IEEE Std. 1459 power quantities ratio approaches for simplified harmonic emissions assessment

The paper investigates the suitability of using power ratio parameters for harmonic emissions assessment at the point of common coupling (PCC). The study is carried out starting from the IEEE Std. 1459-2010 apparent power decomposition, where power factors are defined for evaluating line utilization and harmonic pollution levels. In addition, the study investigates the behavior of new parameters, which are expressed in terms of ratio between IEEE Std. 1459-2010 power quantities. The study is carried out for both single-phase and three-phase case, also considering the presence of capacitors.

SECTION I. Introduction

The assessment of harmonic emissions levels is a very important issue for modern electricity distribution grids, where distortion levels are progressively increasing because of the presence of non linear loads (equipped with power electronic devices) or even distributed generation from renewable energy resources (equipped with inverter-interface for grid connection) [1]. The definition of an effective methodology for harmonic emissions assessment has been deeply debated in literature and it is an essential issue for ensuring normal power quality levels, promoting regulation for harmonic mitigation, sharing responsibility between customers and utilities for power systems disturbances [2]–​[9]. Some of them allow to separate customers and utilities contribution to harmonic distortion, allowing also to investigate the impact of single harmonic components. The limitation of such approaches is that they are difficult to be implemented in practical measurement instruments. On the contrary, some proposed solutions are able to provide less information, giving only indication on the prevailing source of disturbance or on the presence of a disturbing load. The advantage is that such methods can be easily implemented on smart meters or other measuring instruments diffused over the whole network. Current international Standards on power quality and harmonics [13]–​[19] set limits for networks and loads harmonic distortion levels; they define also measurement methods for harmonic distortion evaluation (in terms of THD or single harmonics amplitudes) and electric power quantities for quantifying flow of electrical energy, as in IEEE Std. 1459–2010 [20]. This last Standard provides a set of power definitions (active, nonactive, apparent) and related line utilization, harmonic pollution and load unbalance factors, which can be used for revenue purposes, determination of major harmonic polluters and so on. As regards the line utilization, some power factor definitions are introduced. In sinusoidal conditions, power factor is an important index for power quality evaluation and it is a very suitable parameter, which is effective for power transmission efficiency improvement and it is also simple to be measured (almost all measuring instrumentation for power systems applications can easily implement its measurement). Power factor is well defined in sinusoidal situations, while different definitions exist in nonsinusoidal conditions, for example as those reported in [20]. As regards this, the IEEE Std. 1459 is based on the separation of the fundamental components from the harmonic content of voltage and current. This approach allows to measure the traditional quantities (active, reactive and apparent powers and energies, and related power factor), and to introduce some other quantities for harmonic pollution assessment. Starting from the approach of the IEEE Std. 1459 and the common concept of power factor correction, in this paper a study is presented, aimed at investigating the possibility of using power factor concepts or other power ratio parameters for harmonic emission assessment. The advantage of such solution, in comparison with more complex methods and algorithms is that, even if only qualitatively, it can be easily integrated in common field measurement instruments (smart meters, power quality analyzers, and so on)

SECTION II. Background

A. IEEE Std. 1459–2010 and the Apparent Power Resolution

IEEE Std. 1459 [20] apparent power terms are defined starting from the separation of fundamental components of voltages and currents (at power system frequency) from the harmonics. The apparent power decomposition schemes are summarized in TABLE I. and TABLE II. for single-phase and three-phase systems, respectively. In both tables powers are divided into three basic groups: apparent, active, and nonactive; each group includes combined, fundamental and nonfundamental powers. The last rows report some combined indices for line utilization (power factors) and harmonic pollution assessment (as well as for load unbalance amount, in the three-phase case).

In the single phase case, fundamental active, reactive and apparent powers, represent the apparent power components in the ideal case of a purely sinusoidal system; all the other apparent power terms provide a basis for harmonic assessment. Fundamental power factor $(PP_{1})$ is often referred to as the displacement power factor and it is the most popular parameter to evaluate fundamental power flow condition and to adjust reactive power flow by means of capacitor banks (power factor correction). In nonsinusoidal conditions, power factor $PF$ can be interpreted as the ratio between the energy transmitted to the load and the maximum energy that could be transmitted (with the same line losses), thus it is a line utilization factor, where the maximum utilization is gained when $P=S, \text{i}.\text{e}\cdot PF=1$ (for given values of apparent power $S$ and rms voltage $V$, and even with harmonics). The overall amount of harmonic pollution is evaluated with the ratio $S_{N}/S_{1}$, that is equal to zero in purely sinusoidal conditions. Similar considerations can be made for the three-phase case, where the fundamental power factor PF $1^{+}$ allows evaluating the positive-sequence power flow conditions, while $PF, \ S_{eN}/S_{e1}$ and $S_{U1}/S_{1}^{+}$ factors allow evaluating line utilization, harmonic pollution and load unbalance amounts. In the absence of unbalance, $S_{U1}/S_{1}^{+}=0$, and the effective apparent power decomposition becomes analogous to that of the single-phase case.

B. Summary of Harmonic Emission Assessment Techniques

The most popular indices for evaluating the harmonic distortion level at a given metering section are the total harmonic distortion factors $(\text{THD}_{\text{v}}$ and $\text{THD}_{\text{I}}$ for voltages and currents, respectively. Such parameters are considered also in IEEE Std. 1459; generally speaking, they can measure the amount of the voltage and current distortion, but they don't allow assessing the disturbance source. As regards this last aspect, several methods have been proposed in literature for harmonic sources detection have been presented, based on both single-point and multi-point approaches. Some of them allow quantifying the emission level, providing basis for sharing responsibility between customers and utilities for power system harmonics; however they require the use of complex algorithms, making use also of distributed measurements infrastructure, thus the are not very suitable for diffused and simple practical measuring instruments. On the other hand, simpler solutions have been proposed, which can be able to reveal if a given load is producing harmonics or not, supporting the harmonic source detection, upstream or downstream the metering section. Examples of such approaches are those based on harmonic active power flow direction [3], [4] or on a circuital approach based on impedance measurements [5]–​[8]. Active power flow direction method can provide misleading information, depending on the operating conditions. Compensating effects among harmonic components, phase angles between harmonic voltage and current components or measurement uncertainties can affect the information correctness [9].

On the other hand impedance methods are quite complex to be implemented due to the practical challenge of the evaluation of utility and customer harmonic impedances. Various research works have been conducted to establish methods that can measure these impedances. Unfortunately, impedance measurement is a very difficult problem and research progress has been slow, i.e. independent component analysis method-ICA [10].

Also the authors have dealt with this issue, focusing the attention on the analysis of non-active powers [11]; in very brief the proposed strategy was based on the comparison of three different nonactive power quantities, which were derived form the IEEE Std. 1459 approach and measured at the same metering section. Such method was tested in several situations (both in simulation and experimentally), providing satisfactory results for the detection of the prevailing disturbance source (upstream of downstream the metering section) [12]. However, some difficulties arose in defining the thresholds for comparison, which can depend from different elements, such as the dependence of the power quantities values on the influence of other loads connected to the same PCC, the harmonic state of the system or the presence of capacitors for power factor correction [13].

SECTION III. Proposed Approach and Simulation Results

In order to investigate the possibility to overcome the aforesaid problems, a simplified approach could be used, in accordance with that commonly used for PF correction. This would allow the following advantages:

• Assessing the global harmonic emissions, by means of the comparison with a tolerable threshold for harmonics;

• Providing a simplified tool for billing purposes, regulatory frameworks, incentives for mitigating harmonics on power systems;

• Implementing the corresponding measurement in simple and practical measuring instruments (even the existing meters, with few modifications).

To this aim, in this paper a preliminary simulation study is carried out, with respect to line utilization and harmonic pollution factors of IEEE Std. 1459. The study is carried out for both the single-phase and the three-phase case (see tests systems of Figure 1. and Figure 2. respectively). The behaviour of such indicators is investigated in different operating conditions. Furthermore, the feasibility is also studied of some other simplified new indicators, which are always derived from the IEEE Std. 1459 apparent power resolution.

More in detail, apart from the defined $PF_{1}, PF$ and $S_{N}/S_{1}$, the behaviour of the following new power ratio parameters is investigated: $P_{1}/S, S_{1}/S, Q_{1}/N$ As regards the first parameter, $P_{1}/S$, it can allow evaluating the total amount of line utilization, considering not only the fundamental power flow condition, but also the presence of harmonics (which are included in S); in purely sinusoidal case, $P_{1}/S=PF_{1}$, thus the indicator behaves as a power factor indicator (whose maximum achievable value is equal to $PF_{1}$). As regards the second parameter, $S_{1}/S$, it can allow evaluating the whole harmonic emission level, with respect to both active and reactive power components; in purely sinusoidal conditions, $S_{1}/S=1$, thus the indicator behaves as a power factor indicator (whose maximum achievable value is equal to 1). As regards the last parameter, $Q_{1}/N$, in previous papers [11] the authors showed that the reactive powers behavior depends on the load nature (linear or nonlinear); in a given distorted working condition, $Q_{1}$ is a minimum reference value, since it is the only nonactive power component in the sinusoidal condition; $N$ is a maximum reference value since it groups all the nonactive components of the apparent power [11]; thus $Q_{1}\leq N$. In sinusoidal condition the two quantities are equal. When the load is linear, the amount of current distortion is low and it is due only to the distortion of the supply voltage; in this case the difference between $Q_{1}$ and $N$ is small. If the load is non linear the amount of current distortion is higher, $Q_{1} > N$. Thus, the comparison between $Q_{1}$ and $N$, calculated in the same metering section and in the same working condition, can give a piece of information on the presence of disturbing loads.

Table I. IEEe std 1459–2010 apparent power resolution — single-phase case

Table II. IEEE std 1459–2010 effective apparent power resolution — three-phase case

A. Single-Phase Study

A preliminary validation of the proposed approach was carried out on a simple single-phase test system, which represents a simplified situation, in which both the supply and the load can be responsible for the harmonic distortion [11]. A scheme of the test system is reported in Figure 1. The system consists on: a supply voltage $E_{1}=230 \ \text{V}$ at the fundamental power supply frequency (50 Hz), with a phase angle $\alpha_{1}=0^{\circ}$; a line impedance $Z_{_{-}Line}$ with $R_{L}=0, 1172 \ \Omega$ and $L_{L}=3, 934\cdot 10^{-4}$ H; a resistive-inductive load $Z_{_{-}Load}$ with capacitor $C$ for power factor correction $(\text{In}=5 \ \text{A},\ \cos\varphi=0, 95)$.

Different harmonics can be added on both the supply voltage and the load current, by means of voltage and current generators (represented in the figure with $E_{h}$ and $I_{h}$).; thus, it is possible to simulate the presence of a source of distortion on the supply side and/or the load side.

Several simulations were carried out in different working conditions, which were obtained by introducing various harmonics on voltage and current. Voltage and current were measured at the load terminals (as represented by the voltage and current meters of Figure 1. As an example, the first simulation was carried out by introducing a fifth harmonic on the supply voltage, with rms value $E_{5}=0, 1 \ E_{1}$; no harmonics were injected by the load. The measured quantities are reported in TABLE III. As shown in the table, the values of $PF_{1},\ PF, \ P_{1}/S, \ S_{1}/S$ and $Q_{1}/N$ are between 0.94 and 1, in accordance with the linear load simulated conditions $(S_{N}/S_{1}$ is small, as the distortion amount is low). Further simulations were carried out by introducing the fifth harmonic on both the supply voltage and the load current, with $E_{5}=0, 1\ E_{1}$ and phase angle $\alpha_{5}=0$ and $I_{5}=0, 4\ I_{1}$ and phase angle $\beta_{5},\text{variable}$, from $0^{\circ}$ to $360^{\circ}$. Thus, in this case the simulated load is nonlinear. The obtained results are synthesized in Figure 3. In all cases the values of $PF, \ P_{1}/S, \ Q_{1}/N$ and $S_{1}/S$ are lower than $PF_{1}$ and $S_{N}/S_{1}$ is higher than the previous simulated case, because of the harmonic injected by the load and depending on the phase angle $\beta_{5}$, value.

B. Three-Phase Study

Further simulations were carried out on a simple three-phase test system which is able to simulate different working conditions, with both sinusoidal or distorted supply and linear (RL) or non linear (N.L.) loads [11]. A linear load with capacitor bank for power factor correction (RLC) has been also added at PCC, in order to take under consideration the presence of capacitor banks. A block diagram of the developed system, with its main characteristics, is shown in Figure 2. Simulations were carried out for different working conditions. Some of the obtained results are summarized in Figure 4. They are referred to the following load conditions, all balanced and with nonsinusoidal supply voltage (switch 1 open, switch 2 closed):

• Test A. linear load, RL (switches: 3 closed; 4 and 5 open);

• Test B. linear load with capacitors, RLC (switches: 5 closed; 3 and 4 open);

• Test C. non linear load, N.L. (switches: 4 closed; 3 and 5 open);

• Test D. RL and RLC loads (switches: 3, 5 closed; 4 open);

• Test E. N.L. and RL loads (switches: 3, 4 closed; 5 open);

• Test F. N.L. and RLC loads (switches: 4, 5 closed; 3 open);

• Test G. All loads (switches: 3, 4, 5 closed).

Figure 1.

Single-phase test system.

Figure 2.

Three-phase test system

Table III. Single-phase test— measurements with $E_{5}=0, 1\ E_{1}$

It can be observed that the obtained values for linear load are similar to those obtained in the single phase test of TABLE III. In fact, the values of $PP_{1},\ PF, \ P_{1}/S, \ Q_{1}/N$ and $S_{1}/S$ are high (between 0.94 and 1), while $S_{N}/S_{1}$ is small, as the load harmonic emission is nil. On the contrary, values for non linear load are similar to those obtained in the single-phase test with load harmonic injection. In fact the values of $PF, P_{1}/S, Q_{1}/N$ and $S_{1}/S$ are lower than $PF_{1}$ and $S_{N}/S_{1}$ is higher than that obtained for the linear load, because of the harmonics injected by the non linear load. As regards the behaviour of the load with capacitors bank (RLC), it can be observed that, when the RLC load is the only one load at PCC or it is connected together with the linear RL load, the values of $PF, \ P_{1}/S$ and $S_{1}/S$ are similar to $PF_{1}$ while the most significant difference is obtained for $S_{N}/S_{1}$ and $Q_{1}/N$ because the capacitors amplify the distortion from the nonsinusoidal supply voltage. On the contrary, when both RLC and N.L. loads are connected to the PCC, the values of $PF, \ P_{1}/S$ and $S_{1}/S$ and $Q_{1}/N$ are lower than $PF_{1}$ because the capacitors amplify the distortion injected both by the N.L. load and the supply; thus the RLC load behaves quite similarly to the non linear load, as expected.

Figure 3.

Simulation results. Single-phase case. (a) IEEE 1459 line utilization and harmonic pollution factors; (b) new power ratio parameters

Figure 4.

Simulation results. Three-phase case. (a) IEEE 1459 line utilization and harmonic pollution factors; (b) new power ratio parameters

SECTION IV. Conclusions

The paper has investigated the suitability of using power factors and the other new power ratio parameters for harmonic emissions assessment at the point of common coupling (PCC). The most sensitive power ratio parameter to harmonic emission is $Q_{1}/N$ while $PF_{1}$ could be considered as reference value. The study has been carried out starting from the IEEE Std. 1459–2010 apparent power decomposition, by using only quantities derived from the IEEE Std. 1459 apparent power resolution. The study has been carried out for both single-phase and three-phase case, also considering the presence of capacitor banks. The obtained results show that the proposed approach allow obtaining a qualitative information on the presence of disturbing loads connected at PCC. The employed power ratio parameters are very easy to be measured, thus they could be easily implemented in common instrumentation for power system measurements.