Decision Guidance Approach to Power Network

Analysis and Optimization

Roberto Levy

, Alexander Brodsky

and Juan Luo

Computer Science Department, George Mason University, Va, 22030, Fairfax, U.S.A.

Information Technology Unit, George Mason University, Va, 22030, Fairfax, U.S.A.

Keywords: Decision Support, Decision Guidance, Optimization, HRES, Electric Power Network.

Abstract: This paper focuses on developing an approach and technology for actionable recommendations on the

operation of electric power network components. The overall direction of this research is to model the major

components of a Hybrid Renewable Energy System (HRES), including power generation,

transmission/distribution, power storage, energy markets, and end customer demand. First, we propose a

conceptual diagram notation for power network topology, to allow the representation of an arbitrary complex

power system. Second, we develop a formal mathematical model that describes the HRES optimization

framework, consisting of the different network components, their respective costs, and associated constraints.

Third, we implement the HRES optimization problem solution through a mixed-integer linear programming

(MILP) model by leveraging IBM Optimization Programming Language (OPL) CPLEX Studio. Lastly, we

demonstrate the model through an example of a simulated network, showing the ability to support sensitivity

/ what-if analysis, to determine the behavior of the network under different configurations.

1 INTRODUCTION

We have seen in recent years several trends, which

are significantly transforming the existing

mechanisms for supplying energy to satisfy

electricity demand. At the forefront, environmental

concerns are driving a surge in motivation to integrate

renewable energy sources into the power grid.

Political factors exacerbate this trend, as there is a

significant push for reducing dependency on

imported fossil fuels. Economic aspects take into

consideration the financial viability of operating

those solutions, as well as the need to maintain a

reliable source of supply.

This last factor represents a potential problem for

the effective deployment of some of the most

promising renewable sources, such as wind and solar,

stemming from the uncertain nature of their

generation, which could drive volatility of the energy

supply.

Several complementary elements come into place

to address these issues. The establishment of smart

grids, which expand the more traditional power grids

by using two-way flows of electricity and information

to create an automated and distributed advanced

energy delivery network. Figure 1 (U.S. Energy

Information Administration, 2014), depicts a typical

network configuration for a power grid. As a

specialization of these smart grids, we see the

development of Hybrid Renewable Energy Systems

(HRES), or Integrated Renewable Energy Systems

(IRES), both of which denote an elaborated energy

grid that relies on multiple sources - in general,

renewable ones such as solar, wind, and hydro,

combined with traditional sources such as diesel, and

the placement of storage technology at key locations

on the grid, to establish a reliable, cleaner and stable

flow of supply.

A key problem facing decision makers is to find

the most efficient way to operate such grids, which

are becoming increasingly more complex, including

different types of generation facilities, electricity

storage equipment deployed throughout the network,

transmission and distribution facilities, sources of

demand scattered through a region, and markets for

buying/selling energy and/or capacity. The question

of electricity storage is a particularly important one,

involving the options of placing the right storage

technology at key locations to address multiple needs:

balancing power supply to compensate for potential

fuel shortages and the stochastic nature of renewable

sources; deferring costly upgrades of the

transmission/distribution infrastructure by placing

storage technology next to the end consumer location;

Levy, R., Brodsky, A. and Luo, J.

Decision Guidance Approach to Power Network Analysis and Optimization.

In Proceedings of the 18th International Conference on Enterprise Information Systems (ICEIS 2016) - Volume 2, pages 109-117

ISBN: 978-989-758-187-8

109

allowing frequency regulation; and creating

opportunity for revenue generation through

secondary markets.

This paper focuses on the problem of determining

the optimal operation of the network in the short term,

taking into account the components of power

generation, storage placement, transmission, external

markets, and consumption. The underlying decisions

relate to the optimal flows and mode of operation of

each component of the smart grid. Most of the current

research in the area exhibits several limitations: it

focuses on more specific aspects of the network, as

opposed to an integrated view; is based on mostly

simulation engines or heuristics, not on mathematical

programming optimization; and much is focused on

micro-grids, rather than largely distributed networks.

Addressing those limitations is exactly the focus

of the present research, proposing and implementing

a decision guidance framework for optimal operation

of power networks with renewable resources and

storage. We propose a conceptual diagram notation

for power network topology, to represent Hybrid

Renewable Energy Systems (HRES). We develop a

formal mathematical model that describes the HRES

optimization framework, consisting of the different

network components, their respective costs, and

associated constraints. We implement the HRES

optimization problem solution through a mixed-

integer linear programming (MILP) model by

leveraging IBM Optimization Programming

Language (OPL) and CPLEX Studio. Lastly, we

demonstrate the model through an example of a

simulated network, showing also the ability to

support sensitivity and what-if analysis to determine

the behavior of the network under different

configurations.

There are several benefits to be achieved by the

development of such a model. First, in a context of

uncertain and probable growing demand, by allowing

the planning and simulation of placement of

components (including storage solutions) in different

key locations on the grid, we can make a realistic

assessment of their best utilization, and consequently,

defer a potentially expensive upgrade of distribution

lines. Second, we can minimize overall costs

associated with regular operations due to a more

efficient combination of power flows and use of

storage. Third, we can profitably leverage existing

energy markets, to sell excess capacity at periods of

low demand. And finally, as a clear trend exists for

transitioning from fossil fuels to renewable sources,

the model can support a realistic analysis of how best

to perform this transition.

Figure 1: Distributed power system with storage

technologies (Source: U.S. Energy Information

Administration).

2 RELATED WORK

A significant body of research has been developed in

the past few years to address the smart grid and the

aspects related to its planning and operations. The

first group of research surveys existing work on the

topic rather than proposing new methods. Fang et al.

(2011) define the smart grid as an enhancement to the

traditional power grid of the 20th century, by

leveraging two-way flows of electricity and

information to create an automated and distributed

advanced energy delivery network. They performed a

survey of a large amount of work, classified into three

major categories: Infrastructure System (i.e. the

technologies underlying the Smart Grid for

generation, information control and

communications); Management System

(management techniques for optimal operation of the

grid); and Protection System (security). Our present

work falls mainly in the second category.

Other surveys (Baños et al., 2011; Erdinc and

Uzunoglu, 2012; Chauhan and Saini, 2014) provide a

comprehensive review of optimization and heuristic

methods applied to individual renewable sources of

energy to achieve optimal sizing of components.

Similarly, Deshmukh and Deshmukh (2008) provide

a review of the mathematical modelling of the

different components of an HRES. The methods

covered include traditional methods such as Linear

Programming (LP), Quadratic Programming (QP),

Mixed Integer-Linear Programming (MILP), as well

as heuristics and meta-heuristics approaches,

including Genetic Algorithms (GA), Particle Swarm

Optimization (PSO), Artificial Neural Networks

(ANN), and others. Although robust results were

ICEIS 2016 - 18th International Conference on Enterprise Information Systems

110

achieved in those areas, the research focuses on

optimizing the size of individual sources, and does

not deal with the energy flows between components

involved in the operations of the combined network.

As many of the optimization models deal with

multi-objective optimization, conventional methods

can be used through unification of the objectives into

one consolidated function, or through a Pareto-

optimal set, in which a set of non-dominated solutions

are selected. Alternatively, less traditional methods

are proposed (Katsigiannis et al., 2010), in which a

Multi-Objective Genetic Algorithm is utilized to

minimize the system long term Cost of Energy (COE)

as well as the amount of emission of CO

–

equivalents, using a life-cycle approach that takes

into account emission beyond the production of

energy. This model, however, is designed to address

the optimal combination to be utilized among the

different components, but does not address the design

of a flexible network from an operational perspective,

as we do in our model.

Several models have been developed to explore

other alternative methodologies, with the intent of

deflecting the inherent difficulty of traditional

optimization models. Mahor et al. (2009) provide a

review of multiple papers that attempt to overcome

the problem through the use of Particle Swarm

Optimization (PSO), but those papers focus on the so

called ‘Economic Dispatch’ problem, and on

planning the output of given set of generating units.

For this problem, the network flows did not play a

role. Courtecuisse et al. (2010) propose a

methodology for designing a fuzzy logic based

supervision model for an HRES, based on the

guidance of maximizing the usage of wind power, and

minimizing the use of non-renewable power by

designing a supervisor system that controls the power

generation of each component, and its frequency.

However, they do not attempt to optimize the

functioning of the HRES for cost, environmental

impact, or other objectives.

Much work is focused on the demand side,

ranging from prediction models based on Artificial

Neural networks (Yokoyama et al., 2009; Ekonomou,

2010), to learning consumer behavior through

piecewise regression (Luo et al., 2012; Luo and

Brodsky, 2010), and to mechanisms for Demand Side

Management (DSM) and Demand Regulation (DR) to

counter the constraints on the renewable energy

supply (Moura and de Almeida, 2010). This line of

work complements our solution, in terms of load and

consumption projections, but it does not address our

main area of focus.

Other research focuses on simulating the HRES

model, and on developing optimization strategy to

minimize Net Present Cost (investment costs plus the

discounted present value of all future costs) or the

‘Levelized’ Cost of Energy (total cost of the entire

hybrid system divided by the energy supplied by the

same) (Bernal-Agustin and Dufo-Lopez, 2009).

Although the concept is useful in solving complex

and non-linearized problems, it focuses on stand-

alone hybrid system, not on distributed networks.

Several papers focus on optimization of hybrid

models through Linear Programming approaches

(Cormio et al., 2003), where the model describes the

energy system as a network of flows, by combining

the use of multiple sources (renewable and non-

renewable) of energy services, through a given

planning horizon. The objective function to be

minimized encompasses all fixed and variable costs

(investment and operations), subject to a series of

constraints related to demand, sources, environmental

impacts, etc. The model builds on a comprehensive

modelling of the different elements/components for

generation and consumption, however, it does not

support a modular approach for adding components

located in different parts of the network, with

considerations of distribution flows among possibly

segregated regions.

In the realm of software solution packages, many

comprehensive models were also developed, one of

the best known being HOMER (Lambert et al., 2006),

which provides a robust framework for planning and

simulating an HRES model for a micro-grid, and

driving the identification of the optimal model

through the simulation of discrete number of

scenarios. A good number of packages were

developed in the same vein. HOMER (as well as other

similar packages), offers a user-friendly framework

that allows the flexibility to incorporate the elements

as required, by establishing options for each

component, amount, and sizing, together with the

determination of patterns for the grid load, and

external factors such as wind, sunlight, etc. that affect

the behavior of the components. Their framework,

however, does not address the problem which is the

focus of our research in two respects: it is based on a

simulation approach as opposed to relying on true

optimization techniques, and it solves the problem for

micro-grid planning but does not address a larger

energy distribution network.

Decision Guidance Approach to Power Network Analysis and Optimization

111

3 TOPOLOGY

REPRESENTATION FOR

POWER NETWORKS

Based on the power network depiction in Figure 1, we

generate a topology diagram (Figure 2), which maps

every physical facility in the picture to a

corresponding component in the diagram below,

Orange circles represent generators, blue circles

represent aggregators, yellow circles represent

market, green circles represent storage (for the

purpose of this exercise, we don’t differentiate

between different storage technologies, purple circles

represent transmissions, lines represent power flows,

small ovals represent the power flow identifiers, and

red rectangles represent demand (both residential and

commercial).

Figure 2: Topology Diagram.

This diagram can serve as the basis for establishing

the formal model in the next section, as well as the

case study subsequently, as it provides a modular

view for the components to be assembled in distinct

forms to reflect different network configurations.

The topology diagram can be used for two

interrelated decision problems:

1. Operational (short term) – for every hourly

interval, determine the optimal power flows

across multiple components to satisfy projected

demand during a given time horizon, while

optimizing an objective function (e.g. cost

optimization, emissions, or a combination of

factors). A decision to be made at the beginning

of each hourly interval, as a rolling time horizon.

2. Planning/Investment (mid to long term) – based

on expected demand growth, decide on preferred

investments on network improvements. This

problem normally involves decision on policy,

when evaluating larger scales networks.

This paper focuses on problem 1 – although it can

support the analysis on problem 2, by allowing what-

if analysis on the operations under each option being

evaluated.

In the next section, we will introduce a formal

description of the model, addressing the key

considerations for each component, as well as the

main variables involved.

4 FORMAL MODEL

4.1 HRES Optimization Framework

We define an optimization framework as a tuple:

HRES:

,,,,,,,,,,,

Where:

 T =



1,2,3 … 



is the Time Horizon with

fixed intervals 1, 2,…, N (each with duration

IntervalLength)

 F is the set of flow ids between the

components of the network

 A is the set of aggregator ids

 AIF: →2



is an Aggregator Input Flow

function that, for each aggregator  ∈

,gives a set of its input flows AIF(a)

 AOF: →2



is an Aggregator Output Flow

function that, for each aggregator  ∈

,gives a set of its output flows AOF(a)

 CMP is the set of component ids, including

generators, transmission/distribution,

batteries, demand sources

 CIF:  →  ∪  , where Λ∉,is a

function that, for every component ,

gives:













∈ 















Λ



 COF:  →  ∪  , where Λ∉,is a

function that, for every component ,

gives:













∈ 















Λ



 DS = (D, dF), is the Demand Structure tuple,

where:

ICEIS 2016 - 18th International Conference on Enterprise Information Systems

112

⊆

CMP is a set of demand source IDs;

We require that demand source IDs do not

have output flows, i.e.



∀ ∈















dF:    → 



is the demand function

that, for each demand source d and time

interval t, gives the predicted demand

dF[d,t] in kw.

 GS = (G, fPr, gCap, gEff) is the Generators

Structure tuple, where:

o G

⊆

CMP is the set of generator ids;

we require that generators do not have

input flows, i.e.



∀ ∈ 













o : →



is the price function

that for each generator g and time

interval t, gives the expected fuel price

fPr[g,t] in $/Btu

o : →



is a function that gives

for each generator g, the maximal

capacity of generation gCap(g) in kw

o : →



is the function that gives

for each generator g, the efficiency

gEff(g) in Btu/kw.

  





, , , 



/

, :

o TD

⊆

CMP is the set of

Transmission/ ids

o : → 0,1 is the Loss Ratio of

each Transmission/

o TMC: → 



is the annual

maintenance cost for each

Transmission/ id

o : T→



is the maximal

capacity of transmission in kw for

each Transmission/

 BS = (B, NBC, BLC, BMC, bcF, BIE, M, bmP,

ppC) is the Battery Structure tuple, where:

o B

⊆

CMP is the set of Battery ids

o NBC: →



is the new battery

cost (for replacing each battery id)

o BLC: →



is the Battery

Lifecycle Parameter, for each

battery id

o BMC:B →



is the annual

maintenance cost for each Battery

o bcF: →



is the battery

capacity function that for each

battery b and time interval t, gives

the expected energy storage

capacity bcF(b,t) in kwh

o BIE: B →



is the battery initial

energy level at t = 0

o M is set of market ids being served

by batteries

o bmP: BM → ,  are all

battery-market pairs, for ∀ ∈ 

and ∀ ∈ 

o ppC: B →



is the price that

each market is willing to pay for

committed capacity (in $/kw)

4.2 HRES Optimization Problem

The formal HRES Optimization is stated as:

 Min

,,,,,

 (1)

Subject to Ca, Cg, Ctd, Cd, Cb

Where the decision variables, objective and

constraints are given below:

Decision Variables:

 kw is the matrix of elements kw[f,t], where for

every flow f ∊ F and every time interval t ,

kw[f,t] gives the the amount of kilowatts

transferred between two components

 bE is the amount of energy stored in a battery at

a time interval t

 cFL is the Boolean value (charge flag) that

indicates if a battery is being charged at a time

interval t

 dFL is the Boolean value (discharge flag) that

indicates if a battery is being discharged at a time

interval t.

 c2mFL is the Boolean value (commit to market

flag) that indicates if a battery’s capacity is

committed to a market at a time interval t

 cC is the committed capacity of a battery to a

market at a time interval t

Objective Function:

         (2)

where:

 RevAdjCost is the overall cost through the time

horizon reduced by market revenue

 gC is the cost associated with operating the

power generators during the time horizon (see

section 4.4)

 tC is cost of maintaining the Transmission/

Distribution stations during the time horizon (see

section 4.5)

Decision Guidance Approach to Power Network Analysis and Optimization

113

 bC is the cost of operating the batteries, as well

as the associated battery depreciation cost, based

on usage through the time horizon (see section

4.7.1)

 mR is the revenue associated with committing

batteries to market throughout the time horizon

(see section 4.7.2)

Constraints:

 Ca = Aggregators’ constraints (see section 4.3)

 Cg = Generators’ constraints (see section 4.4)

 Ctd = Transmission/Distribution constraints (see

section 4.5)

 Cd = Demand constraints (see section 4.6)

 Cb = Batteries’ constraints (see section 4.7.3)

4.3 Aggregators

Power Aggregators consolidate power flows

originated from m different sources, and redistribute

the same flows into n different destinations. We

assume no operational costs to be incurred with

power aggregators.

The main constraint for each Aggregator is given by:

Ca:

∑





,





∑





,

∈

∀



,

(3)

4.4 Generators

We assume only output flows from the Power

Generators (in the simplified case of only

combustible fuel generators). The cost of operating

each power generator is given by the fuel cost

(Dollars per BTU), the generator efficiency (BTU per

kWh), and the amount of output flow during the given

time interval:

GenCost[,t] = fPR[,t] * gEff [] * kw[f,

t] * IntervalLength

( ∀, ,















(4)

Total operating cost for all generators across the

whole time horizon is given by the sum of GenCost

across Generator Ids and time intervals t, i.e.

gC =

∑

, 

,

(5)

he only constraint for the output flow is given by

the generator’s maximal capacity:

Cg: kw[f,t]  gCap[]

∀, ,











(6)

4.5 Transmission/Distribution

The total cost associated with

transmission/distribution is given by the sum of the

known maintenance costs for each distribution station

through the time horizon, i.e.

tC =

∑





(7)

A fixed loss ratio is assumed to be known for each

transmission/distribution station. Therefore, it carries

a constraint of a given relationship between output

and input flows based on the loss ratio:

: kw [f

, t] = (1.0 - LR[]) * kw[f

,t]

(∀  ,   ,



1 









2

(8)

A second constraint is given by the maximal

transmission capacity for the station:

kw [f,t]  tCap[]

(∀  ,   ,











(9)

4.6 Demand

Given our assumption that all end demand is satisfied,

and only input flows of electric power are applicable,

the main constraint is that the sum of input flows

equals total demand for any end demand point for any

time interval t:

Cd: kw[f,t] = dF[,t]

(∀,,











(10)

For the same reason, revenue from end demand is

not considered in the cost / Revenue optimization (as

it is unchanged for a given demand load).

4.7 Energy Storage / Batteries

4.7.1 Batteries Cost

Cost of operating each battery for any time interval is

given by adding the maintenance cost for the battery,

and its depreciation cost. The depreciation is given by

the cost of battery replacement (NBC), the

cumulative charge and discharge at the end of the

period (cCD) and a known battery lifecycle parameter

(BLC):

bDep[] =

 ∗   1



(∀  ,   

(11)

The accumulated amount (absolute value) that

charges and discharges through a battery at the end of

each time interval (t+1), is given by:

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cCD[,t+1] = cCD[,t] + (kw[f1,t] + kw[f2,t]) *

IntervalLength

(∀, ,



1









2







(12)

where

cCD[][0] = 0 (13)

For the overall Battery Costs:

batCost[] = BMC[] + bDep[] (14)

bC =

∑



∈

(15)

4.7.2 Batteries/ Market Revenue

If a battery is committed to a market for a given time

interval t, additional revenue is generated, given by

the price per capacity for that market and the

committed capacity for the time interval (cC):

ActualMarketRev [,  ][t] =

ppc[][t] * cC[][t]

(16)

In this model, for sake of simplicity, the capacity

is treated as constant over the time horizon. Note that

during the time intervals where the battery is

committed to a market, the net flow of energy is zero,

i.e. the energy at the end of the period is equal to that

at the beginning of the same period.

The total market revenue (mR) is given by:

mR =

∑



,

(17)

4.7.3 Batteries/ Market Constraints

At any time interval, as the following battery states

are mutually exclusive:

 Charged – only input flows going into the

battery.

 Discharged – only output flows going to

subsequent components in the network.

 Committed to a market (i.e. using existing

unused capacity at any time interval to sell it to

an external market and provide revenue).

Additionally, any battery can be committed to no

more than one market at any given time interval.

This translates into the following constraints,

(∀, , 1







,2







 :

Bc1: cFL[][t] + dFL[][t] +

∑

2, 



1

(18)

Bc2: cFL[][t] = 1 iff kw[f1,])> 0

(0 otherwise)

(19)

Bc3: dFL[][t] = 1 iff kw[f2,] > 0

(0 otherwise)

(20)

Regarding the amount of energy stored in the

battery at any point in time, it starts with a given

amount, ends the time horizon with the same amount,

and oscillates throughout the time horizon based on

charges and discharges of the battery:

Bc4: bE[][1] = bE[



][  1 ] = BIE[] (21)

bE[][1] = bE[][ ] + kw[f1,] – kw[f2,])

* IntervalLength

(22)

5 IMPLEMENTATION AS MILP

AND CASE STUDY

A simple version of this model was developed using

IBM OPL CPLEX Studio.

We proposed different scenarios to provide

insights into the model, and to correspond to the

intuition of what to expect from its behavior for

different combinations of components ads their

characteristics. We also followed a given sequence of

key steps that constitute the methodology: First, we

depict each scenario as the topological representation,

as described in section 3. Next, we capture each of the

component characteristics into the variables defined

by the HRES optimization framework. Lastly, we

implement the MILP problem solution, by translating

these variables into IBM OPL CPLEX Studio, and

running the solver, to derive the solutions.

We examined scenarios in which the different

parameters combinations drive distinct decision

variables for the time horizon. As explained in prior

section, we are examining a 24 hour time horizon,

with a time unit of one hour. For each hourly interval,

in essence, we are determining what would be the

optimal value for power flows, battery states,

commitments and costs, for the full 24-hour time

frame. On real life utilization scenario, two possible

operation modes could be considered: in the first, a

planning engine would run based on the expected

demand for the upcoming day, and after execution,

the planning engine plans the subsequent day

operation; another option, would be to re-evaluate

dynamically the planning within a rolling time

horizon, as every hour we could look at actual values,

as well as adjustments on demand for upcoming 24

hours.

With these insights in mind, we proceeded to scale

up the model, to reflect the topology depicted in

Figure 2, and built (again recurring to synthetic data),

to create the four scenarios depicted below.

 Scenario 1: Generation and transmission

capacity can satisfy the demand.

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115

 Model recommendation: not using batteries

in operation, and always committing them to

market.

 Scenario 2: For some hours in the time horizon,

the fuel cost is very high.

 Model recommendation: discharging

batteries at that time.

 Scenario 3: The generators capacity cannot

satisfy some peak demand (for some hours of

operation).

 Model recommendation: using batteries for

these periods.

 Scenario 4: The transmission capacity is limited,

so that it is not sufficient during some hours of

peak demand.

 Model recommendation: using the batteries

downstream (at the distribution areas), to

offset lack of power from upstream.

6 CONCLUSIONS AND FUTURE

DIRECTIONS

In this work, we demonstrated an approach for

optimizing the operations of components of an

electric power network, including power generation,

transmission/distribution, power storage, energy

markets, and end customer demand (residential and

commercial). A prototype was developed using IBM

OPL CPLEX Studio, to make recommendations for

operating the network, while minimizing revenue-

adjusted overall costs for a given time horizon. A

simple topology was created, and different scenarios

were examined to assess the basic behavior of the

model, in common situations, based on realistic

synthetic data. The initial results demonstrate the

validity of the approach, and provide some promising

directions for future development, including

operations optimization, investment planning /

policy, and the technology aspects of the solution.

Regarding operations optimization, the model can

be refined in several ways: first, by introducing

energy generation through wind and solar power, as

alternate source to the fuel based generators; second,

by incorporating stochasticity in demand (and

possibly supply too, especially with renewable

sources); Third, by introducing real data.

In the realm of long term planning, the framework

should be expanded, to include infrastructure/ capital

investment recommendations to achieve long term

goals. This process would possibly involve multiple

stakeholders / decision-makers, in the public and

private sectors, which could also drive policy

decisions that address multiple goals (including

environmental impact, regional employment, system

reliability, etc.). The model would evaluate the

effects of different policies (e.g. tax incentives,

emissions regulations), as well as the prioritization of

investment in network assets (such as new batteries,

new distribution lines, etc.).

Finally, from a technology perspective, we could

develop more flexible tools, to allow a more intuitive

and reusable model, as well as incorporating other

features such as learning and prediction mechanisms.

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