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参考文献.pdf 2.69MB

}9[~ST_]`1()MV3T6F0RZ}S.png 258KB

考虑储能优化的微网能量管理双层模型

costs

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snd_runningcosts.m 687B

snd_terminalcosts.m 74B

snd_costfunction.m 790B

costfunction.m 551B

runningcosts.m 866B

fcnCalCostonlyDegradation.m 964B

dynamic

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computeOpenloopSolution.m 287B

system_model.m 467B

shiftHorizon.m 286B

snd_dynamic.m 168B

dynamic.m 164B

snd_system_model.m 467B

main_execution1.m 5KB

data

price_sequence_RT.xlsx 64KB

pv_5m_5percent.xlsx 19.13MB

wind_5m_20percent.xlsx 32.11MB

pv_5m_10percent.xlsx 19.16MB

wind_5m_5percent.xlsx 31.94MB

wind_5m_20T30percent.xlsx 32.61MB

wind_5m_10percent.xlsx 32.01MB

Gen_PV_Wind_Data.m 1KB

price_sequence_TOU.xlsx 60KB

pv_5m_20T30percent.xlsx 19.69MB

data_sequence.xlsx 334KB

pv_5m_data.xlsx 434KB

wind_5m_10T20percent.xlsx 32.46MB

data_all.csv 14KB

pv_5m_30T40percent.xlsx 19.74MB

price_seq_RT.csv 6KB

pv_5m_10T20percent.xlsx 19.6MB

wind_5m_30T40percent.xlsx 32.73MB

wind_5min_data.xlsx 1MB

pv_5m_20percent.xlsx 19.22MB

fcnCalCostwithDegradation.m 1KB

fcnSetStageParam.m 3KB

calCost_ALL.m 185B

initiation

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fcnImportData.m 323B

batteryModel.m 398B

fcnChooseOption.m 2KB

solve

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fst_mpc.m 642B

snd_solveOptimalControlProblem.m 863B

solveOptimalControlProblem.m 1KB

constraints

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nonlinearconstraints.m 609B

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printSolution.m 3KB

printClosedloopData.m 614B

1949-3053 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2703126, IEEE

Transactions on Smart Grid

A Two-layer Energy Management System for

Microgrids with Hybrid Energy Storage considering

Degradation Costs

Chengquan Ju, Student Member, IEEE, Peng Wang, Member, IEEE,

Lalit Goel, Fellow, IEEE and Yan Xu, Member, IEEE

Abstract—The integration of renewable energy source (RES)

and energy storage systems (ESS) in microgrids has provided

potential beneﬁt to end users and system operators. However,

intermittent issues of RES and high cost of ESS need to be

placed under scrutiny for economic operation of microgrids.

This paper presents a two-layer predictive energy management

system (EMS) for microgrids with hybrid ESS consisting of

batteries and supercapacitors. Incorporating degradation costs

of the hybrid ESS with respect to the depth of charge (DOD)

and lifetime, long-term costs of batteries and supercapacitors are

modeled and transformed to short-term costs related to real-

time operation. In order to maintain high system robustness

at minimum operational cost, a hierarchical dispatch model is

proposed to determine the scheduling of utilities in microgrids

within a ﬁnite time horizon, in which the upper layer EMS

minimizes the total operational cost and the lower layer EMS

eliminates ﬂuctuations induced by forecast errors. Simulation

studies demonstrate that different types of energy storages can

be utilized at two control layers for multiple decision-making

objectives. Scenarios incorporating different pricing schemes,

prediction horizon lengths and forecast accuracies also prove the

effectiveness of the proposed EMS structure.

Index Terms—Optimization; microgrids; energy storage; en-

ergy management system (EMS); hierarchical control.

NOMENCLATURE

A. Indices and sufﬁxes

i Storage device index.

t Time index.

∆t Time interval.

, t

Time index in upper and lower layer.

∆t

, ∆t

Time interval in upper and lower layer.

B. State Variables

(t) Power of utility grid.

(t) Power of battery.

(t) Power of supercapacitor.

(t) Power of load.

(t) Power of PV.

(t) Power of wind turbine.

This work was under the Adaptive Integrated Hybrid DC-AC Micro Power

Parks System (ERIP04) program with Singapore Economic Development

Board (EDB Singapore) and Energy Research Institute @ NTU (ERI@N).

The authors would like to thank ERI@N for the ﬁnancial support.

C. Parameters

DOD Depth of discharge of battery.

(∆t) Depth of Charge of battery in ∆t.

B.rat ed

Rated battery Capacity.

(t) Energy of battery at time t.

(t) Energy of supercapacitor at time t.

, η

Charging and discharging efﬁciency of

battery.

SCc

, η

SC d

Charging and discharging efﬁciency of

supercapacitor.

a, b, c Curve-ﬁtting coefﬁcients of battery life-

time.

) Battery lifetime with respect to DOD =

Supercapacitor lifetime.

B A

(t) Actual capacity of battery at t.

(t) Accumulative energy of battery at t

Battery replacement cost.

B AC

Battery average degradation cost.

BDC

Battery degradation cost.

Supercapacitor replacement cost.

SC DC

Supercapacitor degradation cost.

, T

Length of prediction horizon in upper

layer and lower layer.

min

(t), P

max

(t) Power limits of utility grid.

min

(t), P

max

(t) Power limits of battery.

min

(t), P

max

(t) Power limits of supercapacitor.

min

(t), S

max

(t) SOC limits of battery.

min

(t), S

max

(t) SOC limits of supercapacitor.

min

(t), P

max

(t) Power limits of battery.

, σ

Cost weighting coefﬁcients.

I. INTRODUCTION

N recent years, growing interest in renewable energy source

(RES) has prompted microgrids to develop towards more

intelligent and modernized entities. Microgrids integrate the

distributed generators including conventional and renewable

sources to supply predicted load of end-users in a decentralized

manner [1]. However, intermittency and undispatchability of

RES outputs induce system robust problems. Energy from

RES might be unavailable due to bad weather conditions when

electricity is needed [2]. Energy storage system (ESS) is usu-

ally integrated in microgrids to compensate power mismatch.

ESS can also act as bidirectional mediators with the utility

Transactions on Smart Grid

grid to store and export energy, providing auxiliary services

and ﬁnancial beneﬁts for end-users based on various control

strategies. In order to meet different operation requirements,

the so-called hybrid ESS which combines different types

of energy storage inherits advantages for each individual to

provide an effective and reliable solution. Researches working

on hybrid ESS in microgrids have covered from real-time

operations that account for instant power sharing [3], [4] and

frequency regulation [5], to scheduling problems that manifest

charging strategies [6] and operational optimization in the long

term [7], [8].

Previous studies for ESS-integrated microgrids have mostly

featured on the design of energy management system (EMS)

to improve energy efﬁciency and operation reliability of mi-

crogrids [9], [10]. Research in [11] decomposes the microgrid

energy management into a unit commitment problem to ac-

count for voltage and frequency regulation and an optimal

power ﬂow problem to provide reactive power support. In

[12], a heuristic method combined with a centralized EMS and

local EMSs is proposed to determine ESS cycling operation at

the household level. However, existing works have narrowly

considered economic effects of the real-time ESS operation

under different resources, load and environment conditions

[13], and ignored or merely assumed a ﬁxed price as the

operational cost [1], [14]. Different from generation resources,

the short-term dispatch for ESS has a signiﬁcant impact

on its lifetime in the long term. For example, battery life

would be considerably deteriorated by frequent charging and

discharging. On the other hand, the conﬂict of economy and

security further complicate the optimal energy management

in microgrids. Increasing the ESS capacity size will provide

larger operating reserves to reduce the probability of loss of

load, however at the expense of extra capital investment [15].

The two-fold requirements enforce the ESS operational cost

to be accurately related to the long-term degradation process

in real-time operation. However, the degradation cost of ESS

was either neglected or modeled on a very rough and general

basis in previous literature [16]–[18].

Hybridization of ESS further urges different dispatch de-

cisions to be made given various operation targets and ESS

characteristics. ESSs with large energy densities such as

batteries are committed to exchange excess energy with other

components and the utility grid, and those with large power

ratings such as supercapacitors are used to compensate the

instant power mismatch. Hence, in the face of different devices

in the hybrid ESS, different time resolutions are required

for the comprehensive design of EMS: the long-term time

horizon manifests operational economy and the short-term

time horizon reﬂects system security. To this end, this paper

proposes a two-layer hierarchical EMS to account for the

above considerations. The main contributions of this paper are

addressed as follows:

1) A noval two-layer EMS for microgrid including the

hybrid ESS is developed. Power dispatch is scheduled to

minimize the operational cost in the upper layer, and forecast

uncertainties and power ﬂuctuations by RES are minimized in

the lower layer.

2) The degradation cost models of battery and supercapaci-

HESS

Battery

Supercapacitor

Aggregated Load

RES

Wind

Utility Grid

Fig. 1. System model of the microgrid.

tor are developed to accurately reﬂect the explicit degradation

process, bridging the long-term capital cost and the short-term

operational cost for real-time economic dispatch.

3) The proposed EMS is applied to a microgrid presented

in considering different electricity pricing mechanisms. The

simulation studies successfully demonstrate that different types

of energy storages including batteries and supercapacitors can

be dispatched at different control layers for multiple decision-

making objectives. Effectiveness of the proposed EMS struc-

ture is proved by various scenarios incorporating pricing

schemes, prediction horizon lengths and forecast accuracies.

The remainder of this paper is organized as follows. In

Section II, the microgrid modeling is proposed, and degrada-

tion cost models of battery and supercapacitor are presented

respectively. Section III is focused on the formulation of

the proposed two-layer EMS. Case studies and results are

discussed in Section IV, in which the proposed two-layer EMS

is simulated with selected scenarios. At last, the conclusion

and main contributions of this paper are summarized in Section

II. MICROGRID MODELING

A. Microgrid Structure

The schematic diagram of a typical microgrid is depicted in

Fig. 1. Without loss of generality, the microgrid in our research

is comprised of the point of common coupling (PCC) to the

utility grid, a hybrid ESS, a RES system and the aggregate

load. Practically, the microgrid can operate either in the grid

tied mode or independently as an islanded grid, depending on

system requirements, RES conditions and electricity market.

Unless speciﬁed otherwise, we will focus on the grid con-

nected mode in the following discussion.

B. Dynamic pricing

The utility grid is operated in an electricity market, where

the electricity price is usually determined by the upper-level

system operator in a static or dynamic way [19]. Static pricing

schemes, such as ﬁxed prices and time-of-use prices, are often

set in advance and do not change with network conditions.

Fixed prices do not usually inﬂuence user patterns in microgrid

since the electricity cost does not change with the quantity

of use, whereas time-of-use prices announced by the market

authorities prompt more electricity to be used in off-peak

hours considering relatively lower rates per kWh. Dynamic

pricing schemes, such as the real-time pricing, are sensitive

to locational marginal prices and are often announced hours

Transactions on Smart Grid

and

(a) (b) (c)

Fig. 2. Different deﬁnitions on DOD [22].

ahead, allowing users to make advanced scheduling so that the

operational cost can be minimized [19]. When the bidirectional

communication is allowed, microgrids can make proﬁts by

selling part of excess electricity to the utility grid.

Two pricing schemes, which are time-of-use pricing and

dynamic real-time pricing, are adopted in this paper. In the

time-of-use pricing model, the electricity price corresponds to

a two-level model which has an off-peak value and an on-peak

value. The speciﬁc values will be provided in Section V. In

the dynamic real-time pricing model, the price is determined

by the system operator according to the bidding of the market

participants. In this paper, the half-hourly price data in EMA

over a year is adopted to form the hourly data, starting from

May 2013 to April 2014 [20]. Moreover, the selling price is

also set in both pricing models, indicating the price per kWh

that the microgrid sell extra generation back to the utility grid,

which is lower than the buying price.

C. ESS Hybridization

Design features of the hybrid ESS vary in terms of power

density, energy density, lifetime and cost [21]. In this paper,

the hybrid ESS in the microgrid is comprised of the battery

and supercapacitor given their complementary characteristics.

The battery is able to store a large amount of electrical energy

for the sake of high energy density, while the supercapacitor

has high power density to give fast response for charging

and discharging events. The main functions of the hybrid

ESS include maintaining the instantaneous power balance

and minimizing the operational cost over a period of time.

Hence, the battery and supercapacitor should target different

objectives, that the battery is scheduled to operate as the

distributed generation unit for economic dispatch while the

supercapacitor should make up the instant power mismatch.

D. Renewable Power Generation

The implementation of RES in the microgrid gives the

EMS a more cumbersome task to track the instantaneous

supply/demand balance. The microgrid is modeled with two

RES systems including PV panels and wind turbines. PV

generation is considered to have a great variation due to

passing clouds. Wind power is closely correlated with wind

speed, which follows different patterns on seasons and even

days. RES forecast error is considered to have a close re-

lationship with the prediction lead time. Solar power ranges

from 20% to 35% root mean square (RMS) error depending

on different irradiance forecast techniques. Day-ahead wind

forecast currently averages at more than 10% RMS error of

the capacity, and progressively reduces half to 5%-6% for one

hour-ahead forecast [23]. Based on this fact, the RES output

in this paper is modeled with a gradient uncertainty level, in

which the forecast error increases when the receding horizon

becomes larger. There are many existing and ongoing studies

on RES forecasting methodologies, however, they will not be

further discussed since different forecasting techniques are not

within the scope of this paper.

III. DEGRADATION COST MODELING

The degradation of ESS is very important to evaluate

economic operation of microgrid analytically [24]. In order to

accurately model the cost properties for microgrid energy man-

agement, the degradation cost of the hybrid ESS is discussed

and mathematically formulated in this section, especially for

the battery and supercapacitor.

A. Modeling of Battery Degradation Cost

The degradation on battery lifetime features on two main

factors, namely, the aging of cycle life that reﬂects the total

achievable cycle count of a battery unit, and the capacity wear

that accounts for the usable energy [25]. Cycling conditions,

such as the number of frequent charging and discharging,

charging and discharging rates and maintenance scheduling,

have a great impact on the battery lifetime [26]. Improper

cycling may cease to battery failure due to accelerated degra-

dation. Apart from cycling conditions, state parameters also

have signiﬁcant inﬂuences on battery lifetime. Excessive high

or low state of charge (SOC) would drastically deteriorate

battery charging and discharging performance. Temperature

may have a negative impact on the battery life as well, that

at high temperatures the decay process will be accelerated. In

practice, the temperature controller is often included in the

battery management system. Therefore, it is assumed that the

battery degradation due to ambient factors can be neglected.

As for the effect of charging rate, its direct impact on battery

lifetime is negligible in comparison of other parameters when

battery is operating within a certain degree of rated current

[27].

To this end, the primary determinants on battery lifetime

are the actual full capacity and the depth of discharge (DOD).

There are two main DOD deﬁnitions in the literature in

accordance with different cycling events, as shown in Fig. 2(a)

and (b). The ﬁrst is the discharged energy from the full

capacity (100% SOC), and the second refers to a full cycle

consisting of one charging and discharging event [22]. Unless

other speciﬁed in this paper, SOC is deﬁned as the leftover

energy compared to the full capacity, and DOD is deﬁned as

the energy in one charging or discharging event with respect to

the full capacity, as illustrated in Fig. 2(c). We also deﬁne the

actual full capacity of the battery as the amount of energy that

can be stored at 100% SOC. Note that a cycle event is counted

whenever the operating modes (charging and discharging)

switch to the opposite sides.

Transactions on Smart Grid

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

2x10

4x10

6x10

8x10

1x10

Number of Cycles

DOD

Battery Life Cycles

Fig. 3. Relationship of number of lifecycles and DOD of a Ni-Cd battery.

Fig. 3 shows a relationship between the number of life

cycles and the DOD of Ni-Cd batteries [27]. The battery

lifetime has the best ﬁtting in the following expression with

DOD=d

) = a × d

−b

× e

−cd

(1)

where a, b, c > 0 are curve-ﬁtting coefﬁcients. As expected,

the number of life cycles decreases with the increasing DOD.

Without loss of generality, this expression is also applied

for other types of batteries with different parameters such

as Lithium-Ion and Lead-Acid batteries [28]. The statistical

data is usually identiﬁed and provided by manufacturing

speciﬁcations, however all charging and discharging cycles in

the statistical data are assumed under conditions with constant

DOD, which is apparently impractical in real-time operation.

Therefore, estimation of battery degradation cost by using

the above information would introduce gross errors. To the

best of our knowledge, however, there is unfortunately no

previous work featuring on direct relationships of variable

DODs and battery lifetime. Therefore, in order to take the

battery degradation cost model in a practical fashion, it is

reasonably assumed that the empirical data of life cycles is

accurate enough to estimate the long-term degradation effect,

in other words, the effect of each charging and discharging

cycle event on the lifetime is irrelevant with the historical

charging and discharging proﬁles.

Given the actual capacity and DOD as two factors, the bat-

tery degradation model is based on the moderate assumptions:

a) The degradation process is considered to be time-linear

throughout the whole battery life [29]; and

b) The degradation cost of each charging and discharging

cycle event with the same level of DOD is the same at different

levels of SOC.

The battery degradation cost model represents a direct

depreciation on its actual capacity and lifetime. Considering

a discharging event starting at time t with the average power

(t) for a time interval ∆t, the DOD during this interval,

(∆t), can be expressed as:

(∆t) =

(t)∆t

B A

(t)

(2)

where E

B A

(t) is the actual capacity at time t. With the

coefﬁcients of charging/discharging efﬁciencies η

and η

the average degradation cost per unit energy in this event in

accordance with Fig. 3 can be formulated as follows [30]:

B AC

(

t, d

(∆t)

)

∆t

(∆t))E

B A

(t)d

(∆t)η

(3)

Note that it is a levelized degradation cost for each charging

and discharging event with DOD=d

. Therefore, we can get

the corresponding battery degradation cost for this discharging

event by simply multiplying the energy exported from the

battery:

BDC

(

t, d

(∆t)

)

= C

B AC

(

t, d

(∆t)

)

(t)

(t)∆t

(∆t))E

B A

(t)d

(∆t)η

(4)

After the cycling event, the actual capacity of the battery at

t+∆t is proportionally deprecated, which can be calculated as

follows:

B A

(t + ∆t) = E

B A

(t) −

B.rat ed

(

(∆t)

)

(5)

where E

B.rat ed

is the rated battery capacity.

In order to address the same degradation effect on the

battery, we consider the cost of the charging event equal to

that of the discharging event. Note that operation at too high

or low SOC for a long time would in fact rise the internal

impedance and decompose electrolyte in the battery, leading

to capacity loss and power fade, however such fade in a short

term would be insigniﬁcant compared with the degradation

caused by chronic charging and discharging events. It is also

noted that the effect of the charging and discharging rate on

battery life will not be considered as a long-term effect as long

as its current does not exceed the limit deﬁned by manufacturer

speciﬁcations, so as for other external parameters such as

temperature and maintenance scheduling [30].

B. Modeling of Supercapacitor Degradation Cost

The lifetime of supercapacitor depends mostly on evapora-

tion rate of liquid electrolyte, which is a principal function of

temperature and terminal voltage [31]. In general, the lifetime

of supercapacitor decreases with increasing central tempera-

ture. Supercapacitor is capable of undergoing thousands of

deep cycles much more than battery and exhibits a much

longer lifetime for more than ten years which is not limited by

cycling stress [32]. Calendar ageing effects of supercapacitor

are mainly resulted from voltage and temperature effects [33].

In particular, thermal conditions may have great inﬂuences on

performance of supercapacitor, that capacitance degradation

would be accelerated when the temperature is too high [34].

On the other hand, charging and discharging rates have little

effect on superacapacitor degradation [35].

Since the supercapacitor lifetime at the maximum working

temperature with proper voltage ranges is always given by

manufacturing speciﬁcations, it can be reasonably assumed

that supercapacitor is expected to last for the estimated life

within normal operating conditions. Therefore, the superca-

pacitor degradation cost can be considered as a linear function

of time despite of DOD of each charging/discharging event.

Given the estimated supercapacitor lifetime L

and the

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