**1. Introduction**

The limitations of fossil fuel reserves and environmental concerns have increased interest in renewable energy resources [1]. Solar photovoltaic (PV) generation is one of the most promising renewable energy approaches. In recent years, PV power generation has increased significantly thanks to the development of cost-effective, higher efficiency semiconductor PV technology, as well as advancements in related power electronics and controls. Solar PV is projected to contribute 16% of the world's total electricity and 43% of the added electricity in the United States (US) by 2050 [2,3]. However, the uncertainty and variability of PV sources constitute the main obstacles against their high level penetration. Furthermore, PV sources do not have inherent rotational inertia to support the grid during the transients [4–6].

The power injected by PV can change suddenly due to cloud movements. In 2011, a study of three PV systems, located in Porterville, Palmdale, and Fontana, California, found that the power ramp rate was as high as 90%, 93% and 75% per minute of their rated power, respectively [7]. The sudden changes in PV power can introduce voltage fluctuations in distribution system and frequency fluctuations in the case of high PV penetration and weak grid, leading to grid stability issues [2,8–10]. Puerto Rico Electric Power Authority (PREPA) limits the ramp rate to 10%/minute of the rated capacity for both wind and PV generation, and the Hawaiian Electric Company (HECO) limits its ramps at ±2 MW/min (even ±1 MW/min during some times) for wind generators under 50 MW [11]. According to IEEE standard 1547, distributed energy resources (DERs) cannot cause voltage fluctuations exceeding 3% for a medium voltage interconnection and 5% for a low voltage interconnection [12].

A large number of distributed PV generators together create a duck-shaped daily net load profile due to the variation in solar irradiation. The duck-shaped net load profile has steep slopes, especially in the evening. This requires bringing a large number of synchronous resources online within a short period of time. Such changes in the net load profile cannot be easily addressed by slow conventional generators and the problem becomes severe with the increased penetration of PVs. The existence of a large number of PV generators also increases the chances of negative net load that requires curtailment of PV power [8,13,14].

The number of PV generators connected to the electric power grid has been rising continuously. Authorities and researchers are considering the development of strategies and approaches to obtain grid services, both transient and long-term, from the aggregation of these distributed resources [15]. Therefore, PV generators have been coupled together with complementary generation and storage technologies to address the intermittencies and the disturbances, and these distributed resources are utilized to obtain grid services. Battery energy storage (BES) systems and super-capacitors are two important energy storage approaches that can be coupled with PV generators [16–18].

Most of the existing approaches that combine BES with household PV-prosumers are concerned with optimization of battery size, and energy management strategies to minimize electricity bills [19–21]. These methods do not address the impact of intermittency and power variation of PVs on the grid. Moving average methods are used to mitigate the impact of abrupt PV power disturbances. However, moving average method does not directly control the ramp rate, depends on historical data, and operates the BES even though BES operation is not required due to the memory effect [22]. The direct ramp control of PV power is an effective method. The ramp-up of PV output is generally not a challenging issue, and it can be achieved using a proper controller without requiring a storage, at the expense of total extracted PV energy [23]. However, the ramp-down is a challenge, and it requires an energy storage to compensate for the PV power drop.

The fluctuations of wind/PV generators are compensated using the BES station in Reference [24]. The control approach calculates the target power for the BES station from the fluctuations of wind/PV generators, and this power is shared by the constituting smaller BES units based on their SOC level. In Reference [22], a BES is coupled with a PV system to mitigate the power fluctuations caused by cloud passing using the ramping method. During PV power fluctuations, the BES is controlled based on the inverse characteristics of the desired ramp-rate. Once the PV power fluctuation is over, the BES power is brought to zero using SOC droop-based ramp rate. The control strategies of References [22,24] are presented at system level, and ignore the dynamics of the converter and details of the control design. Furthermore, the BES reference calculations involve complex algorithms. A hybrid BES and super-capacitor setup is used in Reference [25] to provide frequency support. Although this is combined with a PV generator, it does not directly address the PV power generation variations. Moreover, the frequency does not directly and quickly reflect the PV disturbances at the distribution level.

A battery is integrated in an ac-stack architecture in series with PV converters in Reference [26] to achieve the controlled ramp rate in power. The BES control uses the derivative of the rms of ac string current to determine the fluctuation in PV power. This method does not appear to be able to respond to abrupt PV fluctuations in a timely manner due to the limitations with a derivative operator in practice. Furthermore, this architecture is vulnerable to over-modulation that distorts the output. Finally, the stack architecture compromises the plug-and-play flexibility of the system. In Reference [27], a power management strategy is proposed for a BES in connection to a PV and a local load. If the local load is larger than a predefined minimum value, the combined PV-BES supply the load and the rest of power is offset by the grid. No power ramping is done in this mode. If the local load is less than a predefined minimum, the battery performs a ramp rate control, based on Reference [22], if the PV fluctuations exceed the predefined ramp rate; and the PV-BES operates in constant power feed

mode otherwise. Further details of the control design procedures are not presented. A PV-battery combination connected to an ac grid is presented in Reference [28] where the PV operates at the MPP, a battery controls the dc bus voltage of the inverter and the inverter operates in constant power mode. If the reference power of the inverter is properly determined, it can realize ramping. However, this is not discussed in Reference [28]. One limitation of this approach is that the BES cannot be used for an already operating inverter without altering the control system of the inverter. A similar approach is used in Reference [29] where the BES supplies/absorbs the difference of power between the desired and the PV power. The controller in Reference [29] requires communication of an ac signal which is a major limitation. In Reference [30], a 1 MW/2 MWh BES is connected with a multi-MW PV system to achieve (1) power smoothing using moving average and low pass filter, and (2) frequency regulation using P-f droop control. The power smoothing method of Reference [30] has the disadvantages of the moving average approach mentioned earlier. Also, the frequency regulation may not be useful at the distribution level.

Most of the aforementioned works that implement BES to smooth PV power treat the matter at the system level and ignore the dynamics at the converters level. There is a lack of systematic design of the local controls to accomplish the desired power ramps. This paper presents a BES control system concept to address both the abrupt and daily variations of PV power. The proposed BES connects at the terminals of the PV generator (without requiring a change in the PV inverter) and responds to the disturbances to execute desired power ramp rates. The ramp rate signals are either generated locally or received from the grid operator. The paper presents the complete mathematical model of the system including the dynamics of the converter and provides systematic approach in designing the control. Furthermore, if the BES is only used to filter the abrupt PV disturbances for a short period, it results in low utilization of the BES. Therefore, the ramping capability of the PV-BES system has been utilized in this paper to improve the daily load profile. The grid operator can remotely command the distributed PV-BES units with the desired ramp rate, and the proposed control executes the command. The aggregated effect of the distributed PV-BES units with the proposed ramping capability significantly enhances the daily net load profile in terms of (1) reduced peak, (2) increased minimum, and (3) reduced slopes. The proposed method also includes an outer loop that controls the SOC of the BES. The performance of the proposed system is verified using extensive computer simulation and a laboratory prototype.

The contributions of this paper may be summarized as follows: (1) A simple yet effective battery control philosophy to address both the abrupt and daily photovoltaic generation variations. The two set-points of the proposed controller can be generated locally or through communications for system-wide optimization; (2) Complete modeling and control design of the battery control system; (3) Verification of the proposed approach using simulations and laboratory tests.

The remainder of the paper is organized as follows. The power variabilities, abrupt and daily profile, originated from PV generators are discussed in Section 2. Section 3 presents a proposed battery energy storage (BES) system, its mathematical model, and the proposed control to ramp the output power of the PV. Numerical designs and the results obtained both in simulation and laboratory experiment are presented in Section 4. The paper concludes with concluding remarks and limitations of the proposed control in Section 5.
