Towards Unified Operational Value Index of Energy Storage Services in Power Systems
Anupam A. Thatte and Le Xie
Emails: thatte@tamu.edu, lxie@ece.tamu.edu
Department of Electrical and Computer Engineering, Texas A & M University, College Station, TX
In Automatic Generation Control the governor reference is changed in
response to frequency deviation:
Psmax
Esmax
Esmin
Rs
ηs
N
Δt
Es(k)
λ̂e(k)
λ̂ru(k)
λ̂rd(k)
λ̂sr (k)
Cs(k)
Ps(k)
Psru(k)
Psrd(k)
Pssr (k)
Benefits of Explicit and Implicit Forms of Energy Storage
Services
• Improve utilization of renewables
• Reduce energy imbalances and associated penalties
• Ancillary services such as regulation
Need to Understand Impact of Energy Storage
• Define unique features of heterogenous storage devices
• Pose the problem of analyzing impact of storage
• Assess the value of storage to power system operations
Need to quantify benefits of storage across power system operations using
a unified framework.
System Theoretical Perspective
1
Δω[m] =
Pimb[m]
(5)
βG + βS + βL
where βi represents the droop characteristics of module i. Droop of energy
conversion module i is defined as
Δωi[m]
βi =
(6)
| ref
ΔPi[m] Δωi =0
With the energy storage the overall system droop characteristic becomes
β = βG + βL + βS , where subscripts G, L, S represent aggregated
generation, load, and storage, respectively. Thus energy storage can
contribute to frequency regulation.
Tertiary Control Model
Energy storage can participate in load following and load leveling. Power
absorbed or delivered by the energy storage unit Ps[K], is the decision
variable. Ramping rate is Rs
Psmin ≤ Ps[K] ≤ Psmax
Es[K] = Es[K − 1] − ηPs[K − 1]
0 ≤ Es[K] ≤ Esmax
|Ps[K] − Ps[K − 1]| ≤ Rs
(7)
(8)
(9)
(10)
Operational Value of Energy Storage
• Different types of storage devices can participate at different time scales
in the control action, depending upon their inherent characteristics such
as power rating, energy capacity, droop, ramping etc.
• Participation in multiple control actions has potential for higher profits
for storage service providers
• Contribution by storage can reduce system cost for balancing actions
Energy
Conversion
Figure: Modified IEEE RTS 24 bus system
N
Energy Storage Device
Vs =
BUS 18
Control stage
Primary
Secondary (AGC)
Tertiary (ED, UC)
Time scale Assumption
Within
Dynamics are locally stabilizable
seconds
10 s to minutes Primary dynamics are already
stabilized
5 minutes to Tie line flows and system frehours
quency are at pre-specified values
ref
xv
xnetwork
v
uv
ref
uv
xs
xnetwork
s
us
ref
us
, uv , uv )
ẋv = fv (xv , xnetwork
v
ẋnetwork = g(x)
(λe[k]Ps(k)+λruPsru(k)+λrdPsrd(k)+λsr Pssr (k))+P Vd
(2)
ref
network
, us(xv ), us )
ẋs = fs(xs, xs
(3)
state variables of variable generator
interaction of generator with network
generator control variables
generator controller set points
states of the storage unit
interactions of storage with network
storage control variables
storage control set points
With fast responding energy storage the combined response from both
modules could be improved [2].
50
30
40
30
20
10
20
0
10
-10
0
-10
0
5
10
15
Time (Hours)
20
-20
0
25
5
10
15
Time (Hours)
20
25
Results
Figure: Storage participation in Day-Ahead Market
(a) PEV
(b) Flywheel and Thermal Load
12
6
PEV Power (MW)
PEV Regulation up (MW)
PEV Regulation down (MW)
Thermal Load Power (MW)
Thermal Load SR (MW)
Flywheel Regulation up (MW)
Flywheel Regulation down (MW)
10
8
4
2
BUS 21
BUS 22
-4
0
BUS 23
G
230 kV
B
A
BUS 19
BUS 16
-2
-4
C
BUS 20
D
BUS 14
BUS 11
BUS 12
25
-6
0
5
10
15
Time (Hours)
20
25
Hourly market constrains participation of flywheels. Short duration market would realize full potential of such fast responding storage devices.
PEV
BUS 9
20
Technology Energy Regulation Spinning Reserve
Flywheel
120.30
PEV
495.97
226.95
Thermal Load 63.61
3.21
BUS 13
BUS 3
10
15
Time (Hours)
Table: Day-Ahead Market Revenue ($/MW)
Synch.
Cond.
BUS 24
5
Storage decisions based on forecast prices, revenue on actual prices. Average results for 1000 Monte Carlo runs are:
BUS 10 BUS 6
cable
BUS 5
138 kV
Flywheel
Conclusions
BUS 8
Thermal
load
k=1
T.Psmax
ru
max
rd
sr
BUS 7
BUS 1
BUS 2
Technology Energy Regulation Spinning Reserve
Flywheel
No
Yes
No
PEV
Yes
Yes
No
Thermal Load
Yes
No
Yes
(12)
s.t.
Es(k) = Es(k − 1) − [Ps(k) − ηcPsrd(k)+
1 ru
Ps (k)].Δt
ηd
Ps(k) + Psru(k) + Pssr (k) ≤ Psmax(k)
(14)
Psrd(k) ≤ Ps(k − 1) + Psmax(k)
Esmin ≤ Es(k) ≤ Esmax
−Psmax ≤ Ps(k) ≤ Psmax
Ps(k) − Ps(k − 1) ≤ Rs
Psru(k) ≥ 0
(15)
(16)
(17)
(18)
(19)
Psrd(k) ≥ 0
Pssr (k) ≥ 0
(20)
(21)
(13)
• Unified operational value index - first step for assessment of
benefits of energy storage across different technologies and market
designs
• Cross-market co-optimization model - decision making tool
for energy storage service providers
• Distributed energy storage can improve system flexibility by
providing ancillary services
Future Work
• Empirical study of proposed framework using real world data
Thermal Load Model
N
E[ {λ̂e(k)Ps(k)+ λ̂ru(k)Psru(k)
Ps(k),Ps (k),Ps (k),Ps (k) k=1
+λ̂rd(k)Psrd(k) + λ̂sr (k)Pssr (k) − C(k)(Ps(k))2}]
cable
Table: Storage Technologies and Applications
The decision of the extent of storage participation in markets can be formulated as a co-optimization problem based on forecast of prices. The
following expected value problem is solved, with the objective of profit
maximization [3].
(1)
40
F
Decision Making Framework
Primary Control Model
Differential equations governing the dynamics of variable generator and
storage combination are:
50
-2
BUS 4
(11)
For this case study we consider only the operational value in ISO
market operations.
Table: Temporal decomposition
60
Actual regulation up price ($/MW)
Forecast regulation up price ($/MW)
Actual regulation down price ($/MW)
Forecast regulation down price ($/MW)
0
Proposed operational value index considers multiple revenue streams:
energy, regulation, spinning reserve and benefits from deferral of system upgrades attributed to the energy storage device.
Multi-time-scale Modeling
70
0
Unified Operational Value Index
Controller
60
Actual energy price ($/MWh)
Forecast energy price ($/MWh)
Actual SR price ($/MW)
Forecast SR price ($/MW)
2
E
Electrical
Grid
(b) Flywheel and Thermal Load
80
4
BUS 15
Energy
Storage
Reservoir
(a) Energy and Reserve Prices
6
BUS 17
Figure: Schematic of Energy Storage
Figure: Forecast and Actual Day-Ahead Market Prices
Case Study
Three major categories of energy conversion components are generators, loads, and energy storage
Energy Storage Module Definition [1]
• it lacks a primary energy source,
• −Psmax ≤ Ps ≤ Psmax , i.e., it can either deliver or draw power
from the grid,
s = P is controllable, and
• dE
s
dt
• Esmin ≤ Es ≤ Esmax, i.e., it has a finite storage reservoir whose
level is controllable.
(4)
Maximum charging/discharging power (MW)
Maximum energy storage level (MWh)
Minimum energy storage level (MWh)
Ramp rate of storage
Roundtrip efficiency of the storage device
Number of time periods
Duration of time periods
Energy storage level of device
Forecast energy market price ($/MWh)
Forecast regulation up capacity price ($/MW)
Forecast regulation down capacity price ($/MW)
Forecast spinning reserve capacity price ($/MW)
Charging/discharging cost of energy storage
Energy sold/purchased by storage (MWh)
Regulation up capacity sold (MW)
Regulation down capacity sold (MW)
Spinning reserve capacity sold (MW)
MW
ω ref [m] = βS (ω[m] − ω[m − 1])
Day Ahead Market Simulation
Price
Nomenclature
Price
Challenges with Renewable Generation
• Inter-temporal Variability
• Limited Predictability
Secondary Control Model
MW
Motivation
Using smart controls that act in response to price signals, thermal loads
such as air-conditioning can act as analogues to energy storage. The model
for power consumption is:
P (k)
in
in
out
)
(22)
T (k + 1) = T (k) + (1 − )(T (k) − ηcop
A
T in(k) = inside temperature in period k,
T out(k) = outside temperature in period k,
P (k) = power consumption in period k,
ηcop = coefficient of performance of cooling system = 2.5,
τ = duration of control periods = 1 hour,
T C = time constant of system = 2.5 hours,
= exp[−τ /T C] = factor of inertia,
A = overall thermal conductivity = 0.14 kW/◦F
T min ≤ T in(k) ≤ T max, ∀k.
Smart controls reduce power consumption while maintaining inside temperature within preset limits.
• Regulatory and pricing mechanism design for distributed storage
References
[1] L. Xie, A. A. Thatte, and Y. Gu, “Multi-time-scale modeling and
analysis of energy storage in power system operations,” in Proc.
IEEE Energytech, Cleveland, OH, May 25-26, 2011, pp. 1–6.
[2] A. A. Thatte, F. Zhang, and L. Xie, “Coordination of wind farms and
flywheels for energy balancing and frequency regulation,” in Proc.
IEEE PES General Meeting, Detroit, MI, Jul. 24-29, 2011, pp. 1–7.
[3] A. A. Thatte and L. Xie, “Towards a unified operational value index
of energy storage in smart grid environment,” IEEE Trans. Smart
Grid, accepted.
Acknowledgements
This work was supported in part by Vestas Technology R&D, and in part
by National Science Foundation Grant ECCS #1029873. The authors
greatly appreciate the financial help.