Power Electronics-enabled Autonomous Power ...

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx.doi.org/10.1109/TIE.2017.2677339 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

Power Electronics-enabled Autonomous Power Systems: Architecture and Technical Routes Qing-Chang Zhong, Fellow, IEEE

Abstract—Power systems are going through a paradigm change from centralized generation to distributed generation and further on to smart grids. In this paper, it is shown that future power systems will be power electronics-based, instead of electric machines-based, with a huge number of incompatible players and that the fundamental challenge behind this paradigm change is how to make sure these players could work together and maintain system stability. Then, a lateral architecture based on the synchronization mechanism of synchronous machines (SM), which has underpinned the growth and operation of power systems for over 100 years, is proposed to unify the integration and interaction of these players with the grid, by operating the power electronic converters involved to behave like virtual synchronous machines (VSM). Thus, all the suppliers and the majority of loads can follow the same mechanism to regulate system stability. This paves the way for autonomous operation of future power systems. Moreover, two technical routes, one based on the synchronverter technology and the other based on the robust droop control technology, are proposed to implement the architecture. Real-time simulation results are presented to illustrate the operation of such a system. Index Terms—Smart grid, grid architecture, renewable energy, distributed energy resources (DER), virtual synchronous machines, synchronverter, robust droop control, universal droop control, self-synchronization, control, power electronics, power systems, phase-locked loops

I. I NTRODUCTION N current power systems, the generation of electricity is dominated by centralized large facilities. For example, the lion’s share of electricity in China is provided by just 1500 or so generators rated at 200 MW and above. It is relatively easy to regulate a limited number of generators in a power system to achieve system stability and meet the balance between generation and demand. Due to civilization and economic development, the demand for electricity is constantly growing, leading directly to supply issues and environmental crisis. The large-scale utilization of distributed energy resources (DER), including renewables, electric vehicles and energy storage

I

Manuscript received September 16, 2016; revised December 4, 2016 and January 5, 2017; accepted January 30, 2017. Qing-Chang Zhong is with the Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA. Email: [email protected]. Some ideas of this paper were presented at (semi-)plenary talks, panel discussions, tutorials and workshops at several conferences, including 2016 IEEE PES General Meeting, IEEE ISIE 2016, IEEE ECCE 2015, The 1st Indian Control Conference, ACC 2015, The 2014 Chinese Control and Decision Conference (CCDC), IEEE IECON 2014, IEEE GreenTech 2014, and IEEE PEDG 2013, and distinguished lectures sponsored by IEEE Control Systems Society and IEEE Power Electronics Society.

systems, is regarded as a promising means for lessening these problems [1] and, as a result, power systems are going through a paradigm change from centralized generation to distributed generation. Adding a communication and information network into power systems, hence the birth of smart grids, would help make power systems more efficient, more resilient to threats, and friendlier to the environment [2]. Naturally, the added communication network is expected to provide the infrastructure needed for all power system players to work together, even at the low-level controls. This standard scenario, however, could lead to serious concerns about reliability [3], [4]. If the communication network breaks down then the whole power system could crash. Moreover, when the number of players reaches a certain level, how to manage the communication network is itself a challenge. When a large number of DER are integrated into a power system, the number of players on the supply side will increase considerably. Moreover, a lot of players on the demand side are expected to actively take part in the system regulation as well. Hence, the total number of active players in a power system could easily reach millions, hundreds of millions or even billions. How to integrate all these players so that they are able to work together to maintain the system stability is a great challenge [5]. The Intergrid proposed in [6] adopts the hierarchical nanogrid→microgrid→ . . . →grid structure to achieve dynamic decoupling of generation, distribution, and consumption by using bidirectional power electronic converters as energy control centers. The Integrated Grid [7] is proposed to integrate DER in the planning and operation of the grid and to expand its scope to include DER operation. An integrated smart grid system is proposed in [8] to advocate a synergy of computing and physical resources and envision a trustworthy middle-ware providing services to grid applications through message passing and transactions. The FREEDM system envisions to operate power systems as “Energy Internet” or “Internet of Energy” [9]. The constant seeking for an underlying principle is ongoing. What is equally important is the integration and interaction of loads. At the moment, most loads do not actively contribute to the regulation of system stability. In recent years, demand response has become an active research area to empower some loads to take part in the regulation [10]. However, these are done on the ON/OFF basis. It would be much better if the majority of loads are able to take part in the system regulation in a continuous way, like generators. Similar trend is also happening in shipboard power systems [11], vehicular power systems [12] and aircraft power systems [13], where more and more power electronic converters are

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This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx.doi.org/10.1109/TIE.2017.2677339 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

II. T HE F UNDAMENTAL C HALLENGE B EING FACED BY P OWER S YSTEMS As shown in Fig. 1, the electricity consumption in the U.S. has been constantly increasing in the last sixty years. More and more different types of loads are being added to power systems. According to the US Electric Power Research Institute, the estimated electricity consumption in the U.S. is shown in Fig. 2. The majority of electricity, over 50%, is consumed by motors. The Internet devices consume over 10% and lighting devices consume about 20%. Other loads consume the rest 20% electricity. It has been well known that the adoption of motor drives is able to significantly improve the efficiency

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being added into these smaller scale power systems. A simple mechanism that is able to govern the stability of power systems at different scales is demanded. Since the public power system is already the largest manmade machine in the world [14], it is not feasible to rebuild power systems from the scratch. The ultimate solution is to tame the power electronic converters-interfaced supplies and loads so that they can follow the major principles of the current power systems. It is well known that synchronous machines can synchronize with each other or with the power supply autonomously, without the need of external communication. This has underpinned the organic growth and operation of power systems for over 100 years. In this paper, the architecture that is able to continue adopting the synchronization mechanism of synchronous machines is proposed for future power systems to unify the integration and interaction of all generators and the majority of loads. This allows all active players to communicate with each other at the low level of the power system without relying on a communication network. The function of communication is achieved through control, that is to say, the measurement of local voltage or frequency and the execution of control algorithms, based on the underlying synchronization mechanism of synchronous machines. As a result, the communication system in a smart grid can be released from low-level controls and adopted to focus on high-level functions, e.g. information monitoring and management, electricity market etc. This architecture simply turns all supplies—both conventional and DER—and the majority of loads into (virtual) synchronous machines. They can work together autonomously and make contributions to maintain system stability, leading to the autonomous operation of power systems. Moreover, two technical routes are presented to implement the architecture, one based on the synchronverter technology and the other based on the robust droop control technology. It is worth emphasizing that operating power converters as virtual synchronous machines does not mean to mimic conventional synchronous machines exactly, e.g. to have slow responses because of large inertia, but to mimic the fundamental synchronization mechanism of synchronous machines while maximizing the benefits of power converters, e.g. to have fast responses and flexible controllability. In this way, it is possible to build a more robust, more reliable and more resilient power system.

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Fig. 1. The estimates of U.S. energy consumption by end-use sector (1949-2010) [15] Internet >10% 

 



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Fig. 2. Estimated electricity consumption in the U.S.

of motor applications [16]. Motor drives are equipped with power electronic rectifiers to convert AC electricity into DC electricity, which is then used to drive DC motors or converted into variable-frequency AC to drive AC motors. Hence, the electricity consumed by motors is actually consumed by power electronic rectifiers. Internet devices consume DC electricity, which is converted from AC electricity by power electronic rectifiers as well. As to lighting devices, there is a clear trend in the lighting market to adopt LED lights, which also consume DC electricity as well. Hence, in the future, the majority of electricity will be consumed by rectifiers, whatever the end function is. On the supply side, more and more DER are being connected to the grid through power electronic inverters. For example, most wind turbines generate electricity at variable frequencies and require power electronic converters to control the generation and interaction with the grid. Solar panels generate DC electricity, which needs to be converted into AC electricity to make it compatible with the grid as well. Similarly, electric vehicles and storage systems require power electronic converters to integrate with the grid. In transmission and distribution networks, in order to reduce losses and improve controllability, more and more power electronic converters, e.g. HVDC (high-voltage DC) links [17] and FACTS (flexible AC transmission systems) devices [18], are being added to electronically, rather than mechanically, control future power systems [19]. Putting all the above together, future power systems will be power electronics-based, instead of electric machines-based, with a huge number of relatively small and non-synchronous players at the supply side, inside the network and at the demand side. The fundamental challenge is how to organically grow and operate these systems without jeopardizing the

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This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx.doi.org/10.1109/TIE.2017.2677339 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

system stability, i.e., how to make millions or even billions of different players work together. Because of the huge number of players involved, it will no longer be viable for low-level controls to rely on communication network. It will no longer be viable to manage these systems through human interaction, either. It is crucial to find a mechanism to enable the organic growth and autonomous operation of future power systems. III. T HE F UTURE OF P OWER S YSTEMS A. Synchronization Mechanism of SM — What Underpins the Growth and Operation of Power Systems A vital problem that needs to be answered when the power system are going through the transition from electric machines-based to power electronics-based is whether it is possible to continue adopting the major principles that have already been established in current power systems. If yes, this is going to significantly reduce the cost and effort involved in this transition. Looking at the current power systems, it is easy to find out that the electricity generation is dominated by synchronous generators, at coal-fired power plants, nuclear power plants, hydro power plants etc. There must be a reason why the industry has decided to adopt synchronous machines while there are different types of electric machines. This can be understood from the mathematical model of synchronous generators. A synchronous generator is governed by the well-known swing equation 1 θ¨ = (Tm − Te − D pθ˙ ), (1) J where θ is the rotor angle; θ˙ is the angular speed of the machine; Tm is the mechanical torque applied to the rotor; J is the moment of inertia of all the parts rotating with the rotor; D p is the friction coefficient; and Te is the electromagnetic torque
 θ . (2) Te = pM f i f i, sin Here, p is the number of pairs of poles of the magnetic field; i is the stator current; i f is the field excitation current; M f is the maximum mutual inductance between the stator windings and the field winding; and ·, · denotes the conventional inner  θ , together with cos  θ , are defined, product. The vectors sin respectively, as ⎡ ⎡ ⎤ ⎤ cos θ sin θ  θ = ⎣ sin(θ − 2π ) ⎦ .  θ = ⎣ cos(θ − 23π ) ⎦ , sin cos 3 4π cos(θ − 3 ) sin(θ − 43π ) The three-phase generated voltage e and the reactive power Q are, respectively,  θ, e = θ˙ M f i f sin (3)  θ. Q = −θ˙ M f i f i, cos

(4)

Assume that the terminal voltage is v. Then the stator current is e−v , (5) i= sL + R

where sL + R is the impedance of the stator windings. Note that i, e and v in (5) are the Laplace transform of the corresponding signals. The mathematical model of a synchronous machine described in (1-5) actually performs the function of an enhanced phase-locked loop called the sinusoid-locked loop [1], [21], which includes a frequency channel to synchronize the frequency and the phase and a voltage channel to synchronize the amplitude with the terminal voltage. In other words, synchronous machines have the inherent mechanism of synchronization, which allows them to synchronize with each other or the grid autonomously. The synchronization mechanism of synchronous machines is the mechanism that has underpinned the growth and operation of power systems for over 100 years. B. The Proposed Architecture for Future Autonomous Power Systems The main contribution of this paper is to point out that the synchronization mechanism of synchronous machines can continue to be adopted to underpin future power systems and to propose the corresponding architecture for future power systems shown in Fig. 3. In such a power system, all conventional power plants, including coal-fired, hydro and nuclear power plants, are connected to the transmission and distribution network through synchronous machines (SM), as normally done without any major change. For all DER that need power electronic inverters to interface with the grid, the inverters can be controlled to behave like virtual synchronous machines (VSM), more specifically, virtual synchronous generators, by embedding the mathematical model of conventional synchronous generators as the core of the controllers for these inverters. Hence, these inverters can have the same dynamic behavior, in particular, the synchronization mechanism, of conventional synchronous machines. As for loads, since the majority of them will have rectifiers at the front-end to interface with the grid, these rectifiers can also be controlled to behave like virtual synchronous machines (VSM), more specifically, virtual synchronous motors. For HVDC links, the power electronic converters at both ends can be controlled as VSM, one as a virtual synchronous generator and the other as a virtual synchronous motor, as well. In a power system shown in Fig. 3, all power electronicsbased players, at the supply side, at the demand side and inside the network, are empowered to actively take part in the regulation of system stability in the same way as SM. Because the synchronization mechanism of SM are inherently embedded inside all the active players, they autonomously interact with each other via exchanging power through the electricity network. This paves the way for the autonomous operation of power systems, which means minimal human intervention is needed to maintain the system operation within the designed operational boundaries of the frequency and the voltage. For example, when a coal-fired power plant is tripped off, the system frequency drops. Because of this, all SM/VSM that take part in the autonomous regulation of system stability on the supply side would quickly and autonomously respond to the frequency drop and increase the power output. At the

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Hydro-Electric Plants

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Fig. 3. The proposed architecture for future power electronics-enabled autonomous power systems, which actually offers a technical solution to realize the lateral power that underpins the Third Industrial Revolution as envisioned in [20].

same time, all VSM that take part in the autonomous regulation of system stability on the demand side would autonomously decrease power consumption. As a result, the frequency drop is reduced, which helps reduce the number of loads to be tripped off. If a new power balance cannot be reached after all generators reach the maximum capacity then some VSM that serve non-critical loads further reduce the power consumption. Similarly, if a heavy load is turned off, all SM/VSM that take part in the autonomous regulation of system stability on the supply side would quickly and autonomously reduce the power output and all VSM that can take part in the autonomous regulation of system stability on the demand side would autonomously increase power consumption to help reach new power balance. The increase or decrease of load power can be of short term or long term, depending on the types and functions of loads. Similarly, the variability of DERs can be taken care of by the system players. It is worthy emphasizing that all the SM and VSM have the inherent mechanism of synchronization so there is no need to rely on additional communication network to achieve this lowlevel control. In other words, the communication network can be released from low-level control to focus on highlevel functions of power systems, e.g. SCADA and market operations [22]. This also helps enhance the cybersecurity of the system because no access to low-level control is provided for malicious attackers. This architecture will also facilitate continuous demand response and turn all players into active and responsible players to maintain system stability, which avoids some customers to suffer load shedding and improves quality of service (QoS). Because the key principle that has

underpinned the growth and operation of power systems for over 100 years is adopted, the transition of today’s grid into tomorrow’s is expected to be evolutionary rather than revolutionary. This architecture is scalable and can be applied to power systems at different scales, from single-node systems to million-node systems, from vehicles, aircraft to public grids. When there is a need, small systems can be connected together. If a part of the system is faulty, then it can be disconnected; after the fault is cleared, it can be re-connected to the grid. Unlike the normal hierarchical architecture, e.g. the ones proposed in [6], [9], [23], this architecture is technically lateral, although it could offer a hierarchical management structure on top of the lateral technical structure. This empowers all players to directly take part in the regulation of system stability and enhances system autonomy [24], which is consistent with the worldwide trend of increasing autonomy and declining hierarchy in many fields [25], [26]. As a matter of fact, this offers a technical solution to realize the lateral power that underpins the Third Industrial Revolution as envisioned in [20]. The implementation of this architecture will significantly reduce the infrastructure investment on generation/transmission/distribution network. For example, the capacity of the UK power grid is about 70GW. If the load contributes 2% in contingencies, which is within the tolerance for most individual loads, then the total contribution from all loads is about 1.4 GW, which is at the level of a nuclear power plant. It is also able to release the inertia that already exists in the system and considerably reduce the operational

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IV. T ECHNICAL R OUTE B ASED ON THE S YNCHRONVERTER T ECHNOLOGY A. The Original Synchronverter to Operate Inverters as Virtual Synchronous Generators Synchronverters [35], [34] were originally proposed as inverters that mimic synchronous generators, with the power part shown in Fig. 4(a) and the electronic part shown in Fig. 4(b). The controller includes the mathematical model of synchronous generators described by (1-4). The voltage e generated according to the mathematical model (1)-(4) is converted into PWM pulses to drive the power semiconductor switches in the power part so that the average of voltages  T ea eb ec over each switching period is the same as

+ Ls , R s VDC

vb

ib

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ic

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va

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ea

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cost because of the fast action of power electronic converters. For example, if there are 10 million laptops plugged in a network and each contributes 10 W when needed, then the equivalent reserve amounts to 100 MW. The large amount of big industrial motors, wind turbines, and electric vehicles etc. can all contribute to the system reserve/inertia. This architecture can also considerably reduce the infrastructure investment on communication networks and cybersecurity because the low-level control does no longer rely on the communication network. Different/similar options to implement VSMs have been proposed in the literature. The VISMA approach controls the inverter current to follow the current reference generated according to the mathematical model of synchronous machines [27], [28], which makes inverters behave like controlled current sources. Since power systems are dominated by voltage sources, this may impose potential detrimental impact on the system, in particular, on system stability [29], [30], [31]. The approach proposed in [32] follows the mathematical model of SM but it requires the measurement of the grid frequency, which is often problematic in practice [33]. The synchronverter approach directly embeds the mathematical model of synchronous machines into the controller to control the voltage generated without the need of measuring the grid frequency [34], [35], [36]. The approach proposed in [37] controls the voltage but it also requires the measurement of the grid frequency for the real power-frequency droop control. The synchronverter has the simplest structure with the lowest number of control parameters among all available options today and has been further developed for microrgrids [38], HVDC applications [39], [40], STATCOM [41], PV inverters [42], wind power [43], motor drives [44], and rectifiers [45], [46]. In Section IV, the synchronverter-based technical route is outlined to implement the architecture of power-electronicsenabled autonomous power systems proposed in Fig. 3. Recently, it has been revealed that droop controllers and (enhanced) phase-locked loops are essentially the same thing but operated under different conditions [47], [48]. This means the synchronization mechanism of SM inherently exists in the well-known droop control strategy as well. In Section V, another technical route, which is based on an improved droop control strategy called the robust droop controller is outlined to implement the architecture proposed in Fig. 3.

v fb

vr

(b) Fig. 4. A three-phase synchronverter [35]: (a) the power part, (b) the electronic part

 T e. The currents ia ib ic flowing out of the inverter are measured and treated as the stator current i and fed back to the mathematical model of synchronous machine, which implements (5). Hence, the mathematical model (1)(4) are linked together with the power part shown in Fig. 4(a). Then, the matured technologies developed for SM, e.g. the frequency droop and voltage droop control, can be applied. The friction coefficient D p actually plays the role of frequency droop and, hence, the frequency droop control can be easily implemented via comparing the virtual frequency θ˙ with the reference frequency θ˙r . The field excitation current i f can be regulated by an integrator that controls the reactive power Q, with respect to the reference reactive power Q set . A voltage droop controller is added to the reactive power control loop via the voltage droop coefficient D q . The mechanical torque Tm can be obtained via scaling the real power Pset because the frequency of the inverter is assumed to be regulated within a tight range around the nominal frequency θ˙n . The controller also includes a phase-locked loop (PLL) to provide the grid frequency as the reference frequency θ˙r and the grid phase θg for synchronization before connecting the synchronverter to the grid or when operating it in the set mode to send the desired power to the grid. In addition to operating in the set mode, synchronverters are able to operate in the droop mode to take part in the regulation of system frequency and voltage. Fig. 5 shows the frequency regulation of a synchronverter connected to the grid in the droop mode. The real power sent to the grid is autonomously changed according to the varying grid frequency. When the frequency increases, the real power decreases; when

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1060.0

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the frequency decreases, the real power increases. Similarly, a synchronverter could take part in the regulation of voltage by autonomously changing the reactive power exchanged with the grid according to the varying voltage.

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B. Self-synchronized Synchronverters As reported in [36], the PLL in the synchronverter can be removed after making some changes to the controller. As shown in Fig. 6, the difference between the generated voltage 1 e and the grid voltage v g is put through a low-pass filter Ls+R , which functions like a virtual stator winding, to generate a virtual current i s . After setting Pset and Qset to zero, turning SQ OFF to disable the voltage droop control, and replacing the grid current i g with the virtual current i s , the voltage e can be established to be the same as the grid voltage v g before the synchronverter is connected to the grid, with the help of the PI controller to regulate ∆T to zero. This is equivalent to floating a synchronous generator on the grid without exchanging any real power or reactive power.

motor and a PI controller to regulate the DC-bus voltage V o around the reference voltage V re f and generate the mechanical 1 torque Tm . Similarly, a low-pass filter sL+R is adopted to generate the virtual current i s for self-synchronization, together with the PI controller that regulates the output of the D p block to zero. The voltage droop loop is omitted in Fig. 7 but it can be added if voltage regulation is needed. Some experimental results from a rectifier connected to the grid are shown in Fig. 8. When the reference value for the DC-bus voltage and the load were changed, the virtual frequency of the rectifier was able to track the grid frequency quickly and accurately.

C. Operating Rectifiers as Virtual Synchronous Motors

The electricity generation of current power systems is dominated by synchronous machines, which have inductive output impedances. However, future power systems will be dominated by power electronic converters, of which the output

The same idea can be applied to operate rectifiers as virtual synchronous motors [45], [46]. As shown in Fig. 7, the controller includes the mathematical model of a synchronous

V. T ECHNICAL R OUTE B ASED ON THE R OBUST D ROOP C ONTROL T ECHNOLOGY

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S = P + jQ

ωi

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i

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~

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Pi*

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Qi

(a) ωi

Fig. 9. Power delivered to a voltage source through an impedance

Ei E*

ω* ωi = ω * − mi Pi

impedances change with the design and control of the converters and could be inductive (L-inverters), resistive (R-inverters) [49], [50], capacitive (C-inverters) [51], [52], resistiveinductive (RL -inverters), resistive-capacitive (R C -inverters) or complex around the fundamental frequency. The impedance of converters plays an important role in system stability. Moreover, for inverters with different types of output impedance, the conventional droop controllers have different forms [1]. The robust droop controller [50], initially proposed for R-inverters to achieve accurate power sharing and tight voltage regulation, has recently been proven to be applicable to inverters with output impedance having an impedance angle between − π2 rad and π2 rad [53] and, hence, it is universal. Furthermore, it can be equipped with the self-synchronization mechanism mentioned above so that no additional PLL is needed [54]. In this section, it will be shown at first that droop controllers are structurally the same as phase-locked loops and hence droop controllers have the inherent synchronization mechanism of SM. Then, a technical route based on the robust droop control will be illustrated. A. Inherent Synchronization Capability of Droop Control — Structural Resemblance between Phase-Locked Loops and Droop Controllers An inverter can be modeled as the series connection of an ideal voltage source v r and an output impedance Z o . Fig. 9 illustrates such an inverter delivering power to a voltage source Vo ∠0◦ . Since the current flowing through the impedance is E cos δ − Vo + jE sin δ I¯ = , Zo ∠θ the real power and reactive power delivered to the terminal via the impedance can be obtained as EVo V2 EVo cos δ − o ) cos θ + sin δ sin θ , Zo Zo Zo EVo V2 EVo Q=( cos δ − o ) sin θ − sin δ cos θ , Zo Zo Zo P=(

(6) (7)

where δ is the phase difference between the voltage source and the terminal. It is often called the power angle and has a small value in order to maintain system stability. Based on these, droop control strategies can be developed to regulate the voltage source [1]. For different types of impedances, the conventional droop control principles are different, as shown in Fig. 10 for inductive, resistive and capacitive impedances.

Ei = E * − ni Qi

Capacitive 0

Pi*

Inductive 0

Pi

Qi*

Qi

(b) ωi ω*

Ei E*

ωi = ω * + mi Pi

Ei = E * + ni Qi

Capacitive 0

Pi*

Inductive 0

Pi

Qi*

Qi

(c) Fig. 10. Conventional droop control principles [1]: (a) for resistive impedance; (b) for inductive impedance; (c) for capacitive impedance.

For inverters with resistive impedance (R-inverters), the droop relationship is P ∼ E and Q ∼ −δ , where ∼ means in proportion to, and the conventional droop controller is Ei = E ∗ − ni Pi ,

ωi = ω ∗ + mi Qi . As demonstrated in [47], [48], the equivalent structure of this droop control can be found as shown in Fig. 11(a), which is structurally the same as the enhanced phase-locked loop or the sinusoid-tracking algorithm for synchronization [55], [56], [57], [58] shown in Fig. 11(b). In other words, droop controllers have the inherent synchronization mechanism of SM as well and can be adopted to implement the architecture shown in Fig. 3. B. Robust Droop Control The conventional droop control is not robust against parameter drifts, component mismatches and numerical errors etc. Moreover, there is a fundamental trade-off between the voltage regulation and power sharing accuracy [50]. A robust droop controller, as shown in Fig. 12, is proposed in [50] to address these problems, after introducing an integrator into the voltage amplitude channel and an output voltage feedback. These change the voltage droop from the set point E to the output voltage Vo . As a result, R-inverters can be operated in parallel to achieve accurate power sharing and tight voltage regulation, which makes these inverters to be able to take part in the regulation of system frequency and voltage.

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Ke s

E

2

H (s )

-

1 R

X

v

eq

X

sin

 cos θ − sin θ are cos θ ± j sin θ , of which the real part sin θ cos θ cos θ is positive for any impedance with θ ∈ (− π2 , π2 ). Hence,



e

e

X

˜ P ∼ P˜ and Q ∼ Q. Moreover, according to (8), there are P˜ ∼ E

cos Kf

1 s

θ

H (s )

s

ω

P∼E e

E

2

(9)

X

and Q ∼ −δ .

This is the same as the droop relationship shown in Fig. 10(b) for resistive impedance. In other words, the robust droop controller shown in Fig. 12 is universal for inverters having an impedance angle between − π2 rad and π2 rad [53]. This considerably reduces the complexity of future power systems.

-

1 s

µ1

Q˜ ∼ −δ

for δ ∈ (− π2 , π2 ). As a result,

X

(a)

X

and

v

X

sin

D. Self-synchronized Universal Droop Control

cos 1 s

1 s

θ

µ2 ( µ3 + )

X

(b) Fig. 11. Structural resemblance between the droop control and the enhanced phase-locked loop (EPLL) [48]: (a) A droop controlled system with a resistive impedance, (b) The enhanced phaselocked loop (EPLL)

E*

-

Ke

-

1 s

Pi

ni

Calculation

Ei

RMS

vri

ω it+δ i

1 s

Qi

mi

vo

i

ω*

Fig. 12. Robust droop controller [50], which is universal for inverters with different types of impedances

The self-synchronization mechanism for synchronverters mentioned in Section IV-B can be applied to the universal droop controller discussed above. The resulting selfsynchronized universal droop controller [54] is shown in Fig. 13. In the self-synchronization mode, both S P and SQ are OFF and a virtual current i s is generated by the voltage difference between the output voltage v o and the grid voltage v g . This regulates the real power P and reactive power Q to be zero and forces vo to be the same as vg , i.e. to achieve synchronization. Once the synchronization is achieved, the inverter can be connected and then operated in the set mode to send the desired power Pset and Qset to the grid or in the droop mode to take part in the regulation of system frequency and voltage. Fig. 14 shows the frequency and voltage regulation capability of an inverter equipped with the self-synchronized universal droop controller operated in the droop mode. The real power P is autonomously changed according to the varying voltage E and the reactive power Q is changed according to the varying frequency f . When the voltage increases, the generated real power decreases; when the voltage decreases, the generated real power increases. When the grid frequency increases, the generated reactive power increases; when the grid frequency decreases, the generated reactive power decreases. The inverter has excellent balancing capability for real and reactive power with fast reaction.

C. Universal Droop Control

E. Droop-Controlled Rectifiers

The power delivered to the terminal as characterized by (67) can be rewritten as

The controller shown in Fig. 13 can be applied to rectifiers as well, after adding a controller to regulate the DC-bus voltage Vo around the reference voltage V re f and to generate Pset . This is very similar to Fig. 7, where the output Tm of the controller is replaced with Pset here. Fig. 15 shows the simulation results from a 110 VAC to 200 VDC rectifier rated at 182 W. The voltage varies in the range of 108.9 ~ 112.3 VAC, which makes the real power drawn by the rectifier to change in the range of 168 ~ 245 W. The frequency varies in the range of 59.85 ~ 60.21 Hz, which leads to the reactive power to change in the range of 76 ~ -108 Var. When the voltage increases, the real power drawn by the rectifier



with

P Q



=

P˜ Q˜

cos θ sin θ

 =

− sin θ cos θ



2

cos δ − VZoo o − EV Zo sin δ

EVo Zo

P˜ Q˜



.

(8)

This means the vector P + jQ is obtained via rotating the vector P˜ + jQ˜ by θ . Note that the eigenvalues of

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E* SP

Ke

-

RMS

Pset E

1 s

n

P

-

vr

ω* ω t+δ

1 s

-

m

ωd - K

Q

-

Calculation

Vd

vo is i

1 Ls+R

- vg

SC s g

ig

Qset

s

SQ

1

Fig. 13. Self-synchronized universal droop controller [54].

VI. I LLUSTRATION VIA R EAL - TIME S IMULATIONS

E: [3.667V/div] 150 W 110 V P: [100 W/div]

Q: [100 Var/div]

150 Var 50 Hz

f: [0.1667 Hz/div]

t: [100 s/div]

Fig. 14. Experimental results of an inverter equipped with the selfsynchronized universal droop controller in regulating the system frequency and voltage [54]. P: [50 W/di 200 W

110 V E: [1.833 V/div] Q: [100 Var/div] 0 Var 60 Hz f: [0.2 Hz/div]

t: [1 s/d

Fig. 15. Simulation results of a rectifier equipped with the selfsynchronized universal droop controller in regulating the system frequency and voltage.

increases; when the voltage decreases, the real power drawn by the rectifier decreases. When the grid frequency increases, the reactive power drawn by the rectifier decreases; when the grid frequency decreases, the reactive power drawn increases. The rectifier presents excellent balancing capability for real and reactive power with fast reaction. Comparing Fig. 15 with Fig. 14, it can be seen that the droop-controlled inverters and rectifiers have complementary balancing capability for real power and reactive power and can work together to maintain the stability of voltage and frequency.

In order to illustrate how such a system works, a singlephase test system as shown in Fig. 16 was simulated with an OPAL RT OP5607, which is a powerful real-time simulator having the software environment compatible with MATLAB/Simulink. Since inverters with different types of output impedances could potentially destabilize a system, the test system was designed to include an R-inverter, an L-inverter and a C-inverter with the parameters given in Table I. The inverters are connected to the same AC bus in a weak grid. The line impedance among the inverters are omitted while the line impedance between the AC bus and the grid is modeled as a 0.24 mH inductor in series with a 0.1 Ω resistor [59]. The weak gird was implemented by a 30 kVA R-inverter, which was equipped with the universal droop controller discussed in Section V-C. The three inverters, rated at 15 kVA, 10 kVA and 5 kVA, respectively, were equipped with the self-synchronized universal droop controller shown in Fig. 13. The rated RMS system voltage and frequency are 230 V and 50 Hz, respectively. The parameters of the inverters were not optimized but selected empirically with the intention to demonstrate the robustness of the system. The inverter bridges were implemented as controlled voltage sources. The simulation was carried out with the solver ode3 (Bogacki-Shampine) at a fixed step of 50µ s. The relevant signals, as shown in Fig. 17, were sent out through the digital/analog channels of OP5607 and then captured by a Yokogawa 8-channel signal analyzer DL7480. Note that the real power, the reactive power and the voltage of each inverter and the grid were measured at the terminal for control purposes. The droop coefficients were chosen in such a way that 100% increase of real power P results in 10% decrease of voltage E and 100% increase of reactive power Q results in 1% increase of the frequency f . The inductance of the virtual impedance used in the controller for the three inverters to generate the virtual current for synchronization was 1 mH for all inverters and the resistance was 2 Ω, 3 Ω and 6 Ω for the R-inverter, the L-inverter and the C-inverter, respectively. In order to illustrate the operation of such a system under

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230 V Primary Source

PCC Inverter

L-inverter

R-Inverter (15 kVA)

Vo: [4 V/div]

Load

206V Primary Source

C-inverter t=0 s R-inverter P: [3000 W/div]

grid

Inverter L-Inverter (10 kVA)

Grid (30 kVA)

R-inverter

L-inverter

C-inverter

~

Primary Source

0W Inverter

t=0 s

t: [2 s/div]

C-Inverter (5 kVA)

(a)

PCC

Microgrid

f: [0.02 Hz/div]

t=0 s

Fig. 16. A test system with three inverters connected to a weak grid. 50 Hz

TABLE I

C-inverter L-inverter R-inverter grid

PARAMETERS OF THE SYSTEM SHOWN IN F IG . 16 Weak Grid Rated apparent power S 30 kVA Inductance Ls 0.35 mH 0.02 Ω Resistance Rs Inductance Lg 0.035 mH Resistance Rg 0.002 Ω Capacitance C 10 µ F

R-inverter 15 kVA 0.7 mH 0.04 Ω 0.07 mH 0.004 Ω 10 µ F

L-inverter 10 kVA 1.05 mH 0.06 Ω 0.105 mH 0.006 Ω 10 µ F

C-inverter 5 kVA 2.1 mH 0.12 Ω 0.21 mH 0.012 Ω 10 µ F

grid

R-inverter L-inverter

0W

different modes, a series of actions were taken. The details are described as follows: (1) Black start of the system. At t = 0 s, the weak grid started to supply electricity to the load (3 Ω in series with 1.8 mH). The PCC voltage was 211.6 V, which was about 8% below the rated value 230 V. The voltage drop was due to the line impedance of the weak grid and the droop effect. The system frequency was 50.05 Hz, which was about 0.1% above the rated value because of the 3 kVar reactive power. (2) Synchronization of the inverters to the grid. The selfsynchronization mode was enabled for the R-inverter, Linverter, and C-inverter at 0.5 s, 1.0 s and 1.5 s one by one, all inverters synchronized with the PCC voltage and frequency gradually and quickly. (3) Connection of the inverters to the grid. At t = 3 s, all inverters with Pset = 0 and Qset = 0 were connected to the grid at the PCC. The connection was very smooth, without any noticeable spikes in real power P and reactive power Q. (4) Operation in the set mode. At t = 4 s, Pset was changed to 7.5 kW, 5 kW and 2.5 kW, and Q set to 0.9 kVar, 0.6 kVar and 0.3 kVar for the R-inverter, L-inverter, and C-inverter, respectively. The PCC voltage increased to 227.6 V, which was about 1% below the rated value 230 V because all the inverters started injecting real power to the grid and the grid only supplied about 2.4 kW, i.e., 0.8% of the capacity, to the load. The frequency decreased to 50.02 Hz, which was about 0.04% above the rated frequency, because the grid only supplied about 1.26 kVar, i.e., about 0.04% of the capacity, to the load. As can be seen, all the inverters injected the required

t: [2 s/div] Q: [600 Var/div] C-inverter

t=0 s

(b) Fig. 17. Real-time simulation results from the system in Fig. 16: (a) real power and RMS voltage, (b) reactive power and frequency.

real power and reactive power to the grid and the grid picked up the rest of the load. Note that in this case the inverters did not take part in the regulation of the grid frequency and voltage. The PCC frequency and voltage were regulated by the grid. (5) Operation in the droop mode with non-zero Pset and Qset . At t = 10 s, the droop mode were enabled, which forced the R-inverter, L-inverter, and C-inverter to take more load (proportionally) because the PCC voltage was below the rated value and the frequency was above the rated value. As a result, the real power and reactive provided by the grid decreased, which autonomously brought both the grid voltage and grid frequency closer to the rated values, respectively. Note that the PCC frequency and voltage were still mainly regulated by the grid because of the non-zero power set-points. (6) Operation in the droop mode with zero Pset and Qset . At t = 13 s, the Pset and Qset were changed to 0. The inverters sent less real power to the grid because of the drop of the power set-points, which caused the PCC voltage to drop to 222 V, i.e., about 3.4% of the rated voltage. In this case, for the Rinverter, according to the droop coefficients, i.e., 10% decrease of voltage E results in 100% increase of real power P, the real power was expected to be 3.4% 10% × 15 kW ≈ 5.1 kW. Indeed, as

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shown in Fig. 17, the real power P of the R-inverter was around 5.1 kW. At the same time, the frequency was 50.024 Hz, which was 0.048% above the rated frequency 50 Hz. For the R-inverter, according to the set droop coefficients, i.e., 1% increase of f results in 100% increase of Q, the reactive power was expected to be 0.048% 1% × 15 kVar ≈ 0.72 kVar. As shown in Fig. 17, the reactive power was indeed around 0.72 kVar. Similarly, the L-inverter and C-inverter supplied the real power P and reactive power Q correspondingly. In this case, all the inverters took part in the regulation of the PCC frequency and voltage. (7) Autonomous operation in the droop mode in response to load change. At t = 16 s, an RC load (20 Ω in parallel with 300 µ F) was connected to the system at the PCC. The real power supplied by the grid further increased but the reactive power decreased to a negative value because of the strong capacitive load, which caused the PCC voltage to drop further and brought the frequency below the rated value. All the inverters also autonomously changed the real power and reactive power. Again, all the inverters took part in the regulation of the PCC frequency and voltage. Note that no instability occurred during the whole process although the output impedances of the inverters and the grid had different types and values and the load changed from inductive to capacitive. VII. C ONCLUSIONS Power systems are going through a paradigm change from centralized generation to distributed generation. It has been shown that future power systems will be power electronicsbased with a huge number of incompatible players. The synchronization mechanism of conventional synchronous machines can continue to be adopted in future power systems, after controlling power electronic converters in these players to behave like virtual synchronous machines. A lateral architecture has been proposed for future power systems based on this synchronization mechanism to empower all these players to take part in the regulation of system frequency and voltage. This actually offers a technical solution to realize the later power envisioned in [20]. Two technical routes, one based on the synchronverter technology and the other based on the robust droop control technology, have been presented to implement the proposed grid architecture. Real-time simulation results are presented to illustrate the operation of such a system. ACKNOWLEDGMENTS The author would like to thank Dr. Fred Lee for the stimulating discussions as well as Dr. Wen-Long Ming and Dr. Yu Zeng for their help on the real-time simulations. R EFERENCES [1] Q.-C. Zhong and T. Hornik, Control of Power Inverters in Renewable Energy and Smart Grid Integration. Wiley-IEEE Press, 2013. [2] K. Moslehi and R. Kumar, “A reliability perspective of the smart grid,” IEEE Transactions on Smart Grid, vol. 1, no. 1, pp. 57–64, Jun. 2010. [3] P. Eder-Neuhauser, T. Zseby, and J. Fabini, “Resilience and security: A qualitative survey of urban smart grid architectures,” IEEE Access, vol. 4, pp. 839–848, 2016.

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Qing-Chang Zhong (M’04-SM’04F’17) received the Ph.D. degree in control and power engineering from Imperial College London in 2004 and the Ph.D. degree in control theory and engineering from Shanghai Jiao Tong University in 2000.He holds the Max McGraw Endowed Chair Professor in Energy and Power Engineering at the Dept. of Electrical and Computer Engineering, Illinois Institute of Technology, USA. He is a Fellow of IEEE and IET, a Distinguished Lecturer of IEEE Power Electronics Society, IEEE Control Systems Society and IEEE Power and Energy Society, and the Vice-Chair of IFAC TC Power and Energy Systems. He was a Senior Research Fellow of Royal Academy of Engineering, UK, and the UK Representative to European Control Association. He serves/d as AE for IEEE TAC/TIE/TPELS/TCST/Access/JESTPE. He proposed to continue adopting the synchronization mechanism of synchronous machines to unify the integration of nonsynchronous distributed generators and flexible loads to achieve autonomous operation of power systems.

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