In-situ Reconfiguration for Flexible Distribution of

Energy and Storage Resources

Ajit A. Renjit

Student Member, IEEE

The Ohio State University

Electrical and Computer Engineering

Columbus, OH 43210, USA

renjit.1@osu.edu

Mahesh S. Illindala

Senior Member, IEEE

The Ohio State University

Electrical and Computer Engineering

Columbus, OH 43210, USA

millindala@ieee.org

Abstract—Flexible Distribution of EneRgy and Storage

Resources (FDERS) is a new framework recently proposed for

integrating various distributed resources in a power system. It

provides flexibility in rearranging the interconnected system

resources into formations in order to achieve greater

sustainability as observed in the V-shape formation of a bird

flock or peloton formation of a cycling racing team. One of the

characteristic features of FDERS is in enabling distributed

resources reconfiguration in-situ, i.e., the resources

demonstrate a different dynamic behavior relative to each

other than their (original) physical ‘electrical’ location

otherwise would suggest. This paper presents various schemes

for in-situ reconfiguration along with their advantages. It is

achieved by means of developing novel techniques employing

special functions of compensating reactances. These techniques

help in achieving greater sustainability goals like optimal

energy storage deployment, enhanced controllability, improved

system robustness and increased lifetime of the distributed

energy and storage resources. In-situ reconfiguration is

demonstrated for within-parallel, parallel-to-series and series-

to-parallel connections. Finally, a comparison is also presented between physical and in-situ and reconfigurations.

I. INTRODUCTION

Distributed Energy Resources (DERs) and microgrids

have been proposed in the recent past to improve the power

quality and reliability for critical and sensitive loads [1].

However, the integration techniques developed thus far

relied to a large extent on the traditional power systems

approach that assumes large DERs providing power to

numerous smaller-rated loads. In this case, the individual

load dynamics get smoothed out and there is seldom a need

to make any large and sudden changes in generation. Such

systems are ill-prepared for challenging scenarios of large

and fluctuating demands – as observed when multiple smaller-rated DERs need to supply significant-sized loads,

especially when there is no power from the main (utility)

grid.

A typical example of challenging load scenario is the

crusher load commonly found in metal industries, mining

sites or cement plants [2]. A network of small-rated DERs

needs very detailed and thorough design for reliably

supplying without breakdown any large and fluctuating

loads, especially in the islanded mode of operation. This is

because the dynamic behaviors of such DERs are highly

dependent on their ‘electrical’ locational placement within

the microgrid [3-5]. As a solution, a new framework known

as Flexible Distribution of EneRgy and Storage Resources

(FDERS) was proposed in [6].

FDERS was inspired by the V-shape formation of a bird

flock and peloton/echelon formation of a cycling racing team

where the team members cooperate for deriving greater

shared benefits [6]. It claims to offer several benefits like optimal energy storage deployment, enhanced controllability,

improved system robustness and increased lifetime of all

power system resources. One of the key features enabling the

flexibility is the reconfiguration in-situ, where the distributed

resources demonstrate a different dynamic behavior relative

to each other than their (original) physical ‘electrical’

location otherwise would suggest. This paper presents

various schemes for in-situ reconfiguration along with their

advantages.

The organization of this paper is as follows: Section II

describes the synthesization of virtual reactance that is the

essential first step in realizing in-situ reconfiguration. Also

the simple case of within-parallel in-situ reconfiguration is

explained in this section. In Section III, an in-situ

reconfiguration scheme parallel-to-series is described.

Section IV covers the series-parallel in-situ reconfiguration.

Finally, Section V concludes the paper.

II. SYNTHESIZATION OF VIRTUAL REACTANCE FOR WITHIN-PARALLEL IN-SITU RECONFIGURATION

This section discusses briefly how to realize synthesized

virtual reactances in power electronics based DERs that are

connected parallelly to supply a load [6]. Consider an n-

DER parallel network. In order to realize FDERS, it is

required to achieve relative drafting between two DERs in

the network. This is only possible with a variation in their

2378978-1-4799-0336-8/13/$31.00 ©2013 IEEE

Fig. 1. Synthesis of ‘virtual’ reactance Xk-add in producing inner loop voltage controller reference for each DER in a parallel network

individual interface reactances.

A practical concern over the use of a large physical

reactance in interfacing any DER to the network is its size

and the fact that it cannot be easily varied in the existing

equipment. Therefore, using the method of synthesized

‘virtual’ reactances as shown in Fig. 1 any value of

additional reactance can be built within the DER’s

controller, and thereby changing its voltage reference

from �⃗�𝑘∗ (𝑡) to �⃗�𝑘

′∗(𝑡). It is to be noted that, for the purposes

of simulation, the inner voltage regulator has been

approximated as a first-order lag function whose time-

constant is assumed as (Tv = 5 ms) based on the controller

bandwidth for a PWM inverter operating at 4-kHz switching

frequency [5].

Fig. 2 illustrates a parallel configuration where the

physical reactances X1o=X2o=X30…=Xno=10%, and the

additional reactances Xk-add (where k = 1, 2, .., n) for each

DER are synthesized within its controller card. The value of

the synthesized reactance Xk-add can then be programmed

corresponding to the pecking order of DERs in the

formation – similar to the bird flock/V-formation [7, 8] or

cycling team/peloton formation [9-11]. The pecking order

can be modified based on preferred criteria such as energy

resource availability, prime-mover response characteristics

and lifecycle costs. Thus the method of synthesized

reactances helps the DERs to reconfigure in-situ while their

physical electrical location remains unaltered.

Time-domain simulations were carried out in

Matlab/Simulink/SimPowerSystems for the parallel

DER system. Fig. 3 shows the observed dynamic response

of a parallel-connected 3-phase, 480-V, 60-Hz, 4-DER

islanded system for a large block load change from 80-kW

to 160-kW.

Fig. 2. Single line diagram of parallel configuration of multiple (n > 2) DER system with synthesized reactances.

Act

ive

po

wer

(k

W)

Time (s)

Fig. 3. Response of a 4-parallel-DER system obtained using within-

parallel in-situ reconfiguration to a step change in a large block load from

80kW to 160kW

As anticipated based on the net reactance values (Xko+Xk-

add), the DER1 that is electrically closest to the load

3-phase

space

vector

(synchr. frame)

+

Vk∗

ωk∗

ikd

From “DERk

power

controller”

(inset of this

picture)

From DERk output current measurements

ikq

-1

𝑖𝑘(𝑡)= 𝑖𝑘𝑑 + 𝑗𝑖𝑘𝑞

𝑗𝑖𝑘(𝑡)= −𝑖𝑘𝑞 + 𝑗𝑖𝑘𝑑

+

𝑣𝑘𝑞

∗

Xk-add

�⃗�𝑘′∗(𝑡)

= 𝑣𝑘𝑑′∗ + 𝑗𝑣𝑘𝑞

′∗

�⃗�𝑘′∗(𝑡) = �⃗�𝑘

∗(𝑡) − j𝑋k−add 𝑖𝑘(𝑡)

𝑣𝑘𝑑∗

𝑣𝑘𝑞′∗

𝑣𝑘𝑑′∗

ωk∗

�⃗�𝑘∗(𝑡)

= 𝑣𝑘𝑑∗ + 𝑗𝑣𝑘𝑞

∗ dq/abc

transform. (Effect of

inner voltage controller)

1

1 + 𝑠𝑇𝑣

�⃗�𝑘

′ (𝑡)= 𝑣𝑘𝑑

′ + 𝑗𝑣𝑘𝑞′

𝑣𝑘𝑞′

𝑣𝑘𝑑′

𝑣𝑘𝑎′

𝑣𝑘𝑏′

𝑣𝑘𝑐′

ikd

ikq

nom

+ 1

Dqk

+

+

+

+

+

Vk∗

ωk∗

Vno

m Q

k

Pk

To the inner

loop voltage regulators

1

Mks + Dk

∆Vk∗

∆ωk∗

Qk∗

V /Q

Controller

/P

Controller

Pk∗

1 + 𝑠𝑇𝑎

1 + 𝑠𝑇𝑏

X2o

𝑖2

PL

X1o

DER

1

𝑖1

DER

2

X1-add

X2-add

DER

n

�⃗�1𝑝= V1𝑝ej1pt

�⃗�𝑛𝑝= V𝑛𝑝ejnpt

�⃗�2𝑝= V2𝑝ej2pt

�⃗�1𝑝′ = V1𝑝

′ ej1pt

�⃗�2𝑝′ = V2𝑝

′ ej2pt

�⃗�𝑛𝑝′ = V𝑛𝑝

′ ejnpt

Xn-add

𝑖𝑛

X3o

X1-add

< X2-add

< ••• < Xn-add

X1o

= X2o

= ••• = Xno

= 10%

X1-add = -10%

X2-add = 0%

X3-add = 10%

X4-add = 20%

X1o

= X2o

= X3o

= X4o

=10%

Leading

DER1

Drafting

DER4

2379

DERn

X1o

=0

�⃗�1𝑠= V1𝑠ej1st

X2o

Xno

�⃗�2𝑠= V2𝑠e

j2st

�⃗�𝑛𝑠= V𝑛𝑠ejnst

DER2

DER1

𝑖1

𝑖2

𝑖𝑛 P

L

𝑖2 + 𝑖3 … + 𝑖𝑛

X2o

= X3o

= ••• = Xno

contributes a major share in the transient power flow while the remaining DERs show drafting characteristics.

III. PARALLEL - SERIES IN-SITU RECONFIGURATION

It was earlier reported that the series connection of DERs facilitated a greater amount of drafting than a parallel connection [6]. Consequently, the parallel system in Fig. 4a was reconfigured into an n-DER series connected system in Fig. 4b using the conventional methods of physical reconfiguration using sectionalizers/switchgears. Fig. 6.a illustrates the response of a 4-DER series connected system for a block load change from 80kW to 160kW. Although by such a physical reconfiguration, enhanced drafting could be achieved, a major concern over this kind of reconfiguration technique is that it is not practically feasible to change interconnections to all the DERs that are distributed over long distances in a network. This would require a significant investment due to greater installation costs, communication overhead. Moreover, it also complicates the protection and control strategies. As a solution, the in-situ reconfiguration technique introduced in this paper, helps in reconfiguring the systems between parallel and series configurations and vice versa without any kind of physical interconnection between the DERs.

Fig. 4.a Single line diagram of a parallel configuration for multiple (n > 2)

DER system for equal steady-state sharing of a large block load (PL)

Fig. 4.b Single line diagram of series configuration for multiple (n > 2)

DER system for equal steady-state sharing of a large block load (PL)

For the parallel and series connected n-DER systems in Fig. 4a and Fig. 4b, the network equations are shown in Table I.

TABLE I. NETWORK EQUATIONS FOR THE PARALLEL AND SERIES

CONFIGURATIONS

Comparing the network equations of both the parallel and

series configurations in Table I, it is observed that

reconfiguring in-situ a parallel network to series form requires recreating all the additional voltage drops that are

absent in the parallel configuration’s network equations. In

the previous section, for a within-parallel in-situ

reconfiguration, the additional voltage drops required to

generate drafting characteristics in the parallel network were

built using synthesized reactances Xk-add and their

corresponding branch currents, 𝑖𝑘. However, in the parallel-

to-series case the network equations in Table-I suggest that

in order to achieve an in-situ parallel - series

reconfiguration, it would necessitate each DER to use its

neighbors’ branch currents too. A detailed step-by-step

procedure to realize this in-situ reconfiguration technique is explained below:

Step 1: Recreating the additional voltage drops using the

virtual reactances.

As a first step, the additional voltage drops in the

network equations of the (final state) series configuration

are added to the (initial state) parallel network equations in

Table I. However in a parallel configuration, since the DERs

are tied directly to the point of common coupling (PCC)

through their individual physical reactances Xko the

remaining voltage drops for Xm,o (m = 2, 3, …, k) are

constructed using corresponding virtual reactance Xm-add = Xm,o (m = 2, 3, …, k). Accordingly, the reconfigured

network equations can be represented as:

�⃗�1𝑝∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 )

�⃗�2𝑝∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

�⃗�3𝑝∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖3 ∗ 𝑗𝑋3𝑜) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑) +

(∑ 𝑖𝑘𝑛𝑘=3 ∗ 𝑗𝑋3−𝑎𝑑𝑑)

�⃗�4𝑝∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖𝑛 ∗ 𝑗𝑋𝑛𝑜) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

+(∑ 𝑖𝑘𝑛𝑘=3 ∗ 𝑗𝑋3−𝑎𝑑𝑑) ……. + (∑ 𝑖𝑘

𝑛𝑘=𝑛−1 ∗ 𝑗𝑋(𝑛−1)−𝑎𝑑𝑑)

DER

No

Parallel configuration

(Fig. 4a) Series configuration (Fig. 4b)

1 �⃗�1𝑝∗ = 𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 �⃗�1𝑠

∗ = (𝑃𝐿/ ∑ 𝑖𝑘𝑛𝑘=1 )

2

�⃗�2𝑝∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(𝑖2 ∗ 𝑗𝑋2𝑜)

�⃗�2𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(∑ 𝑖𝑘𝑛𝑘=2 ∗ 𝑗𝑋2𝑜)

3 �⃗�3𝑝

∗ = (𝑃𝐿/ ∑ 𝑖𝑘𝑛𝑘=1 ) +

(𝑖3 ∗ 𝑗𝑋3𝑜 )

�⃗�3𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(∑ 𝑖𝑘𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗

𝑗𝑋3𝑜)

4

�⃗�4𝑝∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(𝑖4 ∗ 𝑗𝑋4𝑜)

�⃗�4𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(∑ 𝑖𝑘𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗

𝑗𝑋3𝑜) + (∑ 𝑖𝑘𝑛𝑘=4 ∗ 𝑗𝑋4𝑜)

n

�⃗�𝑛𝑝∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(𝑖𝑛 ∗ 𝑗𝑋𝑛𝑜)

�⃗�𝑛𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) +

(∑ 𝑖𝑘𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗

𝑗𝑋3𝑜) +… … . + (∑ 𝑖𝑘𝑛𝑘=𝑛 ∗ 𝑗𝑋𝑛𝑜)

X1o

=0

�⃗�𝑛𝑝= V𝑛𝑝ejnt

DERn

�⃗�1𝑝= V1𝑝ej1pt

X2o

�⃗�2𝑝= V2𝑝ej2pt

DER2

DER1 𝑖1

𝑖2

𝑖𝑛 PL

X2o

= X3o

= ••• = Xno

Xno

Vpcc

ejpcct

Vpcc

ejpcct

2380

A typical equivalent circuit corresponding to the above

equations is shown in Fig. 5.a for n=3, DER3.

Fig. 5.a Equivalent circuits showing the transformation of the actual DER3

network in the parallel configuration of Fig. 4.a into a reconfigured

network with the additional voltage drops created using the virtual (Xk-add)

reactances between the source and the PCC.

Step 2: Modifying the virtual reactance drops into

dependent voltage sources to be built inside the DER’s controller card:

Next, all the additional terms depicting voltage drops

(across virtual reactances) are built inside each DER’s

controller as dependent voltage sources, and thereby its

voltage reference is modified from �⃗�𝑘𝑝∗ (𝑡) to �⃗�𝑘𝑝

′∗ (𝑡), as shown

in Fig. 5.c.

�⃗�1𝑝′∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 )

�⃗�2𝑝′∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖2 ∗ 𝑗𝑋2𝑜)

= �⃗�2𝑝∗ − (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

�⃗�3𝑝′∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖3 ∗ 𝑗𝑋3𝑜)

= �⃗�3𝑝∗ − (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)−(∑ 𝑖𝑘

𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑)

�⃗�𝑛𝑝′∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖𝑛 ∗ 𝑗𝑋𝑛𝑜)

= �⃗�𝑛𝑝∗ − (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑) −(∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3−𝑎𝑑𝑑)…….

− (∑ 𝑖𝑘𝑛𝑘=𝑛−1 ∗ 𝑗𝑋(𝑛−1)−𝑎𝑑𝑑)

A simplified equivalent circuit corresponding to the

above equations is shown in Fig. 5.b for k=3, DER3.

The dynamic behavior of a parallel-to-series in-situ reconfigured 4-DER system for an 80-kW load change was

evaluated through a time-domain simulation performed

using MATLAB/Simulink/SimPowerSystems, and the results obtained are displayed in Fig. 6.b. It was

observed that the reconfiguration results matched

reasonably well with the physical series configuration

results displayed in Fig. 6.a. Minor discrepancies are

observed because of the unaccounted resistive drops in the

simulation model (that also exist in real-life). It is to be

noted that the PWM inverter-based DER inner-voltage

regulator controls were approximated as a first-order lag

function whose time-constant is assumed to be (Tv = 5 ms)

based on the controller bandwidth (cf. Fig. 1) typical with a

4-kHz switching frequency [5].

Fig. 5.b Equivalent circuit of the reconfigured network for DER3 with

dependent voltage sources to modify the terminal voltage from �⃗�3𝑝 to �⃗�3𝑝′ .

Fig. 5.c The complete reconfigured parallel-to-series equivalent circuit with

dependent voltage sources implemented inside each DER controller to

modify its voltage reference from �⃗�𝑘𝑝∗ (𝑡) to �⃗�𝑘𝑝

′∗ (𝑡)

IV. SERIES - PARALLEL IN-SITU RECONFIGURATION

Another kind of reconfiguration that may be also of

interest to power engineers is the reverse transformation of

that described in the previous section, viz., a series-to-

parallel reconfiguration. As such, the in-situ reconfiguration

technique was once again employed to reverse reconfigure

the n-DER series network (X1=0, X2 = X3 =... = Xn) in Fig.

4.b into a parallel one (X1=0, X2 = X3 =... = Xn) in Fig. 4.a. The network equations of both the parallel and series

connected n-DER systems are the same as shown before in

Table I. Relating both the system equations, it is observed

�⃗�3𝑝= V3𝑝ej3pt

X2-add

PL

X3o

𝑖3 DER

3

X3-add

𝑖2 + 𝑖3 … +𝑖𝑛

𝑖4 + 𝑖5 … +𝑖𝑛

−𝑖3 + 𝑖4 𝑖5 … + 𝑖𝑛

𝑖2

�⃗�3𝑝∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖3 ∗ 𝑗𝑋3𝑜) + (∑ 𝑖𝑘

𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑)

+(∑ 𝑖𝑘𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑 )

DER3

�⃗�3𝑝= V3𝑝ej3pt

X3o

𝑖3

PL

(R-Load)

𝑖3

Vpcc

ejpcct

Vpcc

ejpcct

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖2 +𝑖3 … . . +𝑖𝑛) �⃗�3𝑝

𝑗𝑋3−𝑎𝑑𝑑 ∗ (𝑖4 +𝑖5 … . . +𝑖𝑛)

PL

X3o

�⃗�3𝑝′ = V3𝑝

′ ej3pt

DER3

𝑖3

�⃗�3𝑝′∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 ) + (𝑖3 ∗ 𝑗𝑋3𝑜)

= �⃗�3𝑝∗ − (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)−(∑ 𝑖𝑘

𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑)

Vpcc

ejpcct

X2o

DER

2

DERn

DER3

DER1

X3o

Xno

Vpcc

ejpcct

�⃗�2𝑝′ = V2𝑝

′ ej2pt

�⃗�1𝑝′ = V1𝑝

′ ej1pt

PL

𝑖1

𝑖2

𝑖3

𝑖𝑛

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖3 +𝑖4 … . . +𝑖𝑛)

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖2 +𝑖3 … . . +𝑖𝑛)

𝑗𝑋(𝑛−1)−𝑎𝑑𝑑 ∗

(𝑖𝑛−1 + 𝑖𝑛) 𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖2 +𝑖3 … . . +𝑖𝑛)

𝑗𝑋3−𝑎𝑑𝑑 ∗ (𝑖4 +𝑖5 … . . +𝑖𝑛) �⃗�3𝑝

′ = V3𝑝′ e

j3pt

�⃗�𝑛𝑝′ = V𝑛𝑝

′ ejnpt

�⃗�2𝑝

�⃗�𝑛𝑝

�⃗�3𝑝

2381

A

ctiv

e p

ow

er (

kW

)

Act

ive

po

wer

(k

W)

Time (s) Time (s)

(a) (b)

Figure 6.a Response of a 4-DER physical series network to a step change in a large block load from 80kW to 160kW

Figure 6.b Response of a 4-DER series network (obtained using parallel-to-series in-situ reconfiguration) to a step change in a large block load from 80kW to 160kW

that reconfiguring in-situ a series system into a parallel form

requires getting rid of all the additional voltage drops that

are present in the network equations of the series

configuration. Following a similar procedure as the previous

section on parallel-to-series reconfiguration, a detailed step-

by-step procedure to realize in-situ series-to-parallel

reconfiguration is explained below:

Step 1: Compensating the additional voltage drops using the

virtual reactances.

Identifying that the (final state) parallel configuration

should be devoid of all the additional voltage drops that are

present in the network equations of the (initial state) series

configuration, their effect is nullified by using compensating

virtual reactances. (Note: The respective network equations

are given in Table I.)

In a series configuration, since the DERs are

interconnected through their individual physical reactances

Xko, the compensating voltage drops for Xm,o (m = 2, 3, …,

k) are constructed using corresponding virtual reactance Xm-

add = Xm,o (m = 2, 3, …, k). Accordingly, the reconfigured network equations can be represented as:

�⃗�1𝑠∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 )

�⃗�2𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) -(∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

�⃗�3𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3𝑜)-

(∑ 𝑖𝑘𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑) -(∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

�⃗�𝑛𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜)+(∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3𝑜) +

… … + (∑ 𝑖𝑘𝑛𝑘=𝑛 ∗ 𝑗𝑋𝑛𝑜) −(∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)-(∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3−𝑎𝑑𝑑)-

… … − (∑ 𝑖𝑘𝑛𝑘=𝑛−1 ∗ 𝑗𝑋(𝑛−1)−𝑎𝑑𝑑)

A typical equivalent circuit corresponding to the above

equations is shown in Fig. 7.a for n=3, DER3.

Step 2: Modifying the virtual reactance drops into

dependent voltage sources to be built inside the DER’s

controller card:

As a next step, all the additional terms depicting voltage

drops (across virtual reactances) are built inside each DER’s

controller as dependent voltage sources, and thereby its

voltage reference is modified from �⃗�𝑘𝑠∗ (𝑡) to �⃗�𝑘𝑠

′∗ (𝑡), as shown

in Fig. 7.c.

�⃗�1𝑠′∗ = (𝑃𝐿/ ∑ 𝑖𝑘

𝑛𝑘=1 )

Fig. 7.a Equivalent circuits showing the transformation of the actual DER3

network in the series configuration of Fig. 3.b into a reconfigured network

with the compensating voltage drops created using the virtual (Xm-add)

reactances.

�⃗�2𝑠′∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜)

= �⃗�2𝑠∗ + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

�⃗�3𝑠′∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3𝑜)

= �⃗�3𝑠∗ + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)+(∑ 𝑖𝑘

𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑)

X2o

�⃗�3𝑠= V3𝑠ej3st

DER3

X3o

𝑖4 + 𝑖5 … + 𝑖𝑛

𝑖3

𝑖2

DER3

𝑖4 + 𝑖5 … + 𝑖𝑛

𝑖2 + 𝑖3

𝑖2 + 𝑖3 + ⋯ 𝑖𝑛

X2o

�⃗�3𝑠= V3𝑠ej3st

X3o

𝑖2 + 𝑖3 … + 𝑖𝑛

𝑖3 + 𝑖4 … + 𝑖𝑛

𝑖4 + 𝑖5 … + 𝑖𝑛

𝑖3

𝑖2

X3-add

X2-add

�⃗�3𝑠∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3𝑜)-

(∑ 𝑖𝑘𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑) -(∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)

𝑖3 + 𝑖4 … + 𝑖𝑛

PL

PL

𝑖2 + 𝑖3 … + 𝑖𝑛

Vpcc

ejpcct

Vpcc

ejpcct

X2o = X3o = X4o

=10%

X2o = X3o = X4o

=10%

X2-add = X3-add = X4-add

=10%

Leading

DER1

Drafting

DER4

Leading

DER1

Drafting

DER4

2382

�⃗�𝑛𝑠′∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3𝑜 ) +… ….

+ (∑ 𝑖𝑘𝑛𝑘=𝑛 ∗ 𝑗𝑋𝑛𝑜)

= �⃗�𝑛𝑠∗ + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑) +(∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3−𝑎𝑑𝑑)…….

+ (∑ 𝑖𝑘𝑛𝑘=𝑛−1 ∗ 𝑗𝑋(𝑛−1)−𝑎𝑑𝑑)

A simplified equivalent circuit corresponding to the

above equations is shown in Fig. 7.b for k=3, DER3. Note the presence of the dependent voltage sources in the

network and their polarity. They are represented in such a

way that they cancel out the additional voltage drops in the

series configuration’s network equation.

Fig. 7.b Equivalent circuit of the reconfigured network for DER3 with

dependent voltage sources to modify the voltage reference from �⃗�𝑘𝑠∗ (𝑡)

to �⃗�𝑘𝑠′∗ (𝑡)

The dynamic behavior of a series to parallel in-situ

reconfigured 4-DER system for a 80kW to 160kW load

change was evaluated through a time-domain simulation in

MATLAB/Simulink/SimPowerSystems, and the results obtained are displayed in Fig. 8.b. For comparison

purposes, the dynamic response of the 4-DER physical

parallel network (of Fig. 4.a) is illustrated in Fig. 8.a for the same block load change from 80kW to 160kW. It was

observed that the in-situ reconfigured system results

matched reasonably well with the physical parallel

configuration results. As observed in the earlier case, minor

discrepancies are observed in this case also because of the

unaccounted resistive drops in the simulation model (that

also exist in real-life). It is to be noted that the PWM

inverter-based DER inner-voltage regulator controls were

approximated as a first-order lag function whose time-constant is assumed to be (Tv = 5 ms) based on the controller

bandwidth (cf. Fig. 1) typical with a 4-kHz switching

frequency [5].

Fig. 7.c The complete reconfigured parallel-to-series equivalent circuit with

dependent voltage sources implemented inside each DER controller to

modify its voltage reference from �⃗�𝑘𝑠∗ (𝑡) to �⃗�𝑘𝑠

′∗ (𝑡).

Act

ive

po

wer

(k

W)

Act

ive

po

wer

(k

W)

Time (s) Time (s)

(a) (b)

Figure 8.a Response of a 4-DER physical parallel network to a step change in a large block load from 80kW to 160kW

Figure 8.b Response of a 4-DER parallel network (obtained using series-to-parallel in-situ reconfiguration) to a step change in a large block load from 80kW to 160kW

𝑗𝑋3−𝑎𝑑𝑑 ∗ (𝑖4 +𝑖5 … . . +𝑖𝑛) �⃗�3𝑠

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖2 +𝑖3 … . . +𝑖𝑛)

PL

�⃗�3𝑠′ = V3𝑠

′ ej3pt

DER3

�⃗�3𝑠′∗ = (𝑃𝐿 / ∑ 𝑖𝑘

𝑛𝑘=1 ) + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2𝑜) + (∑ 𝑖𝑘

𝑛𝑘=3 ∗ 𝑗𝑋3𝑜)

= �⃗�3𝑠∗ + (∑ 𝑖𝑘

𝑛𝑘=2 ∗ 𝑗𝑋2−𝑎𝑑𝑑)+(∑ 𝑖𝑘

𝑛𝑘=4 ∗ 𝑗𝑋3−𝑎𝑑𝑑)

X2o

X3o

𝑖2

+ 𝑖3 …+ 𝑖𝑛

𝑖3

+ 𝑖4 …+ 𝑖𝑛

𝑖2

+ 𝑖3 …+ 𝑖𝑛

𝑖3

+ 𝑖4 …+ 𝑖𝑛

𝑖2 + 𝑖3 … + 𝑖𝑛

𝑖3 + 𝑖4 … + 𝑖𝑛

𝑖2

𝑖4 + 𝑖5 … + 𝑖𝑛

Vpcc

ejpcct

Xno

�⃗�𝑛𝑠′ = V𝑛𝑠

′ ejnt

X1o

=0

�⃗�1𝑠= V1𝑠ej1st

X2o

DER1

𝑖2

𝑖2 + 𝑖3 … + 𝑖𝑛

𝑗𝑋3−𝑎𝑑𝑑 ∗ (𝑖4 +𝑖5 … . . +𝑖𝑛) �⃗�3𝑠

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖2 +𝑖3 … . . +𝑖𝑛)

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖3 +𝑖45 … . . +𝑖𝑛) �⃗�2𝑠

𝑗𝑋(𝑛−1)−𝑎𝑑𝑑 ∗ (𝑖(𝑛−1) + 𝑖𝑛) �⃗�𝑛𝑠

𝑗𝑋2−𝑎𝑑𝑑 ∗ (𝑖2 +𝑖3 … . . +𝑖𝑛)

𝑖3 + 𝑖4 … + 𝑖𝑛

𝑖3

𝑖𝑛

X3o

�⃗�3𝑠′ = V3𝑠

′ ejnt

�⃗�2𝑠′ = V2𝑠

′ ejnt

DER2

DERn

DER3 P

L

Vpcc

ejpcct

X2o = X3o = X4o

=10%

X2o = X3o = X4o

=10%

X2-add = X3-add = X4-add

=10%

Leading

DER1

Drafting DER2,

DER3 and DER4

Leading

DER1

Drafting

DER4

2383

V. CONCLUSIONS

This paper has presented the various in-situ reconfiguration schemes that are possible in Flexible Distribution of EneRgy and Storage Resources (FDERS). It facilitates the flexibility in rearranging and teaming up the interconnected power system resources into cooperative formations like the V-shape formation of a bird flock or peloton formation of a cycling racing team. By the methods presented in this paper, the various distributed resources are made to demonstrate a different dynamic behavior relative to each other than their (original) physical ‘electrical’ location otherwise would suggest. It has been achieved by means of developing novel techniques employing special functions of synthesized virtual reactances. A comparative analysis between the physical and in-situ reconfiguration schemes has been also presented. It was observed that the in-situ reconfiguration results match reasonably well with those of physical reconfiguration. The in-situ reconfiguration can be a viable alternative to the physical reconfiguration as it offers the benefits of saving installation cost, reducing communication overhead and simplifying the protection and control strategies. The proposed methods are particularly helpful in sustainably dealing with the large and fluctuating loads that are typically found in the metal industries, mining sites and cement plants. They help in achieving the greater sustainability goals of FDERS including optimal energy storage deployment, enhanced controllability, improved system robustness and increased lifetime of the distributed energy and storage resources.

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