1. Introduction
Electrical energy is the most widely used source of energy nowadays. Its quality will have a direct impact on industrial production. With the development of automated production lines and precision equipment, high power quality is highly desired. Some kinds of key automation equipment are extremely sensitive to interference in the distribution network, such as just permission to tolerate inferior power to 1–2 cycles [
1]. Among the power quality problems, the voltage sag has caused widespread concern. According to some historical records, in countries, such as Europe and the United States, the economic loss that is caused by voltage sags can reach millions of dollars [
2]. According to statistics, voltage sag contributes about 70%-90% of power quality problems [
3]. How to eliminate the impact of voltage sag on the sensitive load has become an important issue in the field of power quality nowadays.
A dynamic voltage restorer (DVR) is a series voltage compensation device that can effectively tackle power quality problems, such as voltage sag [
4].
Table 1 gives a comparison between the Uninterruptible power system (UPS), Static synchronous compensator (STATCOM), and DVR. It is obvious that DVR has an advantage in dealing with a short time voltage sag, but DVR has a high investment cost because storage capacity is expensive. An advanced compensation strategy is important for reducing the cost of DVR.
As shown in
Figure 1, a DVR is generally composed of a storage capacitor, a pulse-width modulation (PWM) inverter, an LC filter circuit, a series transformer, and a relative control system. When the voltage sag occurs in the system, the voltage drop detection module transmits the detected falling voltage information on amplitude and phase angle to the compensation module, and the compensation part calculates the compensation voltage amplitude and phase angle, according to the reference voltage set by the compensation strategy. Subsequently, a corresponding control signal is generated through the PWM module according to the compensation calculation result, and to make the inverter output the desired compensation voltage waveform. Finally, after filtering, the system voltage is combined and compensated to the sensitive load, so that the voltage amplitude and phase angle of the sensitive load are maintained at normal levels [
5].
The main aspects in the research field of DVR include the DVR topology [
6,
7,
8], the location of the output filter capacitance [
9], the series transformer’s capacity [
10], the control strategies [
11,
12], the voltage detection methods [
13], and the compensation strategies [
14]. The studies about the DVR control strategies [
11,
12] mainly focus on how to improve DVR dynamic performance and harmonic control. The studies about the compensation strategies [
14] mainly focus on how to generate the appropriate reference signal economically and effectively. Plenty of researches concentrate on the DVR compensation strategies. Among them, presag compensation, in-phase compensation, and minimum energy compensation are mainly employed [
15,
16]. The above compensation strategy referenced focus on how to minimize the storage capacitance capacity and increase the DVR effective duration. A new compensation strategy that is based on the combination of minimum energy compensation method and the longest compensation duration method is proposed [
17]. The simulation results prove that this compensation strategy can provide compensation of a longer time under the limited energy storage capacity, but the strategy put forward higher requirements on the detecting speed and the accuracy of the equipment. In [
5], the compensation voltage vector of DVR is represented by polarization ellipse parameters, and the most effective voltage compensation strategy with the minimum DVR capacity can be achieved by partially optimizing the direction of compensation voltage. However, the compensation to the jumping voltage phase angle of the sensitive load is not considered in the strategies that are mentioned above. For such a situation, a new DVR optimization compensation strategy is proposed in [
18], by designing the DVR transition process compensation. As a result, the voltage phase of the sensitive load is compensated, and the compensation time is also significantly increased.
Table 2 shows the comparison between the state-of-the-art compensation methods. At present, the researches on DVR compensation strategies focus on the elimination of phase angle jump and the reduction of energy storage capacity to decrease the DVR investment cost. The possible effect of DVR action on adjacent loads has not been studied.
The current research on DVR compensation strategy focuses on how to better improve the compensation capability and the compensation duration for the voltage sag on the sensitive load, but the impact caused by DVR action on the parallel load, named as the adjacent load thereinafter, to the sensitive load at the same busbar has been rarely investigated so far. When a voltage sag occurs in main gird, DVR as an additional source to compensate the voltage for the sensitive load, might cause secondary impacts on the adjacent load. The adjacent load, in turn, might impair the efficiency of DVR in some unfavourable scenarios. The expected influences of DVR on the adjacent load will be pursued as possible, and in which DVR compensation strategies might play an important role. Therefore, the mechanism of the influence of DVR on the adjacent load is worth studying. Besides, when using DVR to mitigate voltage sags, there is an inevitable controversial issue among users who install DVR and those who do not. A more transparent and fairer method in the economic aspect is proposed to address the issue, which is important when the rights of individual users are highly respected nowadays.
In the field of economics, externality, or the spillover effect, reveals that economic activity not only produces the expected effect, but also has certain impact on other parts, except for the main entity in economic activity. This impact is difficult to embody in currency or price in market transactions [
19]. Nowadays, the study of externality has covered most economic production activities of the society. The two major problems about externality are how to define externality and how to internalize it [
20]. In fact, except for traditional economic activities, some scholars have progressively introduced externality theory into the electrical field. Literature [
21] defines energy externality as a kind of transcendence of traditional power systems and it needs to be considered as one of the important problems when constructing new generation of power systems. Literature [
22] studies the construction of a new optimal power configuration and externality algorithm based on the externality of communication networks. Literature [
23] calculates the external impact of wind power integration on multiple subjects of the power system, and an effective reference is provided for grid operators and in the formulation of subsidies. In the behavior of the DVR compensation for the voltage sag of the sensitive load, the sensitive load is seen as the activity entity, and the adjacent load is the receptor in the whole structure. When the DVR is only carried out compensation when considering the private benefit of the sensitive load, with the presag compensation strategy, for example, the negative externalities or positive externalities might be produced in adjacent loads. In other circumstances when the DVR considers the common interests of the sensitive load and the adjacent load, that is, the normal coordinated strategy to compensate the sensitive load, the compensation effect of the sensitive load itself will be reduced.
From the perspective of traditional equivalent circuit analysis, this paper firstly explores the influence of DVR on adjacent load that is based on the parameters change of network. Subsequently, combined with the theory of externality, a new concept of the first event circle (FEC) is proposed and the externality boundaries are clearly defined when considering network parameters to handle the controversy caused by DVR action among multi entities. Finally, an optimization compensation strategy of DVR based on externality is proposed to ensure different entities’ benefits, and the feasibility and effectiveness of the proposed method is verified by simulation in the MATLAB/Simulink platform.
2. Analysis of Influence of DVR on the Adjacent Load
Figure 2 illustrates the equivalent circuit diagram of the DVR, sensitive load, and adjacent load in order to theoretically analyze the influence of DVR on adjacent load. DVR is regarded as a series voltage source. When there is no voltage sag problem, the switch
S closes, and the DVR is standby mode.
When a voltage sag occurs in the infinite system, the monitoring device of DVR triggers to open the switch S, and the DVR outputs the voltage needed. At this time, there are two sources to supply voltage, i.e., the system source and the DVR. The circuit is divided into two parts, according to the superposition theorem for this linear system in the study, as shown in
Figure 3 and
Figure 4, respectively.
The following relationship is obtained, according to the current distribution principle:
where the ratio
.
In order to simplify the Equation (1), the distribution coefficient
k is defined:
where
p is the amplitude of
k;
is the phase angle of
k.
Substitute (2) into Equation (1), then
Meanwhile,
k is rationally treated, and expressed into a general plural form, as follows:
It shows that k is dependent on the complex impedance of the transmission line and the complex impedance of the adjacent load. The value of k has the following three cases:
(1) k closes to 1 when x approaches zero, meaning is much smaller than . At this case, the might be close to . As the reference direction of the compensation current provided by DVR is opposite to the reference direction of the adjacent load current itself, the existence of compensation current may cause the adjacent load current drop again (secondary current drop) or rise after the first current drop instantaneous response to the voltage sag. The extent of this subsequent current rise or secondary current drop depends on the size of x.
(2) k is a complex number whose real part is less than 1 when x is set as constant , meaning , and the compensation current of the adjacent load can be obtained with the scaling and rotating of the sensitive load compensation current. There is still a secondary current rise or secondary current drop of the adjacent load for this case.
(3) k approaches 0, when x tends to infinity, meaning that can be ignored. In this case, also closes to 0. For the DVR-sensitive load structure with adjacent load, the influence of the DVR on the adjacent load is generally effective, since the equivalent system line impedance is always large enough to be considered in a real case. The larger the k is, the more influence of the DVR on the adjacent load will be.
In the circumstance where the system structure parameters are given, the magnitude and phase angle of the
is affected by
, and the amplitude of
depends on the magnitude and phase angle of the DVR compensation voltage. How the DVR compensation voltage affects the adjacent load behavior in terms of current change with different
would be addressed by the phasor diagram. The phasor diagram analysis can simplify the complex theoretical analysis into an intelligible phasor analysis and it is widely used in the analysis of DVR compensation strategy regarding the DVR compensation strategy [
5,
17,
24,
25]. The analysis of different
is shown, as follows:
(A) When the impedance of the sensitive load is different from that of the adjacent load, namely
, as shown in
Figure 5.
In
Figure 5, as
is opposite to
in the direction, when solving the secondary current change of the adjacent load
, it is necessary to move
along the reverse direction and parallel to the point F to obtain
. In this diagram, the angle between
and
is defined as
. The angle between
and
is defined as
. In
,
, and
, with
is to be searched.
and
can be obtained by the solution of
, and
is the angle between the adjacent load current and the sensitive load current after the voltage sag occurs, which can be obtained by the measuring device of DVR. From
Figure 5, it can be seen that the adjacent load current change highly depends on the relation of the impedance of the sensitive load and that of the adjacent load.
(B) For simplification, while assuming
, the corresponding phasor diagram is shown in
Figure 6. The phasor like
in the
Figure 6 means that
and
are equal. Noticeably, the analysis in
Section 3 is based on the assumption
.
Taking the classical presag compensation strategy of DVR as an example, the corresponding conditions for the secondary current drop, secondary current rise, or keeping current constant for adjacent load are deduced, as follows.
As the reference direction of the compensation current for the adjacent load is opposite to the original current reference direction of the adjacent load, one can obtain
In
Figure 3, it is shown that
is rotated 180 degrees counterclockwise around point F and is then summed with
to obtain
. The Equations (6) and (7) can be deduced, referring to
Figure 4 and
Figure 5 as
When the secondary current drop of adjacent load occurs:
Substitute the Equations (6) and (7) into (8), then
Similarly, if secondary current rises with DVR action after voltage sag and the adjacent load current amplitude is kept unchanged, (11) and (12) can be determined, respectively.
In Equations (10)–(12), except for the amplitude and phase angle of , other variables can be obtained in given real cases. By controlling the amplitude and the phase angle of , the influence of DVR on the adjacent load in terms of current change could be estimated and directed based on different strategies.
4. Design of DVR Optimization Compensation Strategy Considering Externality
Before the optimization compensation strategy is proposed, several hypotheses for the establishment of the strategy need to be explained:
The proposed compensation strategy in this paper is only applicable to the optimization of fundamental signal.
The line impedance should not be ignored, otherwise the externalities will be very small, and the compensation strategy of DVR should not take the possible externalities on adjacent loads into a consideration.
The externalities of the DVR on adjacent loads can only be discussed if the equivalent circuit structure shown in the
Figure 2 is satisfied.
According to the previous section, the range of the externality on the adjacent load that is caused by DVR compensation will be obtained with the sag current of the sensitive load, the sag current of the adjacent load and DVR compensation limit determined by its capacity.
Figure 10 shows the optimized compensation strategy to minimize the externality.
In
Figure 10, If the condition
w < 0 is not met, it indicates that the externality of the initial compensation strategy is non-negative, and the compensation costs will be given to the DVR owner directly, and there is no need to further optimize the compensation strategy. If the judgment
w < 0 is yes, then the initial compensation strategy needs to be optimized. Subsequently, if
is not true, this means that even the pursuing optimization strategy cannot achieve no or positive externality, thus the target is to achieve the minimum negative externality as much as possible.
Immediate compensation is not suitable for the single external economic compensation payment in the flow chart due to its small value. Instead, the grid operator will offer compensation to the DVR owners as soon as the cumulative external economic compensation reaches a certain value. If the externality is positive, the grid operator will reward the DVR owners; conversely, if the externality is negative, the network operator will punish the DVR owners with “Pigovian tax” and compensate the adjacent load of DVR at the same time. The compensation that is caused by negative externality is marked as a negative value, and the compensation that is related to the positive externality is considered to be positive.
Potentially, different compensation ranges might result in scalable externality, but the calculation process is consistent. Taking
Figure 9 as an example, the computational complexity of the model is analyzed. According to
Figure 11, the whole calculation model is divided into two parts: calculation of external compensation range and calculation of external costs. The calculation model does not involve iteration process, but it mainly involves algebraic calculation and a large number of trigonometric function’s operations. When compared with the traditional compensation strategies, the proposed optimization strategy only increases the calculation of some algebraic equations. Its computational complexity and calculated time are controllable, which is within the acceptable range of real projects.