Multi-index and self-approximate-optimal operation for a smart electrical power grid

Multi-index andself-approximate-optimaloperation for a smartelectrical power grid

G. HeY. SunQ. LuT. Li

H. LvW. Yin

J. Dong

An instrumented, intelligent electrical power grid, or smart grid, isunder research and is being preliminarily constructed in many partsof the world to deal with new challenges to modern power systemsbrought on by pressures on environment and resources. In this paper,a smart grid with the ability of multi-index self-approximate-optimaloperation is considered the most distinctive difference between a smartgrid and a traditional power grid. Multi-index is the index set thatconsists of a series of key indices for the grid operating chain, includinggeneration, transmission, distribution, consumption, and dispatching.Self-approximate-optimal refers to the process by which the electricitygrid arrives at a satisfactory operation point from an unsatisfactorypoint by its automated closed-loop control and regulation. In this paper,the general architecture and solution algorithm of multi-indexself-approximate-optimal operation are proposed and developed.Furthermore, two realistic and promising practices in China aredescribed to illustrate how a smart grid can be achieved under theguidance of the proposed multi-index self-approximate-optimaloperation.

IntroductionIn order to respond to energy and climate challenges, aninstrumented, intelligent smart electrical power grid has beenproposed, and its related research and construction are inprogress all over the world [1–14]. IBM has beencontributing to the smart grid since 2004 when it proposed anIntelligent Utility Network [10, 14]. In China, TsinghuaUniversity proposed the concept of a Bdigital power system[

[12] in 1999 and initiated research work on a futureelectricity grid. In 2005, State Grid Corporation of China, thelargest utility company in the world, started to study theframework for a digital electricity grid and digital substationsand began to construct demonstration projects. In the sameyear, Tsinghua University was entrusted by China SouthernPower Grid Corporation to carry out the research for a digitalChina Southern Power Grid [13]. In 2009, State GridCorporation of China proposed its aggressive plan to build aStrong Smart Grid.Undoubtedly, the smart grid has become the direction for

future electricity grids. However, what does smart grid

exactly mean? What are the essential differences between asmart grid and a traditional electricity grid? The smart gridshould be evaluated with systematic indices so that it can beconveniently handled. In the United States, researchersstudying smart grids have decided this through a series ofregional conferences that took place from 2005 to 2010,together with some regional demonstrations such as thePacific Northwest GridWise** Project carried out byIBM Research. Through these efforts, researchers have notonly defined the core values of the U.S. smart grid that theyexpect but also determined how to evaluate the core valueswith corresponding indices. For instance, grid reliability canbe evaluated by the average outage time, the outagefrequency, and the instant outage and power supply quality.Although the conditions of each country could be different,the vision of a smart grid can always be expressed by corevalues, and each value can be evaluated with a series ofindices.In this paper, we synthesize the indices that a smart grid

needs for operation and propose the multi-index andself-approximate-optimal operation architecture for asmart grid. First, we define the multi-index and

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Digital Object Identifier: 10.1147/JRD.2010.2085461

G. HE ET AL. 2 : 1IBM J. RES. & DEV. VOL. 54 NO. 6 PAPER 2 NOVEMBER/DECEMBER 2010

0018-8646/10/$5.00 B 2010 IBM

self-approximate-optimal operation architecture and explainit in detail based on the analysis and synthesis of theexploration and practices on smart grids in the United Statesand Europe. Second, we show that multi-index andself-approximate-optimal operation could be achieved withtwo realistic and promising practices in China. Finally,conclusions are drawn, and future research is proposed.

Multi-index self-approximate-optimal operationThe implementation of smart grids may involve newtechnologies, such as renewable energy generation, energystorage, superconducting transmission, ultrahigh-voltagetransmission, intelligent metering, advanced sensing,communication, and information technology. There are manyindices to be optimized. However, there is only theoreticalmeaning in performing an exact global optimization, whereasin engineering practice, it may be impossible andunnecessary to achieve the exact global optimal operationpoint. Moreover, the electricity grid needs to have the abilityto return to an approximate-optimal status from eventssuch as disturbances through automated closed-loop controland regulation.Based on this, we define a smart grid as an electricity grid

that has the ability of multi-index self-approximate-optimaloperation. In this section, we first present the overallarchitecture. Then, we explain multi-index andself-approximate-optimal. Finally, the goal of multi-indexself-approximate-optimal operation is summarized as anobject function, and the solving algorithm is discussed.

ArchitectureIn Figure 1, each circle represents one of the three categoriesof indices for smart gird operation: stability, reliability, andeconomy. More circles can be drawn if more indices areneeded or a new category can be created for several detailedindices. In fact, there are thousands of indices for gridoperation; thus, there could be thousands of such circles.The BMulti-index[ section describes the most importantindices.Outside a circle means the corresponding index is not

acceptable, but inside means the index is satisfied and theoptimal value must fall into one location there. Thecentral overlap region means all indices are satisfied, andtherefore, this is where a smart grid should operate.A global optimal operation point must be within thisoverlap region, but it is practically impossible to find thissingle point due to the problem dimension, that is, thousands,as indicated above. Moreover, it is unnecessary andimpossible to adjust the system in the optimal state becausethe power system is a complex and large-scale dynamicsystem in which load and operating conditions are changingall the time. It will also influence the service life andeconomic efficiency of the equipment if the adjustment is toofrequent.

As a result, the system can be considered to be operating ina satisfactory state if its state lies in a sufficiently smallneighborhood near the optimal state, that is, within theoverlap region, which is hereafter defined as themultiobjective approximate-optimal operation region(MOOR). In the MOOR, all the indices should be in theacceptable region. Each index has its own range. Theabnormal condition occurs when the index is out of its range.For example, for one node, its voltage magnitude should bekept between 0.9 and 1.1 p.u. Whenever the voltagemagnitude becomes 0.78, an abnormal situation is identified.If one or more indices are not within the MOOR, the controlsystem will act to eliminate the unsatisfying states so that theoperation point of the system returns to the MOOR. As isfurther explained, self-approximate-optimal means the smartgrid can respond to events, including disturbances thathappened in the grid, and return to the MOOR.In order to make this architecture better understood, we

can use a common concept in the smart grid, namely,self-healing [15–20]. As pointed out in [15], BSelf-healingstrategies are control options that are initiated to steer thepower system to a more secure, less vulnerable, operatingcondition.[ This provides us with the following information:First, self-healing focuses on the operating condition of thepower system, which is the focus of this paper; second, theoperating condition should be secure and less vulnerable,which corresponds to Bmulti-index;[ third, Bmore[ meansBapproximate-optimal,[ that is, not to guarantee the globaloptimal; and fourth, Bcontrol options[ and Bsteer[ matchthe Bself[ term used in this paper to represent automated

Figure 1

Architecture of smart grid operation.

2 : 2 G. HE ET AL. IBM J. RES. & DEV. VOL. 54 NO. 6 PAPER 2 NOVEMBER/DECEMBER 2010

closed-loop control. Therefore, self-healing can beconsidered a subproblem of multi-indexself-approximate-optimal operation. Self-healing uses thestability and reliability indices in Figure 1, whereasmulti-index self-approximate-optimal operation hasbroader indices, as provided in Tables 1–3 and in theexamples in the section BPractices toward multi-indexself-approximate-optimal operation for smart grid.[

Multi-indexMulti-index is the index set that consists of a series of keyindices. Mathematically, it can also be called multiobjectiveoptimization (or programming), multicriteria, ormultiattribute optimization, which are processes ofsimultaneously optimizing two or more conflicting objectivessubject to certain constraints [21, 22]. One way to solve thisproblem is to assign corresponding weights to the multiple

Table 1 Typical indices of generation.

Table 2 Typical indices of transmission and distribution.

Table 3 Typical indices of consumption.


objectives, which change the multiobjectives to a singleobjective. Another way is to obtain an optimal spacefor the solution, termed pareto-optimal, in which none ofthe pareto-optimal solutions dominates anotherone [23].In the context of smart grid, the index set may vary for

different countries and regions. Therefore, the first step is todefine the multi-index set according to the nationalconditions and the development level of the electricity grid ofthe corresponding country and region. Tables 1–3 showtypical indices for China, covering the whole energy chain,including generation, transmission, distribution, andconsumption. These indices were obtained throughdiscussion with electric power companies, generationcompanies, and users, as well as international and Chinesenational standards [24–31]. The importance level andcomputational complexity are also provided in these tables.The importance level and computational complexity arenumbered from 1 to 3 and work well in practice, aspresented in the section BPractices toward multi-indexself-approximate-optimal operation for smart grid.[ Werecommend adjusting the importance level andcomputational complexity according to the grid operationenvironment; for example, for a control center equipped with

high-performance computers, the computational complexitydifference can be lowered according to the computationalspeed.

Self-approximate-optimalSelf-approximate-optimal is the process by which a certainobjective arrives at a satisfactory level from an unsatisfactorylevel through automated closed-loop control and regulation.The self-approximate-optimization of the smart grid meansthat the electricity grid can obtain exact knowledge of its ownstate based on all-around self-checking and informationsharing with the support of a well-organized infrastructure,including primary facilities and acquisition, communication,and IT platforms, and that it can make decisions throughintelligent analytics and perform comprehensive regulationand control of itself with the help of the well-organizedinfrastructure in order to make the state of the electricity gridapproach the optimal state.The two key problems of control and regulation of

multi-index self-approximate-optimal operation of anelectricity grid are how to identify the occurrence of abnormalconditions and how to perform control and regulation.To address the first problem, the current operation status

and forecasted operation trajectory are checked with the

Figure 2

Operation state and forecasted trajectory of the MOOR.


MOOR defined in the beginning of this section (Figure 2). Iftheir practical operation states are far away from theirrespective margin of the MOOR, there is no need to considerthem. If the practical operation states are near the margins forsome certain objectives, there are two situations. If the anglebetween the forecasted operation trajectory of a certainobjective and the normal direction of the margin is smallerthan 90 degrees, it will be treated as a constraint. Otherwise,it will not be considered.In order to realize automatic regulation and control as

addressed in the second problem, events should first beclassified into different types. An optimal power flowmodel can then be built aiming at different types ofevents in order to obtain the regulation measure with thelowest control cost. The control measure is then sent to thecorresponding equipment to be implemented so that theabnormal conditions can be eliminated and the automaticregulation of the system operating conditions can befulfilled.As for the classification of events, we can define the

abnormal conditions that will influence the secure, highlyqualified, and economic operation as security events, qualityevents, and economic events. Security events includevoltage security events, active power security events,spinning reserve insufficiency events, and so on. Qualityevents include voltage quality events, frequency qualityevents, and so on. It should be noted that theclassification of events is closely related to the multi-indexset that we expect the electricity grid can achieve and thefactors that can influence the operation of an electricity grid.The systems that deal with these two problems can becalled the event analysis system and the event handlingsystem, respectively. In the practical operation of thesystem, the event analysis system continuously monitors theoperation of the electricity grid, and once an eventoccurs, the event handling system is driven to eliminate theevent and make the system return to the operating state.If there is no event, the electricity grid will be in theMOOR. With the event-driven principle, which can bedescribed as Bevent triggers control[ and Bcontrol eliminatesevent,[ multi-index self-approximate-optimal operation canbe achieved. The power system hybrid control theory,which has this principle as the core, has been proposed[32, 33].

Synthesis of optimization modelWe built the mathematical model with synthesis of themulti-index and self-approximate-optimal principlesdiscussed above to give guidance for how to achievemulti-index self-approximate-optimal operation of smart gridusing available technologies. The objective is that all of theindices stay in acceptable ranges, which form the MOOR. Ifsome index is out of range, that is, an abnormal conditionappears, the model provides a solution to eliminate the

abnormal condition. The optimization model can beformulated as follows:

minx;y

�J ðx; yÞ ¼Xmi¼1

!i�Jiðx; yÞ

with �Ji ¼Ji � J i; when Ji 9 J i

0; when J i � Ji �i

J i � Ji; when Ji G J i

8><>:

s.t. _x ¼ f ðx; yÞ;gðx; yÞ ¼ 0;

hðx; yÞ � 0:

The following list is a description of the variables:

x State variable vector.

y Network variable vector.

�Ji Deviation of the ith index.

!i ¼ ðFi=FmaxÞ=ðSi=SmaxÞ Weight, where Fi is the

importance level of the

ith index and Fmax is the

maximum of all Fi, Si is the

computational complexity of

the ith index, and Smax is

the maximum of all Si.

m Overall number of indices.

Ji Value of the ith index.

J i Upper bound of Ji.

J i Lower bound of Ji.

_x ¼ f ðx; yÞ Equality constraints of the

differential equation.

gðx; yÞ ¼ 0 Equality constraints of the

algebraic equation.

hðx; yÞ � 0 Inequality constraint of the

algebraic equation.

The procedure to solve the aforementioned optimal modelof multi-index self-approximate-optimal operation isillustrated in Figure 3, where the detailed description isgiven here.

Step 1: Obtain all of the variables used in the model,including x, y, J i, and J i.

Step 2: Calculate all of the indices J .Step 3: Check the indices. If an index is out of range,

i.e., �Ji 9 0, go to Step 4. Otherwise, return toStep 1.

Step 4: Analyze the indices that are out of range and groupthem according to their relationship. A group maycontain one or more indices that are coupledwith each other. If an index has no relationship(i.e., they are decoupled from others), then it formsa group with only one index. Each group nowforms a single- or multi-index problem and can be


separately solved. Then, for each multi-indexproblem, use the above optimization model andconvert it into a single-index problem using theweights. Notice that now the dimension of theproblem is greatly reduced as a result of thegrouping.

Step 5: Existing methods can be used to solve single-indexproblems. Different methods might be suitable fordifferent kinds of indices. The results form thecontrol strategy that is needed to eliminate theabnormal conditions occurring in the system.

Step 6: Perform the control strategy such as increasing theactive power of generators, shedding load, andadjusting excitation systems. Then, return toStep 1.

Different indices have different periods; thus, they belongto different timeframe problems. For example, an indexnamed voltage percent of pass could be obtained in seconds,whereas monthly voltage percent should be calculatedonce a month. Thus, different indices with differenttimeframes should be analyzed in different ways.

Practices toward multi-indexself-approximate-optimal operationfor smart gridIn this section, we first use a traditional power system case,i.e., voltage quality, to illustrate the optimal model and how

the solution flowchart introduced in the previous sectionworks. We also present the compatibility of multi-indexself-approximate-optimal operation to traditional powersystem issues. We present two realistic and promisingpractices in China that help the grid become smart with thegoal of multi-index self-approximate-optimal operation. Thefirst practice focuses on the production managementperspective. The Integrated Distribution Outage Planner(IDOP) is based on the closed-loop optimized productionmanagement to make the outage plan more secure, balanced,efficient, and economical. The second practice is theadvanced energy management system (AEMS) [33, 34],which improves the smartness of the grid from a dispatchingperspective and synthesizes the whole architecture of theproposed multi-index self-approximate-optimal operation.

Traditional power system issue: Voltage qualityTake voltage quality as an example to illustrate how to builda self-approximate-optimal model for a traditional powersystem. In the practical operations of the power system, thenodal voltage should be maintained between the upper boundand the lower bound to guarantee the voltage quality. Whena nodal voltage is out of range and lasts for some period,the electricity grid is considered to lie in an unsatisfactorystate and needs to be adjusted immediately. The objective isto keep the actual voltage of nodes between the upper boundand the lower bound.The optimization model of voltage quality can be

constructed as follows:

minP;Q

�V ðP;Q;V ; �Þ ¼Xnbusi¼1

!i�Vi þXnbusi¼1

!0i�ti

with �Vi ¼Vi � V i; when Vi 9 V i

0; when V i 9 Vi 9 V i

V i � Vi when Vi G V i

8><>:

�ti ¼Ti; when �Vi 9 0

0; when �Vi ¼ 0

�

s.t. Pi ¼ Vi

Xj2i

VjðGij cos �ij þ Bij sin �ijÞ;

i ¼ 1; 2; . . . ; nbus

Qi ¼ Vi

Xj2i

VjðGij sin �ij � Bij cos �ijÞ;

i ¼ 1; 2; . . . ; nbus:

The following list is a description of the variables:

P Real power.

Q Reactive power.

V Nodal voltage magnitude.

� Nodal voltage phase.

!i, !0i Weights of the voltage deviation and duration,

respectively, of the ith bus. In this case, we set

them to 1 to treat all buses equally.

Figure 3

Flowchart of multi-index and self-approximate-optimal operation.


Ti Duration of the ith bus whose voltage is out of

range.

Vi Voltage magnitude of the ith bus.

V i, V i Upper and lower bounds of the voltage magnitude

of the ith bus. Their typical values are 1.1 and

0.9 p.u., respectively.

Gij Real part of the element at row i and column j in

the admittance matrix.

Bij Imaginary part of the element at row i and

column j in the admittance matrix.

�ij Phase angle difference between node i and node j.

nbus Number of buses.

j 2 i Denote all the nodes that connect with node i.

Compared with the general model in the section BSynthesisof optimization model,[ power flow equations are the mainconstraints, and differential equations are neglected here.Thus, there is neither a state variable x nor the equalityconstraints of a differential equation. The network variablesare expressed as y ¼ ½PT ;QT ;VT ; �T �T . The index set is in

this case �J ¼ ½�VT ;�tT �T . The equality constraints ofalgebraic equations are now the power flow equations, andthere are no inequality constraints. This model can besuccessfully solved with the modern interior-point method[35], and the convergence and calculation speed can bothsatisfy the requirement for closed-loop automatic control.

Practice 1: IDOPIn 2009, IBM started the smart grid practice, i.e., the IDOP,in Shanghai Electric Power Company in order to improve itsproduction management performance and customerexperience. The multi-index and self-approximate-optimalconcept was successfully applied in the IDOP.Grid maintenance, upgrades, and new user integration are

very important daily work for electric power companies.Most of them require grid device interruptions, which aresometimes harmful to grid security and cause user outages.The challenge is how to arrange these outage tasks optimallyso that they can be finished on schedule with high girdsecurity and user satisfaction. However, outage tasks are

Figure 4

Interaction between outage tasks.


connected by the power grid and interact with each other. Forexample, in Figure 4, outage task Oi will cause theinterruption of switches 101, 102, and 103, whereas Oj hasthe outage scale of switches 103, 104, and 105. They havethe same element 103. Analytics and optimization tools canhelp improve operations by helping the utility developoptimized outage plans that will result in fewer duplicateoutages and workload imbalances, as well as improvedcoordination efficiency among the different organizationsrequired to implement the changes. IBM Research, workingclosely with Shanghai Electric Power Company, hasdeveloped an analytics and optimization solution to producereliable and efficient outage plans.Following the concept of multi-index and

self-approximate-optimal, we built the IDOP models here.Description of variables:

T Total number of outage time slots.

N Number of outage tasks.

S Number of switches in the power grid.

pt Price at the tth time slot.

xi0 Promoted outage time of the ith outage task.

xi Rescheduled/optimized outage time of the ith

outage task. It is a network variable.

c Extra unit charge of changing outage time.

ust Status of the sth switch at the tth time slot,

which is influenced by xi. It is a network

variable.

Pt Total outage load at the tth time slot; it is a

function of ust .

gt Grid structure at the tth time slot; it is a function

of ust.

Lt Grid loss at the tth time slot; it is a function

of ust .

G Set of radialized grid structures.

M Number of nodes in the power grid.

Qm Secure power flow range of the mth node.

qmt Power flow of the mth node at the tth time slot.

Vm Secure voltage range of mth node.

vmt Voltage of the mth node at the tth time slot.

rt Resource requirement at the tth time slot; it is a

function of xi.

R Resource limitation.

Objectives:

Minimize the duplicate outage rate J1: J1 can be simplycounted.Improve the workload balance:

J2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPTt¼1jrt � rj2

T � 1

vuuutþ 1

T

XTt¼1

maxf0; rt � rg;

where r ¼ ð1=TÞPT

t¼1 rt , and maxf0; rt � rg is theworkload penalty function.

Reduce the power sales loss:

J3 ¼XTt¼1

ptPt:

Reduce the grid loss:

J4 ¼XTt¼1

Lt:

Reduce the operation times of the switch:

J5 ¼XSs¼1

XTt¼1

ust � usðt�1Þ�� :

Reduce the changes of the proposed time:

J6 ¼ cXNi¼1jxi � xi0j:

Figure 5

Workload balance in the IDOP. (a) Unbalanced workload. (b) Balancedworkload in the MOOR.


Combined objective:

minx

�J ðx; uÞ ¼X6k¼1

!kJk ;

where !k is the weight of the kth index.

Constraints:

Security constraint: For 8t 2 ½1; T �, qmt 2 Qm.Power quality constraint: For 8t 2 ½1; T �, vmt 2 Vm.Grid structure constraint: For 8t 2 ½1;T �, gt 2 G,which means the distribution part of the grid isradicalized.

In the IDOP model, xi and ust can be regarded as networkvariables. We can see that the scale of this optimizationproblem is very large. In Shanghai Power, there are more

than 10 million variables. It is nearly impossible to find anoptimal solution in a reasonable time.We define several types of events, for example,

workload event, sales loss event, time changing event,security event, and grid structure event. Taking the objectiveof workload balance as an example, in Figures 5(a) and 5(b),the horizontal red line with the workload 16 is the alertline (border of the MOOR). In Figure 5(a), the workloadindex of day 12 exceeds the MOOR, and the IDOP monitorengine detects this abnormal event. Then, the IDOPoptimization engine starts to work to keep the workloadin the secure region, as shown in Figure 5(b). For otherobjectives, for example, duplicate outage rate and sales loss,we can also perform the optimization in the same wayas the workload balance. However, some objectives mayconflict with each other; we use the method described inthe section BSynthesis of optimization model[ to assignthe weight of each single objective. In this practice,

Figure 6

Framework of the AEMS.


duplicate outage rate and sales loss are the most importantobjectives because they have the largest weights.The IDOP has helped Shanghai Power greatly improve

performance. Since project completion in February 2010, therate of the equipment availability factor in Shanghai Powerhas increased to 99.99% (outage rate reduced), and plannedsuspended service of the power grid was reduced by5.24 hours. As a result, the company’s sale of electricityhas increased by 0.65%, which is approximately600 million kWh annual sales, or approximately $50 million(USD) annual revenue increase.

Practice 2: AEMSDue to the difficulty in guaranteeing secure, high-quality, andeconomic operation of the electricity grid simultaneously, thetraditional energy management system only analyzes theoperating status of the electricity grid. The operation modesstill need to be adjusted by dispatchers manually, whichcannot ensure that the electricity grid operates in secure,high-quality, and economic status. The possible misoperationof dispatchers can even cause potential problems in theelectricity grid.With a small investment in 2005, Shanghai Electric

Power Company initiated the construction of an AEMS inorder to obtain overall improvement of grid stability,reliability, and economy by introducing a new controlconcept with the help of Tsinghua University [33, 34]. TheAEMS is a multiobjective self-approximate-optimalclosed-loop control system that is based on the powersystem hybrid control theory and tries to realize the tripleoptimization objectives. The AEMS considers the security,economy, and quality of the power system. It consists ofautomatic generation control (AGC), automatic voltagecontrol, and automatic lower frequency oscillation control.The working process of the AEMS follows the flowchartillustrated in Figure 3.Based on the event-driven principle presented in the section

BSelf-approximate-optimal,[ the AEMS transforms themulti-index optimization problem into several single eventhandling problems and then tries to eliminate the events.After all of the events are eliminated, the system returns tonull-event operating status, and thus, the electricity grid willoperate in secure, high-quality, and economic status. Thetypes of events that the AEMS is able to handle can bedynamically adjusted with the development of the electricitygrid.The framework of the AEMS is illustrated in Figure 6.

The event analysis system performs real-time analysis of thecollected information and judges whether there are events. Ifthere are events, these events are sent to the event handlingsystem, which processes the events and producescorresponding control commands and operating orders andthen transfers them to the lower level AEMS or to thecomponents that are directly controlled by this system. In

normal conditions, the event analysis system and the eventhandling system can realize effective closed-loop control.However, to facilitate the dispatchers’ need of monitoringand controlling the state of the power system, the AEMSshould also be equipped with a decision-making supportsystem. This system is responsible for the followingfunctions:

1. Transferring the key operation state to the dispatchers invisual form to make the dispatchers have an intuitiveknowledge of the system operation state.

2. Making it convenient for the dispatchers to makedecisions in the operation and maintenance schedules.

Here is an example of how the AEMS deals with avoltage-stability unsatisfied event. Consider multiplecontingencies for tests as in Table 4, and following theconcept of multi-index and self-approximate-optimal, theoptimization model minimizes the cost of preventive andemergency control of power system voltage stability with Kcontingencies, i.e.,

min �C Up;U1e ; . . . ;UK

e

� �

¼ !p�CpðUpÞ þXK�¼1

!�e �C�e U�

e

� �

with �CpðUpÞ

¼CpðUpÞ � Cp; when CpðUpÞ 9 Cp

0; when Cp � CpðUpÞ � 0

Cp � CpðUpÞ; when CpðUpÞ G 0

8><>:

�C�e U�

e

� �

¼C�e U�

e

� �� C

�

e ; if C�e U�

e

� �9 C

�

e

0; if C�

e � C�e U�

e

� �� 0

C�e � C�

e U�e

� �; if C�

e U�e

� �G 0

8><>:

s.t. �� Up;U�e

� �

¼P�max Up;U

�e

� �� P� Up;U

�e

� �P�max Up;U

�e

� � � 100 � "

Pi ¼ Vi

Xj2i

VjðGij cos �ij þ Bij sin �ijÞ;

i ¼ 1; 2; . . . ; nbus

Qi ¼ Vi

Xj2i

VjðGij sin �ij � Bij cos �ijÞ;

i ¼ 1; 2; . . . ; nbus

Up � Up � Up

U�e � U�

e � U�e :

Description of variables:� �th contingency.

�� Voltage stability index of

contingency �; in this paper, we

chose load margin.


" Threshold value of the voltage

stability index, i.e., load margin.

�� Power injection vector of

contingency �.

k Increase direction vector of the

power injection vector.

T� Scalar parameterizing power

injection vector of contingency �.

X� State variables of contingency �

such as voltage magnitude and

angles.

Up ¼ ½�T ; cT �T Preventive control vector,

including transformer tap

variations and bus compensation

capacity variations.

�i Tap variation of the

ith transformer.

cj jth bus compensation capacity

variation.

Up, Up Minimum and maximum values of

preventive control, respectively.

U�e ¼ ½ðl�Þ

T ; ðg�ÞT �T Emergency control vector of

contingency �, including load

shedding and generation

regulating.

l�k kth load shedding amount under

contingency �.

g�m mth generation regulating

amount under contingency �.

U�e , U

�e Minimum and maximum values of

emergency control,

respectively, of contingency �.

CpðUpÞ Cost function for preventive control.

C�e ðU�

e Þ Cost function for emergency control

of contingency �.

p� Occurrence probability of

contingency �.

P�ðUp;U�e Þ System’s total load after

preventive control and

emergency control for

contingency �.

P�maxðUp;U�e Þ System’s critical load after

preventive control and emergency

control for contingency �.

In the model, the cost function CpðUpÞ is set as

CpðUpÞ ¼1

2�T�� þ

1

2cT�cc;

where �� ¼ diagð��;1; ��;2; . . . ; ��;M Þ and�c ¼ diagð�c;1; �c;2; . . . ; �c;N Þ, with �� and �c being thecost-coefficient diagonal matrices of transformer tap controland bus compensation control, respectively.The cost function C�

e ðU�e Þ is set as

C�e ðU�

e Þ ¼ ð1=2Þðg�ÞT ðp��g Þ

Tg� þ ðp��l ÞT l�, where

��g ¼ diag ��g;1; ��g;2; . . . ; ��g;P

� �

��l ¼ diag ��l;1; ��l;2; . . . ; ��l;O

� �;

with ��g and ��l being the cost coefficient diagonal matrices ofgeneration regulating control and load shedding control,respectively.The voltage stability constraint is as follows:

��ðU�p ;U

�e Þ¼

P�maxðU�p ;U

�e Þ�P�ðU�

p ;U�e Þ

P�maxðU�p ;U

�e Þ

�100�";

i¼1; 2; . . . ;K;

where P�ðU�p ;U

�e Þ denotes the current load after preventive

control and emergency control, and P�maxðU�p ;U

�e Þ is the

critical load of the system after preventive control andemergency control. U�

p � U�p � U

�p and U�

e � U�e � U

�e are

Table 5 Optimal coordinated control results for themulticontingency case (contingency 1 is the base case).

Table 4 Ten contingencies considered (contingency 1is the base case).


voltage constraints after preventive control and emergencycontrol, respectively.In the Shanghai power grid, the voltage-stability load

margin is required to be kept over 7%; thus, we set " ¼ 7 inthis practice. If there is only preventive control, no feasiblesolution can be found. That is, with only preventive control,the load power margins of all the contingencies cannot beimproved to 7. However, with both preventive control andemergency control, this can be achieved. Table 5 showsthe load power margins before and after control, as well asthe emergency control costs of all of these contingencies.Figure 7 provides the value of every element of theemergency control vectors for contingencies 3, 5, and 6.The emergency control values for the other contingenciesare all zeros. Figure 8 provides the value of every elementof the preventive control vector. A more detailed descriptionof the event analysis system, the event handling system,and the decision-making support system for dispatchers canbe found in [33].In March 2007, the AEMS began operation in Shanghai

Electric Power Company [21]. This was the first time thatmulti-index automatic closed-loop control was achieved inpower dispatching. Currently, the AEMS can control theactive power of all of the AGC units in Shanghai ElectricPower Company and the reactive power of two powerplants (Wujing 2 and Shidongkou) and two substations(Chunshen and Wanrong). In the AEMS phase II project thatwill be finished in 2010, the reactive controlled equipmentwill include all of the major power plants, the mainsubstations, and the flexible alternating current transmissionsystem devices.The AEMS has already resulted in quite good

performance, including improving the disaster prevention

capability, enhancing the system stability, decreasingthe voltage fluctuation rate by 1.2%, and reducing thenetwork losses equivalent to $2.1 million (USD) in2007 [33].The successful operation of the AEMS in Shanghai

Electric Power Company shows that the newautomation system can realize the multiobjectiveself-approximate-optimal operation of the electricity gridand, thus, can provide tremendous secure and economicbenefits. In addition, the AEMS can effectively reduce theburden of dispatchers and minimize the maloperationproblem caused by frequent manual dispatching operations.The implementation of multi-index self-approximate-optimalsmart grid means that we can control an entire large-scalepower system and make it a smart wide area robot(Smart-WAR), which represents a major innovation in thearea of avoiding power system failures.

SummaryIn this paper, we have explained that the biggest differencebetween a smart grid and a traditional electricity grid is theability for multi-index self-approximate-optimal operation.In order to help the electricity grid obtain this ability, we firstdefined the multi-index and self-approximate-optimaloperation architecture. Then, we explained in detail andsynthesized the indices that a smart grid needs foroperation and proposed the general optimization model.We presented two ongoing practices in China, including theAEMS and the IDOP, in order to illustrate how multi-indexand self-approximate-optimal operation could be achieved.Both practices help the electricity grid become smarter, andboth electrical power companies and customers getextraordinary benefit from them.

Figure 7

Emergency control values for contingencies 3, 5, and 6.

Figure 8

Preventive control values.


AcknowledgmentsThe authors would like to thank Ruan Qiantu, the formerDeputy General Manager of Shanghai Electric PowerCompany, who took charge of the coordination andorganization of the projects in the process of theimplementation of Shanghai AEMS and also providedsome instructive advice. The authors would also like to thankthe following employees of Shanghai Electric PowerCompany: Wang Wei, Guo Jiatian, Shen Lijing, ZhangWangyu, Shi Zhixiong, Yu Xufeng, Zhang Jian,Chen Yan, among others, for having put forward very helpfulsuggestions on how to adapt to the practical situation ofShanghai Electric Power Company when implementingthe AEMS and the IDOP. Finally, the authors appreciateinsightful advice and help from Dr. Feng Gao andDr. Haifeng Wang of IBM China Research Laboratoryand Wei Tan of Tsinghua University.

**Trademark, service mark, or registered trademark of BattelleMemorial Institute in the United States, other countries, or both.

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Received December 11, 2009; accepted for publicationSeptember 1, 2010


Guangyu He Department of Electrical Engineering, TsinghuaUniversity, 100084 Beijing, China ([email protected]). Dr. Hereceived his B.S. degree in automation and Ph.D. degree in electricalengineering from Tsinghua University in 1994 and 1999, respectively.His research interests are focused on power system analysis andoperations, as well as linear, and nonlinear optimization for large-scaleproblems. He is currently an associate professor at Tsinghua University.

Yingyun Sun Electrical & Electronic Engineering School, NorthChina Electric Power University, 102206 Beijing, China ([email protected]). Dr. Sun received his B.S. degree in electricalengineering from Shanghai JiaoTong University in 1996 and his M.S.and Ph.D. degrees in electrical engineering from Tsinghua University in2004 and 2007, respectively. His research interests include powersystem optimization and control. He is currently a lecturer at NorthChinaElectric Power University.

Qiang Lu Department of Electrical Engineering, TsinghuaUniversity, 100084 Beijing, China ([email protected]). Dr. Lugraduated from the Electrical Engineering Department of TsinghuaUniversity and is Academician of the Chinese Academy of Sciences,Foreign Member of the Royal Swedish Academy of EngineeringScience, IEEE Fellow, and Professor of Electrical Engineering atTsinghua University. He is now the director of the Academy Committeeof the State Key Laboratory of Power System. He has been mainlyengaged in the fields of power system nonlinear optimal control andadvanced EMS (advanced energy management systems).

Thomas Li IBM China Research Laboratory, ShangDi, 100094Beijing, China ([email protected]). Dr. Li earned a B.S. degree inelectrical engineering from National Taiwan University, an M.S. degreein computer science and operations research from Pennsylvania StateUniversity, and a Ph.D. degree in management of information systemsfrom the University of Texas at Austin. He has taught in variouseducational institutions in the United States and Asia, and he iscurrently an adjunct professor, offering the course in on-demandtransformation technology at Peking University. Dr. Li is the Directorof IBM China Research Laboratory, leading a team of more than 200researchers dedicated to research in the fields of computer hardware,software, industry solutions, and services science.

Hairong Lv IBM China Research Laboratory, ShangDi, 100094Beijing, China ([email protected]). Dr. Lv received a B.E. degree in2002 and a Ph.D. degree in 2007, both in the Department ofAutomation, Tsinghua University, China. Currently, he is working as aResearcher in the IBM China Research Laboratory. His researchinterests include pattern recognition, machine learning, and businessintelligence.

Wenjun Yin IBM China Research Laboratory, ShangDi, 100094Beijing, China ([email protected]). Dr. Yin received his Ph.D.degree from Tsinghua University, China, in 2004 and then joined IBMChina Research Laboratory. He is manager of customer relationshipmanagement and his research interests include supply chainmanagement and logistics, business analytics and optimization, datamining, and business intelligence.

Jin Dong IBM China Research Laboratory, ShangDi, 100094Beijing, China ([email protected]). Dr. Dong is Senior Manager ofSupply Chain Management and Logistics Research in the IBM ChinaResearch Laboratory. He received his Ph.D. degree from TsinghuaUniversity, China, in 2001. Before joining IBM, he was a ResearchAssistant Professor in the Industrial Engineering Department ofArizona State University.


Multi-index and self-approximate-optimal operation for a smart electrical power grid

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