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Impact of the Aggregate Response of Distributed

Energy Resources on Power System Dynamics

Taulant K¨

erc¸i∗,Student Member, IEEE, Mel T. Devine†, Mohammed Ahsan Adib Murad∗,Student Member, IEEE,

Federico Milano∗,Fellow, IEEE

∗School of Electrical and Electronic Engineering,

University College Dublin, Ireland

{taulant.kerci, mohammed.murad}@ucdconnect.ie, federico.milano@ucd.ie

†School of Business,

University College Dublin, Ireland

mel.devine@ucd.ie

Abstract—This paper addresses a current concern of the Irish

transmission system operator, namely, the impact of aggregated

distributed energy resources (DERs) on the dynamic behavior of

transmission systems. The aggregation of DERs is done through

the virtual power plant (VPP) concept. The paper considers two

approaches to operate the VPPs. First, a mixed-integer linear

programming (MILP) that optimally schedules the DERs that

compose the VPP is presented. The MILP is embedded into a time

domain simulator (TDS) by means of co-simulation framework

in order to study its impact on the dynamic response of the

system. Then, an automatic generation control (AGC) approach

is proposed to coordinate the DERs included in the VPP. The

case study based on the IEEE 39-bus system serves to illustrate

the features and dynamic behaviour of the proposed approaches.

Index Terms—Distributed energy resources, virtual power

plant, transmission system, time domain simulation, power sys-

tem dynamics.

I. INTRODUCTION

The large-scale integration of distributed energy resources

(DERs) into power systems allows more electricity generation

from renewable energy sources as well as reduces the impact

on the environment [1]. However, the penetration of DERs

creates additional challenges for transmission system operators

(TSOs) mainly due to their uncertain and variable nature

as well as the lack of visibility (i.e., mostly connected on

the distribution level) [2]. For this reason, it is important

to manage DERs in order to better contribute to electricity

markets [3], and system operation [1].

A way to address this problem is to make use of the virtual

power plant (VPP) concept. A VPP is generally composed

of different DERs technologies, including conventional (e.g.,

gas power plants) and non-conventional (e.g., wind power

plants) generating units, storage systems and ﬂexible loads,

and operates as a single transmission-connected generator.

In the Irish power system, there are many DERs units that

operate as a VPP in the electricity market [4]. EirGrid, the

Irish TSO, requires that the power output of a VPP increases

This work was supported by Science Foundation Ireland, by fund-

ing Taulant K¨

erc¸i, Mel T. Devine and Federico Milano under Grant

No. SFI/15/SPP/E3125; Mohammed Ahsan Adib Murad and Federico Milano

under Grant No. SFI/15/IA/3074.

ts

(0,0) (dg,0) (dg+Rg,0)

τg

cg

(dg+Rg+τg, cg)

Power Generation

Time

Fig. 1: Power production of a single small generator [6].

ts

Cf(t−T0

T1−T0)

n

P

g=1

Cgf(t−dg

−Rg

τg)

Power Generation

Time

(T0,0)

(T1, C)

Fig. 2: Power production of a single large power plant (continuous line) and

that of a collection of small generators (dashed line) [6].

linearly during the ramp-up time [5]. The TSO does not reward

the excess power if the VPP generates more than the agreed

linear ramp. On the other hand, the VPP incurs a ﬁne if it is

unable to provide the scheduled power [6]. This is a challenge

for VPPs as different generators have different characteristics

(e.g., different capacity, response and ramping time), and thus

the aggregate ramping rate may be non-linear. This problem

was raised by a local company to the 141st European Study

Group with Industry workshop held in Dublin, Ireland, on June

2018, that was attended by the ﬁrst two authors [6].

To illustrate the problem faced by the VPPs in the Irish

power system, Figs. 1 and 2, show the power production of

a single small generator, and the power production of both a

single large power plant and that of many small generators,

respectively. The points in Fig. 1 have the following meanings:

•(0,0), is the time when the TSO tells the VPP to go to

the maximum production.

•(dg,0), is the delay time of the VPP, i.e., how long the

VPP takes to send a signal to the g-th generator to start

the production.

•(dg+Rg,0), is the time at which the g-th generator

transitions from the minimum to the ramping production,

and Rgis the response time of the g-th generator of the

VPP, i.e. how long such a generator takes to respond to

the instruction from the VPP.

•(dg+Rg+τg, cg), is the time at which the g-th generator

of the VPP transitions from the ramping to the maximum

production, where τgis the ramping time and cgcorre-

sponds to the maximum capacity of the g-th generator.

The points in Fig. 2 have the following meanings:

•(T0,0), is the time when the ramping of the VPP begins.

•(T1, C), is the time when the ramping of the VPP

stops, where Ccorresponds to the total capacity of the

generators that compose the VPP.

The functions

Cf t−T0

T1−T0,(1)

n

X

g=1

Cgft−dg−Rg

τg.(2)

represent the power generated by a single large power plant

(linear), and the total power output of small generators of the

VPP (piecewise linear), respectively. A thorough discussion on

how to achieve an aggregate ramping rate of the VPP which

is as close to linear as possible is given in [6].

Motivated by the discussion above, we address the following

research questions: (i) what is the impact of linear aggregate

response of a VPP on high voltage transmission grid? (ii) is

there any difference between imposing or not imposing such

a linear ramping response? and what is the best operation and

control of a VPP from the TSO point of view?

To answers these questions, we consider two approaches.

First, an optimization problem based on mixed-integer lin-

ear programming (MILP) that optimally schedules the small

generators of the VPP in order to achieve a linear ramping

is presented. The MILP-based VPP is embedded into a time

domain simulator (TDS) by means of a recent proposed co-

simulation framework, in order to study its impact on the

dynamic behaviour of the system. Second, an approach based

on automatic generation control (AGC) is proposed and used

to coordinate the DERs that form the VPP.

A. Contributions

The contributions of the paper are as follows:

•Study the impact of linear aggregate response of VPPs

on the dynamic behaviour of the system and propose a

simple yet efﬁcient AGC approach for VPPs.

•Show that at low penetration levels of VPPs, there might

be no need to enforce a ramping limit by the TSO.

•Demonstrate that an AGC-based approach leads to a

better dynamic performance of the system as compared

to that of the VPPs based on MILP scheduling.

B. Paper Organization

The remainder of the paper is organized as follows. Section

II describes the mathematical formulation of the VPP based

on MILP; the AGC approach; the power system model for

transient stability analysis; and the co-simulation framework.

Section III discusses the impact of different control approaches

and penetration levels of VPPs on the dynamic response of the

IEEE 39-bus system. Conclusions and future work directions

are given in Section IV.

II. MODELING

A. MILP-based VPP

MILP is commonly utilized by TSOs to solve power system

operation (e.g., unit commitment) and planning problems.

These analyses are facilitated by the signiﬁcant improvements

of the efﬁciency and robustness of MILP solvers in recent

years [7]. In this work, we use the MILP model proposed in

[6] to optimally schedule the single generators of the VPP and

obtain a ramping rate that is as close to linear as possible. The

mathematical formulation of such a problem is as follows.

min X

tpa,t +Kpb,t ,(3)

such that

pg,t ≤Cg,∀g, t, (4)

pg,t =pg,t−1+Rgbg,t −bg ,t,∀g, t, (5)

bg,t ≥bg,t−1,∀g, t, (6)

bg,t ≥bg,t−1,∀g, t, (7)

X

t

(bg,t −bg,t ) = τg,∀g, (8)

X

g

pg,t +pb,t −pa,t =tPgCg

|˜

T|,∀t, (9)

bg,t, bg ,t ∈ {0,1},∀g, t, (10)

pg,t, pa,t , pb,t ≥0,∀g, t. (11)

where pa,t and pb,t represent continuous variables that model

the distances above and below the target linear characteristic

at time t, respectively (see Fig. 2). Krepresents a penalty

multiplier when the actual ramping rate is below the target

line, i.e., this is needed as the VPP is penalized if it provides

less power but that is not true for the other way round. In

this work, a value of K= 10 is considered. Equations (4)

model the capacity limits of single small generators, where pg,t

represents the active power generation of the g-th generator

at time period t. Equalities (5) model the ramping limits

of generating units, where the binary variables bg,t model

the status of generating units when they are generating (1 if

producing and 0 otherwise), while the binary variables bg,t

model the status of generating units when they are generating

at maximum capacity (1 if true and 0 otherwise). Equations

(6) and (7) model the logic of the binary variables. Equations

(8) model the generators ramp time (τg), i.e. the sum of the

differences bg,t −bg,t must equal τg. Equations (9) model

the target ramping line, i.e. tPgCg

|˜

T|, with |˜

T|representing the

total number of time periods. Finally, equations (10) and (11)

represent variable declarations.

B. AGC-based VPP

TSOs rely on secondary frequency regulation or AGC to

restore the frequency to the nominal value as well as keep the

interchange between different areas at the scheduled values

[8]. The AGC operates in the time scale of tens of seconds up

to tens of minutes and eliminates the steady-state frequency

error remained after the primary frequency control [9]. In this

work, we consider an AGC scheme that coordinates the DERs

that belong to the VPP.

The AGC control scheme considered in this paper is shown

in Fig. 3 [8]. For the conventional secondary frequency control,

the measured signal u=ωpilot is the frequency of a pilot

bus of the system, which is then compared to a reference

frequency, i.e. uref =ωref . An integrator block is included

to reduce the steady-state error to zero, with K0being its

gain. Finally, the AGC coordinates each turbine governor (TG)

of the generators proportionally to their droop, i.e. Rg/Rtot,

where Rtot =Pn

g=1.

We propose an AGC scheme for the VPP that instead of

regulating the frequency, regulates the total active power of the

VPP. With this aim, the signal uref =pref

VPP, i.e., the reference

power signal sent by the TSO to the VPP and u=pVPP is

the sum of the measured active power of the DERs included

in the VPP.

_

+

uref

u

∆u

K0

s

1

Rtot

R1

Ri

Rn

to TG 1

to TG i

to TG n

Fig. 3: Basic AGC control scheme for active power regulation of VPPs.

C. Power System Model

Power system dynamics with inclusion of stochastic pro-

cesses can be modelled as a set of hybrid nonlinear stochastic

differential-algebraic equations (SDAEs) [10]:

˙

x=f(x,y,u,z,˙

η)

0=g(x,y,u,z,η)

˙

η=a(x,y,η) + b(x,y,η)ξ,

(12)

where f,gare the differential and algebraic equations,

respectively; x,y,zare the state, algebraic, and discrete

variables, respectively; uare the inputs, e.g. load forecast and

active power schedules; ηrepresents stochastic perturbations,

e.g. wind speed variations, which are modeled through the last

term in (12); aand brepresent the drift and diffusion of the

stochastic differential equations (SDEs), respectively; and ξ

represents the white noise vector.

Equations (12) include the dynamic models of synchronous

machines, TGs, automatic voltage regulators, power system

stabilizers, wind power plants, AGC, and the discrete model

of VPPs based on MILP scheduling. In particular, TGs are

modelled as a conventional droop and a lead-lag transfer

function, whereas wind power plants are represented by ag-

gregated models, which implement a 5-th order Doubly-Fed

Induction Generator (DFIG) with voltage, pitch angle and

MPPT controllers [11].

D. Co-Simulation Framework

Co-simulation allows studying the dynamic behaviour of

modern power systems by coupling different sub-domain mod-

els, e.g. power systems and electricity markets [12]. Figure 4

shows the structure of the co-simulation framework presented

in [13]. Such a framework merges together the model of the

sub-hourly stochastic unit commitment (sSCUC), the model

of MILP- and AGC-based VPPs, as well as the dynamic

model of power systems described in the previous section.

A rolling horizon approach is used to feed back the current

values of the demand, e.g. dj,t, to the sSCUC problem. For

space limitations, we do not present here the sSCUC model

but the interested reader can ﬁnd the complete formulation in

[14]. The solutions of the sSCUC (pg,t,∀g) and the regulating

signals (Rg∆u/Rtot) generated by the AGC, are utilized to

change the power set point of the turbine governors of the

power plants.

sSCUC

DOME Framework

Load,Wind Forecast,

sSCUC & VPP Data Static &

Dynamic Data

TG

TG

SDAEs

VPP Grid

(Gurobi)

pg,t

dj,t

Fig. 4: Co-simulation framework that includes the sSCUC, the dynamic model

of the grid and of the DERs that compose the VPP.

III. CAS E STU DY

To study the effectiveness and the impact of the VPP

operation on the dynamic behaviour of power systems, we

consider a modiﬁed version of the IEEE 39-bus system [15].

The data of the sSCUC are based on [16], whereas VPP data

are taken from [6]. To simulate the VPP, we connect 10 small

generators at buses 10-19. In the following, we assume that the

VPP is only composed of non-renewable generation, i.e. small

gas power plants, as it is the case in the Irish system. The

focus is on the ﬁrst 15 minutes of the planning horizon that

is the relevant time window for the aggregated response of

DERs. Furthermore, in order to create a realistic scenario that

represents the current situation in the Irish power system, the

real-world data of the VPP made available by EirGrid are

used in the simulations below [4]. Based on these data, the

VPP capacity with respect to the total generation capacity is

about 4.3%. For consistency, in the ﬁrst of the case study, we

thus use a VPP/grid capacity ratio of 5%.

TABLE I: DERs data for the MILP-based VPP

Generator Capacity Response time Ramping time

(MW) (min) (min)

1 0.68 2.73 13.17

2 3.16 6.13 49.61

3 3.74 10.71 39.00

4 1.68 6.91 34.51

5 4.32 1.78 35.49

6 3.89 11.34 28.52

7 1.74 11.23 43.04

8 4.92 9.00 15.14

9 1.02 1.51 4.17

10 4.80 9.48 33.20

0 200 400 600 800

Time [s]

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

ωCOI [pu]

Fig. 5: ωCOI for 5% VPP penetration with ramping constraint.

The modeling of wind power uncertainty and volatility

within the sSCUC model, as well as the modeling of stochastic

nature of wind based on SDEs is the same as in [14].

Moreover, 25% wind penetration level is considered, where

the wind generation is given by wind power plants connected

to buses 20-23.

The study carries out Monte Carlo time domain simulations

and 50 simulations are solved for each scenario. The MILP

problem (3)-(11) and the sSCUC model are implemented in

the Python language and solved using Gurobi [17], while all

simulations are obtained using DOME , a Python-based software

tool for power system dynamic analysis [18].

A. 5% Penetration of VPPs

In this scenario, only VPPs with MILP scheduling are

considered. Table I shows relevant data of the 10 DERs that

form the VPP [6]. The total capacity of these generators is

29.95 MW, which means that they represent around 5% of

the total generation in [16] (during the ﬁrst 15 minutes of the

planning horizon). The time period tused in the simulations

is 1 minute. Thus, the VPP provides 29.95 MW at the end of

the 15 minute period. Moreover, we assume that the system

operator requires this power to increase linearly with respect

of time.

1) VPP with ramping constraints: Figure 5 depicts the

trajectories of the frequency of the center of inertia (ωCOI)

and shows that there are signiﬁcant frequency oscillations at

the beginning of the planning horizon due to the ramping

of generators. The value of the standard deviation of the

frequency is σCOI = 0.000556 pu(Hz).

2) VPP without ramping constraints: In this scenario, we

discuss whether removing the ramping limit of VPP leads to

0 200 400 600 800

Time [s]

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

ωCOI [pu]

Fig. 6: ωCOI for 5% VPP penetration without ramping constraint.

0 200 400 600 800

Time [s]

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

ωCOI [pu]

Fig. 7: ωCOI for 20% VPP penetration with ramping constraint.

a worse dynamic behaviour of the system. This will allow

us to check the effect of the ramping limit enforced by the

TSO. Figure 6 shows the trajectories of ωCOI. Compared to

the previous case (Fig. 5), where ramping limits are enforced,

the value of σCOI is 0.000601 pu(Hz) and, hence, there is no

signiﬁcant difference on the dynamic behaviour of the system.

Thus, it appears that, with a low VPP penetration level, there

might be no need to enforce a ramping limit on VPPs.

B. 20% Penetration of VPPs

This scenario is relevant for microgrids and/or future grids

such as the Irish system with high penetration of DERs.

1) VPP with ramping constraints: Figure 7 depicts the

trajectories of the ωCOI for the case when the ramping limit is

enforced. With a standard deviation σCOI = 0.000571 pu(Hz),

frequency variations are slightly higher compared to the 5%

penetration scenario (Fig. 5).

2) VPP without ramping constraints: Similar to Subsec-

tion III-A2, we check the importance of the ramping limit of

the VPP. Figure 8 shows the trajectories of the ωCOI for the

case when the ramping limit is not enforced. This leads to a

worse dynamic behaviour of the system compared to Fig. 7. In

this case, the value of the σCOI is 0.000645 pu(Hz). Hence,

increasing the penetration levels of VPPs, while increasing

their impact on the system, does not constitute a stability issue

for the system.

C. AGC-based VPP

This section discusses the performance of the AGC de-

scribed in Section II-B and assumes a 20% penetration of

VPPs. The gain of the AGC is set to K0= 50. Figure 9 shows

0 200 400 600 800

Time [s]

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

ωCOI [pu]

Fig. 8: ωCOI for 20% VPP penetration without ramping constraint.

0 200 400 600 800

Time [s]

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

ωCOI [pu]

Fig. 9: ωCOI for the AGC-based VPP with 20% penetration.

0 200 400 600 800

Time [s]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Total Mechanical Power [pu]

Fig. 10: Total mechanical power of 10 relevant machines of the AGC-based

VPP.

the trajectories of ωCOI for 15 minutes. The frequency varia-

tions are signiﬁcantly lower, i.e. σCOI = 0.000459 pu(Hz),

compared to those shown in Fig. 7. This is due to the fact that

the AGC coordinates the DERs in such a way that they start

ramping up all at the same time and then smoothly increase

their generation (see Fig. 10). From a system operator point

of view, thus, the AGC-based VPP is preferable with respect

to the conventional scheduling based on a MILP problem.

IV. CONCLUSIONS

This paper studies the impact of a linear aggregate oper-

ation of DERs on the dynamic response of a transmission

system. With this aim, the paper considers two approaches,

namely, an optimization problem based on MILP and an AGC

that coordinate the DERs to achieve a linear ramping. Both

approaches are simulated through a co-simulation platform

recently developed by the ﬁrst and fourth authors.

The case study shows that at a low penetration level of VPPs

(5%) there is effectively no relevant difference on the dynamic

performance of the system when imposing the ramping limit

or not. For a higher penetration level of the VPP (20%), while

frequency variations remain relatively small, ramping limit

leads to a slightly better dynamic behaviour of the system.

A comparison of both approaches with respect to long-term

frequency deviations shows that an AGC is to be preferred

compared to scheduling based on an optimization problem as

it leads to lower frequency variations of the system.

Future work will focus on applying the proposed methods

to microgrids with a high penetration of DERs.

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