The modes of switches during the charging and discharging of CES unit.

## Abstract

The fast acting due to the salient features of energy storage systems leads to using of it in the control applications in power system. The energy storage systems such as superconducting magnetic energy storage (SMES), capacitive energy storage (CES), and the battery of plug-in hybrid electric vehicle (PHEV) can storage the energy and contribute the active power and reactive power with the power system to extinguish the rapid change in load demands and the renewable energy sources (RES). This chapter gives an overview about the modeling of energy storage devices and methods of control in them to adjust steady outputs.

### Keywords

- energy storage devices
- superconducting magnetic energy storage (SMES)
- capacitive energy storage (CES)
- plug-in hybrid electric vehicle (PHEV)

## 1. Introduction

With the increasing of distributed generator (DG) technologies, large numbers of DGs are connected with the grid in different forms, such as wind and solar power systems [1, 2, 3]. Because of the fluctuations of their output power, energy storage devices are utilized to adjust steady outputs [4, 5]. In fact, the characteristics of the different storage devices vary widely, including the amount of energy stored and the time for which this stored energy is required to be retained or released [6, 7]. The superconducting magnetic energy storage (SMES), superconducting capacitive energy storage (CES), and the battery of plug-in hybrid electric vehicle (PHEV) are able to achieve the highest possible power densities. Each storage energy device has a different model. Several control approaches are applied to control the energy storage devices. In [8, 9], model predictive control (MPC) is presented for residential energy systems with photovoltaic (PV) system and batteries. Model predictive control predicts the load and the generation over a certain time horizon into the future and finds the optimum schedule of the battery over that period which can minimize a desired objective. In [10], a voltage regulation in distribution feeders is proposed using residential energy storage units. The control method is carried out by making the charging and discharging rates of the batteries a function in the voltage at the point of common coupling. A fuzzy logic based control method of battery state of charge (SOC) is presented in [11]. This control method regulates the battery SOC at expected conditions, and consequently the energy capacity of BESS can be small. In [12], a state-of-charge feedback control technique is used to keep the charging level of the battery within its proper range while the battery energy storage system make the output fluctuation of a wind farm smooth. The optimal design of MPC with SMES based on the bat-inspired algorithm (BIA) is introduced for load frequency control in [13]. This work is extended to include the MPC with SMES and CES in [14]. Decentralized MPC with PHEVs is utilized for frequency regulation in a smart three-area interconnected power system in [15].

## 2. Superconducting magnetic energy storage

The SMES units are used to compensate the load increments by the injection of a real power to the system and diminished the load decrements by the absorbing of the excess real power via large superconducting inductor [16, 17, 18]. Figure 1a show a schematic diagram of SMES unit consists of superconducting inductor (*L*), Y-Y/Δ transformer, and controlled ac/dc bridge converter with 12-pulse thyristor. A power conversion system (PCS) is used to connect the superconducting inductor with the AC grid. The PCS is a dual-mode converter and it works as a rectifier or as an inverter in the charging and discharging modes of the inductor respectively. Obviously, the mode of operation is detected according to the nature of load perturbation. The charging phase represents the rectifier mode. In the rectifier mode, adjusted positive voltage is applied across the terminals of the inductor. Alternatively, the discharging phase represents the inverter mode. In the inverter mode, adjusted negative voltage is applied across the terminals of the inductor. The controlling in the thyristor firing angle is used to switch either rectifier or inverter modes, the converter output voltage is expressed in kV and it is given in following equation [19]:

where *Ed* is the inductor DC voltage (kV); *Eo* is the converter open circuit voltage (kV); α is the thyristor firing angle (degrees); *Id* is the inductor current (kA); *RC* is the equivalent resistance of commutation (ohm).

### 2.1 Modeling of superconducting magnetic energy storage

According to the rectifier or inverter modes, the polarity of the voltage *Ed* is adjusted while the direction of inductor current *Id* does not change. As mention in the above section, the regulation of the thyristor firing angle is used to controlling the direction and magnitude of the inductor power *Pd*. Initially, a small positive voltage is applied to charge the inductor to its rated current according to the desired charging period of the SMES unit. The inductor voltage is reduced to zero and the inductor current reach to its rated value because the coil is superconducting. When the inductor current reached to its rated value, the SMES unit can be coupled to the power system. The error signal *∆e* represent the input to control the SMES voltage *Ed*. This error signal may be the change of system frequency, the change of system voltage, or the change of system current according to the control object. The incremental voltage and current changes of the SMES coil are given as follows:

where *Tdc* is the converter time constant in sec, *Ko* is the gain of the proportional controller in kV/Hz and *s* is the Laplace operator. As reported in [19], the inductor current reaches to its nominal value very slowly in the SMES unit. So, the fast rate of the current to restore its rated value is required to extinguish the next load perturbation fastly. Therefore, a negative feedback signal is used in the SMES control loop to provide fast current recovery. Thus, Eq. 2 is rewritten in following form:

where

Therefore, the real power incremental change Δ*Pd* of the SMES unit in MW is computed as follows:

The corresponding block diagram of an SMES incorporating the negative feedback of the current deviation is shown in Figure 1b.

Setting the parameters (*L*, *Ko*, *KId* and *Ido*) of the SMES unit to their optimistic values can enhance its role in achieving well-damped to the responses. Herein, the application of artificial intelligence (AI) techniques is suggested to search for the optimal parameters of the SMES and controller simultaneously.

### 2.2 Control techniques of SMES

Modern control techniques such as adaptive control, fuzzy logic control, and model predictive control (MPC) can be applied to control the charging and discharging of the SMES instead of the proportional controller as shown in Figure 2. The controller and SMES parameters must be adjusted by proper optimization technique such as genetic algorithm (GA), particle swarm optimization (PSO), and artificial bee colony (ABC),…etc. to give a good performance.

## 3. Capacitive energy storage

The capacitive energy storage (CES) has an important role to stabilize the power system against to the sudden change in load demand. The static operation of the CES makes its response faster than of the mechanical systems [20, 21, 22, 23]. Parallel storage capacitors form the CES. Figure 3a shows a schematic diagram of a CES unit connected with the AC grid by a PCS. The capacitor bank dielectric and leakage losses are defined by the resistance (R). When the load demand decreases, the capacitor charges up to its rated full value, thus releases an amount of the excess energy in the system. Contrary, the capacitor discharges to its initial value of voltage when the load demand rises suddenly and release the stored energy fastly to the grid through the PCS. A gate turn-off (GTO) thyristors is used as switches to control the direction of the capacitor current during the charging and discharging as shown in Table 1.

Charging mode | Discharging mode | |
---|---|---|

S_{1}, S_{4} | ON | OFF |

S_{2}, S_{3} | OFF | ON |

The controlling in the thyristor firing angle is used to switch either rectifier or inverter modes of CES to adjust the capacitor voltage as defined in Eq. 1.

### 3.1 Modeling of superconducting magnetic energy storage

The CES unit is ready to be coupled to the power system for LFC when the rated voltage across the capacitor is attained. The current *Id* of CES is controlled by sensing the error signal Δe. This error signal may be the change of system frequency, the change of system voltage, or the change of system current according to the control object. The incremental current changes of the CES are given as follows:

where *Kc* is the proportional controller in kA/Hz.

As stated in [20], the CES voltage reaches to its nominal value very slowly. So, the fast rate of the capacitor voltage to restore its rated value is required to extinguish the next load perturbation fastly. Therefore, a negative feedback signal is used in the CES control loop to provide a fast voltage recovery. Thus, Eq. 7 is rewritten in following form:

where

Thus, the real power incremental change Δ*PCS* of the CES unit in MW is computed as follows:

The corresponding block diagram of a CES unit incorporating the negative feedback of the voltage deviation is shown in Figure 3b.

Setting the parameters (*C*, *Kc*, *KEd* and *Edo*) of the CES unit to their optimistic values can enhance its role in achieving well-damped to the responses. Herein, the application of artificial intelligence (AI) techniques is suggested to search for the optimal parameters of the CES and controller simultaneously.

### 3.2 Control techniques of CES

Modern control techniques such as adaptive control, fuzzy logic control, and MPC can be applied to control the charging and discharging of the CES instead of the proportional controller as shown in Figure 4. The controller and CES parameters must be adjusted by proper optimization technique such as GA, PSO, and ABC,…etc. to give a good performance.

## 4. Plug-in hybrid electric vehicle model

The PHEV model is represented as first-order transfers function with very small time constant *TPHEV* as shown in Figure 5(a) [24, 25, 26, 27]. The change of PHEV output power ∆*PPHEV* for charging or discharging is selected according to the control signal *Ui* of the controller. In this chapter, the control signal is determined by modern control techniques such as adaptive control, fuzzy logic control, and model predictive control (MPC). The control signal depends on the error signal to adjust the charging or discharging of PHEVs batteries. Figure 5(b) shows a bi-directional PHEV to charging and discharging power control ‘vehicle to grid (V2G)’. According to the change of error, this V2G release a power to the grid or drain power from the grid. The change of PHEV output power is adjusted by the control signal (U) according to the limit range of output power deviation of PHEV as

where *P*_{max} is the maximum PHEV power.

## 5. Conclusion

In this chapter, classifications of energy storage devices and control strategy for storage devices by adjusting the performance of different devices and features of the power imbalance are presented. The modeling of each storage energy devices is discussed. Furthermore, the control method for each one are cleared. These energy storage devices with modern control techniques such as adaptive control, fuzzy logic control, and model predictive control (MPC) can be applied to extinguish the rapid change in load demands and the fluctuations of RES.