The frequency domain doesn’t tell the complete story. Therefore, the system has also been simulated with disturbance time series that were developed in the RAR-project. From these simulations, the response in relation to the kpis’ is evaluated.
Optimization for four different scenarios and varying the K-factor
FIGURE 37.SUMMARY OF THE DEVELOPED KPIS’ PLOTTED AGAINST EITHER THE PEAK GAIN OF THE NORMALIZED TRANSFER FUNCTION OF ∗ 𝑺 , THE CALCULATED VARIANCE OF THE PHYSICAL SYSTEM OF 𝑮̂∗ 𝑺 OR THE VARIANCE OF THE NORMALIZED TRANSFER FUNCTION
𝒔 ∗ 𝑪 ∗ 𝑮 ∗ 𝑺.
Figure 37 shows some different and interesting things.
KPI: MoNB
i. There is a relationship between the MoNB and the variance of the physical transfer function of 𝑮̂∗ 𝑺 where a reduction of the variance reduces the kpi.
ii. It is also visible that the total FCR-N steady state capacity here has a positive influence in that it supresses the kpi further.
iii. Further suppression of the kpi is attained if the disturbance time constant is reduced from 90 s to 60 s. The efficiency of the time constant is lower though than an increase in the static capacity (ii).
KPI: Balance
i. There is a relationship between the MoNB and the variance of the physical transfer function of 𝑮̂∗ 𝑺 where a reduction of the variance reduces the kpi.
ii. It is also visible that the total FCR-N steady state gain here has a positive influence in that it supresses the kpi further.
iii. Further suppression of the kpi is attained if the disturbance time constant is reduced from 90 s to 60 s. The efficiency of the time constant is lower though than an increase in the static capacity (ii).
KPI: Δf(t)-path
i. There is a clear relation between the relative arc length of the grid frequency deviation vs the peak gain of the normalized transfer function for 𝑮 ∗ 𝑺.
ii. It is also visible that the total FCR-N steady state capacity here has a positive influence in that it supresses the kpi further.
KPI: Δu(t)-path
i. If the total FCR-N steady state capacity is increased then the kpi is increased.
ii. The smaller the resonance peak is for the normalized transfer function 𝑮 ∗ 𝑺, the larger the kpi becomes
iii. There seems to be a minimum value for the peak gain where the kpi is at its smallest value iv. At larger peak gain values the kpi takes on larger values again.
KPI: Variance comparison
i. There seems to be some type of exponential relationship between the variance of the normalized transfer function G*S and s*C*G*S.
KPI: Variance vs. Δu(t)-path
i. There is a general linear relationship between the normalized transfer of s*C*G*S and the relative arc length of the FCR-N controller output.
ii. The linear relationship seems to only hold down to a certain point and then the relative arc length increases.
These kpis’ suggests that
i. The more effort that is put in to suppressing the resonance peak the more work an FCR-N provider has to do.
ii. If the FCR-N provider reduces its bandwidth too much giving a large resonance peak then the work performed starts to increase.
iii. The steady state gain of the FCR-N is more important for the MoNB and balance kpis’ than the bandwidth of the FCR-N provider.
Optimization for four different scenarios and varying the K-factor
FIGURE 38.SUMMARY OF THE DEVELOPED KPIS’ PLOTTED AGAINST EITHER THE PEAK GAIN OF THE NORMALIZED TRANSFER FUNCTION OF 𝑮 ∗ 𝑺, THE CALCULATED VARIANCE OF PHYSICAL SYSTEM OF 𝑮̂∗ 𝑺 OR THE VARIANCE OF THE NORMALIZED TRANSFER FUNCTION
OF 𝒔 ∗ 𝑪 ∗ 𝑮 ∗ 𝑺.
Figure 38 shows some different and interesting things.
KPI: MoNB
i. There is a relationship between the MoNB and the variance of the physical transfer function of 𝑮̂∗ 𝑺 where a reduction of the variance reduces the kpi. It is not linear, however, but seems to be exponential.
KPI: Balance
i. There is a relationship between the Balance and the variance of the physical transfer function of 𝑮̂∗ 𝑺 where a reduction of the variance reduces the kpi. It is not linear however but exponential.
KPI: Δf(t)-path
i. There is a clear relation between the relative arc length of the grid frequency deviation vs the peak gain of the normalized transfer function for 𝑮 ∗ 𝑺.
KPI: Δu(t)-path
i. There is a clear relation between the relative arc length of the FCR-N controller output vs the peak gain of the normalized transfer function for 𝑮 ∗ 𝑺.
ii. The more effort that is put in to suppressing the resonance peak the more work and FCR-N provider has to do.
KPI: Variance comparison
i. There seems to be some type of exponential relationship between the variance of the normalized transfer function of G*S and s*C*G*S.
KPI: Variance vs. Δu(t)-path
i. There is a general linear relationship between the normalized transfer of s*C*G*S and the relative arc length of the FCR-N controller output.
ii. The linear relationship seems to only hold down to a certain point and then the relative arc length These kpis’ suggests that
i. The more effort that is put in to suppressing the resonance peak the more work an FCR-N provider has to do.
ii. If the FCR-N provider reduces its bandwidth too much giving a large resonance peak then the work performed again starts to increase.
iii. The steady state gain of the FCR-N is more important for the MoNB and balance kpis’ than the bandwidth of the FCR-N provider.