}: (

**a**) frequency curves for strategy 2 for different P

_{DC,ref,slave}set points and H

_{eq}values and (

**b**) comparison of frequency peak values among curves in (

**a**).

**Figure 12.**Sensitivity analysis for the variation of D

_{t}: (

**a**) frequency curves for strategy 2 for different P

_{DC,ref,slave}set points and D

_{t}values and (

**b**) comparison of frequency peak values among curves in (

**a**).

Strategies | k_{FSM} | P_{DC,ref,slave} | |||
---|---|---|---|---|---|

Strategy 1 | 0% | 0.25 | 0.5 | 0.75 | 1 |

Strategy 2 | 5% | ||||

Strategy 3 | 7.5% |

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**MDPI and ACS Style**

Haro-Larrode, M.; Santos-Mugica, M.; Etxegarai, A.; Eguia, P.
Methodology for Tuning MTDC Supervisory and Frequency-Response Control Systems at Terminal Level under Over-Frequency Events. *Energies* **2020**, *13*, 2807.
https://doi.org/10.3390/en13112807

**AMA Style**

Haro-Larrode M, Santos-Mugica M, Etxegarai A, Eguia P.
Methodology for Tuning MTDC Supervisory and Frequency-Response Control Systems at Terminal Level under Over-Frequency Events. *Energies*. 2020; 13(11):2807.
https://doi.org/10.3390/en13112807

**Chicago/Turabian Style**

Haro-Larrode, Marta, Maider Santos-Mugica, Agurtzane Etxegarai, and Pablo Eguia.
2020. "Methodology for Tuning MTDC Supervisory and Frequency-Response Control Systems at Terminal Level under Over-Frequency Events" *Energies* 13, no. 11: 2807.
https://doi.org/10.3390/en13112807