microgrid load monitoring using state estimation ...apic/uploads/research/sample4.pdfmicrogrid load...

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Abstract—Smart grid technologies will increase load

management opportunities to customers. As a result, effective

load monitoring is needed to wisely evaluate the load

management options. In response to this need, this paper

presents a solution for microgrid load monitoring using state

estimation techniques based on voltage-sensors installed at the

loads. This solution is special suitable for commercial facilities,

where usually it is difficult to have access to the conductors

responsible for feeding the loads, while the voltages at the

terminal of the loads are easily accessible. A current-based state

estimation algorithm is proposed to estimate the load currents

based on the voltages at the terminals of the loads. Measurements

of currents and power collected from panels are also considered

and provide redundancy for the proposed state estimation

algorithm. A test case is used to show the effectiveness of the

proposed method. The method presents great potential to be

applied in microgrids load monitoring. From the solution

presented in this paper further applications and researches in

this area can be developed.

Index Terms—Microgrids, State estimation, smart grids.

I. INTRODUCTION

With the modernization of the electrical systems, the

concept of microgrids has emerged as one of the solutions for

the future operation of the system as a smart grid. Low-voltage

grids provided with advanced monitoring, control and

automation systems to manage its consumption, generation

and storage can be characterized as microgrids [1]-[2].

Commercial facilities have great potential for the

employment of microgrids solutions. They represent one

segment with significant demand of electricity and potential to

increase efficiency of energy utilization as well as to

participate on demand response programs. Commercial

systems usually present a variety of loads and a high demand

for heating, ventilation, and air conditioning, which usually

can be controlled [3]-[4]. These facilities also deploy small

generators as back-up in case of loss of the utility; additionally

their generation capacity is rising by the increase on solar

photovoltaic generation installed in their systems.

In microgrids, the energy management systems are

responsible for coordinated operation of loads for energy

This work was supported in part by the XX under Grant XX.

X. X. XXX is with XX University, District Hastings, NE 68902 USA (e-

mail: [email protected]).

efficiency improvement and demand response. These

functions can be better performed with detailed power flow

information based on real time measurements. Such

information will allow that a smart algorithm interpret

consumption patterns, which can be used, for instance, to

reduce peak loads, without compromising the customers

comfort, since information about the power consumption of

different segments is known. This information may also allow

monitoring the functioning of fundamental equipment, such as

equipment associated to cooling, ventilation and pumping

functions [4]-[7].

The intuitive solution for monitoring microgrids loads is

the direct measurement of current or power consumed by each

load of the facility installation. However measuring load

current or power in a facility building require access to the

conductors, which can be a difficult task since the power

supply conductors are usually installed in ducts inside the

walls and therefore inaccessible. On the other hand, voltages

at the load terminals are easily accessible and can be measured

by distributed voltage sensors. The voltage sensors should be

able to measure the voltage phasor at each load terminal.

These voltages combined with other measurements available

in the installation can be employed in a state estimation

algorithm to estimate the loads currents. In this context, the

solution for microgrids load monitoring proposed in this paper

is to install voltage sensors at the terminals of the loads and

use these measurements to estimate the currents of the loads.

The treatment of the measurements and the estimation of

the most possible and reasonable values of the system state

can be conducted by a state estimation algorithm. Since

voltage phasors at loads are known, the most appropriate

algorithm for this problem should estimate the currents of

loads, which can be performed by a current-based state

estimation algorithm.

The traditional state estimation methods are applied to

transmission systems and are node-voltage based, that is, the

estimated or state variables are the voltages at the nodes

[8],[9]. The current-based state estimation algorithms present

in the literature have application in power distribution systems

[10]-[13]. In [10] a branch current three-phase state estimation

method was proposed. The algorithm uses the current in the

rectangular form as state variable and it is based on power

injections and power flow measurements. The same state

variables are used for [11] and [12], but they propose a

constant Jacobian matrix by converting the power and

magnitude current measurements to equivalent currents in the

Microgrid Load Monitoring Using State

Estimation Techniques (V1.0)

Author 1, Member, IEEE, and Author 2, Fellow, IEEE

2

rectangular form. In [13] a branch-current based state

estimation is proposed using the magnitude and phase angle of

the branch current as the state variables.

These current-based state estimation algorithms proposed

in the literature cannot be directly applied to estimate the load

currents for this problem. Firstly, the currents estimation

should be based on voltage measurements. Conventional state

estimation algorithms usually employ active and reactive

power measurements to estimate the bus voltages or the

branches currents. Secondly, typically in a facility the main

panel is connected to the secondary side of distribution service

transformer and multiple levels of panels are expanded

downstream until the loads are reached. However, only the

voltages from the load buses and the main panel are known,

since for the most of installations is difficult to have access

and measure the voltage from the panels. Such constrain is a

complicating factor since the currents should be estimated

using only the available voltages.

In this paper a state estimation algorithm is proposed to

estimate the three-phase loads currents of a microgrid. The

algorithm is based on the load voltages and additional

measurements such as power injections and current

magnitudes from the accessible panels. These additional

measurements ensure the state estimation redundancy.

This paper is organized as follows. Section II discusses the

characteristics associated to the typical commercial systems

and the measurements available. Section III describes the

current-based state estimation algorithm proposed. Section IV

presents the test results. Section V summarizes the main

conclusions of this paper.

II. PROBLEM DESCRIPTION

Typically, in a facility the main panel is connected to the

secondary side of distribution service transformer. From the

main panel multiple levels of subpanels are expanded

downstream, and other panels or multiple conductors are

derived from such panels. A typical single-phase equivalent

circuit of a commercial facility is presented in Fig. 1. As can

be seen in this figure, several subpanels are connected to the

main panel. The subpanels are responsible to connect either

other subpanels or the loads. From each one of the bottom

panels a great number of conductors are derived to connect the

loads.

These conductors are confined inside trays or ducts, which

are installed inside the walls. The installation of current or

power measurement devices to monitor the load consumption

requires the access to each one of these conductors. However,

factors such: the difficulty to access the trays or ducts, the

great number of conductors in the same tray, and the difficulty

in identifying or tracking the conductors’ routes became the

installation of power measurement devices impeditive. To

overpass such difficulty, one solution is the measurement of

the voltage at the load terminals. These terminals are easily

accessible and can be measured using plug-in devices. The

voltage measurements of each one of the load terminals can be

synchronized with the voltage from the main panel. So the

voltage magnitude and angle of each load can be considered

known.

Fig. 1. Typical per-phase equivalent facility circuit.

Therefore, once the voltage magnitude and angle at loads

are known, the voltage drop can be used to calculate the load

currents. The configuration of the grid can be easily modeled

by extracting the information from electrical diagrams; and the

electrical impedances from each branch can be calculated

based on the wire gage and length.

The voltages of the intermediate panels or subpanels are

assumed not known, since it may be difficult to access and

measure the voltage from these panels. As the currents

estimation should be based on the voltages at the main panel

and at the loads, a special procedure has to be defined to

compute the load currents with the voltage drop between the

main panel and the loads terminals.

The calculation of the loads current is based on the fact

that all branches currents are a combination of the loads

currents. For example, considering the simple system shown

in Fig. 2, in which the main panel is represented by the bus 1,

the loads are connected to buses 3 and 4. As the voltage at bus

2 is unknown, the equations relating the loads currents to the

voltage drop are:

(1)

(2)

where , and are the phasors of voltage of the main

panel, load 3 and load 4, respectively. and are the load

3 and 4 currents. is the branch current from bus 1 to bus 2.

Z12, Z23 and Z24 are the branches impedances form branch

connecting 1 to 2; 2 to 3 and 2 to 4, respectively.

To solve this system, the number of unknown currents

should be equal to the number of load voltages. So the

solution is to write the branches currents as function of the

load currents. For this example, the branch current is

composed by the sum of the load current with . So, the

branch current can be replaced by a combination of load

Subpanel

Subpanel

Subpanel

Subpanel Subpanel

…

Main panel

Secondary of service

transformer

…

loads

…

loads

…...

…

…...

…...

…...

loads loads loads

loads

Subpanel

Subpanel

Subpanel Subpanel

Subpanel

Subpanel

3

currents, resulting in:

( ) (3)

( ) (4)

Using this assumption, it is possible to calculate all the

currents considering the measured voltages at the main panel

and at the loads terminals. For more complex systems the

solution will require more detailed procedure, which will be

further presented in this paper. This procedure is important for

computing the initial currents estimation for the state

estimation algorithm. The initialization of the variables has a

great impact on the algorithm convergence speed.

Fig. 2. One-line diagram of a simple example system.

Besides the phasor voltages at the loads and at the main

panel, additional measurements are also available from the

main panel and possible from other panels, which can also be

used to estimate the currents. Usually, measurements of active

and reactive power injection are available from the main

panel, the magnitude of some branches currents may also be

available. These measurements should be used with a state

estimation algorithm to estimate the load currents. As already

seen, measurements of voltages in all loads allow to calculate

the load currents, so the extra measurements, such as injected

power and magnitude currents can be used to provide

redundancy to the state estimation algorithm.

III. STATE ESTIMATION FORMULATION

The general form of state estimation problem can be

expressed as:

( ) s.t. c(x)=0 (5)

where z is a m-dimensional vector containing the m

measurements; x is a n-dimensional (n<m) state vector; h(x) is

a m-dimensional vector of functions relating measurements to

state variables; w is a m-dimensional vector containing the

measurement error vector; c(x) is a l-dimensional vector of

functions that model the zero injections as equality

constraints; m is the number of measured quantities; and n is

the number of state variables.

The Weighted Least-Square (WLS) is used to estimate the

state variables, and different weights are selected according to

the accuracy of the measurements, resulting in:

( ) ∑

( ( ))

[ ( )] [ ( )] s.t. c(x) = 0

(6)

where σ2 is the covariance of the measurement and R

-1 is the

inverse matrix of the diagonal matrix with the variances (σ2

i)

in the ith diagonal position, given by:

[

]

(7)

The equality constraints representing the zero injections

measurements are treated by the method of Lagrange

multipliers [14]. The estimated state is obtained by solving the

following system of equations at each iteration:

( ( ) ( )

( ) ) (

)

( ( ) [ ( )]

( ))

(8)

where k is the iteration index, xk is the solution vector at

iteration k, k are the Langrange multipliers at iteration k, H(x)

= (∂h/∂x) and C(x) = (∂c/∂x) are Jacobian matrices and

G(x)=HT(x)R

-1H(x) is the gain matrix.

The problem of State Estimation for microgrids can be

modeled using Fig. 3, which presents a simplified one-phase

facility network. This system is composed by one main panel

and two panels connected downstream from the main. In the

main panel the voltage and the injected power are measured,

the current magnitude may also be measured. In the subpanels

(buses 2 and 3) usually is difficult to have access to measure

the voltage or the power, but sometimes it is possible to

measure the current magnitude. From the last panel before the

load, several circuits are derived to connect the loads. The

terminal voltages are measured, and these measurements are

synchronized with the main panel voltage, making the

magnitude and angle of the loads voltage available. Following

the downstream sequence, numbers are associated to the each

node of the circuit, including panels and load terminals as

nodes, as shown in Fig. 3.

Fig. 3. One-phase diagram Simple system.

A. Measured variables

The loads voltages and the main panel voltage in the

complex domain may be expressed in their rectangular form

by:

1

2

3 4

Main panel

Subpanel

loads

V

0

Z Z

Main Panel 1

V4 V5

Z Z

25

P1+j Q1

I12

I13

1

3 Panel 2 Panel 3

V6

L

V7

I24 I25 I37

I

01

I36

Z

Z

4 5 6 7

I12 I

13

4

(9)

where is the complex voltage and Vq,r and Vq,x are,

respectively, the real and imaginary part of the voltage of a

bus q. The expression of voltage phasor measurements in the

rectangular form improves the convergence properties of the

estimator [15].

Other measurements that also can be collected are the

active and reactive power injection at the main panels, some

branches magnitude currents from the panels. The

measurements vector results in:

[ ] (10)

where Pk and Qk are the active and reactive power injection in

the main panel; Iij is the branch current magnitude from bus i

to j; Vq,r is the real part of the voltage of load connected to bus

q and Vq,x is the imaginary part of the voltage of load

connected to bus q.

B. State variables

The vector x is composed by the currents in the rectangular

form, including the load currents and the branches currents,

such as:

[ ] (11)

where Iij,r and Iij,x are, respectively, the real and imaginary

parts of the current from node i to node j.

C. Functions relating measurement vector to state vector

1) Power injection in the main panel: The equation of the

total power injection in the main panel is given by:

∑

(12)

where Vk is the voltage magnitude of the considered bus, in

this case the main panel and k=1 and Ωk indicates all branches

connected to bus k.

The active power injection is given by:

∑

∑

(13)

The reactive power injection is calculated by:

∑

∑

(14)

2) Equation of the magnitude current branches. The current

magnitude measurement is related to the state variables by:

√( ) ( )

(15)

where Iij is the branch current magnitude, and Iij,r and Iij,x are,

respectively, the real and imaginary parts of the branch current

state variable.

3) Equation of load voltage: The voltage at the load

connected to node q is the voltage at the main panel minus the

voltage drop on the branches between the main panel and the

load. The voltage phasor of the load qth

is given by:

∑

(16)

where is the voltage at the load, is the voltage at the

main panel, zij is the impedance of the branch ij, is the

current of the branch ij and the set Bq contains all branches

where the q-load current flows from the main panels to the

load terminal.

The real part of the voltage is given by:

∑ ( )

(17)

where rij and xij are, respectively, the resistance and reactance

of the branch ij.

The imaginary part is given by:

∑ ( )

(18)

D. Equality Constrains

Zero injection current equality constrains should be

considered for the panels, but the main panel. For the ith

bus,

which is a panel, the real and imaginary parts of the currents

should have a zero injection. For the real part of the current:

∑

(19)

For the imaginary part of the current:

∑

(20)

where Ωi comprises all buses connected to the bus i. The

convention of current signals adopted is currents flowing into

bus i has a positive signal and currents flowing from bus i has

a negative sign.

E. Entries of Jacobin Matrix

The entries of the Jacobian matrix are derived by taking the

differential of the measurement equation with respect to the

state variables.

1) Active power injection measurements: If the branch is

connected to the bus k, for the real part of the current:

(21)


(22)

If the branch is not connected to the bus k, the derivate is

zero.

2) Reactive power injection measurements

If the branch is connected to the bus k, for the real part of

the current:

5

(23)


(24)


zero.

3) Current magnitude measurements. For the real part of

the current:

√( ) ( )

(25)

For the imaginary part:

√( ) ( )

(26)

4) Real part of load voltage phasor measurements. If the

current of the load q flows through the branch ij:

For the real part of the current:

(27)


(28)

5) Imaginary part of load voltage phasor measurements:

If the current of the load q flows through the branch ij:

(29)

And for the imaginary part:

(30)

6) Virtual Measurements: Taking the differential of the

equality constrains in relation to the state variables, used to

construct the C matrix, the following equations for the real and

imaginary parts, respectively, are obtained:

∑

( ) (31)


∑

( ) (32)

If the current is flowing into bus i α=2; if the current is

flowing from bus i α=1.

For current-based state estimation algorithms, the inclusion

of the virtual measurements, representing the zero injections

measurements, are discussed in [14]. In this reference the

authors use zero power injection. For an algorithm which the

state variables are the branches currents, it is more efficient

consider zero current injections, which, as can be seen in the

last equations, result in unit elements in the correspondent

Jacobian matrix elements.

F. Initialization

Initialization of the state variables presents a great impact

on the convergence speed of the algorithm. The first value for

the currents can be calculated using the voltages of the loads

terminals and the voltage of the main panel. The voltage drop

between the main panel and the loads terminals can be

calculated using the impedances and currents of each branch

connecting the load to the main panel. However, it is

necessary to consider that only the voltages at the loads are not

enough to compute all the currents, but if each one of the

branches currents is considered a combination of the loads

currents, the loads currents can be firstly calculated and then

all the branches currents can be calculated.

The first step is to identify the branches that connect each

load to the main panel. So, for a load k, Bk contains the set of

all branches connecting load k to the main panel. The second

step is for each one of the branches the load currents that

flows through it should be identified, for example, in Fig. 3 for

the branch from bus 1 to 2, the currents from loads 4 and 5

flows for it. This information can be saved in a set Lij, which

brings the loads that the current flows for the branch ij.

With this information, the load currents can be calculated

by:

[ ] [ ] (33)

where [ ] is the vector containing the difference between the

measured load voltages and the main panel voltage; [ ] is a

vector containing all the loads currents and Z is the impedance

matrix. The matrix Z is given by:

For the elements out of the diagonal:

( ) ( ) ∑

(34)

where zij is the branch impedance which is part of the path of

the load k and of the load q. If Lq and Lk are already known,

Lqk can be calculated by Lq∩Lk. If both loads don’t share any

branch this element will be null.

For the elements of the diagonal:

( ) ∑

(35)

Once the impedance matrix is calculated the load current

can be calculated by:

[ ] ( ) [ ] (36)

One important aspect to highlight is that the impedance

matrix will not change and its inverse can be saved. Once the

load currents are known, a back sweeping procedure can be

applied to calculate all the branches currents, since the

branches currents are a combination of the loads currents.

6

Some state estimation algorithms in the literature that uses

magnitude currents measurements don’t employ these

measurements in the first iteration [10]. These algorithms use

a flat voltage start for first iteration, and in such cases current

magnitude measurements may lead to convergence problems

if used in the first iteration. For current-based state estimation

algorithms a flat voltage start can be used to calculate the first

iteration currents with a backward sweep procedure. In these

cases the current measurements are also excluded in the first

iteration and then introduced in the successive iterations.

Other solution proposed in [11] was reducing the weights of

current magnitude measurements in the first and second

interactions. The initialization procedure proposed in this

paper avoids problems of this nature and additionally speeds

up the algorithm convergence. So, in the algorithm proposed

in this paper all measurements are used with the properly

weights from the first iteration.

G. Algorithm Steps

The algorithm is implemented as the following steps:

Step 1: Define the system configuration and parameters:

Obtain the system configuration, the branches impedances

and the measurements.

Step 2: Initialization: Calculate the first estimation for the

load currents, x(1), based on the measurements of the

voltage at the loads terminals and the main panel voltage.

Step 3: Using back sweeping calculate all branches

currents.

Step 4: Using forward sweeping calculate all nodes

voltages.

Step 5: Calculate the updates of the system state, Δx(n).

Such updates should be calculated based on Equation (8).

Step 6: Update the system state: x(n+1) = x(n)+Δx(n).

Step 7: If Δx(n) is smaller than a convergence tolerance

(stop criterion), then stop. If the number of iteration is

smaller than the maximum iteration number, go to step 4.

If it is not, it does not converge.

In the state estimation formulation proposed, the state

vector is composed of the rectangular form of the currents.

Such choice avoids ill-conditioning problems, especially, for a

state estimation problem whose solution is highly based on

voltage measurements. The voltage measurements are

transformed from the polar form to the rectangular form, with

the same purpose of the use of the current in the rectangular

form. In fact, the use of currents in the rectangular form during

the solution of the state estimation algorithm has been used in

[10]-[12]. One of the differences is that such algorithms are

based on the power and current magnitude measurements,

differently from this presented algorithm.

The use of the currents and voltages in the rectangular form

simplifies the calculation of the Jacobian elements. In fact, for

the voltage measurements, these elements are composed by

the conductors’ reactances and resistances, as can be seen in

Equations (27)-(30).

IV. METHOD VALIDATION

The proposed load currents state estimation method is

implemented for a commercial system. The system is based on

the electrical diagram of a commercial building, which is

presented in Fig. 4. The system comprises, besides the main

panel, 6 panels and 14 three-phase loads. The main panel is

connected to a service transformer, responsible for converting

the voltage from the distribution level to 600 V, which is the

nominal voltage of all loads represented in the system. The

loads are responsible for ventilation, heating and pumping

functions of the building. The data of the system is presented

in the Appendix.

This system is monitored by measuring the phasors of

voltage of all loads as well as the phasor of voltage of the

main panel. The injected active and reactive power of the main

panel and the magnitude of current from the subpanels are also

measured, as indicated in Fig. 4.

Fig. 4. One-line electrical diagram of the test system.

In order to generate the input data for the state estimation

algorithm, a load flow program was employed to obtain, for

the specified loads and main panel voltage, the voltages

magnitude and angle in the loads terminals, the currents and

the injected power of the main panel. Then, the measured

value is calculated by adding a normally distributed

(Gaussian) error on its true value, as following presented:

(37)

where is the measured value,

is the true value

provided by the load flow and ei is the measurement error. The

error is a random number with a standard deviation of the

error (σi), given by rand×(σi). For a given inaccuracy of the

measurement equipment (error%), the standard deviation can

be computed as follows [16]:

(38)

5

loads

6 7

Main panel 1

2

3

4

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

P+jQ

I12 I13

I24 I25 I36 I37

7

For currents and power measurements the considered

error% is 2, and for the voltage measurements the error% is

0.2 [15]. The variance is computed as the square of standard

deviation of the measurements, which values are used to build

the matrix R.

In Table I the average of the absolute errors for the current

magnitude and angles considering 100 simulations are

presented. For each one of these simulations different errors

are associated to the measurements, since the errors are

created by a random function. The convergence criteria

applied to the state estimation algorithm considers that the

maximum update of the state variable should be smaller than

1.10-4

pu. As the currents resulted from the algorithm are in

the rectangular form, they were converted to the polar form

and compared with the original values obtained by the power

flow program.

TABLE I

AVERAGE OF THE ABSOLUTE ERROR OF THE CURRENT AND ANGLE

Branch or

load

Mag.

(pu)

Angle

(deg.)

1 (1-2) 0.0086 0.2403

2 (1-3) 0.0100 0.3632

3 (2-4) 0.0077 0.5610

4 (2-5) 0.0053 0.4175

5 (3-6) 0.0051 0.5920

6 (3-7) 0.0069 0.4627

8 0.0118 0.8481

9 0.0110 0.7337

10 0.0115 1.5075

11 0.0117 1.9886

12 0.0113 0.7588

13 0.0115 0.7156

14 0.0129 0.8281

15 0.0131 1.5033

16 0.0105 1.4781

17 0.0113 1.5158

18 0.0111 1.7082

19 0.0111 0.5782

20 0.0122 1.0841

21 0.0121 0.7524

22 0.0104 0.7838

For the 100 simulated cases, the initialization of the

program improved the convergence process and all simulated

cases converged. The most cases converged with 3 iterations,

and the maximum number of iterations was 4.

As can be seen from TABLE I, the currents from the panels

present lower average errors than the loads currents. This

behavior is explained by the magnitude current measurements

installed in these panels. Although current magnitude

measurements from the panels were considered to obtain the

results, in case of these measurements are not available, it

won’t interfere in the observability of the system. The

observability is ensured by the voltages measurements and by

the virtual measurements, that is, the zero injection current

equality constrains of the panels. If the current flow

magnitudes are not considered the only redundancy

measurement will be the active and reactive power measured

at the main panel.

The results for a second case (Case II) are presented in

Table II, which shows the average of the absolute errors of

current magnitudes and angles for 100 simulations. In these

simulations no current magnitude measurements in the panels

were considered. As one can notice, comparing Table II to

Table I, the average errors for the loads (8-22) are very

similar, while the panels branches currents (1-6) presented a

higher error in Case II. TABLE II

AVERAGE OF THE ABSOLUTE ERROR OF THE CURRENT AND ANGLE – CASE

II

Branch or

load

Mag.

(pu)

Angle

(deg.)

1 (1-2) 0.0096 0.2431

2 (1-3) 0.0153 0.5172

3 (2-4) 0.0106 0.6931

4 (2-5) 0.0116 0.3623

5 (3-6) 0.0101 0.6100

6 (3-7) 0.0146 0.7033

8 0.0111 0.9409

9 0.0104 0.6357

10 0.0112 1.4913

11 0.0112 1.8498

12 0.0128 0.7977

13 0.0137 0.8013

14 0.0132 0.7868

15 0.0135 1.4796

16 0.0134 1.8120

17 0.0105 1.3460

18 0.0120 1.8296

19 0.0115 0.7278

20 0.0106 1.1198

21 0.0130 0.9770

22 0.0116 0.9489

Fig. 5 presents the comparison of the panels current

magnitude relative errors between Case I and Case II. For

Case I, the panels current magnitude measurements are

considered in the state estimation algorithm and for Case II

these measurements are not considered. As one can notice,

taking the panels current magnitude measurements into

consideration slightly improve the estimation of the currents

of the panels. So, if current magnitude measurements from the

panels are available it is worth to include such measurements

in the state estimation.

Fig. 5. Comparison of relative errors of the estimated current magnitude.

1 2 3 4 5 60

1

2

3

4

branch number

erro

r per

centa

ge

(%)

Case I

Case II

8

V. CONCLUSIONS

This paper has presented a new method for microgrid load

monitoring. The main idea of the proposed method is to

measure the phasors voltages at the terminals of the loads,

which comprises a good solution for facilities which the load

conductors are inaccessible. A current-based state estimation

algorithm is proposed to estimate the currents based on

voltage measurements and other measurements available in

the facility. The method was applied to a test system based on

a real system and the results revealed that the method can be

applied to microgrids load monitoring. From the solution

presented in this paper further applications and researches in

this area can be developed and proposed. The proposed

voltage-sensor based load monitoring can also be extended

and adapted to be applied in residential installations.

VI. APPENDIX

The data of the system presented in Fig. 4 is presented at

Table III and the powers of the loads are presented at Table

IV. A base power of 1MVA is used and a base voltage of 600

V. TABLE III

CONDUCTORS PARAMETERS

From To R(pu) X(pu)

1 2 0.0007 0.0058

1 3 0.0007 0.0056

2 4 0.0031 0.0047

2 5 0.0043 0.0067

3 6 0.0059 0.0092

3 7 0.0041 0.0063

4 8 0.0334 0.0188

4 9 0.0352 0.0198

4 10 0.0220 0.0253

5 11 0.0224 0.0257

5 12 0.0349 0.0197

5 13 0.0342 0.0193

5 14 0.0302 0.0170

5 15 0.0213 0.0245

6 16 0.0202 0.0232

6 17 0.0208 0.0239

6 18 0.0231 0.0266

7 19 0.0356 0.0201

7 20 0.0355 0.0200

7 21 0.0346 0.0195

7 22 0.0337 0.0190

TABLE IV

LOAD PARAMETERS

Bus P(kW) Q(kvar)

8 139.2 53.6

9 149.2 63.6

10 198.9 79.7

11 168.9 59.7

12 128.2 53.0

13 120.9 53.2

14 138.0 58.5

15 178.9 80.8

16 230.0 80.8

17 204.0 80.8

18 197.2 69.7

19 178.9 69.7

20 129.2 43.2

21 139.2 53.2

22 150.2 53.6

VII. REFERENCES

[1] F. Katiraei, R. Iravani, N. Hatziargyriou, and A. Dimeas, “Microgrids

Management,” IEEE Power & Energy Magazine, vol. 6 pp. 54-65.

May/June 2008

[2] H. S. V. S. K. Nunna and S. Doolla, “Energy Management in Microgrids

Using Demand Response and Distributed Storage—A Multiagent

Approach,” IEEE Trans. Power Delivery, vol. 28, pp. 939-947. Apr.

2013.

[3] “Buildings Energy Data Book, Chapter 3: Commercial Sector,” U.S.

Department of Energy [Online]. Available:

http://buildingsdatabook.eren.doe.gov/default.aspx

[4] P. Palensky and D. Dietrich, “Demand Side Management: Demand

Response, Intelligent Energy Systems, and Smart Loads,” IEEE Trans.

Industrial Informatics, vol. 7, pp. 381-388. Aug. 2011.

[5] D. Dietrich, D. Bruckner, G. Zucker, and P. Palensky, “Communication

and Computation in Buildings: A Short Introduction and Overview,”

IEEE Trans. Industrial Electronics, vol. 57, pp. 3577-3584. Nov. 2010.

[6] Y. Du, L. Du, B. Lu, R. Harley, and T. Habetler, “A Review of

Identification and Monitoring Methods for Electric Loads in

Commercial and Residential Buildings,” presented at the Energy

Conversion Congress and Exposition, Atlanta, USA, 2010.

[7] J. L. Mathieu, P. N. Price, S. Kiliccote, and M. A. Piette, “Quantifying

Changes in Building Electricity Use With Application to Demand

Response,” IEEE Trans. Smart Grid, vol. 2, pp. 507-518. Sep. 2011.

[8] A. Monticelli, State Estimation in Electric Power System: A Generalized

Approach, Kluwer Academic Publishers: USA, 1999.

[9] A. Abur and A. G. Exposito, Power System State Estimation: Theory

and Implementation, Marcel-Dekker: New York, USA, 2004.

[10] M. E. Baran and A.W. Kelley, “A branch-current-based state estimation

method for distribution systems,” IEEE Trans. Power Syst., vol. 10, pp.

483–491, Feb. 1995.

[11] C. N. Lu, J. H. Teng, and W. H. E. Liu, “Distribution system state

estimation,” IEEE Trans. Power Syst., vol. 10, pp. 229–240, Feb. 1995.

[12] W. M. Lin, J. H. Teng, and S. J. Chen, “A highly efficient algorithm in

treating current measurements for the branch-current-based distribution

state estimation,” IEEE Trans. Power Delivery, vol. 16, pp. 433–439,

Jul. 2001.

[13] H. Wang and N. N. Schulz, “A Revised Branch Current-Based

Distribution System State Estimation Algorithm and Meter Placement

Impact,” IEEE Trans. Power Systems, vol. 19, pp. 207-213, Feb. 2004.

[14] W. M. Lin and J. H. Teng “State estimation for distribution systems with

zero-injection constraints,” IEEE Trans. Power Syst., vol. 11, pp. 518–

524, Feb. 1996.

[15] G. N. Korres and N. M. Manousakis, “State Estimation and

Observability Analysis for Phasor Measurement Unit Measured

Systems,” IET Gener., Transm. & Distrib., vol. 6, pp. 902-913. Sep.

2012.

[16] R. Singh, B. C. Pal, and R. A. Jabr, “Choice of Estimator for

Distribution System State Estimation,” IET Gener., Transm. & Distrib.,

vol. 3, pp. 666-678. Jul. 2009.

VIII. BIOGRAPHIES

XXXX (M’1888, F’17) xxxx

1

Abstract — A major feature of the smart grid is its diverse

load management opportunities for customers, which calls for

innovative techniques for load monitoring. This paper presents a

method to monitor microgrid loads using a set of voltage sensors

and state estimation algorithms. The technique is especially

suited for commercial facility based microgrids where it is often

difficult to measure loads directly but the load voltages can be

sensed. A current-based state estimation algorithm is proposed to

estimate the load currents using the voltages sensed at the

terminals of the loads. Currents and powers collected from

limited number of panels are also utilized to provide redundancy

for estimation. Case studies have shown that the proposed

method represents a promising alternative direction for

monitoring microgrid loads.

Index Terms—Microgrids, load monitoring, state estimation,

smart grids.

I. INTRODUCTION

ITH the modernization of the electrical systems, the

concept of microgrids has emerged as one of the

solutions for the future operation of the system as a smart grid.

Low-voltage grids provided with advanced monitoring,

control and automation systems to manage its consumption,

generation and storage can be characterized as microgrids [1]-

[2].

One of the representative microgrids is the commercial

facilities, as they are owned by single owners and thus are

much easier to setup microgrid operation. They also represent

one energy-use segment with significant potential to increase

energy efficiency and to participate in demand response.

Commercial systems usually have a wide variety of loads.

They can also deploy small generators using renewable

sources [3]-[4]. For microgrid operations, the energy

This work was supported in part by CNPq and FAPESP of Brazil and

NSERC of Canada.

A. P. Grilo is with University of Alberta, Edmonton, AB T6G 2V4,

Canada, as Post-Doctoral Fellow, and Federal University of ABC, Santo

Andre, SP, Brazil, as Assistant Professor on a leave of absence (e-mail:

[email protected]).

W. Xu is with the Department of Electrical and Computer Engineering,

University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail:

[email protected]).

M. C. de Almeida is with the Department of Electrical Energy Systems,

University of Campinas, Campinas, 13083-852 Brazil (e-mail:

[email protected]).

management systems are responsible for coordinated

operation of loads and generators. A critical piece of

information needed by the system is the real-time power

consumption of various loads. In addition, this information

can be used for equipment condition monitoring, which is

another smart feature of the microgrids [4]-[7].

The direct solution to monitoring loads is to measure

current or power consumed by each load of the facility.

However measuring load current or power requires accessing

to the conductors supplying the loads. This can be difficult or

even impossible for facilities that have already been built. This

is because the power supply conductors are usually installed in

ducts inside the walls and therefore inaccessible. As a result,

except for a few large loads with built-in sensors, most of the

loads in a commercial building cannot be monitored at

present.

On the other hand, voltages at the load terminals are often

accessible and can be measured by distributed voltage sensors.

These voltages, combined with the network topologies and

parameters, can be used to estimate the load currents through

state-estimation-like algorithms. Based on this reasoning, a

distributed voltage sensor based, computational load

monitoring solution is proposed in this paper. By utilizing the

work done in the area of power system state estimation, this

paper has shown that the proposed technique represents a

promising solution to the microgrid load monitoring problem.

This paper is organized as follows. Section II discusses the

challenges of load monitoring for commercial microgrids and

defines the problem to be solved. It also reviews the various

state estimation algorithms that may be adopted for the load

monitoring problem. Section III presents the proposed current-

based state estimation algorithm. Section IV shows the case

study results. Section V summarizes the main conclusions of

this paper.

II. PROBLEM DESCRIPTION

The common electrical configuration of a commercial

facility starts at the main panel. The voltage, current and

power are often monitored at this location. From the main

panel multiple levels of subpanels are expanded downstream,

and other panels or multiple conductors are derived from such

panels. A typical equivalent circuit of a commercial facility is

shown in Fig. 1. As can be seen in this figure, several

subpanels are connected to the main panel. The subpanels are

responsible to connect either other subpanels or the loads.

Microgrid Load Monitoring Using State

Estimation Techniques (Final Version)

Ahda P. Grilo, Member, IEEE, Wilsun Xu, Fellow, IEEE,

and Madson C. de Almeida, Member, IEEE

W

2

From each one of the bottom panels a great number of

conductors are used to supply various loads.

These conductors are confined inside trays or ducts, which

are installed inside the walls. The installation of current

measurement devices to monitor the load consumption

requires the access to each of these conductors. However,

factors such as the difficulty to access the trays or ducts, the

great number of conductors in the same tray, and the difficulty

in identifying or tracing the conductors’ routes make the

installation of power measurement devices very difficult and

costly. On the other hand, the load voltages can be measured

relatively easily since many receptacles are available in a

facility. One can, for example, develop low cost voltage

sensors and install them at various locations. These sensors are

synchronized and networked. It is possible to estimate the load

currents from such measured voltage phasors if the network

topology and conductor impedances are known.

Fig. 1. Typical per-phase equivalent facility circuit.

The topology and impedance data can be obtained from the

building electrical diagrams. The calculation of the loads

current is based on the fact that all branches currents are a

combination of the loads currents. For example, considering

the simple system shown in Fig. 2, in which the main panel is

represented by the bus 1, the loads are connected to buses 3

and 4. As the voltage at bus 2 is unknown, the equations

relating the loads currents to the voltage drop are:

(1)

(2)

where , and are the phasors of voltage of the main

panel, load 3 and load 4, respectively. and are the load

3 and 4 currents. is the branch current from bus 1 to bus 2.

Z12, Z23 and Z24 are the branches impedances from branch

connecting 1 to 2; 2 to 3 and 2 to 4, respectively.

To solve this system, the number of unknown currents

should be equal to the number of load voltages. So the

solution is to write the branches currents as function of the

load currents. For this example, the branch current is

composed by the sum of the load current with . So, the

branch current can be replaced by a combination of load

currents, resulting in:

( ) (3)

( ) (4)

Using this transform, it is possible to calculate all the

currents considering the measured voltages at the main panel

and at the loads terminals. For more complex systems the

solution will require more detailed procedure, which will be

further presented in this paper.

Fig. 2. One-line diagram of a simple example system.

Besides the phasor voltages at the loads and at the main

panel, additional measurements are also available from the

main panel and possibly from other panels, which can also be

used to estimate the currents. Usually, measurements of active

and reactive power injection are available from the main

panel, the magnitude of some branches currents may also be

available. These measurements can be used to increase

redundancy for the estimation algorithm. The voltages of the

intermediate panels or subpanels are assumed not known,

since they are difficult to access for measurement. As the

currents estimation should be based on the voltages at the

main panel and at the loads, a special procedure has to be

defined to compute the load currents with the voltage drop

between the main panel and the loads terminals.

The problem to be solved can, therefore, be defined as an

estimation problem: solve for load currents based on multiple

voltage and power measurements at various locations. This

problem is closely related to the well-known power system

state estimation problem [8],[9]. The difference here is that the

load monitoring problem is to estimate currents (or power)

from voltages whereas the traditional state estimation problem

estimates voltages from powers (or currents).

The majority traditional state estimation methods published

focus on the estimation of transmission system voltages.

Nodal voltages are the unknown to estimate [8],[9]. Reference

[10]-[13] presented current-based state estimation algorithms

for power distribution systems. For example, reference [10]

uses the currents in rectangular coordinates as state variables

and power injections as observable quantities. The same state

variables are used for [11] and [12], but they propose a

constant Jacobian matrix solution algorithm. In [13] a branch-

current based state estimation is proposed using the magnitude

and phase angle of the branch current as the state variables.

Subpanel

Subpanel

Subpanel

Subpanel Subpanel

…

Main panel

Secondary of service

transformer

…

loads

…

loads

…...

…

…...

…...

…...

loads loads loads

loads

Subpanel

Subpanel

Subpanel Subpanel

Subpanel

Subpanel

1

2

3 4

Main panel

Subpanel

loads

3

The above current-based state estimation algorithms are

more closely related to the load monitoring problem. But they

cannot be directly applied. Firstly, the observable quantities

are the voltage measurements here. Conventional state

estimation algorithms usually employ active and reactive

power measurements to estimate the bus voltages or the

branches currents. Secondly, a facility’s main panel is

connected to the secondary side of distribution service

transformer and multiple levels of panels are expanded

downstream until the loads are reached. Only the voltages

from the load buses and the main panel are known. Such

constraint is a complicating factor since the currents should be

estimated using only the available voltages. To solve the

problem of load monitoring, a new state estimation problem is

formulated and new algorithms are proposed to solve it.

III. STATE ESTIMATION FORMULATION

The general form of state estimation problem can be

expressed as:

( ) s.t. c(x)=0 (5)

where z is a m-dimensional vector containing the m

measurements; x is a n-dimensional (n<m) state vector; h(x) is

a m-dimensional vector of functions relating measurements to

state variables; w is a m-dimensional vector containing the

measurement error vector; c(x) is a l-dimensional vector of

functions that model the zero injections as equality

constraints; m is the number of measured quantities; and n is

the number of state variables.

The Weighted Least-Square (WLS) is used to estimate the

state variables, and different weights are selected according to

the accuracy of the measurements, resulting in:

( ) ∑

( ( ))

[ ( )] [ ( )] s.t. c(x) = 0

(6)

where σ2 is the covariance of the measurement and R

-1 is the

inverse matrix of the diagonal matrix with the variances (σ2i)

in the ith

diagonal position, given by:

[

]

(7)

The equality constraints representing the zero injections

measurements are treated by the method of Lagrange

multipliers [14]. The estimated state is obtained by solving the

following system of equations at each iteration:

( ( ) ( )

( ) ) (

)

( ( ) [ ( )]

( ))

(8)

where k is the iteration index, xk is the solution vector at

iteration k, k are the Langrange multipliers at iteration k, H(x)

= (∂h/∂x) and C(x) = (∂c/∂x) are Jacobian matrices and

G(x)=HT(x)R

-1H(x) is the gain matrix.

The equations of State Estimation for microgrids can be

formulated using Fig. 3 as example, which presents a

simplified one-phase facility network. This system is

composed by one main panel and two panels connected

downstream from the main. In the main panel the voltage and

the injected power are measured, the current magnitude may

also be measured. In the subpanels (buses 2 and 3) usually is

difficult to have access to measure the voltage or the power,

but sometimes it is possible to measure the current magnitude.

From the bottom panels, several circuits are derived to connect

the loads. The terminal voltages are measured, and these

measurements are synchronized with the main panel voltage,

making the magnitude and angle of the loads voltage

available. Following the downstream sequence, numbers are

associated to the each node of the circuit, including panels and

load terminals as nodes, as shown in Fig. 3.

Fig. 3. One-phase diagram Simple system.

A. Measured variables

The loads voltages and the main panel voltage in the

complex domain may be expressed in their rectangular form

by:

(9)

where is the complex voltage and Vq,r and Vq,x are,

respectively, the real and imaginary part of the voltage of a

bus q. The expression of voltage phasor measurements in the

rectangular form improves the convergence properties of the

estimator [15].

Other measurements that also can be collected are the

active and reactive power injection at the main panel and some

branches magnitude currents from the panels. The

measurements vector results in:

[ ] (10)

where Pk and Qk are the active and reactive power injection in

the main panel; Iij is the branch current magnitude from bus i

to j; Vq,r is the real part of the voltage of load connected to bus

q and Vq,x is the imaginary part of the voltage of load

connected to bus q.

B. State variables

The vector x is composed by the currents in the rectangular

V

0

Z Z

Main Panel 1

V4 V5

Z Z

25

P1+j Q1

I12

I13

1

3 Panel 2 Panel 3

V6

L

V7

I24 I25 I37

I

01

I36

Z

Z

4 5 6 7

I12 I

13

4

form, including the load currents and the branches currents,

such as:

[ ] (11)

where Iij,r and Iij,x are, respectively, the real and imaginary

parts of the current from node i to node j.

C. Functions relating measurement vector to state vector

1) Power injection in the main panel: The equation of the

total power injection in the main panel is given by:

∑

(12)

where Vk is the voltage magnitude of the considered bus, if the

power injection is at the main panel k=1, and Ωk indicates the

set of all branches connected to bus k. So, the active power

injection is given by:

∑

∑

(13)

The reactive power injection is calculated by:

∑

∑

(14)

2) Equation of the magnitude current branches. The current

magnitude measurement is related to the state variables by:

√( ) ( )

(15)

where Iij is the measured branch current magnitude, and Iij,r

and Iij,x are, respectively, the real and imaginary parts of the

branch current state variable.

3) Equation of load voltage: The voltage at the load

connected to node q is the voltage at the main panel minus the

voltage drop on the branches between the main panel and the

load. So, it is necessary the information about the branches

that connect each load to the main panel, which for the load q

is defined as the set Bq. Such set contains all branches that are

path of the current of load q from the main panel to the load.

For example, in Fig. 3, the set B4 for load 4 contains the

branches 1-2 and 2-4.

The voltage phasor of the load qth

is given by:

∑

(16)

where is the voltage at the load, is the voltage at the

main panel, zij is the impedance of the branch ij, is the

current of the branch ij and the set Bq contains all branches

connecting load q to the main panel.

The real part of the voltage is given by:

∑( )

(17)

where rij and xij are, respectively, the resistance and reactance

of the branch ij.

The imaginary part is given by:

∑( )

(18)

D. Equality Constrains

Zero injection current equality constrains should be

considered for the panels, but the main panel. For the ith

bus,

which is a panel, the real and imaginary parts of the currents

should have a zero injection. For the real part of the current:

∑

(19)


∑

(20)

where Ωi comprises all buses connected to the bus i. The

adopted convention of current signals is currents flowing into

bus i has a positive signal and currents flowing from bus i has

a negative sign.

E. Entries of Jacobin Matrix

The entries of the Jacobian matrix are derived by taking the

differential of the measurement equation with respect to the

state variables.

1) Active power injection measurements: If the branch is

connected to the bus k, for the real part of the current:

(21)


(22)


zero.

2) Reactive power injection measurements

If the branch is connected to the bus k, the differential with

respect to the the real part of the current:

(23)


(24)


zero.

3) Current magnitude measurements. For the real part of

the current:

√( ) ( )

(25)


5

√( ) ( )

(26)

4) Real part of load voltage phasor measurements. If the

branch ij is part of the path of the current of the load q, or if

the branch ij belongs to the set Bq, the differential with respect

to the real part of the current is:

(27)

For the imaginary part of the current it results in:

(28)

5) Imaginary part of load voltage phasor measurements:

If the branch ij is part of the path of the current of the load

q, the differential with respect to the real part of the current is:

(29)

And for the imaginary part:

(30)

6) Virtual Measurements: Taking the differential of the

equality constrains in relation to the state variables, used to

construct the C matrix, the following equations for the real and

imaginary parts, respectively, are obtained:

∑

( ) (31)


∑

( ) (32)

If the current is flowing into bus i α=2; if the current is

flowing from bus i α=1.

For current-based state estimation algorithms, the inclusion

of the virtual measurements, representing the zero injections

measurements, are discussed in [14]. In this reference the

authors use zero power injection. For an algorithm which the

state variables are the branches currents, it is more efficient

consider zero current injections, which, as can be seen in the

last equations, result in unit elements in the correspondent

Jacobian matrix elements.

F. Initialization

Initialization of the state variables presents a great impact

on the convergence speed of the algorithm. The first value for

the currents can be calculated using the voltages of the loads

terminals and the voltage of the main panel. The voltage drop

between the main panel and the loads terminals can be

calculated using the impedances and currents of each branch

connecting the load to the main panel. However, it is

necessary to consider that only the voltages at the loads are not

enough to compute all the currents, the currents from

branches, which no loads are connected, can be considered a

combination of the currents of loads. So, the currents of the

loads can be firstly calculated and then all the currents of the

other branches can be calculated using back sweeping

procedure.

The currents of the loads can be calculated by:

[ ] [ ] (33)

where [ ] is the vector containing the difference between the

main panel voltage and the measured load voltages, [ ] is a

vector containing all the loads currents and Z is the impedance

matrix.

The calculation of the elements of the impedance matrix,

which relates the currents of the loads to the voltage drop from

the main panel to the loads, depends on information about the

branches that connect each load to the main panel. The set Bq,

already defined, contains the branches connecting load q to the

main panel. The nomenclature used so far is the load q is the

one connected to the bus q. However, for the impedance

matrix, the numbers associated to the loads should be in

accordance with the sequence of the voltage and currents of

the loads in the vectors [ ] and [ ]. So the load p

corresponds to the pth

load in the current or voltage drop

vector. So, the elements of the main diagonal of the matrix Z

are given by:

( ) ∑

(34)

where Bp is a set including the branches that connect the pth

load to the main panel.

The elements out of the main diagonal are given by:

( ) ( ) ∑

(35)

where Bpt is a set including the branches shared by currents

from loads p and t. If Bp and Bt are already known, Bpt can be

calculated by Bp∩Bt. If both loads don’t share any branch this

element will be null.

Once the impedance matrix is calculated the load current

can be calculated by:

[ ] ( ) [ ] (36)

One important aspect to highlight is that the impedance

matrix is constant if the system topology is maintained.

Therefore the impedance matrix can be inverted or factored

offline, reducing the computational effort.

Some state estimation algorithms in the literature, which

use magnitude currents measurements, don’t employ these

measurements in the first iteration [10]. These algorithms use

a flat voltage start for first iteration, and in such cases current

magnitude measurements may lead to convergence problems

if used in the first iteration. For current-based state estimation

algorithms a flat voltage start can be used to calculate the first

6

iteration currents with a backward sweep procedure. In these

cases the current measurements are also excluded in the first

iteration and then introduced in the successive iterations.

Other solution proposed in [11] was reducing the weights of

current magnitude measurements in the first and second

interactions. The initialization procedure proposed in this

paper avoids problems of this nature and additionally speeds

up the algorithm convergence. Besides, all measurements are

used with the properly weights from the first iteration.

G. Algorithm Steps

The algorithm is implemented as the following steps:

Step 1: Define the system configuration and parameters:

Obtain the system configuration, the branches impedances

and the measurements.

Step 2: Initialization: Calculate the first estimation for the

load currents, x(1), based on the measurements of the

voltage at the loads terminals and the main panel voltage.

Step 3: Using back sweeping calculate all branches

currents.

Step 4: Using forward sweeping calculate all nodes

voltages.

Step 5: Calculate the updates of the system state, Δx(n).

Such updates should be calculated based on Equation (8).

Step 6: Update the system state: x(n+1) = x(n)+Δx(n).

Step 7: If Δx(n) is smaller than a convergence tolerance

(stop criterion), then stop. If the number of iteration is

smaller than the maximum iteration number, go to step 4.

If it is not, it does not converge.

In the state estimation formulation proposed, the state

vector is composed of the rectangular form of the currents.

Such choice avoids ill-conditioning problems, especially, for a

state estimation problem whose solution is highly based on

voltage measurements. The voltage measurements are

transformed from the polar form to the rectangular form, with

the same purpose of the use of the current in the rectangular

form. Actually, the use of currents in the rectangular form

during the solution of the state estimation algorithm has been

used in [10]-[12]. One of the differences is that such

algorithms are based on the power and current magnitude

measurements, differently from the presented algorithm.

The use of the currents and voltages in the rectangular form

simplifies the calculation of the Jacobian elements. In fact, for

the voltage measurements, these elements are composed by

the conductors’ reactances and resistances, as can be seen in

Equations (27)-(30).

IV. METHOD VALIDATION

The proposed load currents state estimation method is

implemented for a commercial system. The system is based on

the electrical diagram of a commercial building, which is

presented in Fig. 4. The system comprises, besides the main

panel, 6 panels and 14 three-phase loads. The main panel is

connected to a service transformer, responsible for converting

the voltage from the distribution level to 600 V, which is the

nominal voltage of all loads represented in the system. The

loads are responsible for ventilation, heating and pumping

functions of the building. The data of the system is presented

in the Appendix.

This system is monitored by measuring the phasors of

voltage of all loads as well as the phasor of voltage of the

main panel. The injected active and reactive power of the main

panel and the magnitude of current from the subpanels are also

measured, as indicated in Fig. 4.

In order to generate the input data for the state estimation

algorithm, a load flow program was employed to obtain, for

the specified loads and main panel voltage, the voltages

magnitude and angle in the loads terminals, the currents and

the injected power of the main panel. Then, the measured

value is calculated by adding a normally distributed

(Gaussian) error on its true value, as following presented:

(37)

where is the measured value,

is the true value

provided by the load flow and ei is the measurement error. The

error is a random number with a standard deviation of the

error (σi), given by rand×(σi). For a given inaccuracy of the

measurement equipment (error%), the standard deviation can

be computed as follows [16]:

(38)

For currents and power measurements the considered

error% is 2, and for the voltage measurements the error% is

0.2 [15]. The variance is computed as the square of standard

deviation of the measurements, which values are used to build

the matrix R.

Fig. 4. One-line electrical diagram of the test system.

In Table I the average of the absolute errors for the current

magnitude and angles considering 100 simulations are

presented. For each one of these simulations different errors

are associated to the measurements, since the errors are

created by a random function. The convergence criteria

applied to the state estimation algorithm considers that the

maximum update of the state variable should be smaller than

P+jQ

5

loads

6 7

Main panel 1

2

3

4

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

I12 I13

I24 I25 I36 I37

7

1.10-4

pu. As the currents resulted from the algorithm are in

the rectangular form, they were converted to the polar form

and compared with the original values obtained by the power

flow program.

For the 100 simulated cases, the initialization of the

program improved the convergence process and all simulated

cases converged. The most cases converged with 3 iterations,

and the maximum number of iterations was 4.

As can be seen from Table I, the currents from the panels

present lower average errors than the loads currents. This

behavior is explained by the magnitude current measurements

installed in these panels. Although current magnitude

measurements from the panels were considered to obtain the

results, in case of these measurements are not available, it

won’t interfere in the observability of the system. The

observability is ensured by the voltages measurements and by

the virtual measurements, that is, the zero injection current

equality constrains of the panels. If the current flow

magnitudes are not considered the only redundancy

measurement will be the active and reactive power measured

at the main panel. TABLE I

AVERAGE OF THE ABSOLUTE ERROR OF THE CURRENT AND ANGLE

Branch or

load

Mag.

(pu)

Angle

(deg.)

1 (1-2) 0.0086 0.2403

2 (1-3) 0.0100 0.3632

3 (2-4) 0.0077 0.5610

4 (2-5) 0.0053 0.4175

5 (3-6) 0.0051 0.5920

6 (3-7) 0.0069 0.4627

8 0.0118 0.8481

9 0.0110 0.7337

10 0.0115 1.5075

11 0.0117 1.9886

12 0.0113 0.7588

13 0.0115 0.7156

14 0.0129 0.8281

15 0.0131 1.5033

16 0.0105 1.4781

17 0.0113 1.5158

18 0.0111 1.7082

19 0.0111 0.5782

20 0.0122 1.0841

21 0.0121 0.7524

22 0.0104 0.7838

The results for a second case (Case II) are presented in

Table II, which shows the average of the absolute errors of

current magnitudes and angles for 100 simulations. In these

simulations no current magnitude measurements in the panels

were considered. As one can notice, comparing Table II to

Table I, the average errors for the loads (8-22) are very

similar, while the panels branches currents (1-6) presented a

higher error in Case II.

TABLE II

AVERAGE OF THE ABSOLUTE ERROR OF CURRENT AND ANGLE – CASE II

Branch or

load

Mag.

(pu)

Angle

(deg.)

1 (1-2) 0.0096 0.2431

2 (1-3) 0.0153 0.5172

3 (2-4) 0.0106 0.6931

4 (2-5) 0.0116 0.3623

5 (3-6) 0.0101 0.6100

6 (3-7) 0.0146 0.7033

8 0.0111 0.9409

9 0.0104 0.6357

10 0.0112 1.4913

11 0.0112 1.8498

12 0.0128 0.7977

13 0.0137 0.8013

14 0.0132 0.7868

15 0.0135 1.4796

16 0.0134 1.8120

17 0.0105 1.3460

18 0.0120 1.8296

19 0.0115 0.7278

20 0.0106 1.1198

21 0.0130 0.9770

22 0.0116 0.9489

Fig. 5 presents the comparison of the panels current

magnitude relative errors between Case I and Case II. For

Case I, the panels current magnitude measurements are

considered in the state estimation algorithm and for Case II

these measurements are not considered. As one can notice,

taking the panels current magnitude measurements into

consideration slightly improve the estimation of the currents

of the panels. So, if current magnitude measurements from the

panels are available it is worth to include such measurements

in the state estimation.

Fig. 5. Comparison of relative errors of the estimated current magnitude.

V. CONCLUSIONS

This paper has presented a novel and attractive approach

for microgrid load monitoring. The main idea of the proposed

method is to use easily accessible voltage measurements to

estimate load currents. The estimation method is based on the

state estimation algorithms. The proposed technique represents

a good solution for microgrid facilities where the load

conductors are inaccessible for current sensing. The proposed

current-based state estimation algorithm has been applied to a

test system and the results revealed that it is a promising

alternative direction for monitoring microgrid loads. The idea

1 2 3 4 5 60

1

2

3

4

branch number

err

or

perc

enta

ge (

%)

Case I

Case II

8

of using voltages to estimate currents as presented in this

paper has some other applications. For example, it could be

used to monitor home appliance behavior by using distributed

voltage sensors installed at various locations of a home.

VI. APPENDIX

The data of the system presented in Fig. 4 is presented at

Table III and the powers of the loads are presented at Table

IV. The nominal power is 1MVA and the nominal voltage is

600 V. TABLE III

CONDUCTORS PARAMETERS

From To R (pu) X (pu)

1 2 0.0007 0.0058

1 3 0.0007 0.0056

2 4 0.0031 0.0047

2 5 0.0043 0.0067

3 6 0.0059 0.0092

3 7 0.0041 0.0063

4 8 0.0334 0.0188

4 9 0.0352 0.0198

4 10 0.0220 0.0253

5 11 0.0224 0.0257

5 12 0.0349 0.0197

5 13 0.0342 0.0193

5 14 0.0302 0.0170

5 15 0.0213 0.0245

6 16 0.0202 0.0232

6 17 0.0208 0.0239

6 18 0.0231 0.0266

7 19 0.0356 0.0201

7 20 0.0355 0.0200

7 21 0.0346 0.0195

7 22 0.0337 0.0190

TABLE IV

LOAD PARAMETERS

Bus P(kW) Q(kvar)

8 139.2 53.6

9 149.2 63.6

10 198.9 79.7

11 168.9 59.7

12 128.2 53.0

13 120.9 53.2

14 138.0 58.5

15 178.9 80.8

16 230.0 80.8

17 204.0 80.8

18 197.2 69.7

19 178.9 69.7

20 129.2 43.2

21 139.2 53.2

22 150.2 53.6

VII. REFERENCES

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[2] H. S. V. S. K. Nunna and S. Doolla, “Energy Management in Microgrids

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[3] “Buildings Energy Data Book, Chapter 3: Commercial Sector,” U.S.

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[4] P. Palensky and D. Dietrich, “Demand Side Management: Demand

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[5] D. Dietrich, D. Bruckner, G. Zucker, and P. Palensky, “Communication

and Computation in Buildings: A Short Introduction and Overview,”

IEEE Trans. Industrial Electronics, vol. 57, pp. 3577-3584. Nov. 2010.

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[8] A. Monticelli, State Estimation in Electric Power System: A Generalized

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[9] A. Abur and A. G. Exposito, Power System State Estimation: Theory

and Implementation, Marcel-Dekker: New York, USA, 2004.

[10] M. E. Baran and A.W. Kelley, “A branch-current-based state estimation

method for distribution systems,” IEEE Trans. Power Syst., vol. 10, pp.

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[11] C. N. Lu, J. H. Teng, and W. H. E. Liu, “Distribution system state

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VIII. BIOGRAPHIES

Ahda P. Grilo (M’09) received her her Ph.D degree in Electrical

Engineering from the University of Campinas - UNICAMP, Brazil, in 2008.

Since 2009, she is an Assistant Professor at UFABC, Santo Andre, Brazil.

Currently she is a Post-Doctoral Fellow at the University of Alberta,

Edmonton, AB, Canada, on leave of absence from UFABC. Her interests

include analysis of distribution systems and distributed generation.

Wilsun Xu (M’90–SM’95–F’05) received the Ph.D. degree from the

University of British Columbia, Vancouver, Canada, in 1989. Currently, he is

a Professor and a NSERC/iCORE Industrial Research Chair at the University

of Alberta, Edmonton, Canada. His current research interests are power

quality, harmonics, and information extraction from power disturbances.

Madson C. de Almeida (M’07) received the M.Sc. and Ph.D. degrees in

electrical engineering from the State University of Campinas, Campinas,

Brazil, in 1999 and 2007, respectively. He is an Assistant Professor in the

Electrical Energy Systems Department at the State University of Campinas.

His research areas are power systems planning and control.

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