A new method of electric energy metering considering harmonic responsibility

ZHU Si-wei，TIAN Ming-xing，LI Jun，GAO Yun-bo

(1. School of Automation and Electrical Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China；2. Rail Transit Electrical Automation Engineering Laboratory of Gansu Province，Lanzhou Jiaotong University, Lanzhou 730070，China)

Abstract：Aiming at the shortcomings of the existing electric energy metering method, combining with the harmonic responsibility analysis model based on the reference impedance method and the idea of apparent power decomposition in IEEE Std 1459-2010 standard, two new metering indicators—billing active power and billing power factor are defined.A new electric energy metering method is proposed and its specific implementation steps are given.The simulation model is built in Matlab/Simulink, and three different examples are set up.Using the simulation data, the various metering indicators need to be examined by the existing electric energy metering method and the new electric energy metering method are calculated.The calculation results show that the new electric energy metering method not only overcomes the shortcomings of the existing electric energy metering method, but also is very easy to be popularized and applied.

Key words：electric energy metering；harmonic responsibility；billing active power；billing power factor

0 Introduction

With the development of economy and technology, the structure of the power grid has become more and more complex, and the problem of harmonic pollution has become increasingly serious.Due to lots of harmonics existing in the grid, the traditional full active power metering under sinusoidal conditions is no longer applicable.Therefore, exploring a fair and reasonable electric energy metering method suitable for non-sinusoidal conditions is a hot issue in both engineering and academic circles[1-2].

A large number of studies have shown that with the full active power being used to charge electricity fee, the linear customers not only will be harmed by harmonics but also must pay the electricity fee of harmonic active power that they are forced to absorb.While the nonlinear customers convert part of fundamental active power that they absorb into harmonic active power that is sent back to the utility, which harms the utility and other customers.However, the electricity fee that the customers need to pay is less[3-4].Therefore, the fundamental active power has been widely used to charge electricity fee in places with a good deal of nonlinear customers, such as high-power rectification industry[4-6].Power factor is another important metering indicator that electric energy metering method needs to examine.At present in China, the power supply company mainly measures the fundamental power factor of the customer and then adjusts the electricity fee according to the “power factor adjustment electricity fee method”.

However, the disadvantage of the electric energy metering method examining the fundamental active power and fundamental power factor is that it is unable to compensate linear customers that are harmed by harmonics, and it is not possible to punish the nonlinear customers for generating harmonics which will cause losses to the utility and other customers.For nonlinear customers, examining their total power factor can punish them to some extent[7-8].But in practice, it is difficult to determine whether the customer is linear or nonlinear in advance.Furthermore, only examining total power factor can not clearly divide the harmonic responsibility of the utility side and the customer side.Since the utility side may contain background harmonics, it is also unreasonable.

In this paper, we propose a new method of electric energy metering that takes into account harmonic responsibility.It can not only compensate the customers for their behaviors of absorbing harmonics, but also punish the customers for generating harmonics.And the measurements of the metering indicators that the new method need to examine are easy to be implemented in engineering.

1 Metering indicators

A simple single phase circuit is shown in Fig.1, the PCC is called as the point of common coupling.

Fig.1 Single phase circuit

The fundamental active power and fundamental power factor of the customer are

P1=UPCC1IPCC1cosφPCC1,

(1)

(2)

whereUPCC1andIPCC1are the root-mean-square(RMS)values of fundamental component of the voltageuPCCand currentiPCCof the customer, respectively;φPCC1represents the phase displacement between the fundamental voltage and current, andS1is the fundamental apparent power.The harmonic active power under harmonic orderhof the customer is expressed as

Ph=UPCChIPCChcosφPCCh,

(3)

whereUPCChandIPCChare the RMS values of harmonic voltage and current under harmonic orderhof the customer, respectively; andφPCChrepresents the phase displacement between the harmonic voltage and current under harmonic orderh.The total power factor of the customer is

(4)

whereUPCCandIPCCare the total RMS value of the voltage and current of the customer, respectively.They can be calculated by

(5)

(6)

Obviously, the fundamental active power and the fundamental power factor cannot reflect the contents of harmonics.Although examining the total power factor can reflect harmonics, it cannot divide the harmonic responsibility of the utility and customers.

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2 Analysis of harmonic responsibility

2.1 Norton equivalent model based on reference impedance method

Fig.2 Norton equivalent circuit under harmonic order h

According to the reference impedance method, the resistance component of the customer load is taken as the reference impedance of the customer side, and then the calculation formula of the reference impedance of the customer side is

(7)

The sum of the short circuit impedance of the power grid and the impedance of the last transformer before the PCC, which can be directly obtained in practice, is proposed as the utility side reference impedance.Then the equivalent harmonic current sources under harmonic orderhof the utility side and customer side can be calculated with Eqs.(8)and(9), respectively, that is

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

2.2 Decomposition of harmonic active power

Combining Eq.(3)with Eq.(14)and referring to the method in Ref.[7], the harmonic active power under harmonic orderhof the customer can be decomposed as

(16)

wherePUhrepresents the harmonic active power under harmonic orderhthat the customer is forced to absorb from the utility side and is simply referred to as the utility harmonic power under harmonic orderh.And thePChrepresents the harmonic active power under harmonic orderhthat the customer generates and is simply referred to as the customer harmonic power under harmonic orderh.

2.3 Decomposition of apparent power

In accordance with the latest power definition standard IEEE Std 1459-2010[13]which is being adopted by more and more researchers, the total apparent power of the customer can be decomposed as

S2=(UPCCIPCC)2=

(17)

whereD1is the current distortion power,DUis the voltage distortion power,SHis the harmonic apparent power,SNis the nonfundamental apparent power.Their expressions are

(18)

(19)

(20)

Furthermore, the ratio of the nonfundamental apparent power to the fundamental apparent power reflects the degree of harmonic pollution at the PCC.

In order to divide the harmonic responsibility of the utility side and the customer side, the customer side nonfundamental apparent powerSNCis defined as

(21)

(22)

SHCUCHICH,

(23)

SHUUUHIUH.

(24)

3 Electric energy metering method considering harmonic responsibility

3.1 Billing active power and billing power factor

On the basis of examining the fundamental active power, the sum of the utility harmonic power under each order is used as the evaluation index to compensate the customers who are forced to absorb harmonics.Consequently, a new metering indicator, billing active power, is defined andαis its corresponding adjustment coefficient.The larger the value ofα, the greater the degree of compensation.The definition formula of the billing active powerPbis

(25)

On the basis of examining the fundamental power factor, the customer side nonfundamental apparent power is used as the evaluation index to punish the customers who generate harmonics.Consequently, another new metering indicator, billing power factor, is defined andβis its corresponding adjustment coefficient.The larger the value ofβ, the greater the degree of punishment.The definition formula of the billing power factorλbis

(26)

3.2 Selection of adjustment coefficients

The relationship between the customer side harmonic apparent power and the utility side harmonic apparent power can be used as the criterion for judging the position of the main harmonic source[14].Therefore, the adjustment coefficientαmight as well be determined in accordance with the range of the ratio of the utility side harmonic apparent power to the customer side harmonic apparent power, as is shown in Table 1.And the adjustment coefficientβmight as well be determined according to the range of the ratio of the customer side harmonic apparent power to the utility side harmonic apparent power, as is shown in Table 2.

Table 1 Adjustment coefficient α

Table 2 Adjustment coefficient β

3.3 Steps of new electric energy metering method

Step 1)Measuring the data of the voltage and current at the PCC, respectively, then obtaining the harmonic voltage and current under each harmonic order by using fast Fourier transform(FFT)analysis;

Step 2)Calculating the reference impedance of the customer side with Eq.(7);

Step 3)Calculating the equivalent harmonic current sources under harmonic orderhof the utility side and customer side with Eqs.(8)and(9), respectively;

Step 4)Calculating the utility sideh-order harmonic current and voltage contribution and the customer sideh-order harmonic current and voltage contribution with Eq.(10)to Eq.(13), respectively;

Step 5)Judging whether the harmonic orderhis equal to the highest harmonic order concerned.If so, proceeding to step 6; If not, reassigning the harmonic orderh, and then returning to step 3;

Step 6)Calculating the customer side and utility side harmonic apparent power with Eqs.(23)and(24), respectively, and selecting the values of the adjustment coefficientsαandβby looking up Tables 1 and 2, respectively;

Step 7)Calculating billing active power with Eq.(25)and calculating billing power factor with Eq.(26);

Step 8)Using the billing active power of the customer to charge the electricity fee, and then using the billing power factor of the customer to adjust the electricity fee according to the “power factor adjustment electricity fee method”.

4 Analysis of examples

The simulation circuit is built in Matlab/Simulink, and three examples are set in terms of whether the utlity side containing background harmonics and whether the customer being nonlinear.Since the main harmonic components in the power grid are odd harmonics, only the third, fifth, seventh, and ninth harmonics are considered in the simulation.

4.1 Simulation model settings

Example 1: The utility side contains the third and fifth background harmonics, and the customer is a linear resistance-inductance load.Simulation circuit is shown in Fig.3, and the various parameters set in the circuit are shown in Table 3.Through the FFT analysis, the harmonic voltage and current under each harmonic order at the PCC are obtained, as listed in Table 4.

Fig.3 Simulation circuit when customer is linear

Table 3 Parameters of simulation circuit

Table 4 Harmonic voltage and current under each harmonic order at PCC in example 1

Example 2: The utility side does not contain any background harmonic, and the customer is a single phase uncontrolled rectifier circuit.Simulation circuit is shown in Fig.4.And the load parameters of the rectifier bridge areR=5 Ω andL=6 mH.Through the FFT analysis, the harmonic voltage and current under each harmonic order at the PCC are obtained, as listed in Table 5.

Fig.4 Simulation circuit when customer is nonlinear

Table 5 Harmonic voltage and current under each harmonic order at PCC in example 2

Example 3: The utility side contains the third and fifth background harmonics, and the customer is a single phase uncontrolled rectifier circuit.Simulation circuit is shown in Fig.4.Through the FFT analysis, the harmonic voltage and current under each harmonic order at the PCC are obtained, as listed in Table 6.

Table 6 Harmonic voltage and current under each harmonic order at PCC in example 3

4.2 Calculation and analysis of metering indicators

The simulation parameter of the system impedance is selected as the reference impedance of the utility side.And the reference impedance of the customer side of each example is calculated according to the step 2 in Section 3.3.The values of all reference impedances are shown in Table 7.

Table 7 Reference impedances of utility side and customer side in every example

The utility side harmonic current and voltage contribution under each harmonic order and the customer side harmonic current and voltage contribution under each harmonic order in every example are calculated in accordance with step 3 to step 5 in Section 3.3.Then, according to step 6, the adjustment coefficients in every example are determined.Their values are shown in Table 8.Finally, in the light of step 7, all metering indicators that the existing electric energy metering method and new electric energy metering method considering harmonic responsibility need to examine in every example are calculated.The results are shown in Table 9.

Table 8 Adjustment coefficients in every example

Table 9 Metering indicators in every example

It can be seen from Table 9 that in the example 1, the billing active power of the customer is less than the fundamental active power, and the billing power factor of the customer is equal to the fundamental power factor, which manifests that the new electric energy metering method considering harmonic responsibility is able to make the linear customer that is forced to absorb harmonics obtain a certain compensation.In the example 2, the billing active power of the customer is equal to the fundamental active power, and the billing power factor of the customer is less than the fundamental power factor, indicating that the new electric energy metering method considering harmonic responsibility is able to punish the nonlinear customer for generating harmonics.In the example 3, the billing active power of the customer is less than the fundamental active power, and the billing power factor of the customer is less than the fundamental power factor, manifesting that when the utility side contains background harmonics, the new electric energy metering method is able to simultaneously compensate and punish the nonlinear customer.Regardless of the utility side or the customer side, the above results are very fair and reasonable.

5 Conclusion

The new method of electric energy metering considering harmonic responsibility uses the billing active power of the customers to charge the electricity fee, which compensates them for their behaviors of absorbing harmonics.And it uses the billing power factor of the customers to adjust the electricity fee, which can punish them for their behaviors of generating harmonics.Therefore, the new electric energy method can overcome the deficiency of the existing electric energy metering method that examines the fundamental active power and fundamental power factor of the customers.

The practicalities of the new electric energy metering method are reflected in the following three points.Firstly, it avoids compensating the punishing the customers repetitively.Secondly, the existing idea of adjusting the electricity fee in accordance with power factor is continued to use.There is no need to establish a new charging system based on the percentage of harmonic responsibility.Lastly, the metering indicators that the new method need to examine are calculated from the voltage and current data at the PCC.And implementing the calculation method by programming is convenient.So it can be easily applied to the modern smart meters.