Design Considerations of Power Management Control ... · Design Considerations of Power Management Control ... microgrid Power Management Model ... the parallel operation of distributed

2014 Florida Conference on Recent Advances in Robotics 1 Miami, Florida, May 8-9, 2014

Design Considerations of Power Management Control Strategies for Micro-grid Systems

Melendez-Norona, R Computer & Electrical Engineering

& Computer Science Department Florida Atlantic University

[email protected]

Roth, Z Computer & Electrical Engineering


[email protected]

Zhuang, H Computer & Electrical Engineering


[email protected]

ABSTRACT The paper outlines the design considerations for electrical

microgrid Power Management Model (PMM). Design

considerations for decentralized power management control for

a microgrid that operates in an isolated mode disconnected from

the main power grid is the main focus. An example based in part

on a hypothetical scenario of the transformation process of the

No Name Key Island, an island in the lower Florida Keys, into a

microgrid community serves as a typical scenario to formulate

the analysis of optimal power flows and as a consequence the

economical dispatch for photovoltaic arrays and diesel

generators to meet local power demands. Three stage optimal

power flow optimization problem is presented - bidding, unit

commitment and real time adjustment of optimal power flow for

the microgrid. The optimization utilizes simplified models

allowing each optimization to be done using linear programming

implemented in Matlab.

Keywords

Microgrid, microgrid decentralized control, Power Management

Model (PMM), bidding of power sources, unit commitment,

optimal power flow, microgrid nodes and local controllers.

1. INTRODUCTION Design of sustainable alternative energy systems based on

distributed generation has been an active research area for

the last decade. The advantages of distributed generation

in a smart grid performance have been analyzed [1][2].

Distributed generation units usage of renewable energy

sources include photovoltaic, wind power and fuel cells as

part of the variety of sources to supply the local power

demand [3].

Microgrids present an important example of integration of

distributed generation and renewable energy sources into

a sustainable system carrying potential economic benefits

and contributions to the environment [4].

Both isolated and non isolated (islanded) microgrid

schemes may be adopted for operation.

Government, community and power utility companies

around the world have been implementing models and

applications for smart grids creating scenarios to improve

their reliability and security [5]. Several real cases of

microgrid design and implementation have been

presented, specifically those related with geographically

isolated locations. The standalone microgrid in Lencois

Island in Brazil is a good example [6]. That microgid

consists of 99 houses, whereas pv arrays with battery

backup, wind microturbines and diesel generators are part

of the microgrid power sources. It has central control

connected to a SCADA system, sensors for voltage,

power and other important variables are also included.

The objective function for optimal power distribution in

the Lencois island system is to minimize cost of

operation, under power balance constraints.

The control strategies to achieve an optimal performance

for any power system including microgrids have also been

defined. Control schemes include centralized and

distributed power management layout. Decentralized

control involves a free market power exchange based on

bidding processes [32].

A decentralized multiagent method involving smart

control agents to achieve cooperation during both normal

and emergency operating conditions is presented in [7].

In [8] a decentralized multiagent system (MAS) for

optimization of microgrid is proposed. The MAS

framework, concept, control and architecture are


discussed. Java Agent Development (JADE) platform is

used to implement the decentralized control. In this

hybrid distributed control hierarchy several agents for

generation, load, monitoring task, among others, are

created and allowed to communicate with one another to

achieve microgrid cost minimization subject to power

balance constraints. Connection to the main grid

connection is allowed.

For centralized control some local controllers placed on

different locations in the grid communicate with the main

control. In [9] a centralized control system to coordinate

the parallel operation of distributed generation inverters in

a microgrid is studied. In [27] a microgrid hierarchical

control system includes three control levels distributed as

local microsource controllers, local controllers, central

control and distribution management system is presented.

Centralized control also involves control monitoring of

each load, equipment and distribution lines located in the

microgrid. Local controllers to operate loads and sources

as well as a microgrid central controller are included as

part of a hierarchical system architecture. These central

controllers communicate with a distribution management

system. Local optimization is achieved by means of local

controllers and eventually microgrid profit is maximized

by means of the central controller. Connection to the main

grid is most of times present as part of the microgrid

topology and the optimization problem is formulated

differently based on market policies applied to grid

connection and bid rules. Sequential quadratic

programming and artificial intelligence techniques are

applied for optimization for centralized control

applications [27].

Several authors have investigated the design

considerations for agent oriented architecture or software

that supports smart grid operation [10]. Various

optimization techniques and control algorithms have been

studied for control of microgrids. Modern computational

techniques such as Particle Swarm Optimization and Ant

Colony Optimization for microgrid power management

system are introduced in [11]. In [12] a methodology for

optimal allocation of energy storage systems in

microgrids based on genetic algorithm applications is

explained.

For microgrid operation the objective functions to

optimize include microgrid operational cost, microgrid

net profit and reduction of electrical power losses.

This paper proposes a distributed control strategy and

develops a decentralized scheme with power sources

bidding option, taking as an example a hypothetical

scenario involving the conversion of the No Name Key

island to a microgrid community. No Name Key is an

island located in the lower Florida Keys, with a

population of 43 homes. Currently the island is being

served by an electrical distribution system used for some

houses. Other residents use solar photovoltaic systems or

diesel generators only for electricity supply.

2. DEFINITIONS A microgrid is characterized by the coordinated operation

of loads, distributed generation sources and energy

storage systems (Figure 1) [15]. The types of clean energy

sources that can be included in microgrid operations run

from photovoltaic arrays with battery backup and wind

power units to fuel cells [13]. Conventional energy

sources such as diesel generators are used as backup to

improve the reliability of microgrid performance,

enabling it to meet any load demand at any time of the

day during occasional absences or shortages of renewable

power.

In order to achieve an optimal power flow and optimal

dispatch of energy sources and to develop a strategy or set

of rules for microgrid operation it is necessary to define

an appropriate Power Management Model (PMM) [16]. In

many cases the discussion of design considerations for

centralized and decentralized Power Management Model

(PMM) may present an adequate solution for the

challenging task of deciding the best control scheme

option to apply.

Figure 1. Microgrid basic components.

Both centralized and distributed control strategies may be

appropriate for power management (Figure 2). In both

the implementation of a PMM necessitates the study of

the following aspects:

- The nature of power sources used to meet

electrical demand. Intermittent sources (i.e. solar


and wind power generation) and conventional

sources (i.e. diesel generator, gas turbine) are the

most common sources used in microgrid

systems. Fuel cells may be included as well.

- Interconnection of the microgrid to the main

power utility or alternatively an operation of the

microgrid in an isolated mode, with no presence

of a public grid.

- A function related to the microgrid operation

shall be identified as objective function.

Nowadays the criteria of free market for

exchange of power as a result of offer and

demand rules (bid process) is the basis of many

power systems (Figure 3). Free market approach

to optimal power dispatch involves either the

option of maximizing profit or that of

minimizing operational cost.

Figure 2. Overview of centralized and distributed

control scheme for microgrids.

Decentralized control schemes (Figure 3) are based on the

connection of multiple local controllers located at each

different location. For the current study a node [33] is

characterized by a typical residence unit with its

corresponding AC power sources, AC demand and

occasionally DC demand. All decisions are made based

on intercommunication among the local controllers.

Figure 3 shows a 3 node scheme in which each node A, B

and C includes several generation units, loads and local

controllers. Each node may buy or sell energy to other

nodes in the system, by means of accepting or rejecting

bid prices and bid kW offered by each generating source.

Figure 3. Free market power exchange scheme.

3. GENERAL CONSIDERATIONS No Name Key can serve as an example:

- Every house on the island generates its own energy

primarily by means of solar (figure 4) or diesel power.

Solar energy is created as DC power and therefore there

must exist DC to AC inverters to allow this power to

either be consumed at the same node or be transferred to

other nodes in the microgrid.

- Diesel generators are used as back-up power sources.

Diesel generators are known for their capacity to supply

back up power whenever primary sources of energy are

not present or are insufficient [18].

- It is assumed that all pv arrays located at different nodes

operate under the same conditions for temperature and

solar irradiation.

- Currently houses are not energy interconnected. If the

island ever becomes a microgrid it is assumed that such a

system will have a node based architecture [33].

- Presently the system may be observed as a group of

isolated nodes that can potentially share pairwise

interconnections.

- A control strategy will be needed in order to manage the

optimal power flows in the microgrid. That control

strategy will allow the microgrid to operate under safe

and reliable conditions.

The complex operation of the microgrid is achieved in

three optimized steps. The first step consists of Power

Bidding [32], the second stage consists of Unit

Commitment. Unit commitment reflects the planned

microgrid operation in terms of the power that each power

source is committed to produce and its associated cost.

The third stage involves adjustments of the real


economical dispatch of the power sources under real

electrical generation and demand conditions.

- Microgrid is considered as a power system. Therefore

power stability conditions, related to the synchronous

operation of all AC units within a node, as well as

synchronous operation of all the nodes, are important

requirements for microgrid performance [19].

- The configuration of the entire microgrid might be

thought as multiple nodes interconnected via electrical

distribution and communication lines. Each node includes

one or two power sources, an aggregated load (figure 5)

and a local controller. The local controller includes

sensing and monitoring variables. Active power, voltage,

current, frequency, house load demand, among other

variables may all be read by the local controller. Reactive

power will not be considered in this study. Power

variables are shown in Table 1.

- Local controllers also perform communication among

the system nodes, in order to distribute the commands and

take the appropriate actions (i.e. open or close circuit

breakers, turn on or off diesel generators or use storage

batteries energy to supply load requirements).

3.1 INPUT VARIABLES AND DATA

USED Power dispatch strategies for any power system

microgrids are typically presented in terms of sets of

average power system variables [13]. The third stage in a

power flow control relates to the actual economical

dispatch of the generation units due to variations in the

real electrical demand, variations in weather conditions

(i.e. solar irradiation) and unexpected last minute power

sources technical difficulties (i.e. corrective adjustments).

Variables for the unit commitment and real economical

dispatch are presented in Table 1. Pii and Pij are defined as

the power produced in node i to supply part of the load at

that node and the power exchange between nodes i and j,

respectively. Pdge-i and Ppv-i indicate power provided by a

diesel generator and photovoltaic system, at each node.

Plo-i is the load demand at node i. In addition to these

variables, there is a need to include the input data for solar

radiation and for the ambient temperature in order to

calculate the output power for each photovoltaic array in

the microgrid [20][21]. Figure 4 presents an actual solar

power production over a month period as gathered by one

of the residents of the No Name Key island [22].

Figure 4 also presents a typical house load demand. Other

typical energy demand curves are available in [22] [23].

Table 1. Design Variable for microgrid example

Figure 4. PV system Power Production (Sample curve)

and Demand –NNK residence

3.2 NODE CLASSIFICATION

A general consideration for a decentralized PMM design

is that the configuration of the entire microgrid might be

thought as multiple nodes interconnected via electrical

distribution and communication lines. Table 2 proposes a

plausible classification of microgrid nodes.

It indicates that each node shall be classified in direct

relation to presence of pv system, diesel generator and/or

combination of both sources (figure 5). A node is

characterized by the presence of power sources, a local

load demand, a local controller and the connection point

with neighboring nodes in the microgrid.

Table 2. Example of intended node classification for PMM

Node Type

Power Source

PV

array

Diesel

Generator

Wind

Power

Type of Node #1 X X

Type of Node-#2 X

Type of Node-#3 X

Variable

and units

Assigned variable name

AC Power

(W) Pii Pij Pdge-i Plo-i

Ppv-i


Figure 5. Node configuration for microgrid with

decentralized control scheme.

4. ELEMENTS OF THE PMM

The main PMM characterizing elements are the

mathematical models of all loads and generating units, the

power flow diagram and the control policy [16].

Figure 6. PMM Components.

4.1 PMM Mathematical Models

In this study, mathematical model are divided into

subsystem steady-state unit model equations and

optimization set up of the power flow equations. Optimal

power flow equations are developed for each of the three

stages in microgrid planning and operation mentioned

earlier.

4.1.1 Subsystems Models

Subsystem equations describe the static behavior of

microgrid components such as pv arrays [29], diesel

generators, electrical inverters [30] and batteries [29].

Flow charts for Photovoltaic Arrays and Generators

subsystem are presented. Storage mechanisms are not

included as part of this study and are considered as a

future direction; inverters subsystem model is not

included as well and instead efficiencies values represents

inverters operation in equations (14) and (26). Subsystem

equations may be applied to centralized and decentralized

control design process.

For photovoltaic arrays:

Where:

G: solar radiation

Isc: short circuit current parameter of solar cell

IL: photogenerated current due to solar radiation

Icell: current produced by solar cell

Id: saturation current

q: coulomb constant

K: Boltzmann constant

T: solar cell temperature in K0

Vd: DC output voltage one solar cell

Psc-dc: solar cell DC output power

Psc-(module): pv module DC output power

(1)


Psc-(array): pv array DC output power

n: number of cells in one pv module

m: number of modules in one pv array

The temperature parameter (T) affects the solar cell

voltage level, as shown in figure 8. A node may or may

not contain a pv array. For calculation of the current (I)

drawn by a pv array it is known that a pv array is a group

of pv modules connected generally in parallel. Each pv

module is formed by cells. Typically those cells are

interconnected in series configuration to obtain different

combinations of voltages (i.e. 12 DC Volts or 24 DC

Volts). Therefore the total current of an array is calculated

as the current given for one module by a total number of

modules in the array. This applies to every node which

has solar power source. The information on solar

radiation is used as a basis for the application of equations

(1). The total power produced by a pv array is also

affected by changes in the ambient temperature (Figure

7).

Figure 7. Effects of solar radiation and temperature.

For diesel generators in (2):

fuel: fuel input for the diesel engine

P: number of poles of the electrical generator

τapp: applied torque at input of electrical generator

τind: induced torque

ωm: mechanical angular velocity

Mecloss: generator mechanical losses

Ia : armature current

Ra : armature resistance

Pconv: converted power

Pdge: AC output power

f: electrical frequency in Hertz

A: ratio between applied and induced torque, defined by

internal magnetic fields in the machine.

Elecloss: generator electrical losses

The total power produced by the generator is Pdge. Only

active power is considered as part of this study.

4.2.2 Optimal Power Flow Modeling

Another important part of the PMM mathematical model

is the microgrid optimal power flow modeling. In

decentralized microgrid models, the dispatch of the

generation units may be based on a bidding process. A

bidding process [32] consists of rules for offer and

demand on a fair open energy market. Microgrid nodes

offer the production of certain amounts of power at

certain cost taking into account power production costs

and power needed to meet the demands by the node’s own

loads. Usually generators bid during a period of time prior

to the real time operation of the power system. Any bid

process shall be created under economic fairness

conditions or constraints and those conditions might be

)( 2


expressed in terms of design variables Cii, Cij, Pii, Pij,

where Cii and Cij are the cost of producing 1 kW of power

at node i to meet part of local demand and the cost of

produce 1 kW at node i to cover part of demand at node j,

respectively. Pii and Pij were defined in Table 1.

Optimization problem is solved individually at each node

by following a decentralized control scheme. Next,

optimization problem is presented for each stage by

considering the design variables, constraints expressed in

terms of the design variables and the objective function to

minimize as a function of the design variables only.

In the bidding process at the first stage in the planning

process:

- The design variables for each node i are Cpvi(t) and

Cdgi(t) where:

Cpvi(t): the price of generating 1 Kw power from

photovoltaic array located at node i, at time t.

Cdgi(t): the price of generating 1 Kw power from diesel

generator located at node i, at time t.

- The objective function to minimize is the cost of

generation for each node-i:

Where

Ppvi(t): estimated power generated by photovoltaic array

located at node i, at time t.

Pdgi(t): estimated power generated by diesel generator

located at node i, at time t.

The estimates for photovoltaic units depend on typical

time of the day and irradiation dependent production

curves. The estimates for diesel generator produced power

depend on typical power demand curves for the specific

node and expected production of renewable energy.

- Inequality constraints are represented by minimum and

maximum values that cost can take (according to market

cost index for renewable energy sources and traditional

energy sources) for each power unit. References [34] [35]

provide some information related to cost of production for

different power sources.

The maximum cost in (5) is calculated as the product of

the maximum capacities for each power source and the

corresponding unit cost or cost per kW.

Estimates of typical production curves for photovoltaic

systems and projected demand values in kW are the basis

for Unit Commitment:

- The design variables, applied to each node i are Pii(t),

Pij(t), representing the power produced at node i to supply

part of the load at that node and the power produced at

node i to supply part of the load at node j.

- Constraints are represented by the minimum and

maximum values that the design variables can take, in

terms of load requirements for the system and in terms of

the maximum power transfers that the system can support.

Maximum power produces at node i cannot exceed the

given capacities of photovoltaic arrays and generators. In

(6) Li(t) and Lj(t) are the load demand at time t for nodes i

and j while x%, y%, a% and b% represents the portion of

the loads Li(t) and Lj(t).

- In this study it is assumed that part of the load in node i

will be covered by local production. As a consequence

minimum value of Pii is different than zero.

-Unit commitment stage assumes that the local controllers

share information regarding cost parameters and projected

load and also that bidding from first stage is accepted by

each local controller.

- Another constraint is explained by means of the

denominated power balance equations: These equations

reflect the power balance in the system. Decentralized

control dictates that house electrical demand shall be

supplied by microgrid power sources operation. This

statement involves the transferred power Ptransfer and the

self consumed power Pselfconsumed . The power balance

)(cosmax)()( maxmax ttt(t)Pct(t)Pc inodedgidgipvipvi

maxmin

maxmin

dgidgidgi

pvipvipvi

c(t)cc

c(t)cc

)()()( t(t)Pct(t)PctCost dgidgipvipviinode

)()()()( maxmax tPtPtPtP dgipviijii

jijj

iiii

Lb(t)PLa

tLy(t)PtLx

%%

)(%)(%

)( 3

)( 4

)( 5

)( 6

)( 7


equation for PMM is presented in (8), using variables

from Table 1 as the design parameters.

- Pij is equal -Pij since power can only flow in one

direction from one node to another node.

- Pload-i is the load at node i.

- Indexes i, j go from 1 to n, where n is total

number of nodes of the system.

- For this specific study the PMM design process

requires that each node electrical load demand

shall be met while minimizing an objective

function which will be the hourly microgrid cost

in a decentralized operation. As a consequence

individual optimization is developed by each

controller at each node.

- The parameter cij(t) represent the cost of

producing 1 kW in the node i to supply part of

the load at node j, at time t. It is the result from

addition of cost parameters calculated from the

bidding stage 1.

- The parameter cii(t) represent the cost of

producing 1 kW in the node i to supply part of

the load at node i, at time t. It is the result from

addition of cost parameters calculated from the

bidding stage 1.

For actual economical power sources dispatch, as the

third stage in the PMM, solar irradiation and temperature

are the actual values communicated to local controllers

via sensors located at each node. Readings are taken on an

hourly basis. Also differences in electrical demand might

be expected.

- The design variables are PiiR(t), PijR(t),

representing the actual power produced at node i

to supply part of the load at that node and the

actual power produced at node i to supply part of

the load at node j.

- The sum of the PiiR and PijR for each local node i

shall not exceed the maximum operational levels

Pdge-imax and Pinv-imax of diesel and pv systems for

that local node:

- The unit commitment from second stage shall be

honored, with some acceptable tolerance.

Tolerances are decided by owners of the

equipment located at each node.

- Actual Load demand shall be met at anytime.

- Cost is considered for minimization, for each

node of the microgrid. The values of cost

coefficients cii and cij may or may not change

with respect to unit commitment depending on

the real conditions for microgrid operation.

Finally, after calculating the actual value for the design

variables, the calculation of diesel generator power is

iinviscdcpviacpviR EffEff(t)P=(t)P )()(

(t)P+(t)P(t)P+(t)P imaxinvidgeijRiiR max

max,min bid(t)P(t)Pbid ijRiiR

(t)P+(t)P=(t)P(t)P ijRiiRpviRdgiR

)(11

)(12

)(13

)(14

(t)P=(t)P+(t)P

(t)P=(t)P

(t)P=(t)P

(t)P=(t)P

(t)P=(t)P+(t)P

n

=i

ilo

n

j==i

ij

n

=i

ii

n

=i

ilolo

n

j==i

ijtransfer

n

=i

iiedselfconsum

lotransferedselfconsum

111,1

1

11,

1

n

ji

ijijiiiiinode t(t)Pct(t)PcCost,

)()(

)(8

)( 9

n

ji

ijRijiiRiirealnodei t(t)Pct(t)PcCost,

)()(

dgijpvijij

dgiipviiii

ccc

ccc

)(10


In (14) Effsc-i and Effinv-i are the corresponding efficiency

values for pv array and DC-AC electrical inverter for

node i. PpviR-dc is pv array real DC power production.

In case there is some technical difficulty with generation

in one node then some choices are available for the

microgrid:

- Exchange energy with the main power utility

grid

- Generators located in other nodes of the system

may produce more power at a specific time of

day

- Loads in that node have the option to be shifted

to other times of the day

- Energy storage mechanisms may be included and

available to cover loads with no need of

generation from main power sources.

Finally and using subsystems models from (2) the input

for fuel consumption for diesel generator at node i can be

calculated.

As a summary of decentralized control approach, each

node load demand shall be supplied by the total power

produced by pv systems and diesel generators in the

microgrid, during 24 hours a day. Each load at node i in

the microgrid shall be covered by the power produced at

the local node plus all power transfers from other nodes.

Local controllers keep continuous communication to

complete bidding and optimal power flow process. Since

this is a power balance formulation all power consumed is

reflected on generating power by pv units and diesel

generators. Cost is presented as Costnode-i as the function

to minimize and Linear Programming is the tool applied

for optimization purposes.

Optimization process result is translated into a control

strategy for microgrid performance, in terms of power

flows between nodes and power generated by units, at

each time t. For instance, control strategy sets the

commands that each local controller shall send to the

local diesel generator in order to produce more or less

power. In general, the study serves as basis for the future

creation of a set of instructions related to local controllers,

diesel generators, pv systems and loads operation.

Most studies for power management models consider

system stability for the microgrid. Typically power

systems stability conditions are defined in direct relation

to voltage and frequency constraints [19]. A common

PMM should include the establishment of stability

conditions to assure a safe and reliable microgrid

operation, over any sudden changes in load demands at

some nodes. Also, stability issues coming from AC

generator operation [25] shall be treated by PMM at its

lowest hierarchical level. As far as stability is concerned,

electrical frequency values shall be maintained in a

predefined interval. In this study the PMM design process

is that local controllers do not allow any sudden

modifications in the electrical demand, which indicates

that stability issues are beyond of the scope of this paper,

as explained in section 4.2.

4.2 PMM Flow Diagram and Control

Strategy

4.2.1 Hierarchical Levels of the

Decentralized PMM

Flow diagram and control algorithm will show the

consistency of operation of any decentralized or

centralized Power Management Model [24].

For a decentralized approach the control algorithm is

defined by using hierarchical levels (Figure 8). The first

level role is to assure stability conditions for the

microgrid, monitoring the values of voltage and

frequency, as well as controlling the synchronization

process of different AC power sources. As mentioned

before, stability issues are beyond the scope of this paper

and will be addressed in future studies.

- PMM algorithm – first hierarchical level:

First level of the PMM is assures stability

conditions in the microgrid, allowing the

synchronization of different AC generation

sources. Figure 8 reflects that once these

conditions are assured then it makes sense to

consider the higher hierarchy levels. In other

words, if electrical system is stable then

optimization of microgrid power flows is

allowed.

- PMM algorithm – second hierarchical level:

The second hierarchical level manages the

optimization process to achieve the minimum

cost and best economical dispatch of both

photovoltaic systems and diesel units, meeting

house loads requirements, on an hourly basis.

The goal is to maintain a balance between power

generation and power consumption. Several

methods have been used in the literature [11]. In

this paper all optimizations are developed by

using Linear Programming techniques[28].


Figure 8. PMM hierarchical levels.

5. EXAMPLE OF PMM OPERATION An example of a decentralized control is presented as part

of this study by specializing the mathematical model

presented in Section 4. Figure 9 illustrates a microgrid

control structure for three nodes (n=3). Both Nodes 1 and

2 are assumed to include pv systems (3.5kW at node 1

and 2.8kW at node 2, as the maximum capacity) and

diesel generator (4kW at node 1 and 3kW at node 2, as

the maximum capacity). Node 3 only includes a pv

system (2kW). In this example it is assumed that all three

nodes share interconnection among them.

Figure 9. PMM- applied to nodes (n=3) . Example.

It is assumed that the microgrid is off the main grid and

that the cost minimization is performed by each local

controller. Each node possesses a cost function based on

production and cost per kw generated at each power unit.

Matlab simulation provides an environment for PMM

implementation. The main inputs of the simulation are

given by photovoltaic system AC power production and

load demands for each node (figure 10 and figure 11).

Based on realistic solar irradiation data for Florida the pv

production for a pv system is calculated.

Figure 10. PV system scheduled production (node 1).

Load demands vary from node to node, reflecting the

different characteristics of electrical appliances at each

house and also different load peaks during the day.

Figure 11.Projected Load Demand per node.

In the first stage for the planning or definition of cost for

bidding process, design variables are represented by each

cost per kW for each power source, in this case

photovoltaic and diesel generator C1pv, C1dg, C2pv, C2dg,

C3pv.

Cpv1: price of generating 1 kW power from photovoltaic

array located at node 1





Cdg1: price of generating 1 kWw power from diesel

generator located at node 1

Cdg2: price of generating 1 kW power from diesel

generator located at node 2


- Objective functions to minimize are related with

cost of generation for each node:

Ppv1: power generated by photovoltaic array

located at node 1, in kW





Pdg1: power generated by diesel generator located

at node 1, in kW

Pdg2: power generated by diesel generator located

at node 2, in kW

- One of the inequality constraints involves the

minimum and maximum dollar per kW values

that each unit can cover as part of the cost. These

extreme values were defined following standard

or average market cost for photovoltaic units and

diesel generators. Each min, max has US$ per

kW as part of Table 3.

Table 3. Constraints for Cost Parameters

Cost

Variable

Cost constraints

Minimum

Limit (US$

per kW)

Maximum

Limit (US$ per

kW)

Node

Cpv1 Cpv1min=5000 Cpv1max=10000 Node 1



Cdg1 Cdg1min=1200

0 Cdg1max=15000 Node 1

Cdg2 Cdg2min=1200

0 Cdg2max=15000 Node 2

- Another constraint reflects the maximum cost

that each node shall assume for the generation at

that point. In this case cost is the product of unit

cost and generated power in kW.

After inserting constraints inequalities and equalities in

Matlab code, calculation of results for the first stage in the

bidding process is performed.

Figure 12. Bid results from first stage.

)(*)(

)(*)(*

)()(

)()(*

)()(

max3max333

max2max2max2max2

2222

max1max1max1max1

1111

tPct(t)Pc

tP(t)ctPc

t(t)Pct(t)Pc

t(t)PctPc

t(t)Pct(t)Pc

pvpvpvpv

dgdgpvpv

dgdgpvpv

dgdgpvpv

dgdgpvpv

)(

)()(

)()(

333

22222

11111

t(t)PcCost

t(t)Pct(t)PcCost

t(t)Pct(t)PcCost

pvpvnode

dgdgpvpvnode

dgdgpvpvnode

max33min3

max22min2

max22min2

max11min1

max11min1

pvpvpv

dgdgdg

pvpvpv

dgdgdg

pvpvpv

c(t)cc

c(t)cc

c(t)cc

c(t)cc

c(t)cc

)(15 )(16

)(17


The output of the bidding process serves as the input for

Unit Commitment phase. Here the design variables switch

from cost per kW generated to power generated in that

node to supply that node demand and p in kW (P11, P12,

P13, P22, P23, P33).

- Constraints for lower and upper limits in the

design variables indicate the minimum and

maximum amount of power that each node will

generate to supply its own load and the minimum

and maximum exchanges of power between

nodes 1-2, 2-3 and 1-3. These limits are

calculated in terms of load demand requirements,

following a policy that each node shall meet its

own limits under certain conditions and

exchange power from other point in the

microgrid if required. L1(t), L2(t) and L3(t) are load

demand at each node.

- Another constraint is related to the maximum

power that physically the node can produce, due

to operational limits for the photovoltaic system

and diesel generators, given in kW, according to

Table 4.

Table 4. Constraints for Power Variables

Power

Variables

Maximum

Values

(kW)

Notation

P11+ P12+ P13 3.5+4 Ppv1max+ Pdg1max

P22+ P23 3+2.8 Ppv2max+ Pdg2max

P33 2 Ppv3max

- Finally, load demand of the microgrid shall be

supplied at anytime:

)()()(

)()()()()()(

321

332322131211

tLtLtL

tPtPtPtPtPtP

- The objective function subject to optimization is

each node power production cost.

For actual economical dispatch, the decision variables are

represented by the real power flow exchanges between the

nodes and the real power consumed at each node, at any

time of the day (P11R, P12R, P13R, P22R, P23R, P33R).

- First constraint: power balance in the microgrid,

based on actual load demand.

- Operational levels of diesel and pv systems for

each node cannot be exceeded. See Table 4.

- The unit commitment shall be honored.

- The objective function subject to optimization is

each node power production cost as shown in

(25):

(t)P(t)P(t)P

(t)P(t)P(t)P

(t)P(t)P(t)P

(t)P(t)P(t)P

(t)P(t)P(t)P

(t)P(t)P(t)P

R

R

R

R

R

R

232323

121212

131313

333333

222222

111111

98.0

96.0

005.198.0

33.1%98.0

05.198.0

05.195.0

)( 22)(9.0)(6.0

)(1.0)(05.0

)(8.0)(6.0

)(1.0)(05.0

)(2.0)(1.0

)()(6.0

3333

3233

2222

3133

2122

1111

tL(t)PtL

tL(t)PtL

tL(t)PtL

tL(t)PtL

tL(t)PtL

tL(t)PtL

)()(

)()()()(

)()()()()(

max333

max2max22322

max1max1131211

tPtP

tPtPtPtP

tPtPtPtPtP

pv

dgpv

dgpv

)(

)()(

)()()(

33333

232322222

1313121211111

t(t)PcCost

t(t)Pct(t)PcCost

t(t)Pct(t)Pct(t)PcCost

node

node

node

)(19

)( 21

)()()( 321

332322131211

tLtLtL

(t)P(t)P(t)P(t)P(t)P(t)P

RRR

RRRRRR

)(18

)( 24

)( 20

)()(

)()()()(

)()()()()(

max333

max2max22322

max1max1131211

tPtP

tPtPtPtP

tPtPtPtPtP

pvR

dgpvRR

dgpvRRR

)( 23


Figure 13 offers the overview for real power production

in the real economical dispatch of power sources, after

considering the bidding and unit commitments determined

by the communication between local controllers. Here,

real time transfer power from Node 1 to Node 2 and Node

3 are identified as P12R and P13R. Figure 14 indicates the

same power productions and transfers corresponding to

Node 2.

Figure 13. Real Power Production Node 1.

Figure 14. Real Power Production Node 2 and 3.

After power flow variables are established by following

optimization process then calculation of electrical power

generation is shown in figure 15.

Figure 15. Power produced by generator at node 2.

Efficiencies for pv array and inverter together is defined

as 0.6 as typical value for solar systems operation in (26).

6. CONCLUSSIONS In the case study of the No Name Key island, a

conversion of the island community into a microgrid will

necessitate a capital investment to create a basic

infrastructure for electrical connectivity as a microgrid. A

decentralized PMM represents the tool to technically

define microgrid performance and schedule of operation,

as a basis of any decision linked to that investment.

Centralized scheme is also an alternative and it takes into

consideration many of the aspects related with the

decentralized approach. Additional testing and

simulations will be developed in order to prove the

validity of the model and algorithms. Future directions

include the modeling and calculation of storage systems

(i.e. batteries or super capacitors), the detailed

presentation and analysis for inverters and batteries

mathematical models, sensitivity analysis for constraints

limits, microgrid performance for connection with main

utility grid and failure mitigation.

7. ACKNOWLEDGMENTS Our thanks to Dr. John Morris for data used as part of this

formulation problem.

)(

)()(

)()()(

33333

232322222

1313121211111

t(t)PcCost

t(t)Pct(t)PcCost

t(t)Pct(t)Pct(t)PcCost

Rrealnode

RRrealnode

RRRrealnode

)( 25

6.0

6.0

6.0

3

ac3

2

(t)P=(t)P

(t)P=(t)P

(t)P=(t)P

EffEff(t)P=(t)P

3scinv

2scpv

1scacpv

iinvisciscacpvi

(t)P(t)P(t)P(t)P(t)P RRRinvdge 13121111̀

)( 26


REFERENCES

[1] Singh, A.K.. Parida, S.K.. Need of distributed generation

for sustainable development in coming future. IEEE

International Conference on Power Electronics, Drives

and Energy Systems (PEDES), Dec. 2012.

[2] Qiang, J., Shuo, Z., Young-Li, L. A study on capacity of

distributed generation and its effect on short circuit

current at micro-grid operation mode. 4th International

Conference on Electric Utility Deregulation and

Restructuring and Power Technologies (DRPT). 1109 –

1112. 2011.

[3] Kennedy, S., "Bridging the gap between energy research

and energy development impact," Power and Energy

Society General Meeting, 2011 IEEE, pp.1,1, 24-29 July

2011.

[4] Pudjianto, D. et al. “Investigation of Regulatory,

Commercial, Economic and Environmental Issues in

MicroGrids.” [Online]. Available:

http://www.microgrids.eu/micro2000/presentations/37.pdf

.

[5] Chopra, A., Kundra, V., and Weiser, P. (2011, July 13).

[Online]. Available:

http://www.nist.gov/smartgrid/upload/nstc-smart-grid-

june2011.pdf.

[6] de Souza Ribeiro, L.A.; Saavedra, O.R.; de Lima, S.L.;

Gomes de Matos, J., "Isolated Micro-Grids With

Renewable Hybrid Generation: The Case of Lençóis

Island,” IEEE Transactions on Sustainable Energy, vol.2,

no.1, pp.1,11, Jan. 2011.

[7] Colson, C.M.; Nehrir, M.H.; Gunderson, R. W.,

"Distributed multi-agent microgrids: a decentralized

approach to resilient power system self-healing,"2011 4th

International Symposium on Resilient Control Systems

(ISRCS), pp.83,88, 9-11 Aug. 2011.

[8] Eddy, F.Y.S.; Gooi, H. B., "Multi-agent system for

optimization of microgrids," 2011 IEEE 8th International

Conference on Power Electronics and ECCE Asia (ICPE

& ECCE), pp.2374,2381, May 30 2011-June 3 2011.

[9] Tan, K.T.; Peng, X. Y.; So, P. L.; Chu, Y.C.; Chen, M. Z

Q, "Centralized Control for Parallel Operation of

Distributed Generation Inverters in Microgrids,"IEEE

Transactions on Smart Grid, vol.3, no.4, pp.1977,1987,

Dec. 2012.

[10] Ghosn, S.B.; Ranganathan, P.; Salem, S.; Jingpeng Tang;

Loegering, D.; Nygard, K.E., "Agent-Oriented Designs

for a Self Healing Smart Grid," 2010 First IEEE

International Conference on Smart Grid Communications

(SmartGridComm), pp.461,466, 4-6 Oct. 2010.

[11] Colson, C.M.; Nehrir, M.H.; Pourmousavi, S.A.,

"Towards real-time microgrid power management using

computational intelligence methods," Power and Energy

Society General Meeting, 2010 IEEE, pp.1,8, 25-29 July

2010.

[12] Changsong Chen; Shanxu Duan; Tao Cai; Bangyin Liu;

Guozhen Hu, "Optimal Allocation and Economic Analysis

of Energy Storage System in Microgrids," IEEE

Transactions on Power Electronics, vol.26, no.10,

pp.2762,2773, Oct. 2011.

[13] Caisheng Wang; Nehrir, M.H., "Power Management of a

Stand-Alone Wind/Photovoltaic/Fuel Cell Energy

System," IEEE Transactions on Energy Conversion,

vol.23, no.3, pp.957,967, Sept. 2008.

[14] Allen, G. “Tiny Fla. Island Debates Joining Electric

Grid.” [Online]. Available:

http://www.npr.org/2010/11/23/131543151/tiny-fla-

island-debates-joining-electric-grid.

[15] Jia, D., Wei, Q., Song, L;, Huo, G.‘’Brittleness Analysis of

Microgrids’’. College of Electrical and Electronic

Engineering, Harbin Un iversity of Science and

Technology. IEEE. 2011

[16] Melendez, R; Design of a Power Management Model for

a Solar/Fuel Cell Hybrid Energy System; Master’s Thesis;

Florida Atlantic University; 2010.

[17] IEEE Recommended Definitions of Terms for Automatic

Generation Control on Electric Power Systems," IEEE Std

94-1991, pp.1, 1991.

[18] Theubou, T.; Wamkeue, R.; Kamwa, I., "Dynamic model

of diesel generator set for hybrid wind-diesel small grids

applications," 2012 25th IEEE Canadian Conference on

Electrical & Computer Engineering (CCECE), pp.1,4,

April 29 2012-May 2 2012.

[19] Proposed Terms and Definitions for Power System

Stability Task Force on Terms & Definitions System

Dynamic Performance Subcommittee Power System

Engineering Committee," IEEE Power Engineering

Review, vol. PER-2, no.7, pp.28, 28, July 1982.

[20] National Renewable Energy Laboratory [Online] Data for

solar radiation, Florida Keys. Available:

http://rredc.nrel.gov/solar/old_data/nsrdb/1961-

1990/redbook/sum2/state.html

[21] Florida Climate Center. The Florida State University.

Available:

http://climatecenter.fsu.edu/products-services/data/1981-

2010-normals/key-west

[22] Morris, J., Power produced by a typical Photovoltaic

array, Non Name Key, Data.

[23] Parker, D. S. “Research Highlights from a Large Scale

Residential Monitoring Study in a Hot Climate.” [Online].

Available:

http://www.fsec.ucf.edu/en/publications/html/FSEC-PF-

369-02/.

[24] Testa, A.; De Caro, S.; Scimone, T., "Optimal structure

selection for small-si ze hybrid renewable energy plants,"

Proceedings of the 2011-14th European Conference on

Power Electronics and Applications (EPE 2011), pp.1, 10,

Aug. 30 2011-Sept. 1 2011.

[25] Liu, L., Zhou,Y., Li, Hui.; ‘’Coordinated Active and

Reactive Power Management Implementation Based on

Dual-stage PLL Method for Grid-connected PV System



http://www.nist.gov/smartgrid/upload/nstc-smart-grid-june2011.pdf

http://www.nist.gov/smartgrid/upload/nstc-smart-grid-june2011.pdf

http://www.npr.org/2010/11/23/131543151/tiny-fla-island-debates-joining-electric-grid

http://www.npr.org/2010/11/23/131543151/tiny-fla-island-debates-joining-electric-grid

http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/sum2/state.html

http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/sum2/state.html

http://climatecenter.fsu.edu/products-services/data/1981-2010-normals/key-west

http://climatecenter.fsu.edu/products-services/data/1981-2010-normals/key-west

http://www.fsec.ucf.edu/en/publications/html/FSEC-PF-369-02/

http://www.fsec.ucf.edu/en/publications/html/FSEC-PF-369-02/


with Battery’’.Center for Advanced Power Systems,

Florida State University. IEEE. 2010.

[26] Florida Keys Electric Cooperative Association.

Available:

http://www.fkec.com/Cooperative/history.cfm

[27] Tsikalakis, A.; Hatziargyrious, N.; ‘’Centralized control

for optimizing microgrid operation’’; IEEE Transactions

on Energy Conversion, vol 23, no.23,March.2008.

[28] Haimes, Y.; ‘’Hierarchical Analyses of Water Resources

Systems. Modeling and Optimization of Large-Scale

Systems’’; Mc.Graw Hill series in water resources and

environmental engineering; 1977.

[29] Masters, G.;’’Renewable and Efficient Electrical Power

Systems’’; Wiley Intersience and John Wiley & Sons, Inc.,

publication; 2004.

[30] Williams, B.W., "Power Electronics: Devices, Drivers &

Applications ", first edition, 1987.

[31] Jo kic,A.,Van den Bosch,P.,Lazar,M., "Distributed price-

based optimal control of power systems ", 16th IEEE

International Conference on Control Applications, Part of

IEEE Multiconference on Systems and Control,

Singapore, 1-5 October 2007

[32] Urkimez,A., Cetinkaya, N., "Determining spot price and

economic distpatch in deregulated power systems ".

Mathematical and Computational Applications, Vol 5,

No.1, PP 22-33,2010.

[33] Peharda,D.,Hebel Z.,Barta,A., "Power system topology

assessment and pre-estimation in an object oriented

environment ", IEEE, 2007.

[34] Lawrence Berkeley National Laboratory; News Center

[Online]available: http://newscenter.lbl.gov/news-

releases/2013/08/12/installed-price-of-solar-photovoltaic-

systems-in-the-u-s-continues-to-decline-at-a-rapid-pace/

[35] Friedman, B., Ardani, K, Feldman,D., Citron,R.,Margolis,

R., Zuboy,J., "Benchmarking Non-Hardware Balance-of-

System (Soft) Costs for U.S. Photovoltaic Systems, Using

a Bottom-Up Approach and Installer Survey",National

Renewable Energy Laboratory, second edition, 2013.

http://www.fkec.com/Cooperative/history.cfm

http://newscenter.lbl.gov/news-releases/2013/08/12/installed-price-of-solar-photovoltaic-systems-in-the-u-s-continues-to-decline-at-a-rapid-pace/



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