Volume 6, Issue 7 p. 1329-1338
Article
Open Access

Power flow control of intertied ac microgrids

Inam Ullah Nutkani

Corresponding Author

Inam Ullah Nutkani

Experimental Power Grid Centre, Agency for Science, Technology and Research, Singapore

School of EEE, Nanyang Technological University, Singapore

Search for more papers by this author
Poh Chiang Loh

Poh Chiang Loh

School of EEE, Nanyang Technological University, Singapore

Search for more papers by this author
Frede Blaabjerg

Frede Blaabjerg

Department of Energy Technology, Aalborg University, Denmark

Search for more papers by this author
First published: 01 August 2013
Citations: 31

Abstract

Microgrids are small reliable grids formed by clustering distributed sources and loads together. They can, in principle, operate at different voltages and frequencies like 50, 60, 400 Hz or even dc. Tying them together or to the mains grid for energy sharing would therefore require the insertion of interlinking power converters. Active and reactive power flows of these converters should preferably be managed autonomously without demanding for fast communication links. A scheme that can fulfill the objectives is now proposed, which upon realised, will result in more robustly integrated microgrids with higher efficiency and lower reserve requirement. The scheme presented has been tested in experiments with results captured and discussed in a later section.

1 Introduction

Global demand for energy and rising environmental concerns have brought forward the concept of distributed generation by various unconventional sources like photovoltaic, wind, tidal, geothermal and high-speed diesel generators [1, 2]. These sources are known to have their own advantages and disadvantages with no one source suiting all requirements. That prompts the intentional grouping of a few distributed sources and loads together to form small microgrids [3, 4], which in principle, also include distribution grids found in electric ships and aircrafts [5-8]. The formed microgrids are, by nature, independent entities, whose operating voltages and frequencies can be set to suit their respective source and load characteristics. The microgrids can then operate in isolation or tied to the utility grid. Among themselves, there can also be intertying to reinforce their reserve sharing, security and energy trading. Such intertying would definitely require the insertion of power converters [9-12], whose main responsibility is to harmonise the different operating conditions of the microgrids. Usual line-frequency transformers can also be used, but only for different voltages and not frequencies within the microgrids. Adding of power converters is therefore a more universal approach likely to draw more interest.

Besides harmonising different operating conditions, control schemes used with the inserted power converters can be designed with reactive power support and active power transfer among the microgrids. These power flow control mechanisms should preferably be efficient and autonomous without demanding for fast communication links. The latter is important since distributed sources are widely dispersed, and hence impossible or too costly to link using fast communication links. Methods that can avoid fast communication links are usually based on the droop operating principles, whose control decisions are deduced from locally measured variables only. Although droop control has presently been developed into many variants, they are mostly discussed for accurate power sharing within a single ac microgrid. Its extension to multiple intertied microgrids is presently lacking even though there might be a few references moving along that trend.

For example, in [13], the tying of a microgrid to the utility grid through an ac–dc–ac converter is discussed with two droop modes applied to them. In mode 1, sources in the microgrid are droop-controlled, whereas the utility grid is regulated at a constant contractual power through the ac–dc–ac converter. Their roles are reversed in mode 2 with the microgrid sources operating at their fixed full-rated power and the ac–dc–ac converter operating like a droop-controlled source. Although the system studied might appear more complex, the underlying droop scheme remains the same as for a single ac microgrid, since at any instant, only one grid is droop-controlled, whereas the other behaves like a constant power source. In addition, the utility grid in [13] is treated like an infinite bus with its load conditions not affecting control decisions within the microgrid. Management of this utility-tied microgrid is thus close to that of a single ac microgrid. A second example can be found in [14, 15], where the intertying of two single-phase microgrids has been discussed. The focus there is, however, more on improving transient response and minimising power pulsation at the dc-link of the intertying converter. These are no doubt important performance considerations applicable to most power electronic applications, rather than specifically related to intertied microgrids. They are therefore not directly related to the power flow management of intertied microgrids, which is presently lacking.

This study now extends the droop power control scheme from a single ac microgrid to the intertying of at least two microgrids having their own preferred operating voltages and frequencies. The added operating complexity is mainly directed at the interlinking power converters found between any two of the intertied microgrids. These converters, upon implemented appropriately, will result in more flexible active power transfer and reactive power support within the microgrids based only on locally measured variables. Their operations can also be planned such that they operate only when necessary, rather than continuously. Unnecessary operating time and losses can therefore be minimised on average, resulting in a more efficient intertied system. Generating capacity available within each microgrid is also higher and better shared even with no costly standby generators added. Theories and experimental results have thoroughly been discussed in the paper with the scheme demonstrated for both islanded and grid-connected modes.

2 Droop scheme in single microgrid

Fig. 1 shows an example, where two microgrids are intertied by two back-to-back connected converters. Within each microgrid, sources are usually droop-controlled if autonomous operation based only on locally measured variables is preferred. The droop scheme has long been used with the conventional ac power systems for achieving power sharing among multiple electromechanical generators [16]. Its underlying principles are related to the simplified active P and reactive Q power flow expressions listed in (1) and (2) for a predominantly inductive transmission line (line resistance ignored)
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0001(1)
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0002(2)
where V1<δ1 and V2<δ2 are the voltage phasors at the two ends of the line, and Xl is the reactance of the line. Since the phase difference (δ1δ2) is usually small, the sine and cosine terms in (1) and (2) will tend towards (δ1δ2) and 1, respectively. On substituting these approximations, (1) and (2) spell that active and reactive powers can linearly be regulated by tuning the phase difference and voltage magnitude, respectively. The former can in turn be changed by varying frequency.
Details are in the caption following the image

Illustration of intertied microgrids

The same linear active and reactive power variations can be introduced to a non-electromechanical source by programming its controller to have the droop characteristics shown on the right of Figs. 2 and 3 for microgrid ‘B’ quoted as an example. For ‘i’ sources in parallel, their linear gradients, also known as droop coefficients, can then be computed using (3a) and (4a), where fmax, fmin, Vmax and Vmin are the common maximum and minimum frequencies and voltages assumed by the sources. If maximum active power Pi,max and reactive power Qi,max are further set proportional to the source kVA ratings (Pi,maxSi,max and Qi,maxSi,max), (3a) and (4a) expand to (3b) and (4b), which must be satisfied to obtain proportional power sharing among the sources based on their respective kVA ratings
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0003(3a)
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0004(3b)
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0005(4a)
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0006(4b)
where mi and ni are the active and reactive droop coefficients, respectively. At times, (4b) might not be sufficient for guaranteeing proportional reactive power sharing among the generating sources because of different feeder voltage drops and other parameter mismatches. Modifications to compensate for the mismatches have already been studied [17-19], and will hence not be discussed further. The scope here is more on autonomous power flow control among multiple microgrids, rather than source control within a single microgrid.
Details are in the caption following the image

Active droop characteristics of microgrids and interlinking converters

Details are in the caption following the image

Reactive droop characteristics of microgrids and interlinking converters

3 Interlinking droop scheme

When microgrids are tied together like in Fig. 1, there are some features that they can jointly demonstrate. These features are explained below, whose purposes are mainly to enhance the overall system reliability, efficiency and performance.
  • Active power flow from under-loaded to overloaded microgrid for reinforcement. At any instant in the steady state, active power balance must be maintained at the two ends of the interlinking converters to keep their common dc-link voltage Vdc stable.
  • Reactive power reinforcement provided by interlinking converters upon requested. Reactive power reinforcement need not be balanced at the two ends of the interlinking converters, and can hence be independently performed.
  • Priority tuning between active and reactive power generations. Depending on the load types and their associated power factors, priority to supply active or reactive power by the interlinking converters can be set accordingly.
  • Unnecessary operating time and losses of interlinking converters can be minimised. This happens when the intertied microgrids are either all under-loaded or heavily overloaded. The former means the microgrids do not need additional generation, while the latter means they are close to their ratings, and hence do not have additional generating capacities for sharing.
The above-mentioned features and requirements can be fulfilled by the following proposed scheme for the interlinking converters. The scheme is autonomous with only locally measured voltages and frequencies involved.

3.1 Islanded mode

To isolate the intertied microgrids, the static switch connected to the utility in Fig. 1 must be opened. With no utility grid, supply–demand balancing within the microgrids is generally more stringent since any surplus cannot be channeled to the grid and any deficit cannot be replenished from it. It is hence necessary for the interlinking converters to measure generating conditions of the two microgrids in Fig. 1, before deciding on the amount of power to transfer between them. The eventual goal is to arrive at a supply–demand balance for the intertied microgrids in the steady state. Before proceeding further, it is helpful to clarify that this method of interlinking control is different from that explained in Section 2 for a single source in a single microgrid. The former requires measurements from two microgrids before appropriately combining them to produce the necessary interlinking control action, which to date has not been reported in the literature. The latter, on the other hand, measures operating conditions within a single microgrid with no interlinking intelligence needed. It is hence much simpler, and no doubt has already been well established.

Returning to the measurement of microgrid generating conditions, its frequency and voltage can be measured instead because of those ‘cumulative’ microgrid droop lines shown in Figs. 2 and 3. It is hence important for each interlinking converter to have its own phase-locked-loop for extracting frequency and magnitude information from its measured terminal voltages. In addition to that, it should be mentioned that the term ‘cumulative’ has been used with the microgrid droop characteristics to reflect the fact that the interlinking converters cannot see the individual source details of the microgrids at their terminals. Only the summed responses of the microgrids are visible to the interlinking converters at their terminals. A set of power request curves can next be defined for the interlinking converters, whose pictorial representations are shown in the middle of Figs. 2 and 3. Power request (both active and reactive) here is defined as the anticipated positive power demanded by microgrid ‘x’ (x = A or B) to flow into it when it is either overloaded or heavily overloaded. The request can certainly be negative with power demanded to flow out of microgrid ‘x’ when it is under-loaded, but for this paper, it is simply set to zero without compromising the effectiveness of the scheme. Beginning now with the active droop requests shown in Fig. 2 and notated as Px,IC, their representative equations and defined ranges can be expressed as (5) shown at the bottom of the page.
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0007(5)
In (5), mx is the droop coefficient for the active request, and subscripts OL and HOL are for notating thresholds below which the microgrids are considered overloaded and heavily overloaded, respectively. Also included in (5) is the variable Px,IC,max for representing the maximum active power that can be requested, which based on the earlier definition for power request, is always positive. This maximum, together with the concepts brought forward by (5), is better explained with an example, but before addressing it, it is important to clarify that active power requested Px,IC in (5) might not be the actual active power urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0008 produced by interlinking converter ‘x’. The requested active power Px,IC is simply a value that interlinking converter ‘x’ would expect microgrid ‘x’ to request from it based on the detected frequency fx. Requested values from both microgrids must promptly be considered before interlinking converter ‘x’ and its back-to-back companion know how much actual active power urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0009 to inject to the microgrids.
The actual active power urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0010 can in fact be computed from (6), whose value is positive when power is flowing out of interlinking converter ‘x’. This notation causes urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0011 and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0012 in (6) to have equal magnitude but opposite polarity needed to stabilise the dc-link voltage of the interlinking converters. In practice, a small difference urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0013 is also added to account for losses in the converters. Value for urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0014 can automatically be produced by passing error between the dc-link voltage and its reference through a proportional–integral (PI) controller. The obtained urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0015 can then be added to urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0016, urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0017 or divided between them in order to draw the necessary active power needed to keep the dc-link voltage constant. Other reasons on why urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0018 is formulated like in (6) will, as mentioned earlier, are more obvious when describing the example to be followed next
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0019(6)
Assuming the two microgrids shown in Fig. 1 are initially not loaded, their frequencies will then be at their respective maximum notated as fx,max. Loading in microgrid ‘A’ is subsequently increased, followed promptly by its source generation to meet the load demand. From its source droop line shown on the left of Fig. 2, frequency fA of microgrid ‘A’ will then fall. The interlinking converters, after sensing fA and fB ( = fB,max since not yet loaded), will compare them with those ranges defined in (5). If fA remains in the under-loaded range, powers requested by the two microgrids are estimated as PA,IC = PB,IC = 0 based on (5) or the interlinking droop characteristics shown in the middle of Fig. 2. Since the microgrids are not asking for additional active power, the actual active power transferred by the interlinking converters should be zero, which is in agreement with the result obtained from (6). The requested active power PA,IC will only be non-zero when loading in microgrid ‘A’ is further increased, pulling fA into the overloaded range. Its value eventually saturates at PA,IC,max when fA enters the heavily overloaded range. Since microgrid ‘B’ is still not loaded, it has the capacity to generate active power requested by microgrid ‘A’, but only up to its rated capacity notated as PB,max. The maximum active powers that microgrids ‘A’ and ‘B’ can request are therefore capped by (7), and the actual active power transferred is set as urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0020 based on the described example. This is indeed the outcome obtained from (6)
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0021(7)
Assuming next that loading of microgrid ‘B’ is gradually increased, causing its source generation to rise and its frequency fB to fall. Upon fB entering the overloaded range, requested power PB,IC starts to increase above zero. Since PA,IC and PB,IC are both non-zero, they must be compared. If PA,IC > PB,IC, microgrid ‘A’ is loaded more, and should hence be helped with actual active power flowing into it urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0022. The flow should reverse when PB,IC > PA,IC (or when urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0023). These requirements are again in line with result obtained from (6). If loading of microgrid ‘B’ is further increased until fB enters the heavily overloaded range, both requested powers would be at their maximums, expressed as PA,IC = PA,IC,max and PB,IC = PB,IC,max. Since both microgrids are heavily overloaded, they do not have excess generating capacities for sharing. The actual active power transferred should hence decrease to zero, which is again accounted for by (6). Other loading sequences can similarly be tried with (5)–(7) still giving the anticipated results. They are hence appropriate for controlling the active power flow of the interlinking converters in an autonomous manner.

To further strengthen confidence with (5)–(7), a simple case to show how they can be applied is described here, where it is assumed that the two microgrids can produce the same maximum power Pmax. Other relevant maximum power values mentioned earlier can hence be set as Px,IC,max = Px,max = Pmax (x = A or B). It can next be assumed that the microgrids are loaded such that their requested powers are related by PA,IC = 1.5PB,IC. Substituting into (6) then gives rise to K = 0.5PB,IC/Pmax and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0024. The latter simply means that the interlinking converters must transfer 0.5PB,IC from microgrid ‘B’ to assist the more overloaded condition in microgrid ‘A’, as intended, hence proving the effectiveness of the proposed scheme.

Apart from active power flow, the interlinking converters can provide reactive power support to the microgrids, when requested. Unlike active power though, reactive powers at the terminals of the two interlinking converters need not be balanced. They can hence be independently controlled using, for example, the interlinking reactive droop characteristic drawn in Fig. 3 for interlinking converter ‘B’. The same reactive droop characteristic with different axial values can be used for interlinking converter ‘A’. Collectively, they can be represented by the common mathematical expression (8) shown at the bottom of the page.
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0025(8)
where nx is the interlinking reactive droop coefficient. Their common operating principles are similar to those of the active request droop characteristics represented by (5). However, unlike (5), the value obtained from (8) is already the actual reactive power urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0026 produced by interlinking converter ‘x’ for microgrid ‘x’. No further processing like in (6) is needed since reactive power balance is unnecessary. Modification to the maximum reactive power Qx,IC,max that interlinking converter ‘x’ can supply is, however, needed to account for the fixed converter kVA rating Sx,IC,Rated and its varying actual active power urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0027 transferred. This can be done according to (9), whose resulting variation is better shown by those dashed lines drawn in Fig. 3
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0028(9)
The combined power expression produced by the interlinking converters can hence be written as
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0029(10)
When urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0030 is zero, its associated interlinking converter ‘x’ can be turned off to avoid unnecessary operating losses. It will only be turned on when urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0031 with microgrid ‘x’ receiving the generated power.

3.2 Grid-connected mode

The intertied microgrids shown in Fig. 1 can be tied to the utility grid by turning on the static switch placed between them. The same interlinking droop scheme discussed in Section 3.1 can still be used with the interlinking converters without changes. It should, however, be noted that microgrid ‘B’, being directly connected to the grid, is now having a fixed frequency fB and terminal voltage VB determined by the grid. Any surplus or deficit in power in microgrid ‘B’ will also be balanced by the grid, which in a way, acts like an infinite bus. If the frequency and voltage of microgrid ‘B’ are further designed to be in the under-loaded ranges defined in (5) and (8), their corresponding requested powers would be PB,IC = 0 and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0032. The actual active power transferred can hence be simplified from (6) to (11), while urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0033 is still given by (8). It should, however, be noted that (11) is written here for illustration only. The actual implementation is still realised with (6), which works fine in both islanded and grid-connected modes
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0034(11)

3.3 Other variations

The above interlinking control description is based on the assumption of Pf and QV droop lines used within each microgrid. This is, however, not always the case. For example, PV and Qf droop lines can be used for microgrids, whose line impedances are mostly resistive. Regardless of that, the same interlinking droop principles can still be used, but with V now measured to determine P and f measured to determine Q. The same reasoning can be applied to other hybrid droop relationships used with microgrids having equally prominent resistive and inductive line impedances. The only slight changes expected are the interlinking P and Q commands are now determined by applying the desired interlinking droop relationships to both f and V.

4 Experimental results

A scaled-down version of the example intertied microgrids shown in Fig. 1 was assembled in the laboratory for experimental testing with their ratings and base values used for per-unit (p.u.) conversion spelled in Table 1. Per-unit conversion of powers and voltages was based on the standard formula of actual divided by the chosen base value. Conversion for frequencies was, however, done differently. Instead of normalising the frequencies, the conversion shown by (12) normalised their variations from their respective mean values. This had the effect of putting them in the same − 1 to 1 range for easier comparison of results regardless of what frequency values had been chosen for the microgrids (e.g. 50 and 60 Hz, 50 and 400 Hz, … etc.). It will also not modify the interlinking droop concepts proposed in the paper
urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0035(12)
Table 1. Ratings and base values for experimental testing
Entities/Parameters Ratings/Values
Interlinking Converters 2 kVA per converter, 350 V (dc-link)
Microgrid ‘A 2 kVA, 190.5 V (ac rms), 3-phase (60 ± 1)Hz ⇒ fA,max = 61 Hz, fA,min = 59 Hz
Microgrid ‘B 2 kVA, 190.5 V (ac rms), 3-phase (50 ± 1)Hz ⇒ fB,max = 51 Hz, fB,min = 49 Hz
Droop Coefficients mA = mB = 1.25 and nA = nB = 0 to 19.2
Base Power 2 kVA
Base Voltage 190.5 V (ac rms)

For the experimental setup, it should also be mentioned that each microgrid was emulated with a source inverter and a local resistive-inductive load bank for adjusting its loading. The source inverter was within the considered microgrid, and should hence not be confused with the interlinking converters tying the two microgrids together. The source inverter was controlled using the droop scheme reviewed in Section 2 with a usual outer voltage and inner current double-loop controller whose design could be found in [20]. The interlinking converters, on the other hand, were implemented with two six-switch converters sharing a common dc-link. Their common droop scheme was discussed earlier in Section 3. Unlike the source droop scheme whose output was a voltage reference, references from the interlinking droop scheme were represented by the power expression given in (10). Its tracking controller must therefore be modified accordingly with the outer being the power tracking loop and the inner being the usual voltage–current tracking loop.

The outer power loop was realised with two PI controllers for acting on the active urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0036 and reactive urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0037 power errors. Their outputs were the frequency and voltage magnitude commands, which could then be combined to give the three-phase voltage commands urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0038 for tracking by the inner voltage–current tracking loop. Including this outer power loop, illustration of the overall control scheme for the interlinking converters could be found in Fig. 4. DC-link voltage tracking was not shown in the figure because it had already been accounted by urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0039 explained in Section 3.1. The experiment was performed with five scenarios, whose responses had been intentionally slowed down. This was to allow for continuous tracking of operating points on the interlinking active and reactive request lines, which like all droop schemes, applied only to steady-state responses. Snapshots of the tracking were then shown in appropriate figures to be discussed next.

Details are in the caption following the image

Block diagram of interlinking droop scheme

4.1 Islanded scenario 1 (Fig. 5, and 0–100 s in Fig. 6)

The experiment was started with the interlinking converters not yet activated from 0 to approximately 20 s. During this time, the respective load banks in the microgrids were adjusted such that frequency of microgrid ‘A’ was at fA = − 0.5 p.u., whereas that of microgrid ‘B’ was at fB = 0.6 p.u. They corresponded to those operating points marked as ‘1a’ in Fig. 5(a). Microgrid ‘A’ was thus classified as overloaded, whereas microgrid ‘B’ was considered as under-loaded. The actual active power transferred should hence be from microgrid ‘B’ to ‘A’, which indeed happened when the interlinking converters were activated from 20s onwards. This transfer of active power caused frequency of microgrid ‘B’ to drop since it was generating the transferred power. Frequency of microgrid ‘A’, on the other hand, rose since it was receiving the transferred power. Operating points ‘1a’ therefore moved to points ‘1b’ in the steady state, whose actual power values read from Fig. 6a were urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0040 These values were not exactly equal in magnitude because of a small difference urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0041 needed to keep the dc-link capacitor voltage in Fig. 6c constant.

Details are in the caption following the image

Operating point trajectories on

a Frequency against active power and

b Voltage against reactive power characteristics when in islanded mode

Details are in the caption following the image

Experimental results showing

a Frequency and active power

b Voltage and reactive power

c dc-link voltage of interlinking converters during islanded mode

Terminal voltages wise, their respective initial values were read from Fig. 6b as VA = VB = 0.97 p.u. from 0 to 20 s, before activating the interlinking converters. They corresponded to those operating points, also marked with ‘1a’ in Fig. 5b. The two microgrids were thus classified as overloaded, and would hence request for reactive powers from the interlinking converters once they were activated from 20 s onwards. This was observed in Fig. 6b, where the common steady-state reactive power injected to each microgrid was read as urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0042 from 20 s onwards. With this reactive support provided by the interlinking converters, the microgrid terminal voltages rose slightly to those operating points marked with ‘1b’ in Fig. 5b. These operating points laid on the dashed droop lines, whose common maximum value computed from (9) was given by urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0043

4.2 Islanded scenario 2 (Fig. 5, and 100–200 s in Fig. 6)

Active loading of microgrid ‘A’ in scenario 2 had been lowered such that its frequency rose to fA = 0 p.u. Operating points of the microgrids were therefore those marked with ‘2’ in Fig. 5a, whose corresponding active powers requested, and hence actual active powers transferred were all zero. This was observed in Fig. 6a, where both actual powers transferred urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0044 and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0045 were noted to gradually drop to zero from 100 s onwards. Reactive loadings in both microgrids were also decreased in scenario 2, causing them to move to operating points ‘2’ in Fig. 5b. Their reactive power generations urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0046 and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0047 were thus zero, as confirmed by the second plot in Fig. 6b. Since active and reactive powers demanded from the interlinking converters were zero, they could be turned off to keep operating costs low rather than operating them continuously.

4.3 Islanded scenario 3 (Fig. 5, and 200–250 s in Fig. 6)

In scenario 3, the only change introduced was to increase the reactive loading of microgrid ‘B’ until its terminal voltage entered the overloaded range. Reactive power urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0048, read from Fig. 6b, was thus generated by interlinking converter ‘B’ for microgrid ‘B’ from 200 s onwards. Interlinking converter ‘A’, on the other hand, remained off since no reactive power was requested from it and the actual active power transferred by the two converters remained at zero. Steady-state operating points of the two converters were thus those marked with ‘3’ in Figs. 5a and b.

4.4 Grid-connected scenario 4 (Fig. 7, and 0–180 s in Fig. 8)

Scenario 4 was tested with microgrid ‘B’ tied to the utility grid, emulated by a threephase programmable ac source for the experiment. Its voltage and frequency were therefore fixed at 190.5 V and 50 Hz, corresponding to 1 and 0 p.u. in the under-loaded ranges. Active and reactive powers requested from interlinking converter ‘B’ were hence zero according to (5) and (8). Microgrid ‘A’, on the other hand, was loaded such that its voltage and frequency entered their respective overloaded ranges marked by operating points ‘4a’ in Figs. 7a and b. It remained at these operating points from 0 to 20 s, during which the interlinking converters were not yet activated. Active and reactive powers generated by the converters from 0 to 20 s were thus zero, as seen from Figs. 8a and b, respectively. The converters were activated only from 20 s onwards, after which interlinking converter ‘A’ started to generate actual active and reactive powers for microgrid ‘A’. Their values were read as urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0049 and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0050 from Figs. 8a and b, respectively. With these added capacities provided to microgrid ‘A’, its source generation could relax slightly, leading to slight increases in its voltage and frequency. Operating points ‘4a’ therefore moved to ‘4b’ in the steady state. Throughout the trajectory, dc-link voltage of the interlinking converters had been kept constant, as seen from Fig. 8c.

Details are in the caption following the image

Operating point trajectories on

a Frequency against active power

b Voltage against reactive power characteristics when in grid-connected mode

Details are in the caption following the image

Experimental results showing

a Frequency and active power

b Voltage and reactive power, and

c dc-link voltage of interlinking converters during grid-connected mode

4.5 Grid-connected scenario 5 (Fig. 7, and 180–250 s in Fig. 8)

From 180 to 250s, active and reactive loadings of microgrid ‘A’ were reduced until its frequency and voltage rose to fA = 0 p.u. and VA = 1.05 p.u., indicated by those steady-state operating points marked with ‘5’ in Figs. 7a and b. Since they were in the under-loaded ranges, their requested and hence actual active and reactive power flows were zero. These were clearly seen in Figs. 8a and b, where urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0051 and urn:x-wiley:17554535:media:pel2bf02342:pel2bf02342-math-0052 gradually dropped to zero.

5 Conclusion

An interlinking droop scheme for tying microgrids at different nominal frequencies and voltages has been proposed. With the scheme implemented, interlinking converters between microgrids will autonomously transfer an appropriate amount of active power from the under-loaded to overloaded microgrid for reinforcement. Independent reactive power reinforcement can also be provided by the interlinking converters for supporting terminal voltages of the microgrids during high reactive loading conditions. These power flow features are achieved with no requirement for fast communication links and at a minimised operating cost for the interlinking converters. Theories and experimental results have been presented to validate the performances anticipated.