Impact of the Aggregate Response of Distributed Energy Resources on Power System Dynamics

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.

Full text

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
Cgft−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
tpa,t +Kpb,t ,(3)
such that
pg,t ≤Cg,∀g, t, (4)
pg,t =pg,t−1+Rgbg,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.
REFERENCES
[1] D. Pudjianto, C. Ramsay, and G. Strbac, “Virtual power plant and
system integration of distributed energy resources,” IET Renewable
Power Generation, vol. 1, no. 1, pp. 10–16, March 2007.
[2] R. Quint, L. Dangelmaier, I. Green, D. Edelson, V. Ganugula,
R. Kaneshiro, J. Pigeon, B. Quaintance, J. Riesz, and N. Stringer,
“Transformation of the grid: The impact of distributed energy resources
on bulk power systems,” IEEE Power and Energy Magazine, vol. 17,
no. 6, pp. 35–45, Nov 2019.
[3] S. Ghavidel, L. Li, J. Aghaei, T. Yu, and J. Zhu, “A review on the
virtual power plant: Components and operation systems,” in 2016 IEEE
International Conference on Power System Technology (POWERCON),
Sep. 2016, pp. 1–6.
[4] EirGrid, “Tomorrow’s Energy Scenarios 2017,” 2017. [Online]. Avail-
able: http://www.eirgridgroup.com/site-files/library/EirGrid/EirGrid-
Tomorrows-Energy-Scenarios-Report-2017.pdf
[5] ——, “EirGrid Grid Code. Version 8,” 2019. [Online]. Available:
http://www.eirgridgroup.com/site-files/library/EirGrid/Grid-Code.pdf
[6] P. Beagon, M. D. Bustamante, M. T. Devine, S. Fennell, J. Grant-Peters,
C. Hall, R. Hill, T. Kerci, and G. O’Keefe, “Optimal scheduling of
distributed generation to achieve linear aggregate response,” Proceedings
from the 141st European Study Group with Industry, 2018, available at:
http://www.maths-in-industry.org/miis/758/.
[7] G. Morales-Espa˜
na, J. M. Latorre, and A. Ramos, “Tight and compact
milp formulation for the thermal unit commitment problem,” IEEE
Transactions on Power Systems, vol. 28, no. 4, pp. 4897–4908, Nov
2013.
[8] P. Kundur, Power System Stability and Control. New York: McGraw-
Hill, 1994.
[9] F. Milano, F. D ¨
orfler, G. Hug, D. J. Hill, and G. Verbi ˇ
c, “Foundations
and challenges of low-inertia systems (invited paper),” in Power Systems
Computation Conference (PSCC), Dublin, Ireland, Jun 2018, pp. 1–25.
[10] F. Milano and R. Z´
arate-Mi˜
nano, “A systematic method to model
power systems as stochastic differential algebraic equations,” IEEE
Transactions on Power Systems, vol. 28, no. 4, pp. 4537–4544, Nov
2013.
[11] F. Milano, Power System Modelling and Scripting. London: Springer,
2010.
[12] P. Palensky, A. A. Van Der Meer, C. D. Lopez, A. Joseph, and K. Pan,
“Cosimulation of intelligent power systems: Fundamentals, software
architecture, numerics, and coupling,” IEEE Industrial Electronics Mag-
azine, vol. 11, no. 1, pp. 34–50, March 2017.
[13] T. K¨
erc¸i and F. Milano, “A framework to embed the unit commitment
problem into time domain simulations,” in IEEE International Confer-
ence on Environment and Electrical Engineering, June 2019, pp. 1–5.
[14] T. K¨
erc¸i, J. S. Giraldo, and F. Milano, “Analysis of the Impact of Sub-
Hourly Unit Commitment on Power System Dynamics,” Submitted to the
Int. J. of Electric Power & Energy Systems, September 2019, available
at: http://faraday1.ucd.ie/archive/papers/suctds.pdf.
[15] Illinois Center for a Smarter Electric Grid (ICSEG), “IEEE 39-Bus Sys-
tem,” URL: http://publish.illinois.edu/smartergrid/ieee-39-bus-system/.
[16] M. Carri´
on and J. M. Arroyo, “A computationally efficient mixed-integer
linear formulation for the thermal unit commitment problem,” IEEE
Transactions on Power Systems, vol. 21, no. 3, pp. 1371–1378, Aug
2006.
[17] L. Gurobi Optimization, “Gurobi optimizer reference manual.” [Online].
Available: http://www.gurobi.com
[18] F. Milano, “A Python-based software tool for power system analysis,”
in IEEE PES General Meeting, Vancouver, BC, July 2013.