Princess Garasi, Yaser Qudaih, Raheel Ali, Masayuki Watanabe, and Yasunori Mitani

Coefficient Diagram Method Based Load Frequency Control for a Modern Power System

Princess Garasi, Yaser Qudaih, Raheel Ali, Masayuki Watanabe, and Yasunori Mitani

—With the increasing penetration of renewable energy sources with a wide range of operating conditions causing power system uncertainties, conventional controllers are incapable of providing proper performance to keep the system stable. However, controllable or dispatchable loads such as electric vehicles (EVs) and heat pumps (HPs) can be utilized for supplementary frequency control. This paper shows the ability of plug-in hybrid EVs, HPs, and batteries (BTs) to contribute in the frequency control of an isolated power system. Moreover, we propose a new online intelligent approach by using a coefficient diagram method (CDM) to enhance the system performance and robustness against uncertainties. The performance of the proposed intelligent CDM control has been compared with the proportional-integral (PI) controller and the superiority of the proposed scheme has been verified in Matlab/Simulink programs.

Index Terms—Battery, coefficient diagram method, electric vehicles, heat pump, load frequency control, renewable energy sources.

1. Introduction

Microgrid technology is the integration of distributed generation (DG), energy storage systems, and loads. It is an effective approach to the interconnection of large-scale DGs with large power systems[1]. Implementation of microgrid systems can be advantageous to both the users and electric utility providers. It can improve the network, reduce emissions, and cut down costs for the user. Also, since microgrid systems can reduce the power flow on transmission and distribution lines, there is a reduction in losses[2].

It is expected that more renewable energy sources (RES) will be installed in the microgrid in the near future. Since RES causes output fluctuations over time, additional control methodologies are necessary to keep the system stable. This problem is addressed by adding more control to other generation systems such as energy storage systems, or by forming hybrid systems[2]. Recent studies include the utilization of existing customer appliances such as heat pumps (HPs)[3],[4], and electric vehicles (EVs)[5]-[7]as supplementary frequency control. However, with various system operating conditions and unpredictable patterns which can cause system uncertainties, conventional controllers may no longer be able to damp the frequency deviation brought by the RES output and load fluctuations that deteriorates the system stability. To solve this problem, a coefficient diagram method (CDM) has been developed.

The basic principle of CDM has been known in the industry and control community for more than 40 years and it has been successful in the applications of servo control, steel mill drive control, gas turbine control, and spacecraft attitude control. CDM provides more reliable parameter section rules, and by using CDM, the simplest controller to satisfy specifications can be designed efficiently[8]. In this paper, the CDM polynomials parameters have been designed based on the dynamic model of the power system following the methodology described in [9] and [10].

This paper is organized as follows: Section 2 describes the smart micro grid system. Section 3 discusses the system simulation condition and structure in detail. Section 4 describes the general consideration about CDM and its structure. The load frequency control (LFC) model strategy with the proposed controllers is shown in Section 5. Section 6 analyzes the time-domain simulated results of three studied cases of the proposed controller with an isolated small power system under various operating conditions. Finally, conclusions are drawn in Section 7.

2. Microgrid System

2.1 Microgrid Model

The microgrid system in this paper is composed of loads, gas engine generator, photovoltaic (PV), and wind turbine (WT). The gas engine generator is the main generator of this system. It is controlled based on LFC and governor free control (GF). LFC has been carried out to balance the generation and demand. The obtained LFC signal is fed to batteries (BTs), EV, HP, and gas power generators as shown in Fig. 1. Moreover, the block diagram of the gas engine is shown in Fig. 2.

2.2 Power Fluctuation of RES and Load

The aggregated load model defined in [11] is shown in Fig. 3. The standard deviation in MW of the load can be expressed by

whereloadPis the load power output.

The fluctuation period considered in this paper is 5 minutes to 30 minutes. Random fluctuations are generated from the white noise block where the fluctuation periods lower than 5 minutes and higher than 30 minutes are eliminated by low-pass and high-pass filters, respectively. It is then multiplied by the standard deviation and base load capacity to calculate the output fluctuation in the system. Wind and solar power generations are represented in the same manner where their power outputs are 25 MW and 6 MW in this paper, respectively.

The corresponding load fluctuation is shown in Fig. 4. As for the installation sites of wind and solar power, it is assumed that the wind turbine and solar system are widely dispersed in the area. In this case, the maximum output fluctuation over a 20-minute interval is about 60% of the rated output due to the smoothing effect[5]. However, the smoothing effect depends on the climate and installation conditions. Hence, it is assumed in this paper that the fluctuation band of wind power is 70% of the rated output.

2.3 BT Model

The BT model shown in Fig. 5 is designed considering the inverter capacity and battery capacity. The control and communication delays are approximated by the first-order model with a one-second time delay denoted byTb. The BTs will charge and discharge according to the LFC signal.

Fig. 1. Frequency analysis model.

Fig. 2. Gas engine generator dynamics.

Fig. 3. Load model.

Fig. 4. Load fluctuation.

2.4 HP Model

An HP is a high-efficiency and energy-saving appliance used by customers to store hot water in a tank for a day. It is assumed in this paper that the power consumption of the HP can be controlled within 20% to 80% of the rated power consumption according to the input control signal (LFC signal). Also, the per-unit rated power consumption is assumed according to the capacity of the tank. HP consists of a start unit and thermal unit as shown in Fig. 6.

Fig. 5. BT model.

Fig. 6. Aggregated model of HP.

Table 1: Detailed parameters of HP

The HP parameters are given in Table 1[3],[4]. The start unit is modeled to operate from zero to the steady state power consumption, which is approximated by the first-order model with a 60-second time delay. The thermal storage unit expresses the amount of total capacity of the hot water tankCmax. In this paper, it is assumed that there are 10000 HP units in the power system. The total power consumption can then be calculated as

2.5 EV Model

Evs, which have electric motors instead of gas engines, have gained much attention as the next generation vehicles. Charging and discharging of EVs corresponding to the LFC signal can be controlled in the same manner with BTs through bidirectional power converters. The state of charge (SOC) of EVs under study is kept between 60% to 90%. Outside this range, the EVs do not respond to any signal. In the described system, 60% of the EVs are defined as a controllable state and can be discharged with an LFC signal. The EV model[7]is described in Fig. 7.

It is assumed that 10000 EV units are connected in the area under study. Also, it is assumed that the SOC of each unit is synchronized. Parameters of the EV are shown in Table 2[8]. Within its given power capacity, EVs can charge and discharge with a time lag of 5500 seconds corresponding to an input signal.

Fig. 7. EV model.

Table 2: Parameters of EV

3. System Parameters and Formulation

The smart microgrid power system introduced in this paper has gas engine generators as well as PV and WT as renewable energy sources. For simulation conditions, the nominal parameters of a practical single smart microgrid power system are listed in Table 3.

Table 3: Simulation conditions for frequency analysis

The overall generator-load dynamic relationship between the supply errorand the frequency deviationcan be expressed as

whereMis the equivalent inertia constant, ?Pdis the diesel power change, andDis the damping constant. Also,can be expressed as:

wherePEV,PBT,PHP,PWP, andPPVare the EV, BT, HP, water pump, and PV powers, respectively.

The dynamic of the gas generator can be expressed as

where ?Pgis the governor output change andTtis the turbine time constant.

The dynamic of the governor can be expressed as

where ?Pcis the output power of the controller,Ris speed droop characteristic, ?PgandTgare governor power deviation and generator time constants.

Rated capacities of gas engine generator, wind, and solar are shown in Table 4.

Table 4: Generation data

4. Coefficient Diagram Method

CDM is a technique to arrange the poles of a closed loop transfer function in order to get a wanted response in the time domain[9]-[11]. In the coefficient diagram, the logarithmic vertical axis shows the coefficients of characteristic polynomial (ai), stability indices (γi), and equivalent time constant (τ) whereas the horizontal axis shows the values of ordericorresponding to each coefficients. The degree of convexity obtained from coefficients of the characteristic polynomial gives a measure of stability, whereas the general inclination of the curve measures the speed of response. On the other hand, the shape of theaicurve due to the plant parameter variation measures the robustness.

The block diagram of a single input single output (SISO) linear time invariant system with CDM control is shown in Fig. 8.N(s) is the numerator polynomial andD(s) is denominator polynomial of the plant transfer function.A(s) is considered as the forward denominator polynomial.F(s) andB(s) are considered as the reference numerator and feedback numerator polynomials. In the CDM controller, the transfer function of the controller has two numerators, which implies the two degrees of freedom (2DOF) system structure. In this methodris taken as the reference input to the system,uas the controller signal,das the external disturbance signal, andydenotes the output of the control system:

in which the conditionp≥qmust be satisfied andilandikare cofficients. To get the characteristic polynomialP(s), the controller polynomials from (7) are substituted in (6). Then (6) becomes

Fig. 8. Block diagram of a CDM control system.

CDM needs some design parameters with respect to the characteristic polynomial coefficients. They are the equivalent time constantτwhich gives the speed of closed loop response, the stability indicesγiwhich gives the stability and the shape of the time response, and the stability limitsiγ?. The relations between these parameters and the coefficients of the characteristic polynomial (ai) can be described as

According to Manabe’s standard form, the values ofγiare selected as {2.5, 2, 2 ,2}. According to the requirement,γivalues can be changed by the designer. By using the key parameters (τandγi), the target characteristic polynomial,can be framed as

The parameters of the CDM controller are set as follows and the time constantτcan be taken as 2 s, so

Choosingk0=1, then

5. LFC System Model

The main function of the LFC system is to adjust the load reference points of the governors of selected units in the control area. As a result, the mechanical power is adjusted according to these load reference points. These measurements are used to evaluate the area requirement (AR), which is the basis for the control signal sent to the generators equipped with LFC. The reference LFC output signal of each generator is generated by passing the AR signal through a proportional integral (PI) controller. In the LFC control method, the flat frequency control (FFC) is applied. In this control technique, the LFC signal is distributed to the gas engine generator, BTs, EVs, and HPs in the microgrid according to the response speed and controllable capacity. The block diagram of the proposed LFC is illustrated in Fig. 9.

Fig. 9. LFC model block diagram.

The calculation cycle of AR is approximated by the first-order model with a delay of 5 seconds denoted byTAR. Controllable capacity (LFC capacity) of the gas engine generators is expressed in %Kg/MW/Hz, whereCBTandCEVare the inverter capacity of the BTs and the controllable capacity of the EVs, respectively. First, the LFC signal is dispatched to the EVs in which the response speed is the fastest compared with that of the other three sources. Next, the components of the LFC signal that cannot be covered by the EVs due to its limited controllable capacity are fed to LFC generators and HPs as LFC1 (with a time delay constant TLFC) and LFC2 (with the time delay constantTHP), respectively. Then, the component which cannot be covered by the LFC generators and HPs due to the slow response speed is then fed to the BT system (with a time delay constantTBT).

6. Results and Discussions

Computer simulations have been carried out in order to validate the effectiveness of the proposed scheme. The Matlab/Simulink software package has been used for this purpose.

6.1 Superiority of Proposed CDM Controller

The system performance with the proposed CDM controller at nominal parameters is tested and compared with the conventional controller in a system with HPs, EVs, and BTs cooperated with the LFC signal strategy. Fig. 10 shows that the frequency of the microgrid system is fluctuating. However, in Fig. 11, it can be noticed that with the proposed LFC-based CDM controller, the frequency is more stable and has faster stabilization compared with the conventional controller.

Fig. 11. Suppressed frequency fluctuation with LFC signal using CDM and PI controller.

For showing the adaptive property of the proposed CDM controller, the main system parameters in the frequency response model (see Fig. 1), such as the damping coefficientD, inertia constantM, turbine time constantTt, and generator time constantTg, are significantly changed as shown in Table 5. The closed-loop frequency response after applying these changes to the microgrid system parameters are shown in Fig. 12. It is seen that the conventional controller cannot handle the applied parameter perturbation while the CDM controller is proved to be more superior, which has a rapid response to keep the smart microgrid system frequency to 60 Hz.

Table 5: Uncertain parameters and variation range

Fig. 12. Frequency in parameters uncertainty.

6.2 Effectiveness of Controllable Loads (EV and HP) and BTs

Table 6 summarizes the maximum deviation and the root mean square (RMS) values of the frequency deviation in 1.5 hours in three cases. In case 1, the EVs, HPs, and BTs are not part of frequency control. In case 2, the EVs, HPs, and BTs are part of LFC with the conventional controller. In case 3, the EVs, HPs and BTs are part of LFC with the CDM controller. As shown in Table 6, the frequency control with CDM becomes more effective with the help of the EVs, HPs, and BTs.

Table 6: Estimated indices of frequency fluctuation

6.3 Power Exchange

Fig. 13 shows the total power capacity exchange of the EVs, HPs, and BTs and the required power demand of LFC signal in the system. The total required power given in the system is estimated about 10 MW to 40 MW by LFC signals, while the negative sign in Fig. 13 shows the deficiency in the required power demand against the load caused by RES. The EVs discharge power to the system rapidly and share the maximum power in the system throughout the period of 1.5 hours, while BTs share the minimum power.

Fig. 13. Total power forecast in microgrid system.

Also, the contribution of the EVs on the LFC is larger than that of the HPs. It is important to note that this contribution depends on the assumed number of units and the assumed controllable capacity of these appliances. Since BTs have the slowest response, it can be said that the required BT capacity to suppress the frequency fluctuation can be partly reduced by a number of EVs and HPs. The proposed LFC method will be effective if the cost of the control of both EVs and HPs is cheaper than that of the BT installation.

Fig. 14 and Fig. 15 show the changes of the SOC of the EVs and that of the BTs, respectively. Fig. 14 illustrates that the SOC of EVs are controlled in the range of (86±0.75)%. Moreover, the SOC of the BTs fluctuates within 66% to 78%. It can be seen that the SOC does not vary rapidly since EVs shared the most power capacity in the system. It indicates that the LFC with EVs and HPs can decrease the utilization ratio of the BTs and also reduce the capacity of the BTs.

Fig. 14. Total SOC% of EVs.

Fig. 15. Total SOC% of BTs.

7. Conclusions

This paper studies the merging of RES with output fluctuations, such as EVs, HPs, and BTs, in a microgrid controlled by a robust LFC based CDM controller. Digital simulations have been carried out to validate the effectiveness of the proposed scheme. The proposed controller has been tested for the mismatched generation. The simulation results demonstrate that the closed-loop LFC system with a CDM controller has better performance in comparison with the classical integral control design in all test scenarios and is robust against system perturbation. Also, it has shown that HPs, EVs, and BTs have a positive effect on the total response of the smoothing effect of renewable energies and can play a vital role to balance the power supply and demand in the system.

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Princess Garasireceived her B.S. degree in electrical engineering from University of the Philippines in 2011. She is currently pursuing her M.Eng degree in electrical and electronic engineering at Kyushu Institute of Technology (KIT), Japan. Her research interests include power system, smart grid, and renewable energy sources.

Yaser Qudaihgraduated from the University of Engineering and Technology, Pakistan in 1996 in electrical engineer. He received his M.S. and Ph.D. degrees both from Kumamoto University, Japan. He is currently a researcher at KIT. His research interests including power system, renewable energy, and smart grid applications.

Raheel Alireceived his bachelor degree in electrical engineering from the Quaid-e-Awam University of Engineering, Science & Technology, Pakistan in 2010. He completed his M.Eng degree in electrical engineering at KIT, Japan. He is currently working as an electrical engineer at JGC Corporation. His research interests include power system operation and control with the integration of renewable energy sources in smart grid systems.

Masayuki Watanabereceived his B.S., M.S., and D.Eng. degrees all in electrical engineering from Osaka University, Japan in 2001, 2002 and 2004, respectively. Currently, he is an associate professor at the Department of Electrical and Electronic Engineering, KIT, Japan. His research interests are in the area of analysis of power systems.

Yasunori Mitanireceived his B.S., M.S., and D. Eng. degrees all in electrical engineering from Osaka University, Japan in 1981, 1983 and 1986, respectively. He is currently a professor at the Department of Electrical Engineering and Electronics, KIT, Japan. At present he is the Head of Environmental Management Center, KIT, Japan. His research interests are in the areas of analysis and control of power systems. He is a member of the Institute of Electrical Engineers of Japan and IEEE.

Manuscript received May 15, 2014; revised July 24, 2014.

P. Garasi is with the Department of Electrical and Electronic Engineering, Kyushu Institute of Technology, Fukuok, Japan (Corresponding author e-mail: pggarasi@gmail.com)

Y. Qudaih, R. Ali, M. Watanabe, and Y. Mitani are with the Department of Electrical and Electronic Engineering, Kyushu Institute of Technology, Fukuok, Japan.

Digital Object Identifier: 10.3969/j.issn.1674-862X.2014.03.006