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Maximizing the Potential of Energy Storage to Provide Fast Frequency Control Olivier M´egel, Johanna L. Mathieu, G¨oran Andersson Power Systems Laboratory, ETH Z¨urich, Switzerland {megel, jmathieu, andersson}@eeh.ee.ethz.ch
Abstract—Due to their fast responsiveness, energy storage units such as batteries can provide fast frequency control to power systems. However, when the control signal is biased or substantially autocorrelated, they cannot provide services for extended periods of time because they have limited energy capacities. To improve the ability of batteries to provide frequency control, we can offset their frequency response so that they only respond to fast and zero-mean frequency deviations, while passing slower and biased deviations to other resources. We propose two new heuristics to offset frequency control signals, and a method to compare these heuristics to previously developed heuristics. This method allows us to quantify the heuristics from the point of view of both the storage unit operator (return on investment, ROI) and the transmission system operator (impact on the power system). Considering battery degradation, the new heuristics yield better ROIs, and we find that our results are not very sensitive to the battery’s energy-to-power ratio around its optimum. We also find that the best choice of heuristic depends on what impact matters most to the transmission system operator.
I. I NTRODUCTION The number of energy storage units within power systems is likely to increase in the future as they can be used for a variety of applications including photovoltaic integration in distribution grids, peak shaving, infrastructure upgrade deferral, and powering electric vehicles. When not being actively used for one of these applications, a unit could provide other services to power systems [1], such as frequency control. In this paper, we explore methods to improve the potential for batteries to provide primary and secondary frequency control. Specifically, we investigate new methods to modify a battery’s frequency control response in order to maintain its state of charge (SoC) around an acceptable range, as shown in Fig. 1. This is done by adding a time dependent offset to the frequency control signal to form the battery’s response. The offset is canceled out by slower plants that modify their operating point in the opposite direction. These plants could be activated through either a slower time scale frequency control mechanism, intraday market, or via bilateral contracts. Therefore, batteries would help compensate fast components of supply-demand mismatch while passing on the slow components to slower units. Different methods for computing frequency response offsets are presented in [2]–[5] and we compare our new heuristics (referred to as the C1 and D1 heuristics) to the ones developed in [2]–[4]. All of the heuristics can be classified as either continuous, if the offset profile can change at any time, such as the Oudalov [2], Borsche [4] and C1 heuristics; or as discrete, if the offset profile can only change at times corresponding to
intraday market intervals, such as the California Independent System Operator (CAISO) [3] and D1 heuristics. Compared to the CAISO and Borsche heuristics whose goal is to maintain the SoC at a precise value (SoCref ), the C1 and D1 heuristics allow the SoC to vary freely within a given interval, reducing battery degradation. Our heuristics also explicitly limit the maximum offset power, therefore limiting the related power capacity investment. Section II describes the input data, scenarios, heuristics and battery degradation model. Section III describes the simulations and results and Section IV concludes the paper. II. M ETHODS We applied the heuristics on three years (2009, 2011, 2012) of frequency data from the European Continental Synchronous Area for primary control simulation and on one year of load frequency control (LFC) signals from the Swiss Transmission System Operator (TSO) for secondary control simulation. We assume that these data are representative of future conditions, though we will discuss the validity of this assumption in Section III. These data are sampled with a timestep, ∆k, of 10s, which is also the timestep used for the simulations. We compare the heuristics in two ways. First, we extend a method developed in [2] to optimally size storage units (in terms of the energy-to-power ratio, E P ) by adding a lithiumion battery degradation model, which allows us to maximize the return on investment (ROI) under realistic conditions. This approach represents the point of view of storage operators seeking to maximize profits. Secondly, we develop metrics to quantify the impact of offset mechanisms on the power system. This approach represents the point of view of TSOs. A. Offset Scenarios In the intraday market scenario, the storage unit’s response can deviate from the control signal (i.e. the standard frequency response for primary control or the LFC signal for secondary control) if the offset is the result of energy sale or purchase on the intraday market. Due to market structures, there is a delay between the last moment one can place a buy or sell order and the beginning of power delivery. We call this delay the lead time and it corresponds to the minimum time required for a change of the offset value. Furthermore, the offset value must stay constant during a market interval. In the smooth deviation scenario, the offset can vary continuously, without lead time, but it should be smooth enough for slower plants to cancel out. Here, we assume that the offset is
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billed according to the balance energy price, but it could also be billed according to a bilateral contract with a slower plant. In the later case, the sum of the responses of the two units would match the control signal. Continuous heuristics are designed for the smooth deviation scenario, while discrete heuristics are designed for the intraday market scenario. B. General Equations E P:
(1)
where E>0 is the energy capacity, P >0 the physical power capacity of the battery, PA >0 the part of P committed to the ancillary service and PO >0 the part of P that is available for the offset. In our analysis, only the ratios between these quantities are important; therefore, our results can be applied to batteries of any absolute size. We define p(k) to be the power requested from (p(k) positive) or sent to (p(k) negative) the storage unit at time k: p(k) = pA (k) + pO (k) + pR (k),
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Fig. 1. Illustration of the offset principle, C1 heuristic. The offset is added to the primary control response to form the total response. Hence, the response is offset in order to maintain the SoC around an acceptable range.
E E = , P PA + P O
Offset (pO(k)) 0.3
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Time
The most significant parameter for a storage unit is
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Primary Control (pA(k))
SoC and SoC Thresholds [%]
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(2)
where pA (k) is the power requested by the ancillary service, pO (k) the offset, and pR (k) the power sent to a dissipative resistance, when applicable (see Section II-E). Note that power capacities in (1) are upper bounds for the respective instantaneous power values in (2): |p• (k)|≤P• ∀k. Our goal in this paper is to develop methods to compute pO (k). We compute the SoC, defined as a percentage, as follows: ( 1 p(k) if p(k) > 0, ∆k ηd ηc p(k) otherwise , (3) SoC(k + 1) = SoC(k) − E where ηc and ηd are charging and discharging efficiencies, which we set equal to 90%. C. Description of Existing Heuristics 1) Borsche (continuous) [4]: The offset is computed based on previous values of pA (k): Pk (−pA (i) − ploss (i) − pR (i)) pO (k + d1 ) = i=k−a1 +1 , (4) a1 where a1 is the time averaging parameter, d1 the delay between measurement and reaction, and ploss the charge or discharge
Fig. 2. Illustration of the offset principle, D1 heuristic. Ticks on the x-axis represent the beginning of intraday market intervals.
losses. This heuristic was created for primary control, but can also work for secondary control if the parameters are modified. The minimum feasible PO is found empirically based on historic control signals: PO should be large enough so that |pO (k)| ≤ PO ∀k. 2) CAISO (discrete) [3]: This heuristic makes use of the intraday market to manage the SoC. The parameter a2 is the market interval duration and d2 the lead time between market closure and beginning of delivery. The offset is calculated only at k ∗ which represents a market closure time. Based on the difference between SoCref and SoC(k ∗ ) and considering future values of pO that have already been set, the heuristic sets pO to a constant value over the interval [k ∗ +d2 , k ∗ +d2 +a2 −1]. This value is computed so that the SoC would reach SoCref at the end of the interval, if pA is zero over the interval. This heuristic was created for LFC in California, but it can also work for primary and secondary control in Europe if the parameters are modified. We assess the minimum feasible PO in the same way as for the Borsche heuristic. 3) Oudalov (continuous) [2]: The offset is activated when the SoC exceeds specific thresholds SoCT , and only if the frequency is in the deadband of the primary control response. The offset value can change from 0 to 100% of PO at any timestep, meaning that slower plants may struggle to follow it. In this paper, we assume that the frequency band within which the heuristic can modify the response is ±10mHz instead of ±20mHz, as in the original paper, because the tighter value is in line with new ENTSOE guidelines [6]. This heuristic is only used for primary control, as it based on the primary control deadband. D. Description of New Heuristics 1) C1 (continuous): If the SoC exceeds SoCT , then the heuristic orders a ramp of fixed slope (rO ) for a fixed duration (PO /rO ) for the next timesteps, as shown in Fig. 1. Specifying the value of rO ensures that offset variations are slow enough for slower plants to follow. To make the offset easier to follow, it can not be too volatile: it has to stay flat for at least PO /rO between two ramps of opposite signs. The steady state values of PO (k) are chosen by the storage unit operator. This heuristic introduces two improvements over the Borsche method. First, it imposes a constraint on pO (k), which reduces the need for large PO (investment cost saving) and ensures that response distortion is not too large. Secondly, allowing the SoC to fluctuate between the lower and upper thresholds reduces the battery’s responsiveness, which reduces battery degradation.
TABLE I H EURISTIC -S PECIFIC PARAMETERS Parameters Reference SoC (SoCref ) SoC Thresholds (SoCT ) Offset Ramp Constraint (rO )
Values Normal With DR 53.7% 68.7% 44.0/61.5% 55.3/72.8% 1 P [MW/s] 300 O 1 P 1800 O
Market Interval Duration (a2 ) Market Closure Lead Time (d2 ) Average Duration (a1 ) Reaction Delay (d1 ) DR Power (PR ) DR Threshold (SoCDR )
-
[MW/s]
5min 1h 7.5min 45min 15min 1h 5min 0.3·PA 84%
Heuristics C1, D1, CAISO C1, D1, Oudalov C1-f C1-s D1-f, CAISO-f D1-s, CAISO-s D1-f, CAISO-f D1-s, CAISO-s Borsche-f Borsche-s Borsche all all
2) D1 (discrete): D1 is the discrete equivalent of C1, as shown in Fig. 2. As in C1, the offset is activated at specific SoCT , can only take discrete and pre-defined values, and the SoC can fluctuate between the two thresholds. As with the CAISO heuristic, pO remains constant over a market interval, the response is not subject to ramp constraints but delayed by the market lead time, and the computation considers the future values of pO that have already been set. E. Dissipative Resistance Based on [2], we also ran simulations with a dissipative resistance (DR), which prevents battery overcharging. When the SoC goes above a certain threshold SoCDR , a resistor is activated to dissipate energy at a fix rate PR until the SoC is again below the threshold. F. Heuristic Parameters The main parameters and their values are shown in Table I. Most of the heuristics were implemented in fast and slow versions, denoted by suffix “-f” and “-s”. When the suffixes are omitted, the values apply to both versions. The slow versions apply for both primary and secondary control. The fast versions apply only for primary control because their time constants are at least as fast as the typical secondary control signal. We chose SoCref to be in the middle of the battery SoC safe zone (see Section II-G), when considering charging and discharging efficiency. SoCT values are placed relative to SoCref , also considering efficiencies. When simulating the use of the DR, we increase SoCref by 15%. G. Battery Degradation Model Since there is not a single widely-accepted model for lithium-ion battery degradation [7], we implemented a simple model that captures key degradation behavior. We assume that degradation depends linearly on the amount of energy cycled, as long as the SoC stays in a “safe zone” (15-85%). In this case, the End of Life (EoL) is reached when the battery has cycled a specific amount of energy, referred to as its Operative Lifetime, which we assume is 3000 70% Depth-of-Discharge (DoD) cycles (i.e. 3000 · 0.70 · E kWh). Outside the safe zone, we assume degradation increases also linearly with respect to
the SoC, and so the degradation by f (k): 1 f (k) = f1 ·(SoC(k)−85%) f ·(15%−SoC(k)) 1
impact of p(k) is multiplied
if 15% ≤ SoC(k) ≤ 85%, if 85% < SoC(k), if 15% > SoC(k) (5) where f1 is calibrated so that EoL is reached after one 100% DoD cycle. The number of years used for ROI computation is limited by two factors: calendar life (assuming a maximum of 10 years), and operative lifetime (degradation resulting from usage), whichever comes first. H. ROI and Offset Impact Metrics The ROI is used to assess the profitability of the system PN RAS −Co k=1 (1+r)y(k)
, (6) Cinv where RAS is the annual revenue from provision of ancillary services (revenue per kW for both primary and secondary control, and revenue per kWh for secondary control), Co is the annual cost of offset energy, r the discount rate (8%), y(k) maps the simulation timestep to the numbers of years between the timestep and the beginning of the simulation, N is the number of timesteps until the EoL, and Cinv is the investment cost for the full system. For continuous heuristics, Co is based on the balance energy price and, for discrete heuristics, it is based on the intraday market price. To provide TSOs with a method to quantify the impacts of the heuristics on the power system, we propose three metrics: Q1 , the ratio between the energy cycled through the offset and the energy exchanged for frequency control P |pO (k)| ; (7) Q1 = Pk k |pA (k)| ROI =
Q2 , the root-sum-square of the offset ramps, which gives us a sense for how hard it is for slower plants to cancel out the offset sX Q2 = (pO (k + 1) − pO (k))2 ; (8) k
and Q3 , the degree to which the offset directly cancels the control signal, which tells us how much the offset degrades the requested response: 1 X Q3 = (− min(0, pA (k) · pO (k))) . (9) 1000 k
A lower impact value corresponds to a better heuristic. Q2 is only used for continuous heuristics as we assume that, for discrete heuristics, the ramping impact is included in the intraday market prices. I. Assumptions, Parameters and Data We assumed a constant hourly revenue of 16e/MW for both primary and secondary control. This corresponds to the mean marginal price for primary control in Germany and Switzerland over last year, and is between the German and Swiss
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Fig. 3. Battery ROI with C1-f heuristic, primary control. Dashed lines correspond to constant E values. P
secondary control mean marginal prices for the same period. The energy price for secondary control is calculated according to [8]. We use balance energy prices from Switzerland, and intraday market prices from Germany. Cinv is assumed to depend linearly on a battery’s power and e energy capacities: Cinv = C1 ·E +C2 ·P , with C1 = 330 kW h e and C2 = 170 kW , which is in line with the energy capacity price range of [9] for 2015-2020. Whenever a heuristic produces control actions that attempt to push a battery’s SoC below 0% or above 100%, we say that that heuristic (for that battery size) is “infeasible”. III. S IMULATIONS AND R ESULTS A. Primary Control Figure 3 shows the ROI for primary control as a function of computed with the C1-f heuristic. We ran simulations over a large set of (E, PO ) couples, by varying PPO between 0.05 A E and 1.4 and PA between 0.2h and 6h. Each (E, PO ) couple corresponds to an E P value and to a specific ROI (when the heuristic is feasible). We divided the E P axis into bins and, for each bin, we display the highest ROI associated with that bin. Given a battery with a particular E P , one can look for the maximum ROI along the dashed lines of Fig. 3. We repeated the analysis shown in Fig. 3 for each heuristic. In Fig. 4 and 5 we show that, when comparing separately the continuous and discrete heuristics, the C1-f and D1-f heuristics outperform all other heuristics in terms of ROI, over the whole E P range. In part, this is because it is beneficial to allow the SoC to drift within a interval. Targeting a precise SoC (as with the Borsche and CAISO heuristics) leads to more energy exchanged through the offset mechanism and subsequently more battery degradation. For a different problem, [10] also found that an optimal storage policy should not aim to maintain the SoC at a fixed value, but rather within an interval. Therefore, as shown in Table II, the C1-f and D1-f heuristics require a smaller PEA than the other heuristics. Additionally, the bound on PO in the C1 and D1 heuristics also helps decrease the power capacity-related investment costs. Since most of the curves are fairly flat near their peak, we find that the results are not very sensitive to a battery’s E P around its optimum. However, we do find that the results are highly sensitive to the operative lifetime. Doubling it would significantly increase the optimal ROI for each heuristic (for
1
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Fig. 4. Battery ROIs as a function of E/P, for continuous heuristics, primary control, no dissipative resistance.
D1−f D1−s CAISO−f CAISO−s
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Fig. 5. Battery ROIs as a function of E/P, for discrete heuristics, primary control, no dissipative resistance.
instance, +44% for C1-f) and shift the optimal E P to a smaller value (for instance, to 0.5h for C1-f). In this case, the C1-f and D1-f heuristics still achieve higher ROIs than the other heuristics. To analyze the sensitivity of our results to the frequency data used within the simulations, we applied the C1-f heuristic to each of the three years of data separately, and compared the results to those generated by applying the heuristic to three consecutive years of data (as done in our other analyses), as shown in Fig. 6. The ROI from the one-year runs differ by no more than 9% of the ROI from the three-year run, indicating that the results are not particularly sensitive to the underlying frequency data. We found that using a softer degradation function, where one hundred 100%-DoD-cycles lead to EoL, has a negligible impact for most of the heuristics. This is because all of the heuristics manage to maintain the SoC in a relatively narrow band around SoCref . For the same reason, adding the DR only marginally modifies the results, since it is not often activated. TABLE II O PTIMAL BATTERY S IZE & O FFSET I MPACTS , PRIMARY CONTROL , NO DISSIPATIVE RESISTANCE . continuous heuristics
discrete heuristics
C1-f C1-s Borsche-f Borsche-s Oudalov D1-f D1-s CAISO-f CAISO-s E PA PO PA
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TABLE III O PTIMAL BATTERY S IZE , SECONDARY CONTROL , NO DISSIPATIVE RESISTANCE .
C1−f 2009 C1−f 2011 C1−f 2012 C1−f 3 years
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Fig. 6. Battery ROIs as a function of E/P, C1-f heuristics, primary control, one or three years of frequency data, no dissipative resistance.
Additionally, we found that removing the 10 year limit on battery life also has a small impact. Although a larger energy capacity would allow for a longer lifetime (without the 10 year limit), beyond a certain point the discount rate makes the additional revenues smaller than the marginal capacity investment. This tipping point usually corresponds to a lifetime of approximately 10 years. We found that the cost of energy exchanged through the offset mechanism for all the heuristics is always below 10% of RAS . Therefore, the offset energy could become more expensive without jeopardizing the profitability of the scheme. Given our current assumptions for offset energy costs, frequency control revenues, and so forth, we found that the battery breake e even costs for the C1-f heuristic are 450 kW h and 230 kW , C1 assuming that C2 remains the same as in Section II-I. The offset impacts are displayed in Table II. For Q1 , our heuristics outperform the Borsche and CAISO heuristics because allowing the SoC to vary freely within an interval reduces the total offset energy. Note that for all of the heuristics, 9% come from 1) the fact that the primary control signal is not exactly zero-mean and 2) the charge and discharge losses associated with the response. Similarly, for Q3 , the C1 and D1 heuristics outperform the Borsche and CAISO heuristics because they are less sensitive to small SoC variation and therefore degrade the requested response less. On the other hand, for Q2 , the Borsche heuristic does better than the C1 heuristic, and so it would be easier for a slower power plant to cancel out an offset from a battery operating the Borsche heuristic. The Oudalov heuristic is clearly a different type of heuristic. For Q2 , its impact is two orders of magnitude above the other continuous heuristics, (Q2 values for discrete heuristics would even be one order of magnitude below the Oudalov heuristic’s impact), whereas for Q3 it realizes a perfect score, as the offset is only activated when no primary control response is requested. These findings highlight that the best choice of heuristic depends on what matters most to the TSO. B. Secondary Control All of the slow heuristics are far from being cost effective given near-term battery price expectations, as the optimal ROI is always below 0.6. Since the LFC signal can be non zeromean for long periods of time, the offset power is much = 1 (as can be seen in higher than for primary control. PPO A Table III) means that the offset can completely cancel out the full LFC signal, which was not the original intention of the offset heuristics. They were designed to only slightly modify
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the response, and for faster signals (primary control or U.S. LFC signals) which tend to be zero-mean on a much shorter time scales. Given these results and expected battery prices over the next few years, we do not expect secondary control in Europe with batteries to become cost competitive in the near term. As mentioned, this result does not hold for U.S. LFC since those signals are faster and reset by intrahour markets. IV. C ONCLUSION We have shown that batteries could provide primary frequency control in a cost-effective way in the near-term. In order to do so, they would need to be allowed to offset their frequency response, which might require the TSOs to develop new regulations. We designed two new offsetting heuristics and showed through simulation that they outperform previously developed heuristics in term of ROI because they reduce battery degradation. We also proposed three different metrics that allow the TSOs to assess how various heuristics would impact the power system. A sensitivity analysis highlighted that battery operative lifetime is a critical parameter. Therefore, more research on battery degradation models is needed, especially since primary control leads to small and frequent SoC swings, and most of degradation models focus on medium or large DoD. ACKNOWLEDGMENT The authors would like to thank the Swiss Commission for Technology and Innovation (project no. 14478). R EFERENCES [1] J. Eyer and G. Corey, “Energy storage for the electricity grid: Benefits and market potential assessment guide,” SAND2010-0815, Sandia National Laboratories, Tech. Rep., 2010. [2] A. Oudalov, D. Chartouni, and C. Ohler, “Optimizing a battery energy storage system for primary frequency control,” Power Systems, IEEE Transactions on, vol. 22, no. 3, pp. 1259 –1266, 2007. [3] D. Tretheway, “Regulation energy management draft final proposal,” CAISO, Tech. Rep., 2011. [4] T. Borsche, A. Ulbig, M. Koller, and G. Andersson, “Power and energy capacity requirements of storages providing frequency control reserves,” in Proceedings of the IEEE PES General Meeting, 2013. [5] C. Jin, N. Lu, S. Lu, Y. Makarov, and R. Dougal, “Coordinated control algorithm for hybrid energy storage systems,” in Proceedings of the IEEE PES General Meeting, 2011, pp. 1–7. [6] ENTSOE-E Operation Handbook, Chapter 1 : Load-Frequency Control and Performance, ENTSOE-E Std., 2009. [7] L. Lam, “A practical circuit-based model for state of health estimation of li-ion battery cells in electric vehicles,” Master’s thesis, TU Delft, 2011. [8] Swissgrid, Basic principles of ancillary service products, Std., Rev. 6.5, 2013. [9] McKinsey & Company, “A portfolio of power-trains for europe: a factbased analysis,” 2010. [10] N. Gast, D.-C. Tomozei, and J.-Y. Le Boudec, “Optimal storage policies with wind forecast uncertainties,” Proceedings of Greenmetrics 2012, Imperial College, London, UK,, 2012.
Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Digital Object Identifier:
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Maximizing the Potential of Energy Storage to Provide Fast Frequency Control Olivier M´egel, Johanna L. Mathieu, G¨oran Andersson Power Systems Laboratory, ETH Z¨urich, Switzerland {megel, jmathieu, andersson}@eeh.ee.ethz.ch
Abstract—Due to their fast responsiveness, energy storage units such as batteries can provide fast frequency control to power systems. However, when the control signal is biased or substantially autocorrelated, they cannot provide services for extended periods of time because they have limited energy capacities. To improve the ability of batteries to provide frequency control, we can offset their frequency response so that they only respond to fast and zero-mean frequency deviations, while passing slower and biased deviations to other resources. We propose two new heuristics to offset frequency control signals, and a method to compare these heuristics to previously developed heuristics. This method allows us to quantify the heuristics from the point of view of both the storage unit operator (return on investment, ROI) and the transmission system operator (impact on the power system). Considering battery degradation, the new heuristics yield better ROIs, and we find that our results are not very sensitive to the battery’s energy-to-power ratio around its optimum. We also find that the best choice of heuristic depends on what impact matters most to the transmission system operator.
I. I NTRODUCTION The number of energy storage units within power systems is likely to increase in the future as they can be used for a variety of applications including photovoltaic integration in distribution grids, peak shaving, infrastructure upgrade deferral, and powering electric vehicles. When not being actively used for one of these applications, a unit could provide other services to power systems [1], such as frequency control. In this paper, we explore methods to improve the potential for batteries to provide primary and secondary frequency control. Specifically, we investigate new methods to modify a battery’s frequency control response in order to maintain its state of charge (SoC) around an acceptable range, as shown in Fig. 1. This is done by adding a time dependent offset to the frequency control signal to form the battery’s response. The offset is canceled out by slower plants that modify their operating point in the opposite direction. These plants could be activated through either a slower time scale frequency control mechanism, intraday market, or via bilateral contracts. Therefore, batteries would help compensate fast components of supply-demand mismatch while passing on the slow components to slower units. Different methods for computing frequency response offsets are presented in [2]–[5] and we compare our new heuristics (referred to as the C1 and D1 heuristics) to the ones developed in [2]–[4]. All of the heuristics can be classified as either continuous, if the offset profile can change at any time, such as the Oudalov [2], Borsche [4] and C1 heuristics; or as discrete, if the offset profile can only change at times corresponding to
intraday market intervals, such as the California Independent System Operator (CAISO) [3] and D1 heuristics. Compared to the CAISO and Borsche heuristics whose goal is to maintain the SoC at a precise value (SoCref ), the C1 and D1 heuristics allow the SoC to vary freely within a given interval, reducing battery degradation. Our heuristics also explicitly limit the maximum offset power, therefore limiting the related power capacity investment. Section II describes the input data, scenarios, heuristics and battery degradation model. Section III describes the simulations and results and Section IV concludes the paper. II. M ETHODS We applied the heuristics on three years (2009, 2011, 2012) of frequency data from the European Continental Synchronous Area for primary control simulation and on one year of load frequency control (LFC) signals from the Swiss Transmission System Operator (TSO) for secondary control simulation. We assume that these data are representative of future conditions, though we will discuss the validity of this assumption in Section III. These data are sampled with a timestep, ∆k, of 10s, which is also the timestep used for the simulations. We compare the heuristics in two ways. First, we extend a method developed in [2] to optimally size storage units (in terms of the energy-to-power ratio, E P ) by adding a lithiumion battery degradation model, which allows us to maximize the return on investment (ROI) under realistic conditions. This approach represents the point of view of storage operators seeking to maximize profits. Secondly, we develop metrics to quantify the impact of offset mechanisms on the power system. This approach represents the point of view of TSOs. A. Offset Scenarios In the intraday market scenario, the storage unit’s response can deviate from the control signal (i.e. the standard frequency response for primary control or the LFC signal for secondary control) if the offset is the result of energy sale or purchase on the intraday market. Due to market structures, there is a delay between the last moment one can place a buy or sell order and the beginning of power delivery. We call this delay the lead time and it corresponds to the minimum time required for a change of the offset value. Furthermore, the offset value must stay constant during a market interval. In the smooth deviation scenario, the offset can vary continuously, without lead time, but it should be smooth enough for slower plants to cancel out. Here, we assume that the offset is
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−0.3
30 SoC SoC thresholds
−0.6
billed according to the balance energy price, but it could also be billed according to a bilateral contract with a slower plant. In the later case, the sum of the responses of the two units would match the control signal. Continuous heuristics are designed for the smooth deviation scenario, while discrete heuristics are designed for the intraday market scenario. B. General Equations E P:
(1)
where E>0 is the energy capacity, P >0 the physical power capacity of the battery, PA >0 the part of P committed to the ancillary service and PO >0 the part of P that is available for the offset. In our analysis, only the ratios between these quantities are important; therefore, our results can be applied to batteries of any absolute size. We define p(k) to be the power requested from (p(k) positive) or sent to (p(k) negative) the storage unit at time k: p(k) = pA (k) + pO (k) + pR (k),
70
Total Response (p(k))
0
50
−0.3 SoC SoC thresholds
−0.6
30
10 Time
Fig. 1. Illustration of the offset principle, C1 heuristic. The offset is added to the primary control response to form the total response. Hence, the response is offset in order to maintain the SoC around an acceptable range.
E E = , P PA + P O
Offset (pO(k)) 0.3
10
Time
The most significant parameter for a storage unit is
Primary Control (pA(k))
SoC and SoC Thresholds [%]
0.3
90 0.6 Power [MW]
Primary Control (pA(k))
SoC and SoC Thresholds [%]
90 0.6
(2)
where pA (k) is the power requested by the ancillary service, pO (k) the offset, and pR (k) the power sent to a dissipative resistance, when applicable (see Section II-E). Note that power capacities in (1) are upper bounds for the respective instantaneous power values in (2): |p• (k)|≤P• ∀k. Our goal in this paper is to develop methods to compute pO (k). We compute the SoC, defined as a percentage, as follows: ( 1 p(k) if p(k) > 0, ∆k ηd ηc p(k) otherwise , (3) SoC(k + 1) = SoC(k) − E where ηc and ηd are charging and discharging efficiencies, which we set equal to 90%. C. Description of Existing Heuristics 1) Borsche (continuous) [4]: The offset is computed based on previous values of pA (k): Pk (−pA (i) − ploss (i) − pR (i)) pO (k + d1 ) = i=k−a1 +1 , (4) a1 where a1 is the time averaging parameter, d1 the delay between measurement and reaction, and ploss the charge or discharge
Fig. 2. Illustration of the offset principle, D1 heuristic. Ticks on the x-axis represent the beginning of intraday market intervals.
losses. This heuristic was created for primary control, but can also work for secondary control if the parameters are modified. The minimum feasible PO is found empirically based on historic control signals: PO should be large enough so that |pO (k)| ≤ PO ∀k. 2) CAISO (discrete) [3]: This heuristic makes use of the intraday market to manage the SoC. The parameter a2 is the market interval duration and d2 the lead time between market closure and beginning of delivery. The offset is calculated only at k ∗ which represents a market closure time. Based on the difference between SoCref and SoC(k ∗ ) and considering future values of pO that have already been set, the heuristic sets pO to a constant value over the interval [k ∗ +d2 , k ∗ +d2 +a2 −1]. This value is computed so that the SoC would reach SoCref at the end of the interval, if pA is zero over the interval. This heuristic was created for LFC in California, but it can also work for primary and secondary control in Europe if the parameters are modified. We assess the minimum feasible PO in the same way as for the Borsche heuristic. 3) Oudalov (continuous) [2]: The offset is activated when the SoC exceeds specific thresholds SoCT , and only if the frequency is in the deadband of the primary control response. The offset value can change from 0 to 100% of PO at any timestep, meaning that slower plants may struggle to follow it. In this paper, we assume that the frequency band within which the heuristic can modify the response is ±10mHz instead of ±20mHz, as in the original paper, because the tighter value is in line with new ENTSOE guidelines [6]. This heuristic is only used for primary control, as it based on the primary control deadband. D. Description of New Heuristics 1) C1 (continuous): If the SoC exceeds SoCT , then the heuristic orders a ramp of fixed slope (rO ) for a fixed duration (PO /rO ) for the next timesteps, as shown in Fig. 1. Specifying the value of rO ensures that offset variations are slow enough for slower plants to follow. To make the offset easier to follow, it can not be too volatile: it has to stay flat for at least PO /rO between two ramps of opposite signs. The steady state values of PO (k) are chosen by the storage unit operator. This heuristic introduces two improvements over the Borsche method. First, it imposes a constraint on pO (k), which reduces the need for large PO (investment cost saving) and ensures that response distortion is not too large. Secondly, allowing the SoC to fluctuate between the lower and upper thresholds reduces the battery’s responsiveness, which reduces battery degradation.
TABLE I H EURISTIC -S PECIFIC PARAMETERS Parameters Reference SoC (SoCref ) SoC Thresholds (SoCT ) Offset Ramp Constraint (rO )
Values Normal With DR 53.7% 68.7% 44.0/61.5% 55.3/72.8% 1 P [MW/s] 300 O 1 P 1800 O
Market Interval Duration (a2 ) Market Closure Lead Time (d2 ) Average Duration (a1 ) Reaction Delay (d1 ) DR Power (PR ) DR Threshold (SoCDR )
-
[MW/s]
5min 1h 7.5min 45min 15min 1h 5min 0.3·PA 84%
Heuristics C1, D1, CAISO C1, D1, Oudalov C1-f C1-s D1-f, CAISO-f D1-s, CAISO-s D1-f, CAISO-f D1-s, CAISO-s Borsche-f Borsche-s Borsche all all
2) D1 (discrete): D1 is the discrete equivalent of C1, as shown in Fig. 2. As in C1, the offset is activated at specific SoCT , can only take discrete and pre-defined values, and the SoC can fluctuate between the two thresholds. As with the CAISO heuristic, pO remains constant over a market interval, the response is not subject to ramp constraints but delayed by the market lead time, and the computation considers the future values of pO that have already been set. E. Dissipative Resistance Based on [2], we also ran simulations with a dissipative resistance (DR), which prevents battery overcharging. When the SoC goes above a certain threshold SoCDR , a resistor is activated to dissipate energy at a fix rate PR until the SoC is again below the threshold. F. Heuristic Parameters The main parameters and their values are shown in Table I. Most of the heuristics were implemented in fast and slow versions, denoted by suffix “-f” and “-s”. When the suffixes are omitted, the values apply to both versions. The slow versions apply for both primary and secondary control. The fast versions apply only for primary control because their time constants are at least as fast as the typical secondary control signal. We chose SoCref to be in the middle of the battery SoC safe zone (see Section II-G), when considering charging and discharging efficiency. SoCT values are placed relative to SoCref , also considering efficiencies. When simulating the use of the DR, we increase SoCref by 15%. G. Battery Degradation Model Since there is not a single widely-accepted model for lithium-ion battery degradation [7], we implemented a simple model that captures key degradation behavior. We assume that degradation depends linearly on the amount of energy cycled, as long as the SoC stays in a “safe zone” (15-85%). In this case, the End of Life (EoL) is reached when the battery has cycled a specific amount of energy, referred to as its Operative Lifetime, which we assume is 3000 70% Depth-of-Discharge (DoD) cycles (i.e. 3000 · 0.70 · E kWh). Outside the safe zone, we assume degradation increases also linearly with respect to
the SoC, and so the degradation by f (k): 1 f (k) = f1 ·(SoC(k)−85%) f ·(15%−SoC(k)) 1
impact of p(k) is multiplied
if 15% ≤ SoC(k) ≤ 85%, if 85% < SoC(k), if 15% > SoC(k) (5) where f1 is calibrated so that EoL is reached after one 100% DoD cycle. The number of years used for ROI computation is limited by two factors: calendar life (assuming a maximum of 10 years), and operative lifetime (degradation resulting from usage), whichever comes first. H. ROI and Offset Impact Metrics The ROI is used to assess the profitability of the system PN RAS −Co k=1 (1+r)y(k)
, (6) Cinv where RAS is the annual revenue from provision of ancillary services (revenue per kW for both primary and secondary control, and revenue per kWh for secondary control), Co is the annual cost of offset energy, r the discount rate (8%), y(k) maps the simulation timestep to the numbers of years between the timestep and the beginning of the simulation, N is the number of timesteps until the EoL, and Cinv is the investment cost for the full system. For continuous heuristics, Co is based on the balance energy price and, for discrete heuristics, it is based on the intraday market price. To provide TSOs with a method to quantify the impacts of the heuristics on the power system, we propose three metrics: Q1 , the ratio between the energy cycled through the offset and the energy exchanged for frequency control P |pO (k)| ; (7) Q1 = Pk k |pA (k)| ROI =
Q2 , the root-sum-square of the offset ramps, which gives us a sense for how hard it is for slower plants to cancel out the offset sX Q2 = (pO (k + 1) − pO (k))2 ; (8) k
and Q3 , the degree to which the offset directly cancels the control signal, which tells us how much the offset degrades the requested response: 1 X Q3 = (− min(0, pA (k) · pO (k))) . (9) 1000 k
A lower impact value corresponds to a better heuristic. Q2 is only used for continuous heuristics as we assume that, for discrete heuristics, the ramping impact is included in the intraday market prices. I. Assumptions, Parameters and Data We assumed a constant hourly revenue of 16e/MW for both primary and secondary control. This corresponds to the mean marginal price for primary control in Germany and Switzerland over last year, and is between the German and Swiss
3
ROI 1.2
2
1
maximum ROI
0.8 1
1.2 ROI
E/PA [h]
1.5
1
1
0.6 0.5
0.8
0.4
infeasible
0.4
0.6 0.5
0.6
PO/PA [−]
Fig. 3. Battery ROI with C1-f heuristic, primary control. Dashed lines correspond to constant E values. P
secondary control mean marginal prices for the same period. The energy price for secondary control is calculated according to [8]. We use balance energy prices from Switzerland, and intraday market prices from Germany. Cinv is assumed to depend linearly on a battery’s power and e energy capacities: Cinv = C1 ·E +C2 ·P , with C1 = 330 kW h e and C2 = 170 kW , which is in line with the energy capacity price range of [9] for 2015-2020. Whenever a heuristic produces control actions that attempt to push a battery’s SoC below 0% or above 100%, we say that that heuristic (for that battery size) is “infeasible”. III. S IMULATIONS AND R ESULTS A. Primary Control Figure 3 shows the ROI for primary control as a function of computed with the C1-f heuristic. We ran simulations over a large set of (E, PO ) couples, by varying PPO between 0.05 A E and 1.4 and PA between 0.2h and 6h. Each (E, PO ) couple corresponds to an E P value and to a specific ROI (when the heuristic is feasible). We divided the E P axis into bins and, for each bin, we display the highest ROI associated with that bin. Given a battery with a particular E P , one can look for the maximum ROI along the dashed lines of Fig. 3. We repeated the analysis shown in Fig. 3 for each heuristic. In Fig. 4 and 5 we show that, when comparing separately the continuous and discrete heuristics, the C1-f and D1-f heuristics outperform all other heuristics in terms of ROI, over the whole E P range. In part, this is because it is beneficial to allow the SoC to drift within a interval. Targeting a precise SoC (as with the Borsche and CAISO heuristics) leads to more energy exchanged through the offset mechanism and subsequently more battery degradation. For a different problem, [10] also found that an optimal storage policy should not aim to maintain the SoC at a fixed value, but rather within an interval. Therefore, as shown in Table II, the C1-f and D1-f heuristics require a smaller PEA than the other heuristics. Additionally, the bound on PO in the C1 and D1 heuristics also helps decrease the power capacity-related investment costs. Since most of the curves are fairly flat near their peak, we find that the results are not very sensitive to a battery’s E P around its optimum. However, we do find that the results are highly sensitive to the operative lifetime. Doubling it would significantly increase the optimal ROI for each heuristic (for
1
1.5 E/P [h]
2
2.5
Fig. 4. Battery ROIs as a function of E/P, for continuous heuristics, primary control, no dissipative resistance.
D1−f D1−s CAISO−f CAISO−s
1.2 ROI
0.2
E P
C1−f C1−s Borsche−f Borsche−s Oudalov
1
0.8
0.6 0.5
1
1.5 E/P [h]
2
2.5
Fig. 5. Battery ROIs as a function of E/P, for discrete heuristics, primary control, no dissipative resistance.
instance, +44% for C1-f) and shift the optimal E P to a smaller value (for instance, to 0.5h for C1-f). In this case, the C1-f and D1-f heuristics still achieve higher ROIs than the other heuristics. To analyze the sensitivity of our results to the frequency data used within the simulations, we applied the C1-f heuristic to each of the three years of data separately, and compared the results to those generated by applying the heuristic to three consecutive years of data (as done in our other analyses), as shown in Fig. 6. The ROI from the one-year runs differ by no more than 9% of the ROI from the three-year run, indicating that the results are not particularly sensitive to the underlying frequency data. We found that using a softer degradation function, where one hundred 100%-DoD-cycles lead to EoL, has a negligible impact for most of the heuristics. This is because all of the heuristics manage to maintain the SoC in a relatively narrow band around SoCref . For the same reason, adding the DR only marginally modifies the results, since it is not often activated. TABLE II O PTIMAL BATTERY S IZE & O FFSET I MPACTS , PRIMARY CONTROL , NO DISSIPATIVE RESISTANCE . continuous heuristics
discrete heuristics
C1-f C1-s Borsche-f Borsche-s Oudalov D1-f D1-s CAISO-f CAISO-s E PA PO PA
[h]
1.4 1.6
1.7
1.5
2.9
1.5 1.8
1.9
1.9
[−]
0.2 0.2
0.7
0.5
1
0.2 0.25
0.7
0.35
35
45
94
52
15
16
36
18
Q1 [%]
36
42
80
52
24
Q2 [MW]
5.7 1.4
4.9
1.0
375
35
22
0
Q3 [MW2 ] 21
17
ROI*
1.4
TABLE III O PTIMAL BATTERY S IZE , SECONDARY CONTROL , NO DISSIPATIVE RESISTANCE .
C1−f 2009 C1−f 2011 C1−f 2012 C1−f 3 years
1.2
C1-s Borsche-s D1-s CAISO-s
1
0.5
1
1.5 E/P [h]
2
2.5
Fig. 6. Battery ROIs as a function of E/P, C1-f heuristics, primary control, one or three years of frequency data, no dissipative resistance.
Additionally, we found that removing the 10 year limit on battery life also has a small impact. Although a larger energy capacity would allow for a longer lifetime (without the 10 year limit), beyond a certain point the discount rate makes the additional revenues smaller than the marginal capacity investment. This tipping point usually corresponds to a lifetime of approximately 10 years. We found that the cost of energy exchanged through the offset mechanism for all the heuristics is always below 10% of RAS . Therefore, the offset energy could become more expensive without jeopardizing the profitability of the scheme. Given our current assumptions for offset energy costs, frequency control revenues, and so forth, we found that the battery breake e even costs for the C1-f heuristic are 450 kW h and 230 kW , C1 assuming that C2 remains the same as in Section II-I. The offset impacts are displayed in Table II. For Q1 , our heuristics outperform the Borsche and CAISO heuristics because allowing the SoC to vary freely within an interval reduces the total offset energy. Note that for all of the heuristics, 9% come from 1) the fact that the primary control signal is not exactly zero-mean and 2) the charge and discharge losses associated with the response. Similarly, for Q3 , the C1 and D1 heuristics outperform the Borsche and CAISO heuristics because they are less sensitive to small SoC variation and therefore degrade the requested response less. On the other hand, for Q2 , the Borsche heuristic does better than the C1 heuristic, and so it would be easier for a slower power plant to cancel out an offset from a battery operating the Borsche heuristic. The Oudalov heuristic is clearly a different type of heuristic. For Q2 , its impact is two orders of magnitude above the other continuous heuristics, (Q2 values for discrete heuristics would even be one order of magnitude below the Oudalov heuristic’s impact), whereas for Q3 it realizes a perfect score, as the offset is only activated when no primary control response is requested. These findings highlight that the best choice of heuristic depends on what matters most to the TSO. B. Secondary Control All of the slow heuristics are far from being cost effective given near-term battery price expectations, as the optimal ROI is always below 0.6. Since the LFC signal can be non zeromean for long periods of time, the offset power is much = 1 (as can be seen in higher than for primary control. PPO A Table III) means that the offset can completely cancel out the full LFC signal, which was not the original intention of the offset heuristics. They were designed to only slightly modify
E PA PO PA
[h] 4.25
2.75
5.5
5.5
[−] 0.7
1
0.9
1
the response, and for faster signals (primary control or U.S. LFC signals) which tend to be zero-mean on a much shorter time scales. Given these results and expected battery prices over the next few years, we do not expect secondary control in Europe with batteries to become cost competitive in the near term. As mentioned, this result does not hold for U.S. LFC since those signals are faster and reset by intrahour markets. IV. C ONCLUSION We have shown that batteries could provide primary frequency control in a cost-effective way in the near-term. In order to do so, they would need to be allowed to offset their frequency response, which might require the TSOs to develop new regulations. We designed two new offsetting heuristics and showed through simulation that they outperform previously developed heuristics in term of ROI because they reduce battery degradation. We also proposed three different metrics that allow the TSOs to assess how various heuristics would impact the power system. A sensitivity analysis highlighted that battery operative lifetime is a critical parameter. Therefore, more research on battery degradation models is needed, especially since primary control leads to small and frequent SoC swings, and most of degradation models focus on medium or large DoD. ACKNOWLEDGMENT The authors would like to thank the Swiss Commission for Technology and Innovation (project no. 14478). R EFERENCES [1] J. Eyer and G. Corey, “Energy storage for the electricity grid: Benefits and market potential assessment guide,” SAND2010-0815, Sandia National Laboratories, Tech. Rep., 2010. [2] A. Oudalov, D. Chartouni, and C. Ohler, “Optimizing a battery energy storage system for primary frequency control,” Power Systems, IEEE Transactions on, vol. 22, no. 3, pp. 1259 –1266, 2007. [3] D. Tretheway, “Regulation energy management draft final proposal,” CAISO, Tech. Rep., 2011. [4] T. Borsche, A. Ulbig, M. Koller, and G. Andersson, “Power and energy capacity requirements of storages providing frequency control reserves,” in Proceedings of the IEEE PES General Meeting, 2013. [5] C. Jin, N. Lu, S. Lu, Y. Makarov, and R. Dougal, “Coordinated control algorithm for hybrid energy storage systems,” in Proceedings of the IEEE PES General Meeting, 2011, pp. 1–7. [6] ENTSOE-E Operation Handbook, Chapter 1 : Load-Frequency Control and Performance, ENTSOE-E Std., 2009. [7] L. Lam, “A practical circuit-based model for state of health estimation of li-ion battery cells in electric vehicles,” Master’s thesis, TU Delft, 2011. [8] Swissgrid, Basic principles of ancillary service products, Std., Rev. 6.5, 2013. [9] McKinsey & Company, “A portfolio of power-trains for europe: a factbased analysis,” 2010. [10] N. Gast, D.-C. Tomozei, and J.-Y. Le Boudec, “Optimal storage policies with wind forecast uncertainties,” Proceedings of Greenmetrics 2012, Imperial College, London, UK,, 2012.
