Sizing optimization for island microgrid with pumped storage system considering demand response Zhaoxia JING 1 , Jisong ZHU 1 , Rongxing HU 2 Abstract Currently, small islands are facing an energy supply shortage, which has led to considerable concern. Establishing an island microgrid is a relatively good solu- tion to the problem. However, high investment costs restrict its application. In this paper, micro pumped storage (MPS) is used as an energy storage system (ESS) for islands with good geographical conditions, and deferrable appliance is treated as the virtual power source which can be used in the planning and operational processes. Household acceptance of demand response (DR) is indi- cated by the demand response participation degree (DRPD), and a sizing optimization model for considering the demand response of household appliances in an island microgrid is proposed. The particle swarm optimization (PSO) is used to obtain the optimal sizing of all major devices. In addition, the battery storage (BS) scheme is used as the control group. The results of case studies demonstrate that the proposed method is effective, and the DR of deferrable appliances and the application of MPS can significantly reduce island microgrid investment. Sensitivity analysis on the total load of the island and the water head of the MPS are conducted. Keywords Demand response, Micro pumped storage, Battery storage, Island microgrid, Sizing optimization 1 Introduction Islands usually have relatively abundant renewable resources (such as solar, wind and tide energy, etc.), but still most of them are powered by diesel engines [1, 2], which has poor supply reliability and can cause noise and atmospheric pollutants. Microgrid is a flexible and efficient renewable energy utilization method and has advantages in guaranteeing the security of the power supply, improving the renewable energy utilization rate and the power quality. Therefore, renewable energy sources in the microgrid are considered as the best choice to solve small island energy supply problems [2, 3]. Due to the randomness and intermittent nature of renewable energy [4], as well as the load fluctuation, energy storage systems are required to be configured in an isolated microgrid. Most of the existing researches employ battery energy storage in the microgrid [5]. However, battery storage has the disadvantages of short life, high cost, environmental friendliness and difficult maintenance. By contrast, because of their high reliability, friendly environment and low cost, pumped storage is the main energy storage form in a large power grid. In addition, the joint operation of a pumped storage power station and renewable energy station has been proved to be helpful in reducing the phenomenon of discard wind and solar [6]. In [7–12], the application of a small or micro pumped storage system in an isolated microgrid is studied. A seawater desalination system powered by renewable energy and a pumped storage system are designed in [7]. In [8], the feasibility of the technology of a island wind/solar/pumped CrossCheck date: 17 October 2017 Received: 31 August 2016 / Accepted: 17 October 2017 / Published online: 30 December 2017 Ó The Author(s) 2017. This article is an open access publication & Zhaoxia JING [email protected]Jisong ZHU [email protected]1 School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China 2 Foshan Power Supply Bureau, Guangdong Power Grid Co., Ltd., Foshan 528000, China 123 J. Mod. Power Syst. Clean Energy (2018) 6(4):791–801 https://doi.org/10.1007/s40565-017-0349-1
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Sizing optimization for island microgrid with pumped storagesystem considering demand response
Zhaoxia JING1, Jisong ZHU1, Rongxing HU2
Abstract Currently, small islands are facing an energy
supply shortage, which has led to considerable concern.
Establishing an island microgrid is a relatively good solu-
tion to the problem. However, high investment costs
restrict its application. In this paper, micro pumped storage
(MPS) is used as an energy storage system (ESS) for
islands with good geographical conditions, and deferrable
appliance is treated as the virtual power source which can
be used in the planning and operational processes.
Household acceptance of demand response (DR) is indi-
cated by the demand response participation degree
(DRPD), and a sizing optimization model for considering
the demand response of household appliances in an island
microgrid is proposed. The particle swarm optimization
(PSO) is used to obtain the optimal sizing of all major
devices. In addition, the battery storage (BS) scheme is
used as the control group. The results of case studies
demonstrate that the proposed method is effective, and the
DR of deferrable appliances and the application of MPS
can significantly reduce island microgrid investment.
Sensitivity analysis on the total load of the island and the
water head of the MPS are conducted.
Keywords Demand response, Micro pumped storage,
Battery storage, Island microgrid, Sizing optimization
1 Introduction
Islands usually have relatively abundant renewable
resources (such as solar, wind and tide energy, etc.), but
still most of them are powered by diesel engines [1, 2],
which has poor supply reliability and can cause noise and
atmospheric pollutants. Microgrid is a flexible and efficient
renewable energy utilization method and has advantages in
guaranteeing the security of the power supply, improving
the renewable energy utilization rate and the power quality.
Therefore, renewable energy sources in the microgrid are
considered as the best choice to solve small island energy
supply problems [2, 3].
Due to the randomness and intermittent nature of
renewable energy [4], as well as the load fluctuation,
energy storage systems are required to be configured in an
isolated microgrid. Most of the existing researches employ
battery energy storage in the microgrid [5]. However,
battery storage has the disadvantages of short life, high
cost, environmental friendliness and difficult maintenance.
By contrast, because of their high reliability, friendly
environment and low cost, pumped storage is the main
energy storage form in a large power grid. In addition, the
joint operation of a pumped storage power station and
renewable energy station has been proved to be helpful in
reducing the phenomenon of discard wind and solar [6]. In
[7–12], the application of a small or micro pumped storage
system in an isolated microgrid is studied. A seawater
desalination system powered by renewable energy and a
pumped storage system are designed in [7]. In [8], the
feasibility of the technology of a island wind/solar/pumped
CrossCheck date: 17 October 2017
Received: 31 August 2016 / Accepted: 17 October 2017 / Published
online: 30 December 2017
� The Author(s) 2017. This article is an open access publication
[16, 25] and improving the utilization of renewable energy
[19]. To the best of our knowledge, there are few resear-
ches concentrated on microgrid configuration considering
demand response. In [20, 21], island microgrid sizing
optimization considering demand response is studied, but
the demand response resource is the fixed seawater
desalination load without considering different demand
response participation degrees. The demand response par-
ticipation degree (DRPD) [15, 18] is closely related to the
interests of the demand response, but many of the current
researches ignored the impact of the DRPD. For an island
microgrid with the residential load as the main load, the
demand response resources are primarily the deferrable
load of the household appliances.
In this paper, the configuration refers to the sizing of all
major devices in an island microgrid including the number
of wind turbines, number of solar arrays, pump unit
capacity, turbine unit capacity and reservoir volume. And
the optimal configuration model is established for the
island microgrid with a solar–wind-pumped storage system
considering demand response, which is solved by using a
particle swarm optimization algorithm. Compared with the
existing island microgrid configuration researches, the
main contributions of this paper include: � The scheme of
pumped storage is adopted, and the quantity of the power
source and the capacity of the energy storage system are
optimized. ` The effect of demand response on capacity
configuration is considered. ´ The microgrid capacity
configuration of the battery storage scheme and pumped
storage scheme is compared. ˆ The effects of demand
response participation degree, the household number, the
demand response compensation cost and the water head of
the pumped storage system on the microgrid configuration
are analyzed.
The rest of this paper is organized as follows. Microgrid
components and modeling including PV, wind turbine and
pumped storage systems are explained in Section 2. Sec-
tion 3 presents the optimal configuration model consider-
ing demand response. A case study and its related analysis
are presented in Section 4. Finally, the conclusions are
given in Section 5.
2 Main components of an island microgrid
2.1 Island microgrid structure with pumped storage
system
A typical structure of an island microgrid with a pumped
storage system is shown in Fig. 1. Power sources consist of
a photovoltaic array and wind turbine. The pumped storage
system is used to store surplus power during the day time
and generate power during the night time. The island load
is composed of the non-deferrable load and the deferrable
load. The frequency limitation problem of an island
microgrid is attracting the attention of researchers. As the
double-penstock system helps to regulate voltage and
maintain a stable frequency with suitable control strategies
DC bus
AC bus
Inverter
PV array
Load
Upper reservoir
Sea (Lower reservoir)
Turbine Generator
(Day time)
(Night time) (Day time) (Night time)
Wind turbine
Fig. 1 Structure of island microgrid
792 Zhaoxia JING et al.
123
[8] and as there is no suitable generator unit for a micro
reversible pumped storage system, this paper adopts the
double-penstock seawater pumped storage system rather
than the single-penstock pumped storage system [12].
2.2 Wind turbine
The output power of the wind turbine is related to the
wind speed, and it can be calculated by [22]:
PWTðtÞ ¼
0 VðtÞ\Vci
NWT V3ðtÞ � V3ci
� �Pr
ðV3r � V3
ciÞVci\VðtÞ\Vr
NWTPr Vr\VðtÞ\Vco
0 VðtÞ[Vco
8>>>><
>>>>:
ð1Þ
where NWT is the number of wind turbines; Pr is the rated
power of the wind turbine (kW); VðtÞ is the local wind
speed (m/s); Vciis the cut-in wind speed (m/s); Vr is the
rated wind speed (m/s); Vco is the cut-out wind speed (m/s).
2.3 PV array
The fundamental component of a PV array is the solar
cell, which can be connected in series and/or parallel to
form PV modules. A typical module will have 24/72 cells
connected in series. The PV modules are then combined in
series and parallel to form PV arrays. Photovoltaic output
power is affected by the solar light intensity, working
temperature and the cleanliness of the photovoltaic panels.
The output power of the PV array can be expressed as:
PPVðtÞ ¼ NPVgPVPSTC
IradðtÞISTC
ð2Þ
where NPV is the number of photovoltaic panels; IradðtÞ isthe ambient solar intensity; ISTC is the solar intensity under
standard test conditions; PSTC is the photovoltaic panels
power under standard test conditions; gPV is the system
efficiency that relates to the working temperature and
cleanliness of panel.
2.4 Pumped storage system
Although the island freshwater resources are not abun-
dant, it can be very convenient to store gravitational
potential energy by elevating the seawater. A seawater
pumped storage system utilizes the sea as a lower reservoir,
and we need to build a tank as the upper reservoir to reduce
the cost of the pumped storage system. The volume of
water remaining in the upper reservoir can be determined
as:
Wðt þ 1Þ ¼ WðtÞ þ ½QPðtÞ � QTðtÞ�Dt ð3Þ
QPðtÞ ¼3600 � 1000gPgWPPPðtÞ
qgh¼ KPPPðtÞ ð4Þ
QTðtÞ ¼3600 � 1000PTðtÞ
gTgWPqgh¼ KTPTðtÞ ð5Þ
Where WðtÞ is the volume of residual water in the upper
reservoir at the end of the tth time interval (m3); QPðtÞ is thepumping speed (m3/h); QTðtÞ is the discharge water speed
(m3/h); Dt is the time interval (h); gWP is the pipeline
conveyance efficiency; gP is the pump efficiency; PPðtÞ isthe pumping power (kW); gT is the efficiency of generator
unit; PTðtÞ is the power of generator unit (kW); q is the
density of water (1000 kg/m3); g is the gravitational
acceleration (9.8 m/s2); h is the water head (m); KP and KT
are respectively the ratios of flow rate to the pumping
power and the generation power (m3/kWh).
Reservoir capacity constraint:
Wmin �WðtÞ�Wmax ð6Þ
Working state constraint of pumping and generating
unit:
UPðtÞ þ UTðtÞ� 1 ð7Þ
Power constraints of pumping and generating units:
UPðtÞPminP �PPðtÞ�UPðtÞPmax
P ð8Þ
UTðtÞPminT �PTðtÞ�UTðtÞPmax
T ð9Þ
where Wmax and Wmin are respectively the maximum and
minimum storage capacity of the reservoir; UPðtÞ and
UTðtÞ are respectively the working state variables of the
pump and generator unit, both of which are binary vari-
ables; PmaxP and Pmin
P are respectively the maximum and
minimum powers of the pumping unit; PmaxT and Pmin
T are
respectively the maximum and minimum powers of the
generator unit.
3 Sizing optimization model considering demandresponse
3.1 Bi-level optimization
The bi-level optimization model is used to describe the
sizing optimization of the island microgrid. The basic
mathematical model is expressed as:
S1¼minx
Fðx; zÞ ¼ a1xþb1z ð10Þ
C1x� d1 ð11ÞS2¼min
zf ðx,zÞ ¼ b2z ð12Þ
Sizing optimization for island microgrid with pumped storage system considering demand response 793
123
C2xþD2z� d2 ð13ÞEðxÞz� d3 ð14Þ
where the upper-level optimization model can be formu-
lated as (10) and (11), and its optimization objective is to
minimize the total cost. The decision variable x is an n-
dimensional column vector representing the quantity or the
capacity of the device. The formula (11) describes the
constraints of the upper-level optimization. That is, the
number or capacity constraints of the devices. Formulas
(12), (13) and (14) describe the lower-level optimization,
namely operational optimization, for which the optimiza-
tion objective is to minimize the total shortage of elec-
tricity. The decision variable z is an m-dimensional column
vector that represents the microgrid operational states. The
lower-level optimization constraints include the power
balance constraints, energy storage system operational
constraints and demand response constraints, which can be
divided into linear constraints (13) and nonlinear con-
straints (14). a1; b1; b2; d1; d2; d3;C1;C2;D2 are the matrix
of the coefficient.
3.2 Sizing optimization
Generally, the rated power of the PV and wind turbine is
fixed, and the optimization variables are NPV and NWT.
Similarly, the number of pumps, hydro-generator and
reservoir are set to 1, and the optimization variables are
PmaxP , Pmax
T and Wmax. The inverter capacity is matched
with the total installed capacity of the PV and wind turbine,
so there is no need to set the variable for the inverter.
According to the above statements, the upper-level deci-
sion variables are:
x ¼ ½NPV;NWT;PmaxP ;Pmax
T ;Wmax� ð15Þ
The economic analyses of the microgrid are conducted
using the annualized cost method. The annualized costs
include the annual average cost of the initial investment,
and the cost of replacement, operation, maintenance and
demand response compensation and power shortage
penalty. The objective function of the upper-level
optimization can be described in detail as follows:
S1 ¼ minFðx;zÞ¼
X
x12G1
CNAVx ðNx1 ;Cx1 ; ux1Þ
þX
x22G2
CNAVx ðRx2 ;Cx2 ; ux2Þ þ aEDRðzÞ þ bEnoðzÞ
ð16Þ0�Nx1 �Nmax
x1 ð17Þ
0�Rx2 �Rmaxx2 ð18Þ
G ¼ ½G1;G2� ð19Þx 2 G ð20Þ
where G is a collection of devices to be configured for the
microgrid; G1 is a collection of devices, the number of which
needs to be optimized, including photovoltaic panels, wind
turbine and inverter; G2 is a collection of devices, the
capacity of which needs to be optimized, including water
pump, generator and reservoir; Nx1 is the number of device x1with a maximum value of Nmax
x1; Rx2 is the capacity of device
x2 with a maximum value of Rmaxx2
; Cx is the annualized
investment costs of device x; ux is the annual operational and
maintenance cost of device x; CNAVx is the annualized cost of
device x; a is the compensation for deferrable load to par-
ticipate in demand response per kWh; b is the economic loss
cost of the unit shortage electricity; EDR is the electricity of
demand response; Eno is the total shortage of electricity and
its calculation is introduced in detail in the next section.
CNAVx can be calculated by the following formulas:
CNAVx ¼ Nx Cx
r0ð1þ r0Þm
ð1þ r0Þm � 1þ ux
� �ð21Þ
CxðPmaxx Þ ¼
Xm
y¼1
CxðPmaxx ; yÞ
ð1þ r0Þy� SxðPmax
x Þð1þ r0Þm
ð22Þ
SxðPmaxx Þ ¼ CxðPmax
x ; 1Þ lxðNr þ 1Þ � m
lx
� �ð23Þ
where r0 is the discount rate; m is the engineering life; Nx is
the number of devices; Sx is the residual value of the devi-
ces; CxðPmaxx ; yÞ means the initial installation cost of the
devices put into use at the beginning of the year y with the
rated capacity of Pmaxx ; lx is the life span of device x; Nr is
the number of devices replaced during engineering life.
In this paper, it is assumed that the investment and
operating costs of the device are linearly dependent on the
rated capacity, that is:
CxðPxÞ ¼ CxðNxP0xÞ ¼ NxCxðP0
xÞ ð24Þ
where P0x is the unit rated capacity of the devices.
3.3 Operational optimization considering demand
response
In this paper, the island load is divided into the non-
deferrable load and the deferrable load. The non-deferrable
load must be met during each time interval. The deferrable
load, such as washing machines, can be flexibly arranged in
another period. What needs to be emphasized is that
deferrable appliances must get the user’s authorization to
participate in demand response, and unauthorized parts will
794 Zhaoxia JING et al.
123
be considered as the non-deferrable load. Obtaining a
minimum total shortage of electricity is the objective
operational optimization.
S2 ¼ minEno ¼XT
t¼1
ðPnoðtÞDtÞ ð25Þ
where T is the optimization period, and PnoðtÞ is the powershortage during the tth time interval.
Supposing there are a kind of deferrable household
appliances (such as an electric water heater, washing
machine, dishwasher, etc.) whose rated power is DP and
total number is N, and all of them need to work once a day.
Usually, the operating time of the appliances has the
characteristic of randomness. To simplify the analysis, this
paper assumes that when the demand response is not
considered, the number of appliances working for a period
time can be characterized by a known distribution
according to the specific characteristics of the appliances.
NðtÞ is the number of running deferrable appliances during
the tth time interval. The lower layer decision variables z
includes the power consumed by the pump (PpðtÞ), the
power generation (PTðtÞ), the shortage power (PnoðtÞ), thevolume of residual water in the upper reservoir (WðtÞ),state variables of the pump (UPðtÞ) and state variables of
the generator (UTðtÞ) for each time interval.
Without considering the demand response, in addition to
the aforementioned pumped storage system operational
constraints, it is also necessary to meet the system power