Modelling and Management Approaches for Smart Grids

8/12/2019 Modelling and Management Approaches for Smart Grids

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Research Attachment Two: Modelling andManagement Approaches for Smart Grids

Farshad RassaeiDepartment of Electrical and Computer Engineering

National University of Singapore

Abstract

In this report, the fundamental concepts of modelling and management

approaches for smart p ower grids are explained. The generic model of the

optimization problems is presented as well as the mathematical frameworks

and strategies to deal with them. Furthermore, examples are provided to

show how these methods can be applied to manage the power grids under

their specific characteristics and constraints.

1 Introduction

The main objective for the transition towards the smart grids is undoubtedlyto increase the controllability of the behaviour of the electrical power grid. Bybeing able to manage the power grid more efficiently, better performances can beachieved from the existing sources and infrastructures in terms of cost, qualityand capacity which in turn can reduce extra unnecessary investments in powergeneration and delivery [17].

The electric power grid has conventionally been built using a supply followsdemand strategy, where the consumer has the right to demand any amount ofelectricity and pays a constant, pre-specified, and infrequently updated or reportedprice per kilowatt-hour of electricity consumed.

As long as the peak electricity demand does not exceed the total capacity of dis-patchable electricity suppliers, it is possible to generate more electricity to adjustsupply to the real-time demand. Until large-scale electricity storage becomes morecost-effective, electricity generation capacity must always exceed peak electricity

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R.A. Two: Modelling and Management Approaches for Smart Grids

demand to ensure the reliability of the service. However, managing electricity sup-ply and demand in this way leads to inefficient use of fuel supplies, extra systemcapacity that is only used to meet peak loads, consumers without any incentive to

conserve or plan energy usage, and an electric power system vulnerable to failureduring adverse weather events, peak-use periods, and fuel supply disruptions [2].

Managing storage devices itself, has attracted lots of research efforts in thesmart grids literature e.g., [3], [7], and [16]. The researchers have tried to findappropriate answer to the following questions regarding storage devices: How muchcan storage help reduce the need for conventional generation? How much can ithelp improve reliability? How much storage is needed to reach these benefits?What are the optimal control strategies that achieve these limits? Of course,appropriate answers to the mentioned questions can yield to better architectures

for the smart grids as well as in operating them more efficiently and more reliably[16].

With upgrades and improvements likely coming to the electric power grid in theform of the so-called smart grids, there is a near certainty that demand-sensitivepricing of electricity will soon become the standard pricing mechanism or tariff.As other service industries like the airline industry have found, demand-sensitivepricing is a proven method to encourage a demand follows supply strategy,which allows the service systems infrastructure to be used more efficiently withoutrequiring to incur exorbitant investments to build more infrastructure just to meet

the peak demands [9].

By going towards the smart grids, the utility will have more options to managethe grid rather than just the generation adjustments. The first option is storagedevices by which the grid operator can store the extra energy for further con-sumptions during peak demand periods. The second main option is demand sidemanagement (DSM) which lets the consumer side to participate actively in thegrid management [4], [18]. There are delay-tolerant devices as well as devices thatcan provide some levels of flexibility to be operated. Therefore, the main problemis how to manage these devices to achieve better performances [16].

The electrical grid power optimization is to find the right balance between relia-bility, availability, efficiency, comfort, and cost while satisfying the grids physicalconstraints (like transmission and distribution capacity). This is done by theproper use of the control variables available to the grid operator. Meanwhile,the probabilistic nature of generation and consumption (e.g., PEVs) needs to beconsidered. Thus, the optimization problem in general gets a stochastic multi

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variable multi objective multi constraint form. In this report, some math-ematical preliminaries about this problem is presented and a general form of thegrid modelling is provided.

Outline The following sections of this report cover a brief literature review tothe modelling and management approaches for the smart grids. In section 2, ageneral hierarchical agent-based model appropriate for the management purposesis described. In section 3, the concept of multi objective optimization (MOO)is briefly introduced. In section 4, the fundamentals of stochastic dynamic pro-gramming (SDP) is explained. In section 5, an example of a small scale powermanagement system is presented to show the application of MOO and SDP. Fi-nally, conclusion and further research work conclude this report in section 6.

2 Hierarchical Modelling of the Grid

In this section a general hierarchical model for smart power grids is provided.The main advantage of the hierarchical model is of course its scalability [13]. Inthis model, different levels with different scopes of responsibility are defined. Ineach level some agents are in charge of managing the devices or the agents thatare connected to them from the lower level. In this case, lower agents send their

power profiles to the agent in the upper level. This agent in turn aggregates allthe power profiles into one power profile to be sent to the upper level. This actionis repeated through different levels up to the uppermost agent. The position ofthis agent determines the scale of the management system (e.g., within a house, adistrict or a city)[6].

By receiving all the power profiles describing total power request in the wholegrid versus time in an aggregated form, the uppermost agent begins to managethe power allocation to its connected agents based on its available energy sourcesand the reported flexibilities that different connected agents sent previously. Af-terwards, it sends out the control signals to the agents in the lower level [13]. Thiscontrol signal can be just a pricing signal [18] or a steering signal carrying someturn on/off information. Figure 1 demonstrates this model.

Likewise, each agent in the lower level in turn can manage its own connectedagents to achieve the best possible service it can offer based on the steering signalreceived from the upper levels connected agent, the available power profiles of thelower level agents, and its own sources e.g., local generators or storage devices [11].

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Figure 1: Hierarchical Modelling of the Grid.

3 Multi Objective Optimization

Multi Objective Optimization (also known as multi objective programming,multi criteria optimization, and Pareto optimization) is the process of simultane-

ously optimizing two or more conflicting objectives subject to certain constraints[5]. As discussed before, for smart grids, a general optimization problem is re-quired to consider reliability, cost, comfort, and sustainability ob jectives together.Generally, these objectives are conflicting and even opposite. The optimal pointwould be of course a trade-off among all the defined objectives and can be adjustedbased on some predefined preferences.

The general mathematical form for multi objective optimization problems canbe formulated as:

x

= arg minx [1(x), 2(x),...,n(x)]s.t.

g(x) 0h(x) = 0xl x xu

(1)

The solution is a set of so-called Pareto points. A Pareto set or Pareto front is theset of choices that are Pareto efficient. By restricting attention to the set of choices

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that are Pareto efficient, a designer can make trade-offs within this set, rather thanconsidering the full range of every parameter. Pareto efficient or Pareto optimumis, simply speaking, an allocation for which there are no possible alternative alloca-tions whose realization would cause every individual to gain. Thus an alternativeallocation is considered to be a Pareto improvement only if the alternative allo-cation is strictly preferred by all individuals [10]. Figure 2 demonstrates a simpleexample of a Pareto frontier.

Figure 2: Example of a Pareto frontier (Source: Wikipedia).

As can be observed in figure 2, The boxed points represent feasible choices, andsmaller values are preferred to larger ones. Point C is not on the Pareto frontiersimply because it is dominated by both point A and point B. Points A and B arenot strictly dominated by any other, and hence do lie on the frontier. Algorithmsfor computing the Pareto frontier of a finite set of alternatives have been studiedin computer science, sometimes referred to as the maximum vector problem or theskyline query [15].

There is a number of solution methods for multi objective optimization problems.However, an intuitive simple method is to construct a single aggregate objectivefunction (AOF) from all of the objectives. This is usually done by making aweighted linear sum of the objectives. Also, there are other possible methodse.g., Successive Pareto Optimization (SPO), Multi-objective Optimization usingEvolutionary Algorithms (MOEA), Reactive Search Optimization, etc., which canlead to better performances. But, in general, they are much more complicated[10].

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4 Stochastic Dynamic Programming

In Stochastic Dynamic Programming (SDP), the objective functions and the

constraints depend on the optimization variables x and some random variables. In general, this can model parameters variations and uncertainties (likegeneration availability of renewable energy sources) as well as randomness in mea-surements, implementation, and operation [14].

The exact value of some variables are not known apriori to use regular determin-istic optimization approaches. Instead, some statistical information are available.In this case, the goal is to find the optimization variable x such that constraintsare satisfied on average or with high probability (defined by the application). Like-wise, the objective itself gets minimized on average or with high probability [1],

[14].

In particular, for the electrical grid, the constraints need to be met with highenough probability to avoid instability and failures and an on-average strategymay not be appropriate. But, for the objective the on-average method can beconsidered. This matter will be discussed further in section 3.

The basic stochastic programming problem can be stated as follows [14]:

minimizex

F0(x) = E{f0(x, )}

subject to Fi(x) = E{fi(x, )} 0 i= 1, 2,...,m (2)

or it can be expressed as:

minimizex

F0(x) = E{f0(x, )}

subjectto Fi(x) =prob{fi(x, ) 0} 1 i= 1, 2,...,m(3)

where is some factor of tolerance.

Generally, in dynamic programming there are five main concepts: decisions,states, stages, stage-to-stage state transition rules and rules for following an op-

timal policy [12]. In the smart grid context, decisions are the control optionsfor the operator (e.g., turning on/off, charging/discharging signals, pricing, etc).States refer to the current conditions on the grid like current price of electricity,current weather conditions, current storage capacity and so on. Each stage is seenas a decision-making point in time. The time duration between successive stageswill vary by location depending on the frequency of information updates availablefor the states of the system or by the preference of the operator. Stage-to-stage

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state transition rules are used in the dynamic programming model to calculate theprobability of a state variable attaining a certain value at the next stage based onthe state of the system at the current stage and the immediate decision(s) imple-mented at the current stage. These rules are mathematical, probabilistic depictionsof weather conditions, electricity price, and other conditions on the electric grid.

The rule for following an optimal policy guides the dynamic programming al-gorithms decision-making process by balancing the comfort preferences, availablesources, and cost preferences both now and in the future via the optimal sequenceof use, store and sell control decisions given the current and forecasted states ofthe system.

The dynamic program is solved via the principle of optimality by working back-wards from the terminal stage of the process to generate optimal decision rulesfor each preceding stage, culminating with the optimal decision for the currentmoment in time.

Taking all forecasts of future state values into consideration would require con-sidering an infinite number of stages. These challenges underlie many dynamicprogramming models, and the challenges as a whole are often referred to as thecurse of dimensionality. To avoid this to happen, usually an approach called Ap-proximate Stochastic Dynamic Programming is used. In this approach only somevalues out of the probability distributions are used to present them and hence the

number of possible states that the algorithm may face is reduced [14]

5 The Energy Box

In this section, a simple example of stochastic dynamic multi objective program-ming is presented. In this so-called Energy Box[8], the purpose is to managehome scale power consumption and interactions with the electrical grid. But, ac-cording to the hierarchical model presented in section 2, it is scalable to otherlevels of the grid management as well. The energy box, here, is a software en-ergy management system that can coordinate the management of electricity use,storage and selling back to the grid for the typical small consumer of electricity 3.

The use, store and sell decisions chosen by this energy box will ultimately de-pend on the current and forecasted states of the system, which for this modelincludes the home, the electric grid and the weather. At the home, it is assumedthat a number of sensors, appliances and devices will be able to communicate in-formation about the state of the home to this energy box. A few examples of the

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information that might be needed to be collected and sent to the energy box arethe occupancy patterns, the temperature and its variations inside the house, theamount of electricity currently in a storage device, whether or not a plug-in vehicleis plugged-in at the time, and whether an appliance such as the dishwasher or thelaundry machine is loaded and ready to run.

On the other hand, for the electric grid, information may include the currentprice and forecasted prices of the electricity, the portfolio of generation sourcesproducing electricity. Last but not the least is the weather, from which tempera-ture, wind speed and sunlight intensity are a few examples of the information thatwould be collected when considering the thermal comfort of the homes occupants,the amount of electricity available from wind (via the utility and/or a local smallwind turbine), and the amount of electricity available from the sun (again, via the

utility and/or solar panels on the roof).

This energy box model here is limited to three devices at the home for thesake of simplicity: an air conditioner with a controllable thermostat, an always-connected battery array, and a wind turbine. The wind turbine is presumed togenerate electricity whenever the wind is blowing with sufficient speed, so thereis no decision to be made regarding the wind turbine. Therefore, the decisionsavailable to the dynamic programming model are: setting the set point of thethermostat, charging or discharging the battery array, and selling or not sellingelectricity back to the grid. Furthermore, the planning horizon is considered to be

a day divided into 24 one-hour stages.

A set of seven states will be of interest to the model: the indoor temperatureof the home, the amount of electricity stored in the battery array, the amount ofuncontrolled electricity being used in the home, the amount of power generatedby the wind turbine, the temperature outside the home, the wind speed, and theprice of electricity from the electric grid. For this model, the interval betweenstages is set at one hour. Therefore, the stage-to-stage state transition rules willreflect hourly changes in the state information.

In this example, two objectives are defined for the problem: cost and comfort.Here, comfort is defined to maintain the temperature in the range of the desiredtemperatures for the home occupants as often as possible and cost would be mini-mized if the electricity is purchased whenever the price is low with a total minimumand is sold whenever the price is high with a total maximum. Thus, the problemcan be expressed as follows [8]:

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Figure 3: The Energy Box.

maximize{d0,d1,...,d24}

24

i=0

(E[comforti .ucomforti (si, di) +

costi .u

costi (si, di)]) (4)

where, the expectation is on all the possible states during the whole planning hori-zon and the optimization problem is to find appropriate decisions for the defined

24 stages {d0, d1,...,d24} such that the objective which in turn is expressed as aweighted summation of two objectives (ucomforti and u

costi (si, di)) is maximized on

average.

This problem can be solved after defining the appropriate stage-to-stage statetransition rules by starting the dynamic programming algorithm from the 24th

stage and work the way backwards for all possible state combinations at that 24 th

hour, the combination of decisions that can maximize:

E[comfort24

.ucomfort24

(s24, d24) +cost24

.ucost24

(s24, d24)] (5)

is stored as the optimal decision combination for that particular stage. Oncethe optimal decisions are established for stage 24, the process is repeated for stage23 recursively. This process is repeated for each stage until the optimal decisionfor the current moment in time is determined for all state combinations. For thisspecific model, the final results are given for fourteen different scenarios in figure4 [8].

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Figure 4: The Energy Box performance for different scenarios [8].

As can be observed in figure 4, for the fourteenth scenario, in which the man-agement flexibility is maximum the total cost can be reduced almost close to fiftypercent while preserving the comfort which is defined, here, to keep the indoortemperature in the range of 74-76 degrees Fahrenheit as much often as possible.

6 Conclusions and Future Work

6.1 Conclusion

In this report, the modelling and management approaches for the smart powergrids were addressed. A general hierarchical agent-based model for managementpurposes was described. In this model, grid management is done through differentlevels. Additionally, by introducing the general type of grid optimization prob-lems as a stochastic dynamic multi objective problem, the basic concepts of multiobjective optimization problems were explained as well as the basics of stochastic

dynamic programming. Afterwards, to show an application of these methods inpower management the concept of Energy Box introduced whose purpose is tomanage the electrical power at a home scale.

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Modelling and Management Approaches for Smart Grids

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