Assessment of Primary Frequency Control through Battery Energy Storage Systems

This article focuses on the impact of the primary frequency control that can be provided by Battery Energy Storage Systems (BESSs) on the transient response of electric grids. A procedure based on the Fourier transform is used for synthesizing a realistic frequency signal based on the variations of load consumption and generation. The impact of BESSs is evaluated with respect to the storage capacity installed and the regulation strategy adopted and then compared with the regulation provided by conventional sources. The impact of a variabledroop strategy on the dynamic response of the grid and the BESSs State of Charges (SOCs) is also evaluated. A novel index to quantify the performance of the BESSs is proposed and discussed. The case study is based on a detailed dynamic model of the all-island Irish transmission system.


Introduction
The contributions of this paper are as follows: 68 • quantify the impact of the primary frequency control provided by BESSs 69 and compare it to CG contribution through the use of a novel quantitative 70 index. It is also studied the impact of a VD control strategy used by 71 BESSs.

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• a novel procedure, whose preliminary version appeared in [28], to generate 73 realistic synthetic frequency scenarios. The remainder of the paper is organized as follows. Section 2 presents the 76 stochastic models included in the grid, whereas Section 3 describes the adopted 77 frequency control of the BESS. Section 4 outlines the procedure to create real-78 istic scenarios. Section 5 describes various indexes, included the proposed one, 79 to evaluate the performance of the control provided by BESSs and other energy 80 resources. Section 6 describes the case study and discusses simulation results. 81 Finally, Section 7 provides conclusions and outlines future work.  Load models are assumed to be voltage-dependent, i.e., exponential or ZIP models, and either static or dynamic voltage recovery [30]. The reference power consumption of a load, say p load , is defined as the sum of two components: where p det is the "deterministic" consumption which is assumed to vary linearly 108 between assigned values in a given period, e.g. 15 minutes; p sto is a stochastic

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Wind generators are modelled as doubly-fed induction generators (Type C).
α is the mean reversion speed that dictates how quickly the w s,sto tends to the 114 given mean value µ w (in our case 0). ξ w is the white noise, formally defined   . Depending on these parameters, a certain frequency error ∆f max causes the full provision of the regulation band. In general the droop for a CG and a BESS unit is computed as follows [34]:

BESS Control
where P F C band represents the regulator band in pu (in this study, we set P F C CG band = 0.1 pu(MW) and P F C BESS band = 1 pu(MW)). Taking ∆f max equal for both resources and dividing equation (5) by (4), we obtain the relationship which correlates both the droops: R = 0.0050 R = 0.0020  R min is large.

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The VD strategy here proposed cannot achieve a perfect SOC regulation   In order to reproduce real data harmonics, we make use of power stochastic  Finally, the stochastic processes of loads, wind speeds and CG power set points are summed together and the resulting profile, say p tot , is thus identified by a given unique set of parameters that define the four stochastic processes.
The harmonic contents of the frequency trajectories obtained with p tot are then compared with the real data through the estimation of an error f , which is defined as follows: the procedure is shown in Fig. 10.  and v2 refer to different noise profiles with equal |∆pmax| value. ∆tCG is equal to 3-7 minutes for SSP1 and 13-50 minutes for SSP2. To quantify the contribution of each stochastic process to the overall frequency fluctuations, we consider the sum variance law of the frequency signal which defines the variance of a signal composed by N stochastic independent variables as:

Indexes
To compare the impact of each process, it is convenient to consider a normalized variance per process, namely: in such a way, from Equ. (9), we can write:

Impact of BESSs on frequency fluctuations 244
This index provides a measure of the relative improvement to the dynamics response due to the BESSs. It is defined as: where σ B is the standard deviation of the frequency of the system with inclusion where and |∆f (r)| [Hz] is the frequency error including the deadband. E ref k represents 251 the integral of the exact real-time power profile requested by the PFC service in 252 a given period T , E + k represents the actual energy produced by the resources for 253 ∆f > 0, whereas E − k is the energy produced for ∆f < 0 in the same period T .

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The condition in Section 4. With this aim, we make use of the Irish transmission system [37].
267 Table A.5 in the appendix summarizes the main elements of the grid. The CG 268 active installed capacity in S1 is 4347 MW while wind active installed capacity 269 is 2123 MW. In S2 and S3 CG capacity is decreased by 25%.  The time horizon of the three scenarios is 12 hours, from 6:00 to 18:00.
with respect to the real data. Sample frequency fluctuations of the three sce-291 narios are shown in Fig. 12 In Fig. 7 the harmonics of real data and S1 scenario are compared and as  The simulations that include BESSs are divided in two groups: the first     Figure 14 shows the index h B for the various scenarios. The improvement of 328 the frequency signal is more relevant for both scenarios S2 and S3 (see Fig. 15 329 for an example) than for S1. This has to be expected as, in S1, frequency has  Table 3 shows the index e k for the available resources that provide PFC. In   conventional power plants is higher in scenarios S1 and S2 than S3 in that 345 the frequency signal is slower and easier to follow even for slower resources.

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The result of the simulations is that in scenario S1, which represents the  S2 hard mode S1 hard mode FD R BESS = 0.0035 VD hard mode Figure 19: Example of SOC profiles in the S1 scenario with 100 MW of BESS installed S1 100MW S1 200MW S1 300MW S2 100MW S2 200MW S2 300MW  For what concerns SOC, in Table 4 the mean SOC value µ(SOC) of several 378 simulations is shown. VD strategies, especially for S2, are able to keep the 379 SOC statistically closer to SOC ave with respect to FD strategies. Fig. 19 shows 380 as an example two profiles related to the different strategies. As can be seen, 381 the VD strategy is not able to perfectly regulate the SOC, but manages to 382 decrease its standard deviation with respect to the FD case avoiding too high 383 or too low charge levels. Fig. 20 shows the SOC standard deviation for all the 384 scenarios studied in the case η BESS = 0.8. The decrease in standard deviation 385 is slightly better in S2 where the alternation between over and under-frequency 386 periods is faster, therefore the VD strategy changes values often (as shown 387 in Fig. 18), reaching better performances. The possibility of using a bigger 388 difference between R max and R min can further improve the SOC dynamics (e.g.

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R min = 0.002 and R max = 0.008 ), but its effect on the frequency must be 390 carefully evaluated.