Quantitative and Qualitative Evaluation of Flexible

Distribution of Energy and Storage Resources

Hussam J. Khasawneh and Mahesh S. Illindala

Department of Electrical and Computer Engineering

The Ohio State University

Columbus, OH, USA

h.khasawneh@ieee.org, millindala@ieee.org

Abstract— Flexible distribution of energy and storage resources (FDERS) offers the benefits of increased resource lifetime, optimal energy storage deployment, enhanced controllability and improved system robustness. It is enabled through the use of reconfiguration, variable interface reactances and/or adjustable distributed energy resource (DER) controls to create a cooperative framework among multiple interconnected DERs in meeting the system load demands. This paper presents a systematic approach towards analysis of FDERS dynamic behavior to qualitatively and quantitatively evaluate the above benefits and provide design recommendations. It includes developing theoretical small-signal system models along with detailed time-domain simulations in

MATLAB/Simulink environment for an FDERS consisting of multiple interconnected DERs in various cooperative formations.

Keywords— Distributed Energy Resources, Distributed

Generation Control, Energy Storage Systems, Fuel Cells

I. INTRODUCTION

The rapid increase in prices of depleting fossil fuels and newer environmental regulations and concerns has accelerated the need to develop a smart grid. The penetration of distributed energy resources (DERs) is being increasingly preferred to meet the growing needs of local customers. This penetration has its own economic, environmental, and technical impacts on the modern electrical grid. A microgrid is a smart electrical grid that consists of several DERs together with loads and energy storage devices, such as flywheels, super capacitors and batteries [1]. Such DERs may utilize different kinds of prime-mover technologies like internal combustion (IC) engines, gas turbines, photovoltaic, wind turbines, microturbines and fuel cells [2]. The microgrid is intended to operate in two operating conditions, viz., grid-connected mode and islanded mode [3].

Recently, a new framework was introduced known as Flexible Distribution of EneRgy and Storage Resources (FDERS) – where multiple DERs, when present in a network, team up in a formation that secures energy

stabilization through optimal utilization of distributed energy and storage resources [4]. FDERS transforms the fixed electrical power network into a flexible one for achieving potential savings in terms of increased resource lifetime, reduced energy storage requirement, enhanced controllability and improved system robustness. It was inspired by the V-shape formations of flocks of birds [5] and peloton/echelon formation of cycling racing teams [6], [7]. The pecking order of DERs is determined on the basis of their relative strength at any time. In a system consisting of equals, a periodic rotation of positions helps in reinvigorating all team members. The importance of applying FDERS in microgrid manifests itself when large and fluctuating loads are considered. Numerous industrial applications have their loads changing substantially in less than a second [8]. Examples of such applications are found at any cement, mining or metal industrial sites such as crushers, excavators and steel rolling mills [9].

FDERS is particularly useful in a microgrid that is operating under islanded-mode; i.e. when there is no power flow from the main (utility) grid. In such cases, the dynamic behavior of the network of DER units is highly influenced by their ‘electrical’ positions within the microgrid along with their controls [4],[10]-[11]. This paper considers small-rated DERs on a low-voltage distribution that have a slow response characteristics to produce energy for meeting huge and fluctuating loads; for instance, some fuel cells require about 10s for a 15% change in power output [12]. Therefore, it is essential to complement the DERs with energy storage for reliable operation under islanded mode of operation, in particular. This means that DERs are supplemented with distributed energy storage (DES) that is sized for meeting the load demand when the prime mover/energy source availability and dynamics precludes load following. In this paper, the DER and DES at any node will be collectively termed as Distributed EneRgy and Storage Resources (DERS). The dynamic response is illustrated in Figure 1, where the solid area depicts the energy provided by the DER, while the hatched area represents the energy supplied by the DES.

In this paper, a quantitative and qualitative evaluation of FDERS is presented. Section II presents a linearized

43978-1-4799-0336-8/13/$31.00 ©2013 IEEE

Po

we

r (k

W)

Time (s)

Figure 1. Dynamic response of Distributed Energy and Storage Resource

(DERS)

mathematical small-signal model for a parallel-connected microgrid. Results from analysis of the small-signal model are also presented and compared with those obtained from

detailed large-signal MATLAB/Simulink model. These models are used to perform qualitative and quantitative evaluation of the system behavior under various scenarios in Sections III and IV. Finally, the conclusions are presented in Section V.

II. SMALL-SIGNAL MODELING AND ANALYSIS OF

FDERS

In this section, the operation of an n DERS system interconnected in parallel is analyzed and a mathematical model for the dynamic (small-signal) behavior of such a system is developed and presented. The management of power generation in microgrids has been presented earlier in the literature [1],[13]-[14]. Each DERS shares part of the load according to decentralized controls by means of

frequency/active power (/P) and voltage/reactive power (V/Q) droop controls, as shown in Figure 2 [3],[10],[15]. Normally, these droop characteristics are designed such that interconnected DERS under islanded conditions share the total power among themselves in a way comparable with their power ratings.

On the other hand, the dynamic behavior of any DERS is greatly influenced by its ‘electrical’ locational placement within the microgrid. Each DERS is interfaced with the point of common coupling (PCC) through a combination of physical and synthesized reactances. The synthesized ‘virtual’ reactance, Xk-add for the k

th DER (where k = 1,2,…)

can be added to the DER controller by modifying its voltage reference from to , as shown in Figure 3. Such a synthesized additional reactance allows changing the pecking order or hierarchy within the FDERS by means of programming the variation of parameters based on predetermined criteria. Figure 4(a) shows the single line diagram featuring “physical” (Xko) and “virtual” (Xk-add) reactances that together make up a total reactance of Xk. It is important to note that the maximum DERS power is limited by its value of net interface reactance [15]-[18] as follows:

(1)

Figure 2. DERS power controller block diagram [4].

Figure 3. Synthesis of variable reactance in the DERS controller [4]

In this paper, a first order transfer function that mimics the effect of the inertia in a synchronous generator based DER was added to the system. The transfer function is:

(1)

where Mk is related to “virtual” inertia added to the system, while Dk is the inverse of steady-state frequency vs. power slope. This transfer function takes an active role in the

frequency/active power (/P) droop control (cf. Figure 2). It provides the DERS with the ability to get a larger response time without exceeding the power limits mentioned in (1).

Figure 4(b) depicts the small-signal state-variable schematic of the parallel-connected FDERS. The system of differential equations can be written as follows:

(2)

(3)

nom

+

q

+

+

+

+

+

Q

ω

Vnom

Qk

Pk

To the

inner loop

voltage

regulators

V /Q

Controller

/P

Controller

ω

3-phase

vector

+

ω

i

From “DER power

controller”

From DER output current

measurements i

-1

+

v

v

Xk-add

j Xk-add

Response time

DES

DER

PL

44

The output power equations are given by:

(4)

∑ (5)

is the tie-line stiffness between Point of Common

Coupling (PCC) and kth

DER and is determined by:

(6)

Finally, the state-space model of the parallel configuration was computed using MATHEMATICA® software. The order of the system without considering the “virtual” inertias is equal to the number of DERS units minus one; however, each “virtual” inertia adds one state variable to the system. For instance, a system consisting of 3 DERS units by enabling the “virtual” inertia feature for the leading DERS is a 3

rd order system. This system can be

written in the matrix format assuming the state vector to be [ ] , the input matrix [ ], and the output matrix [ ] :

(7)

(8) where

[ ]

[ ]

[ ] [ ]

In order to test the mathematical model, a sample 90kW step change in load was applied to see the effect of having the “virtual” inertia on the power response of the system. Figure 5 displays the results and the parameters are tabulated in Table I for more details on generation control and dynamic behavior of a microgrid refer to [10] and [17].

The small-signal mathematical model presented in this section is representative of the parallel-connected FDERS. It has been verified to match fairly closely with a large-signal detailed model built in MATLAB®/Simulink

TM/

SimPowerSystemsTM

toolbox. These results have been omitted for brevity. In later sections, the detailed

MATLAB/Simulink/SimPowerSystems toolbox that takes into account the bandwidth limitations of voltage and power regulators of each DERS [10] is employed for

evaluating the various benefits of FDERS. A snapshot of the employed model is shown in Figure 6.

(a) Single-line diagram

(b) Small-signal state-variable schematic

Figure 4. FDERS in a parallel connection

Po

we

r (k

W)

Time (sec) Figure 5. Mathematical model response characterictics – without inertia

(dashed) and with inertia (solid)

0 5 10 150

20

40

60

80

DERS 1

DERS 2

DERS 3

X1o

PL

DERS1

P1

P2

X1-add

X2o

DERS2

X2-add

= ej2t

= ej1t

Vpcc

ejpcct

⋮ P

k

Xko

DERSk

Xk-add

= ejkt

⋮ ⋮

= ej2t

= ejkt

= ej1t

-

-

-

-

-

k = 3,4,5,…

- Σ

Σ

Σ

Σ

Σ

45

TABLE I. PARAMETERS FOR TESTING MATHEMATICAL MODEL

X1

Ω X2

Ω X3

Ω D1

(J/rad) D2

(J/rad) D3

(J/rad) M1

(J.s/rad2)

0 3.5 7.5 30K /π 30K /π 30K /π 400K

Figure 6. Parallel FDERS model in MATLAB/ Simulink/SimPowerSystems environment

III. QUANTITATIVE EVALUATION

In this section, a parallel-connected FDERS consisting of three identically rated units will be quantitatively evaluated via a detailed time-domain dynamic simulation using MATLAB®/Simulink

TM/SimPowerSystems

TM toolbox. This

evaluation starts with studying the effect of changing virtual reactances on the response characteristics. After that, the influence of the “virtual” inertia on the system is discussed. Finally, this section compares the results of two cases of non-equally rated DER units.

A. Evaluating the effect of varying virtual reactance

Response characteristics of the FDERS model for a 90kW step load change are shown in Figure 7, with the parameters tabulated in Table II. From the characteristics, it is evident that DERS3, and to some extent DERS2, receive ride-through support from DERS1 – because of the interface reactances X3 and X2, respectively. Consequently, an increase of the same reactances would prolong the ride-through period within the FDERS system. While this change in reactance is difficult to realize physically, it can be comfortably achieved from controller by simply adjusting the virtual reactance values [4]. Such an in-situ reconfiguration provides several benefits, e.g. minimization of energy storage deployment for drafting DERS2 and DERS3 units. This helps optimizing the energy storage deployment, and thereby reducing the installation cost and enhancing the efficiency of overall FDERS system.

To study the effect of FDERS on energy storage deployment, in particular, DERS3 is assumed to be a fuel cell-battery hybrid system (cf. Figure 8). It is well known that electrochemical DERS such as fuel cells have long start-

up time and poor transient response because of their intrinsic characteristics [19]. As such, they are supported with energy storage, i.e. batteries, to meet the transient load demand. Such fuel cell-battery hybrid systems have been earlier analyzed in [20]. Dynamic models employed for fuel cell and Li-ion battery can be found in [21] and [22], respectively. It is observed that when the battery provides energy to the system, its inherent energy drops and so does its state-of charge (SOC), which may change from a value of 100% (fully charged) to a value of 0% (fully discharged). Depth of discharge (DOD) is mathematically the complement of SOC and it is an alternative way to indicate a battery's SOC.

In order to perform the analysis of variation in reactance X3, the virtual reactance X3-add was adjusted. At each value of X3, the battery DOD was calculated and the relationship thus observed is visualized in Figure 9. When X3 is zero, the system functions with identical responses for all three DERS. By increasing the value of reactance X3, the DERS3 starts receiving a ride-through support from DERS1 which shrinks the area between the requested power and the fuel cell output power, thereby reducing the stress on the battery of DERS3. A good parameter to monitor this stress is the DOD - the more the battery is stressed, the higher is its DOD. In this particular case, the DOD continues to decline until it reaches a point where the value of X3 is about to violate the power limitation restriction in (1). It is observed that the maximum allowed value of total (physical+virtual) reactance X3 is equal to 7.51Ω, and the corresponding DOD that was achieved is 12.6% from 26% (when X3 = 0). These savings in battery energy get accumulated over many load cycles of the FDERS operation, which can potentially result in a substantial extension of the battery life [23]-[24].

46

Po

we

r (k

W)

Time (sec) Figure 7. Dynamic response of a 3 DERS parallel configuration

TABLE II. DESIGN PARAMETERS FOR RESULTS OF SECTION II.A

DERSk

Reactance

(Xk =Xko+ Xk-add) Mk

(J.s/rad2)

Dk

(J/rad)

(VAR)

Dqk

(VAR/V) Ohms

Physical

(Xko)

Virtual

(Xk-add)

Total

(Xk)

DERS1 0 0 0 0 (30K)/π 0

DERS2 0.76 2.76 3.52 0 30K / π 25K 1000

DERS3 0.76 6.75 7.51 0 30K / π 50K 1000

Figure 8. Fuel cell-battery hybrid system

De

pth

of

Dis

cha

rge

(D

OD

) (%

)

Value of reactance X3 Ω Figure 9. Relationship between DOD and virtual reactance X3

De

pth

of

Dis

cha

rge

(D

OD

) (%

)

Value of inertia M1 (J.s/rad2)

Figure 10. Relationship between DOD and virtual inertia M1

B. Evaluating the effect of varying virtual inertia

Another interesting parameter in FDERS is the virtual inertia that is achieved by adding a first order transfer function in the active power/frequency droop controller. This parameter mimics the effect of the inertia in a large rotating machine generator. This actually provides the system with the ability to increase drafting without exceeding the maximum power limits discussed earlier.

The virtual inertia was gradually increased to study its effect on the battery of DERS3. The results in Figure 10 show that the DOD decreases when inertia (M1) increases. The DOD corresponding to M1 = 0 is close to where it ended for X3 = 7.51Ω in Figure 9. For increasing values of M1, DOD continues to decline until it reaches a point where the response of DERS3 becomes equal to the fuel cell response time (this happens at M1 = 5.57x10

5). For any value of M1

equal or beyond this value (i.e. M1 = 5.57x105), the fuel cell

located at DERS3 can operate solo without the need of the energy storage system, meaning DERS3 can be reduced to DER3 (i.e. DES3 = 0).

C. Evaluating the effect of varying frequency droop

As mentioned earlier, the steady-state power sharing by each DERS in the system is well known to be impacted by its frequency droop curve [15]. Accordingly, non-identically sized FDERS is quantitatively evaluated in this subsection. A step load change of 120kW will not result in equal sharing by the three DERS.

There are two cases studied in this section: first case considers DERS3 as the smallest within the system (i.e. 30kW), whereas the second is for DERS3 being the largest (i.e. 50kW). Note that in both cases, DERS3 needs to draft due to fuel cell characteristic. The results of the first case are shown in Figure 11 where DERS3 is rated smallest of the three, and the corresponding parameters are tabulated in Table III. On the other hand, Figure 12 displays the results of the second case when DERS3 is the largest rated DER, and the configuration parameters are tabulated in Table IV. This

0 5 10 15 200

20

40

60

80

100

DERS 1

DERS 2

DERS 3

0 1 2 3 4 5 60

5

10

15

20

25

0 1 2 3 4 50

2

4

6

8

10

12

14

Ifc

DC

DC

DC

DC

DC

AC

Vabc +

_ Vdc +

_

Idc I1

I2 Ibatt

+

_

Vf

Vbatt

Fuel Cell

Li-ion Battery

x 105

47

Po

we

r (k

W)

Time (sec) Figure 11. Power response of non-identical units – Fuel cell-battery system

being the smallest rated unit

TABLE III. DESIGN PARAMETERS FOR RESULTS SHOWN IN FIGURE 11

DERSk

Reactance

(Xk =Xko+ Xk-add) Mk

(J.s/rad2)

Dk

(J/rad)

(VAR)

Dqk

(VAR/V) ohms

Physical

(Xko)

Virtual

(Xk-add)

Total

(Xk)

DERS1 0 0 0 0 (30K)/ 0

DERS2 0.76 2.76 3.52 0 (40K)/ 75K 1000

DERS3 0.76 6.75 7.51 0 (50K)/ 100K 1500

difference in steady-state outputs is achieved through the frequency droop (1/Dk). Note that the value of reactance X3 reached its maximum power limitation faster when the power share of DERS3 was increased. In Figure 13, a comparison was carried out between these two cases as well as the identical-units case (discussed in Subsection II.A). As a result, it was found that the DOD curves do not change appreciably between cases where the steady-state load share is same – this is evident when comparing the 30kW load share of dashed blue line representing the case in Subsection II.A with the black line representing the 30kW case mentioned earlier in this subsection. On the other hand, having the fuel cell-battery DERS3 system contributing in a higher load share resulted in a significant stress on the battery and reduced the feasible range of “virtual” reactance (cf. Figure 13). In such circumstances, the solution is to apply the “virtual” inertia (cf. Table V) to the system to achieve a reduced energy storage deployment in fuel cell-battery hybrid system of DERS3. This “virtual” inertia effect on the system response is illustrated in Figure 14.

Po

we

r (k

W)

Time (sec) Figure 12. Power response of non-identical units – Fuel cell-battery system

being the largest rated unit

TABLE IV. DESIGN PARAMETERS FOR RESULTS SHOWN IN FIGURE 12

DERSk

Reactance

(Xk =Xko+ Xk-add) Mk

(J.s/rad2)

Dk

(J/rad)

(VAR)

Dqk

(VAR/V) ohms

Physical

(Xko)

Virtual

(Xk-add)

Total

(Xk)

DERS1 0 0 0 0 (50K)/ 0

DERS2 0.76 2.76 3.52 0 (40K)/ 75K 1000

DERS3 0.76 3.75 4.51 0 (30K)/ 100K 1500

De

pth

of

Dis

cha

rge

(D

OD

) (%

)

Value of reactance X3 Ω Figure 13. Comparison between: identically-sized units (dashed) and non-

identically sized units – DERS3 being the smallest (for black), and that

being the largest (for purple)

0 5 10 15 200

20

40

60

80

100

120

DERS 1

DERS 2

DERS 3

0 5 10 15 200

20

40

60

80

100

120

DERS 1

DERS 2

DERS 3

0 1 2 3 4 5 6 7 7.4

0

10

20

30

40

48

Po

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r (k

W)

Time (sec) Figure 14. Power response of non-equal units – Fuel cell-battery system

being the smallest with virtual inertia

TABLE V. DESIGN PARAMETERS FOR RESULTS SHOWN IN FIGURE 14

DERSk

Reactance

(Xk =Xko+ Xk-add) Mk

(J.s/rad2)

Dk

(J/rad)

(VAR)

Dqk

(VAR/V) ohms

Physical

(Xko)

Virtual

(Xk-add)

Total

(Xk)

DERS1 0 0 0 1433K (50K)/ 0

DERS2 0.76 2.76 3.52 0 (40K)/ 75K 1000

DERS3 0.76 3.75 4.51 0 (30K)/ 100K 1500

IV. QUALITATIVE EVALUATION

In this section, the Quality Function Deployment (QFD) methodology is employed to qualitatively evaluate the various features of FDERS. QFD is a concept that employs a means of translating the demanded quality elements (“What’s” of the customer) into the provision for the demanded quality (“How’s” of the quality team) [25]. It was originally introduced in 1972 by Dr. Mizuno of Japan and later in 1984 was brought to USA by Dr. Clausing of Xerox [26]. QFD works through a set of matrices to quantify customer requirements (“What’s”) and engineering characteristics /technical descriptors (“How’s”), and for this reason it is also called the House of Quality [27].

The various “What’s” and “How’s” along with the strengths of relationships between them for the FDERS system are tabulated in Table VI. The relative importance/weight of each technical descriptive toward production is finally calculated by simple algorithm that correlates “What’s” to “How’s”. The values for strengths of relationships used in the QFD are described in Table VII.

Unlike the quantitative evaluation, the qualitative evaluation offers a relative assessment to some of the technical metrics towards meeting the customer’s requirements. The QFD of this paper shows that by controlling the “virtual” reactances and inertias, the customer needs can be more satisfactorily met. Also, the house of

quality shows that it is not feasible to implement FDERS using physical reactances rather than virtual ones; this is mainly because of cost and controllability issues. Finally, changing the droop gets a significant negative weight since although it has an influence it is practically not the preferred approach – as it also affects the steady-state load sharing among various FDERS constituents, which can potentially result in damaging consequences in the long run.

TABLE VI. HOUSE OF QUALITY

Design

Requirements

How’s

Customer

Re ui e e ts What’s

Imp

ort

an

ce (

1-5

)

Reactance

Dro

op

Vir

tua

l In

ert

ia

Ph

ysi

cal

Vir

tua

l

Increase

DER Lifetime 5 3 3 -1 9

Energy Storage

Deployment 5 9 9 -3 3

Controllability 4 -9 9 -3 9

Robustness 3 3 3

Decrease

Cost 5 -9 -1 -1 -1

Power Loss 3 -1 3 3 3

Complexity 5 3 -3 -3 -3

Maintain Steady State 4 -9

Absolute Weight -9 85 -52 94

TABLE VII. RELATIONSHIPS BETWEEN “WHAT’S” AND “HOW’S”

Factor Value

Strong Positive +9

Medium Positive +3

Weak Positive +1

Neutral 0

Weak Negative -1

Medium Negative -3

Strong Negative -9

V. CONCLUSIONS

This paper presented a mathematical small-signal model as well as a detailed large-signal simulation model developed in MATLAB®/Simulink

TM environment for Flexible

Distribution of EneRgy and Storage Resources (FDERS). FDERS features the use of synthesized interface reactances, “virtual” inertias, and controllable frequency/active power

(/P) droop gains in interfacing multiple distributed energy and storage resources (DERS). This new concept provides enough flexibility to optimize the controller of each DERS and its interactions with other unit. The parameter settings in

0 5 10 15 20 25 300

20

40

60

80

100

120

DERS 1

DERS 2

DERS 3

49

FDERS can be based on various factors such as energy resource availability, response characteristics and lifecycle costs of participating resources. The ultimate objective of FDERS is to increase resource lifetime, optimize energy storage deployment, enhance controllability and improve system robustness.

A quantitative as well as qualitative evaluation of FDERS was presented in this paper. The quantitative evaluation was based on analysis of a parallel configuration that included a fuel cell-battery hybrid distributed energy resource. The results showed that by increasing the value of the “virtual” reactance, the fuel cell-battery hybrid system received a ride-through support from the leading DERS units which reduced the stress on the battery and therefore increased its lifetime. Furthermore, this paper has evaluated the effect of “virtual” inertia and found that it has a greater influence on the system performance. The results showed that a fuel cell can operate solo without any need of a battery. This is possible when a certain value of “virtual” inertia is added to the controller of the leading DERS that has adequate energy storage capability. Also, this paper evaluated the effect of varying frequency droop for two major cases. Finally, the paper wrapped up with a qualitative assessment of FDERS in the form of a Quality Function Deployment (QFD).

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50