The FFR model

In general, for the provision of frequency response, a storage system can inject energy into the network during low frequency events or reduce output/absorb energy from the network in case of high frequency events. The nature of the service provision that is to provide low or high frequency response is determined bilaterally between National Grid and participants, through a process of tender rounds. These participants can thus offer low frequency response, high frequency response or both. Similarly, availability payments are agreed bilaterally. Using data from the tender rounds in 2013, published by National Grid (2013), a total of 5488MW of contracts were awarded for the year for the provision of low frequency response. In the case of high frequency response, this figure was 1913MW, showing a bias in favour of the procurement of low frequency response. Furthermore, additional difficulties arise in considering the provision of high frequency response; from the tender round data, participants providing both high and low frequency response are paid a total fee as availability payment. It is therefore difficult to distinguish between the proportion that is paid solely for the provision of high or low frequency response as each tender is bilaterally agreed and varies. Hence, for simplicity, the storage system is assumed to provide low frequency response throughout this thesis. Using data for the two generators at Dinorwig PHES (DINO-1 and DINO-5), adjusted for power capacity and the number of hours the PHES system is available, an availability payment was calculated. This was approximately £5/MW/h of power capacity. This value is similar to those relating to the provision of Mandatory Frequency Response (MFR) whereby most availability payments were in the range of £2.5/MW/h to £7/MW/h. It should be stressed that both generators at Dinorwig power station offered only low frequency response.

The FFR model is based on the assumption of a fully dedicated unit which only provides frequency response under the Firm Frequency Response service, which National Grid currently procures (National Grid. n.d.). In the previous section, the APX and BM models derived revenues through arbitrage which was determined by optimisation. In this case, the FFR model derives revenues from ancillary services payment and derived through simulation. While there are additional forms of payment made to the FFR provider, the model only takes into account an availability payment and a utilisation payment which corresponds to the term ‘response energy payment’; these are scaled by a factor of 1.25 times wholesale prices during low frequency and 0.75 times that of wholesale prices during high-frequency events as per section 4.1.3.9 of the Connection and Use of System Charges (National Grid 2015a). This low-frequency scaling factor is included in the model but not the high-frequency scaling factor, as the

FFR model is only assumed to provide power during low-frequency events. Other payment types have been omitted given that these are rarely specified, based on the post-tender reports gathered. As an FFR dedicated system, the model includes a self-discharge factor to account for long periods of idle time. During non-idle times, charging and discharging losses are assumed to include the self- discharge losses. Other than the self-discharge parameter, the other storage system parameters for the FFR model are identical to the APX and BM models.

Due to the lack of data on actual frequency response utilisation for a similar sized generator (to the storage system), a probability function is derived similar to the approach undertaken by Loisel et al. (2011). The authors studied wind-storage configuration providing reserves in France; they cite primary reserves as power required within 30 seconds whereas secondary reserves require immediate activation following a disturbance and reaches full capacity within 5 minutes. Tertiary reserves are required to reach their full capacity within 15 minutes. Due to their choice of technology, CAES, only secondary and tertiary reserve are considered for the provision of reserves; the authors use a 15% probability of being used for secondary reserves and 2% for tertiary reserve. In this thesis, a probability of being utilised for the provision of FFR of 20% is chosen. This is slightly higher than Loisel et al. (2011)’s values to include the primary reserve service probability since the FFR timescales encompasses those of primary, secondary and tertiary reserve. Furthermore, in an EPRI report (Rastler 2011), an 18-20% capacity factor was assumed when storage system’s function was to provide T & D support. Since, in Chapter 5, it is shown that major source of revenue is availability rather than utilisation payments, revenues are unlikely to be strongly sensitive to changes in this probability factor.

An artificial utilisation profile is generated using a random binomial distribution to determine when frequency response is required and a random discrete uniform distribution to determine the volume of frequency response required when called for. These signals are assumed to occur 20% of the time and require capacity between 1 and 50 MW.

Equations (4.11) and (4.12) show the FFR revenue and SOC of the system shown as ‘𝜋𝐹𝐹𝑅’ and ‘STt’ respectively. 𝜋𝐹𝐹𝑅= ∑ 𝛾𝑡∗ 𝑒𝑓𝑓𝑑 ∗𝐴𝑉𝐹𝐹𝑅+ 𝛾𝑡∗ 𝜎𝑡∗ SF ∗ 𝑒𝑓𝑓𝑑 ∗ 𝐷𝐹𝐹𝑅,𝑡∗ 𝑃𝐴𝑃𝑋,𝑡− (1 − 𝛾𝑡) ∗ 𝐶𝐹𝐹𝑅,𝑡∗ 𝑃𝐴𝑃𝑋,𝑡 𝑛 𝑡=1 (4.11) 𝑆𝑇𝑡 = 𝑆𝑇𝑡−1−𝑆𝑇𝑡−1∗ 𝑠𝑒𝑙𝑓𝑑𝑖𝑠 + 𝑒𝑓𝑓𝑐 ∗ 𝐶𝐹𝐹𝑅,𝑡+ 𝛼 ∗ 𝐷𝐹𝐹𝑅,𝑡 (4.12)

𝐶𝐹𝐹𝑅,𝑡: { 𝐶𝐹𝐹𝑅,𝑡 = 25 𝑖𝑓 𝑆𝑇𝑀𝐴𝑋− 𝑆𝑇𝑡−1 ≥ 25 𝑎𝑛𝑑 𝛾𝑡 = 0 𝐶𝐹𝐹𝑅,𝑡 = 𝑆𝑇𝑀𝐴𝑋− 𝑆𝑇𝑡−1 𝑖𝑓 0 < 𝑆𝑇𝑀𝐴𝑋− 𝑆𝑇𝑡−1 < 25 𝑎𝑛𝑑 𝛾𝑡 = 0 0 ≤ 𝐶𝐹𝐹𝑅,𝑡≤ (1 − 𝛾𝑡∗ 𝜎𝑡) ∗ 25 ∀ 𝑡 𝐶𝐹𝐹𝑅,𝑡= 0 Otherwise (4.13) 𝑈𝑇 = 𝑓(𝐵𝑖𝑛(𝑛, 𝑞), 𝑈𝑛𝑖𝑓{𝑎, 𝑏}) (4.14) 𝐷𝐹𝐹𝑅,𝑡: { −25 ≤ 𝐷𝐹𝐹𝑅,𝑡 ≤ 0 ∀ 𝑡 𝐷𝐹𝐹𝑅,𝑡= UT 𝑖𝑓 𝛾𝑡 = 1, 𝜎𝑡= 1 𝐷𝐹𝐹𝑅,𝑡 = 0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (4.15) Whereby

𝜋𝐹𝐹𝑅: Revenues from the provision of FFR in £

a: Parameter of the discrete uniform distribution representing the minimum range (1 MWh) 𝐴𝑉𝐹𝐹𝑅: Availability payment in £/MW/h. Initially this is set at £5/MW/h.

b: Parameter of the discrete uniform distribution representing the maximum range (25 MWh)

𝐶: Charge Volume in MWh

𝐷: Discharge Volume in MWh 𝑒𝑓𝑓𝑑: Discharge Efficiency 𝑒𝑓𝑓𝑐: Charge Efficiency

𝑃𝐴𝑃𝑋: Half-hourly APX spot market price in £/MWh

q: Binomial distribution parameter representing the probability of success (20%) 𝑠𝑒𝑙𝑓𝑑𝑖𝑠: Self-charge factor equivalent to 0.001 per half-hour

𝑆𝑇: Storage Volume (Level) in MWh

𝑆𝑇𝑀𝐴𝑋: Maximum Storage Volume (Level) in MWh initially set at 600 MWh

𝑆𝐹: Low frequency scaling factor, for utilisation payments. equivalent to 1.25 𝑈𝑇: Utilisation Volume for the provision of FFR service in MWh

𝛾: Binary variable taking a value of 1 when an FFR window is active, zero otherwise.

𝜎: Binary variable taking a value of 1 when the FFR service is utilised, zero otherwise. 𝑛: Total number of time periods, equivalent to 17520 half-hourly periods in 2013.

In equation (4.11), 𝛾 is a binary variable, taking a value of 1 during a FFR window and zero otherwise. Another binary variable 𝜎 determines the actual utilisation of the service, that is when storage is discharging. ‘selfdis’ refers to the self-discharge rate of 0.1% per half-hour. This value is broadly representative of a lithium battery which loses about 5% of its energy in the first 24 hours (Technical University of Munich 2016).

From equation 4.12, charging occurs as soon as the 12-hour FFR window terminates. This could imply charging at unnecessarily high prices, hence by varying period covered by the 12 hour window FFR revenues can increased (This is shown later in figure 5.9). In other words, even though the FFR model is not an optimisation model, by varying the starting time, it is possible to determine which 12-hour window generates the most revenues. With a half-hourly resolution, there are 48 possible start times for the 12-hour windows and since the system is designed to charge by purchasing power from the APX market, the storage system is able to reduce its costs depending on charging times.

Figure 4.1: Schematic representation of the FFR simulation model.

Figure 4.1 shows the simulation of revenues from the FFR model. Frequency response windows are set in advance for a duration of 12 hours starting initially for the period from midnight to noon. This represents the windows whereby the SO could require the power from the storage system, referred to as FFR window. During the first day of operation, the storage system needs to be fully charged, to its maximum energy capacity shown as ‘STmax’. For each half-hourly period, there is a self-discharge

factor and if this period falls outside of its FFR window and the state of charge is below its maximum energy capacity, charging occurs. Otherwise, the storage system remains on standby until either its service provision is required or the self-discharge reduces the state of charge.