1 Introduction

Along with the accelerated development of distributed generation (DG), such as photovoltaic solar arrays, wind turbines, etc., the microgrid has gradually become a promising framework for distributed energy harvesting and utilization, especially in rural and remote areas that a utility grid cannot reach [1,2,3]. A microgrid is typically a low voltage network consisting of DGs, local loads, energy storage, and other auxiliary infrastructure, aiming to power a certain area (e.g., an island, an industrial park, or a residential quarter) [4,5,6].

To achieve power balance and further economical operational objectives, centralized to distributed control frameworks can be applied [7, 8]. Centralized control requires an advanced central controller, which is responsible for achieving common goal(s) of the system. Through communication facilities, the central controller manages all units by collecting information, making decisions, and sending instructions [9, 10]. Control is always implemented hierarchically with two or three layers. The microgrid in [11] applies a master/slave architecture, where a master converter is assigned to dominate the AC bus and also performs as the central controller to drive other slave converters. Droop-based control is another system for organizing microgrid, which enables active and reactive power sharing without communications. However, the system frequency and voltage in steady state deviate from their nominal values with load changes, which must be restored using a communication-based secondary control loop [12,13,14]. In [15], two secondary control schemes, a model predictive controller and a Smith predictor-based controller, are investigated. In [16], two control techniques, based on H∞ and μ-synthesis theory, are developed as the secondary correction loop.

Distributed control has no central controller, and the information-collecting and decision-making authority is delegated to DGs and flexible loads, forming a multi-agent control architecture. In this case, DGs can operate with more autonomy, but communications, especially between adjacent units, are still necessary for accurate power sharing, frequency restoration, or to achieve economic targets [17, 18]. Reference [19] proposes a supervisory control scheme based on neighboring message exchange, which can achieve either precise power sharing or economic dispatch of a microgrid. In [20], construction rules for communication networks and their agents in a microgrid are proposed together with a systematic method to design control laws, which is verified in the study.

Generally, energy management of a microgrid with centralized or distributed control always relies on wired or wireless communications to achieve power balance, frequency restoration, or to achieve profitable targets, which will be costly and prone disturbances when it attempts to contact every unit in a complex, scattered, and unorganized system. If faults occur in the communication channels (for example, total net power information errors), the microgrid will have difficulties balancing the power within this system, likely leading to system collapse. Furthermore, the communication network, which has a particular structure and specific protocols, is relatively exclusive and not flexible for plug-and-play. Reducing the communication dependency in microgrid operations is always a challenging problem.

This work proposes a novel system deployment principle for master/slave type islanded alternating current (AC) microgrids, with which fully decentralized control without communications can be achieved. The total net power, including active and reactive power, can be metered and compensated for locally and independently by the microgrid units. This design can benefit a microgrid regarding system expandability, flexibility, and plug-and-play. A typical small-scale AC microgrid is considered for demonstration. The assumed units include a diesel generator set, renewable generation, critical loads, hybrid energy storage (battery and ultra-capacitor), and flexible loads. The diesel generator set runs to build up and dominate the AC bus, assuring constant frequency and voltage. With the deployment principle and the designed power flow control scheme, net power of the microgrid is separated into fast-varying and slow-varying components, which are then shared and compensated independently and locally.

The rest of this work is organized as follows. Section 2 presents the proposed system deployment principle in a typical master/slave type islanded AC microgrid. Section 3 illustrates the decentralized power flow control scheme without communications, and Section 4 provides the simulation results in typical scenarios using the MATLAB/Simulink platform. Finally, Section 5 presents the conclusions.

2 System deployment principle of islanded AC microgrids

2.1 Units of microgrid

Up to now, diesel generators remain the de-facto power supplies for emergency and remote area power utilization with proven reliability [21, 22]. A typical islanded AC microgrid is constructed in this work using a diesel generator set with constant speed governor and static exciter to act as the grid-forming unit (master unit). Hybrid energy storage and renewable generation (wind turbines in this work) operate in the grid-feeding mode (current control as the slave unit). Furthermore, the wind turbine works in the maximum power point tracking (MPPT) mode to harvest energy.

As a rotating machine set, the diesel generator set has the following characteristics:

  1. 1)

    Dynamic response takes seconds or even longer, and it cannot follow the volatile renewable power fluctuations in a microgrid. Furthermore, frequent accelerations and decelerations will increase the risk of engine failures.

  2. 2)

    Low load-rate running (below 30% of the rated capacity) generates excessive exhaust gases due to incomplete combustion of fuel. Low efficiency also leads to premature aging of the engine owing to carbon deposits and liner glazing.

To compensate for the volatile power variations from DGs and local loads, energy storage is always essential. According to the theory applied to Ragone plots, any single type of storage device with limited capacity is not well-qualified [23]. A battery has large energy density but limited power rating and further has a short life cycle. In contrast, an ultra-capacitor can absorb/deliver large power in a short time and has a relatively long-life cycle. Their combination forms a hybrid energy storage system, providing a feasible solution in power compensation that performs effectively over an extended lifetime [24, 25].

To avoid low load-rate operation of a diesel engine, minimum power output is limited to 30%-40% of its rated capacity. Consequently, a flexible load is equipped as a companion to dump the surplus power when renewable generation is at a high production rate rather than reducing the diesel engine output below 30%. Flexible loads can be heat production, hydrogen production, or sea water desalination systems, for example, and the type of load used depends on local conditions. To illustrate the main significance of the deployment principle and power flow control scheme, this work will not detail each dumping technology and preferentially takes a power converter interfaced nonlinear load as a general flexible load.

2.2 System deployment principles

This work proposes three system deployment principles for master/slave type islanded AC microgrids.

  1. 1)

    Deploy the diesel generator set together with flexible loads on one side of the main AC bus, working as the grid-forming unit.

The diesel generator set works as the grid-forming unit to build up and dominate the main AC bus. It connects to one terminal together with its flexible loads and downstream sub-feeders are used to connect the DGs and loads. A typical microgrid skeleton is the result.

  1. 2)

    Sub-feeders are used to connect renewable sources and loads. They are deployed on the opposite side of the main AC bus.

The total power production from renewable sources is defined as Pgen and the total load (except for the flexible load) is defined as Pload. Then the total net power of the microgrid can be expressed as:

$$P_{net} = P_{gen} - P_{load}$$
(1)

To achieve power balance, Pnet should be calculated in real-time by collecting information from DGs and loads. In a conventional scattered and unorganized complex AC microgrid, a communications facility is indispensable.

In contrast, when clusters of renewable generation sources and local loads are connected together, renewable generation Pgen is set preferentially to satisfy the local loads represented by Pload, and they will then perform as a single entity. If this entity is interfaced to the AC bus through a single point, the surplus power Pnet will be delivered directly to the AC bus through this junction. Pnet can thus be calculated simply by metering the voltages and currents of this single point. With this deployment principle, the Pnet calculation does not rely on any communications.

  1. 3)

    Deploy the hybrid energy storage.

Hybrid storage is deployed between the two systems (diesel generators and renewable sources) on the main AC bus. Through power sharing and compensation, the hybrid storage system can balance the net power of the microgrid and also maintains high efficiency in the diesel engine set.

2.3 Typical islanded AC microgrid layout

With the above three deployment principles, the configuration of a typical master/slave type islanded AC microgrid is schematically displayed in Fig. 1. A diesel generator set connects to the left side of the main AC bus with its flexible load nearby. Feeders of wind turbines, R and L loads, and converter loads are arranged on the right side of the AC bus as a single entity, which connects to the AC bus through a single point. Then battery and ultra-capacitor units, interfaced to the main AC bus through DC/AC converters, are located in between. The line impedances are defined as Z1, Z2, Z3, Z4, and Z5.

Fig. 1
figure 1

Deployment of typical islanded AC microgrid

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As depicted in Fig. 1, five typical power components with associated directions, Pnet, Pcap, Pbat, Pflex, and Pde, are defined. Pnet is the power gap between Pgen and Pload, and is also the active net power of the microgrid. Pcap and Pbat are defined as the power shares (portions) of the ultra-capacitor and the battery. Pflex is the power dissipation of the flexible load and Pde is the power production of the diesel generator set. In addition, the minimum power production limit of the diesel engine is defined as PDE, which is within 30%-40% of its nameplate capacity.

For a fully decentralized control framework, the ultra-capacitor, the battery, and the flexible load only need local measurement and control loops to achieve power balance without communications. As displayed in Fig. 1, the local metering points of the three units are A, B, and C, respectively. The three-phase voltages and currents of point A (vA, iA) are detected by the ultra-capacitor unit for local power calculation. Similarly, (vB, iB) and (vC, iC) at B and C are respectively metered by the battery and flexible load unit independently.

3 Decentralized control scheme of islanded AC microgrid

3.1 Local power calculation

To derive the power shares of each unit through metered voltages and currents in a three-phase AC microgrid, phase angles of the grid voltages φ should first be estimated through a phased-lock-loop (PLL) algorithm. As displayed in Fig. 2, (va, vb, vc) are transformed to vd and vq under a synchronous rotating reference frame (d-q-0) with transformation matrix Tabc/dq0 in (2). ωf is the nominal value of the grid frequency, which is a constant, and ωa is the estimated frequency. By designing a feedback control loop, vq is regulated to zero and phase angle φ is finally captured.

Fig. 2
figure 2

PLL algorithm in three-phase AC microgrid

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$$\varvec{T}_{abc/dq0} = \frac{2}{3}\left[ {\begin{array}{*{20}l} {\cos (\varphi )} \hfill & {\cos (\varphi - \frac{{2\uppi}}{3})} \hfill & {\cos (\varphi + \frac{{2\uppi}}{3})} \hfill \\ { - \sin (\varphi )} \hfill & { - \sin (\varphi - \frac{{2\uppi}}{3})} \hfill & { - \sin (\varphi + \frac{{2\uppi}}{3})} \hfill \\ {\frac{1}{2}} \hfill & {\frac{1}{2}} \hfill & {\frac{1}{2}} \hfill \\ \end{array} } \right]$$
(2)

With known estimated phase angle φ and Tabc/dq0, currents (ia, ib, ic) are transformed to id and iq, and then active and reactive power can be calculated through (3) and (4). This power calculation process is displayed in Fig. 3 below.

Fig. 3
figure 3

Local power calculations and shares of ultra-capacitor unit

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$$P = \frac{3}{2}(v_{d} i_{d} + v_{q} i_{q} )$$
(3)
$$Q = \frac{3}{2}(v_{q} i_{d} - v_{d} i_{q} )$$
(4)

3.2 Local control of ultra-capacitor unit

In the decentralized control framework, power detecting and sharing of all units are implemented locally and independently without communications. For the ultra-capacitor unit, as displayed in Fig. 1, voltage vA and current iA of point A are metered locally by the voltage source converter (VSC) controller. The active and reactive power calculated by (3) and (4) are exactly equal to the net power Pnet and Qnet.

Ultra-capacitors have a large power density and long-life cycle, and can be charged or discharged even with large current. The hybrid system is used to suppress the fast-varying components of Pnet and Qnet. The power sharing process is presented in Fig. 3, Pnet is separated into high and low frequency components (Phigh and Plow) through a low pass filter (LPF). Qnet also applies the same technique to derive Qhigh and Qlow. The transfer function of the LPF is G(s) = 1/(1 + τs) and its bandwidth is ωb = 2π/T = 1/τ. The time constant τ determines the segmentation of Plow and Phigh. This work sets τ = 30/π so that the period T at ωb equals 60 s. This indicates that power fluctuations whose varying periods are within 60 s will be extracted.

Qhigh is then translated to i*qC and is directly fed to the VSC controller as the reactive current reference. In contrast, Phigh is added with another power component PAC, and their sum is the final Pcap, which is translated to i*dC as the active current reference.

The additional power term PAC is designed to rebalance the ultra-capacitor. As aforementioned, the ultra-capacitor is used to suppress any fast-varying Phigh. Owing to irregular power variation and self-discharge operations, its terminal voltage vcap can become out of balance over extended operation. Therefore, a rebalance approach is developed. The main point is to define a tolerable voltage range (no rebalance is needed in this range) with an upper limit Vup and a lower limit Vlow, and adjust the power flowing in and out to regulate its terminal voltage.

The exact curve of PAC is shown in Fig. 4, and it displays a hysteretic character. If the ultra-capacitor voltage is equal to the nominal value Vrated, PAC is zero, whereas if its voltage goes beyond either limit, a corresponding PAC proportional to the voltage deviation is generated for voltage restoration until the ultra-capacitor’s voltage returns to within the defined range. Then PAC becomes constant until the voltage reaches Vrated, at which time PAC returns to zero.

Fig. 4
figure 4

PAC used to rebalance ultra-capacitor

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3.3 Local control of battery unit

With local metering and control, the fast-varying components in Pnet and Qnet are extracted and suppressed by the ultra-capacitor unit independently. The slow-varying components Plow and Qlow remain to be considered for further compensation. As deployed in Fig. 1, the battery unit is located behind (downstream of) the ultra-capacitor unit and by metering voltage vB and current iB at point B, Plow and Qlow can be calculated locally by the VSC of the battery. Then the battery unit endeavors to share the slow-varying power based on its storage and output capacity.

Generally, a battery’s maximum charge current varies with its state of charge (SOC) and its discharge has limited power rating. In this work, a three-stage approach is followed for battery charging without SOC estimations. As shown in Fig. 5a, stage 1 involves constant current ICHA with limited voltage VCHA until the battery’s voltage rises to VCHA. Then stage 2 follows, which is a constant voltage (VCHA) process with the charge current decreased to a trickle value. At this time, the battery is considered to be fully charged and enters stage 3. Through setting a smaller voltage set-point VF, the full state of the battery is maintained in this stage. As to the discharge process, it depends on system demands, which should not exceed the discharge limit IDIS.

Fig. 5
figure 5

Charging and discharging of a battery

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The referred rules are integrated into the battery power sharing process, and referring to the schematic in Fig. 6, two profiles, Plow + PDE and Pbat, are included. It should be noted that the diesel generator is forced to output PDE even without load demands, and it is preferable to charge the battery rather than dumping its charge. Therefore, the battery takes power Pcap from Plow + PDE. If Plow + PDE > 0, the battery absorbs power segment C according to its present capability. If Plow + PDE < 0, the battery is discharged to compensate for power deficit D without exceeding its discharge limit PDIS. This diagram demonstrates how to extract Pbat from Plow + PDE and is achieved through local control of the battery VSC.

Fig. 6
figure 6

Power sharing of battery unit

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The battery VSC works as a rectifier and the control scheme is schematically displayed in Fig. 7, where an inner current loop and an outer voltage loop are designed with a saturation block between them.

Fig. 7
figure 7

Control of battery VSC

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The voltage loop changes set-points VCHA and VF to switch between charging stages 2 and 3. A controller (PI3) with an upper limit ICHA and a lower limit IDIS is designed. Its output i*B is assumed to be the reference charging and discharging current of the battery, whereas in the current control loop, feedback idB is the inductor current of the VSC under a d-q-0 frame. Therefore, battery current i*B is first converted to VSC current i**B through a coefficient m, and is then input to a dynamic saturation block. m is given by (5), where vbat is the terminal voltage of the battery and vdB is the voltage of point B under the d-q-0 frame.

$$m = \frac{2}{3}\frac{{v_{bat} }}{{v_{dB} }}$$
(5)

The dynamic saturation block has a constant lower limit IdDIS and a dynamic upper limit ilow, given by (6) and (7), respectively.

$$I_{dDIS} = \frac{2}{3}I_{DIS} \frac{{v_{bat} }}{{v_{dB} }}$$
(6)
$$i_{low} = \frac{2}{3}\frac{{P_{low} + P_{DE} }}{{v_{dB} }}$$
(7)

If Plow + PDE > 0 and the battery stays in stage 1 of the charge process, then VCHA > vbat is always satisfied and PI3 outputs its maximum value of ICHA. Through the saturation block, the current reference i*dB is derived as (8).

$$i_{dB}^{*} = \hbox{min} \left\{ {mI_{CHA} ,\;i_{low} } \right\}$$
(8)

In contrast, if the battery stays in stages 2 or 3 of the charge process, PI3 generates a positive value between 0 and ICHA and i*dB is derived as (9).

$$i_{dB}^{*} = \hbox{min} \left\{ {i_{B}^{**} ,i_{low} } \right\}$$
(9)

If Plow + PDE < 0, then VCHA > vbat is also satisfied and PI3 outputs its maximum value of ICHA. Through the dynamic saturation block, the reference current i*dB is derived as (10), where ilow is negative.

$$i_{dB}^{*} = \hbox{max} \left\{ {I_{dDIS} ,\;i_{low} } \right\}$$
(10)

From the above analysis, C and D in Fig. 6 can be extracted and compensated by the battery through local control of the VSC without requiring SOC estimations. Areas A, B, E, and F remain for further compensation.

The reactive power Qlow should be fully compensated by the battery VSC. To accomplish this, Qlow is directly transformed to i*qB and assigned to the VSC controller as the reactive current set-point.

3.4 Local control of flexible load

The flexible load is located on the left side of the main AC bus with the diesel generator set. It is equipped to dump the power surplus from Plow and from the diesel generator. Through local metering of point C, vC and iC are detected. The remaining slow-varying power from Plow is calculated and defined as Pgap. With consideration for the diesel minimum power production limit PDE, the total power that needs to be dumped is determined by (11).

$$P_{flex} = \left\{ {\begin{array}{*{20}l} {P_{gap} + P_{DE} } \hfill & {P_{gap} + P_{DE} \ge 0} \hfill \\ 0 \hfill & {P_{gap} + P_{DE} < 0} \hfill \\ \end{array} } \right.$$
(11)

PDE is a positive constant, which is within 30%-40% of the diesel capacity, and if Pgap + PDE > 0 (A and B in Fig. 6), the flexible load will dissipate all power. Otherwise if Pgap + PDE < 0, the flexible load is shut down.

Flexible load can be heat production, hydrogen production, or sea water desalination systems for example. In this work, a VSC interfaced controlled-current source (CCS) is employed as a general flexible load. The VSC is regulated as a rectifier and the DC side voltage is maintained at Vflex through another voltage control loop, with Pflex/Vflex sent to the CCS as the source signal.

3.5 Local control of diesel generator set

The diesel generator set works as the grid-forming unit (master unit) of the microgrid to support the main AC bus. The actuator is modeled using a third-order transfer function, and T4, T5, T6 are its coefficients. Then a transport delay unit models the diesel engine with a time constant TD. The diesel generator set is equipped with a constant speed governor, which ensures constant frequency of the output voltages. The governor is a second-order transfer function with three coefficients T1, T2, and T3. Furthermore, the generator set is equipped with a static exciter, which ensures constant amplitude of the output voltages. The exciter is modeled using another transfer function with two confidents T7 and T8. The control scheme is schematically displayed in Fig. 8, where two feedback control loops (ω in p.u. and E in p.u.) are included.

Fig. 8
figure 8

Schematic of diesel generator set

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The diesel generator set is an AC voltage source and its power output is regulated indirectly without communications. If Plow > 0, the diesel generator set produces PDE and this power is totally dumped by the flexible load. If Plow < 0 and is within the scope of PDE (a net load exists), the diesel generator set provides PDE, one part is used to satisfy the load demand and any remaining power is dumped. However, if Plow < 0 and exceeds the range of PDE, the diesel generator set only outputs PDE, and the demand gap is filled by the battery. If the battery is functioning at its maximum capability and more power is needed, the diesel generator set will supply the increment automatically (E and F in Fig. 6).

4 Results and verifications

A simulation model of an islanded AC microgrid with the same structure as Fig. 1 is built, which consists of a diesel generator set, three feeders (wind turbine, linear load, and converter load), an ultra-capacitor unit, a battery unit, and a flexible load. As to the line impedances Z1-Z5, each has a resistance of 0.092 Ω and an inductance of 125 μH, which simulate a 50 m transmission line (line diameter is about 15 mm). The nominal AC bus voltage is 380 V/50 Hz (line-to-line) and the capacity of each unit is listed in Table 1.

Table 1 Capacity allocation of each unit
Full size table

In simulation, the diesel generator set is started first to build and dominate the main AC bus and then the ultra-capacitor unit, the battery unit, and the flexible load unit are activated at 1 s, 2 s and 3 s, respectively. The linear load is imposed at 5 s and the wind turbine is switched on at 10 s, which is a step-up power increase to simulate gusting winds. Then the heavy converter load is imposed at 20 s. With these designed scenarios, the power detecting and sharing process of each unit can be presented comprehensively and incisively.

Active power variations under the defined conditions are displayed in Fig. 9. The power generation of the wind turbine Pgen, linear load PRL, converter load Pcov, and the total active net power Pnet are presented.

Fig. 9
figure 9

Designed power variation scenarios

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Under the power variation conditions, the performance of the microgrid system is verified. Figure 10a shows the frequency of the system, which is maintained at 50 Hz, Fig. 10b shows the voltage amplitude of the diesel generator output, and it is also maintained constant at 311 V, and Fig. 10c shows the waveforms of the grid voltage vgrid when 80 kW active power at 10 s is added by the wind turbines, which only causes some slight distortions.

Fig. 10
figure 10

Performance of microgrid system frequency f, voltage amplitude of diesel generator set vm, and voltage waveforms at 10 s

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The decentralized control scheme without communications is verified and the active power sharing results of each unit are provided in Fig. 11. Figure 11b shows the fast-varying power that is extracted and suppressed by the ultra-capacitor unit. The ultra-capacitor is activated at every power perturbation. It should be noted that for this complex simulation model, we choose T = 2 s for ωb of the LPF to reduce the computational burden imposed by the simulation.

Fig. 11
figure 11

Active power sharing of each unit with decentralized control schemes

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The slow-varying power sharing results are displayed in Fig. 11c–e. As described previously, the diesel generator set is started first and no power is produced until the battery is activated at 2 s. Then the diesel generator set generates power PDE to charge the battery. When the linear load is imposed at 5 s, PDE is maintained at constant level and the battery provides power for any shortage. When the 80 kW renewable power source joins the microgrid at 10 s, the diesel set continues to work at 30% load-rate and the battery returns to a charging state. Stages 1 and 2 of the profiles in Figs. 5 and 6 are clearly demonstrated and verified. Any excess power is dumped by the flexible load. At 20 s, a heavy converter load is imposed, which means that user demand has increased. Then the flexible load is shut down accordingly and the battery begins to discharge, supplying power up to its maximum capability, PDIS. Once PDIS is reached, the diesel generator set supplies the power increment needed to satisfy user demand.

With the proposed system deployment principle and the decentralized control scheme, active power requirements of the microgrid can be detected and power is shared locally and independently.

As to the reactive power, approximately 10 kvar is imposed at 5 s (the R and L linear loads). As in Fig. 12a, the reactive power Qnet fluctuates during operation mainly because of the terminal voltage change of the linear loads under different conditions. The fast-varying reactive power Qhigh is suppressed by the ultra-capacitor unit through the same power calculation technique as Phigh, and is displayed in Fig. 12b, where Qcap represents fast-varying power suppression of the ultra-capacitor. The remaining slow-varying reactive power Qlow is compensated by the battery unit totally, as displayed in Fig. 12c, where Qbat represents slow-varying power sharing of the battery.

Fig. 12
figure 12

Reactive power sharing of each unit under decentralized control schemes

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The ultra-capacitor is used to suppress fast-varying active power variations, and its terminal voltage can be out of balance over long-term operation owing to irregular power variation and self-discharge. As illustrated in Section 3, a rebalance algorithm is designed. The verification results are displayed in Fig. 13.

Fig. 13
figure 13

Rebalance of ultra-capacitor

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The rated voltage is 700 V and the tolerable operation range is defined as [Vlow, Vup] = [695 V, 705 V] in this simulation model. The rebalance results are presented in Fig. 13. Without and with the rebalance algorithm, the ultra-capacitor voltage behaves as shown in Fig. 13a, b, respectively. With the proposed approach, the ultra-capacitor voltage can always be rebalanced to the rated value and the power component PAC needed for voltage rebalance under the defined conditions is shown in Fig. 13c.

5 Conclusion

Microgrid control always relies on communication facilities to achieve power balance and economic targets. This work proposes an innovative system deployment principle based on a decentralized power flow control scheme without communication facilities for a master/slave type islanded AC microgrid. This difference will benefit the flexibility and plug-and-play of a microgrid. A small-scale AC microgrid with diesel, wind, hybrid storage, critical loads, and flexible loads is investigated. Without using any communications among units, the net power, including active and reactive power, are detected and compensated locally and independently considering the diesel set’s low load-rate operation, battery charging, and ultra-capacitor rebalance issues. Finally, simulation results are provided to verify the validity of the proposed deployment principle based on decentralized control.