Cooperative Control of Active Power Filters in Power Systems without Mutual Communication

Abstract

The procedure for calculating controller parameters of the APFs implemented into a multibus industrial power system for harmonic voltage mitigation is presented. The node-voltage-detection control strategy is applied and the basic controller parameters are found under the condition that the demanded THD factors at the buses where the APFs are placed will be obtained. A cooperative control of several APFs without mutual communication is proposed, simulated, and experimentally verified. By tuning the controller gains without considering the power circuit parameters, all APFs used tend to share harmonic load currents approximately equally regardless of the operation modes of the nonlinear loads in different parts of the power system.

1. Introduction

The performance and effectiveness of the active power filter (APF) depends on the point of its connection in the multibus power system [1–3].

The effectiveness of the bus voltage and branch current detection control strategies of the APFs used in multibus power systems was analyzed and compared in [4]. In [5] the single APF-multiple harmonic optimization problem was formulated in such a way that its solution yields optimum PI controller parameters of the APF for both the control methods.

In [6], an analytical solution of the multiple APF-single harmonic problem in the frequency domain was formulated. In the case study presented in [6] optimal compensator currents for individual harmonics in case of two APFs were calculated, interaction of the APFs analyzed and, finally, the best places for two APFs recommended.

In [7], an automatic gain adjustment of the APFs was introduced to make each APF damp out harmonic propagation throughout power distribution systems without considering the circuit parameters. The gain adjustment can reduce the APF compensating currents and losses.

In [8], a cooperative control of several APFs with the help of a communication system was proposed. Again, the APFs damp out harmonic propagation throughout power distribution systems. The APFs control gains are tuned by a computer on the basis of voltage total harmonic distortion (THD) at each APF place of installation. The control reduces the voltage THD at buses of the APFs installation and balances the compensating currents as well, irrespective of the power system conditions.

An instantaneous current control loop to ensure proper sharing of harmonic components of nonlinear loads among inverters in distributed generation systems is included in wireless controllers of these inverters [9]. Contrary to [7, 8], the output-voltage THD of distributed inverters are not directly included into the gain adjusting mechanism, although the algorithm helps to hold the voltage THD at a reasonable level.

Also in [10], a harmonic droop scheme for sharing harmonic content of the load currents among distributed generation systems is proposed, being a part of a load-sharing controller that uses only low-bandwidth data communication signals among individual generation systems.

Finally, a distributed APF system for mitigating the harmonic distortion in power systems is proposed in [11]. A droop control strategy based on the VA rating of individual APFs ensures the distribution of the harmonic filtering workload in proportion to the rated capacity of every APF unit. The algorithm does not need the real-time communication among APF units. Again, the output-voltage THD of distributed inverters are not directly included into the gain-adjusting mechanism in [10, 11].

So, no wireless cooperative control strategy considering both the output-voltage THD of distributed inverters and the rated capacity of every APF has been reported till now.

Here, the multiple APF-multiple harmonic problem in case of applying the node-voltage-detection control strategy is formulated. A cooperative control without any communication of several APFs is proposed, simulated, and experimentally verified. The control aims, by tuning the controller gains without considering the power circuit parameters, at attaining the demanded THD of the voltages at the buses where the APFs are placed, provided that the VA ratings of individual APFs are not exceeded. If the load of an APF tends to be higher than its rated capacity, the algorithm tunes the APF controller gain further to hold the APF below its nominal rating. Additionally, the APF is prevented from a too low load as well by applying this procedure. Thus, all APFs used tend to share harmonic load currents approximately equally regardless of the operation modes of the nonlinear loads in different parts of the power system.

2. Multibus Industrial Power System

An example of the multibus industrial power system shown in Figure 1 consists of overhead lines, cables, transformers, induction motors, rectifiers, and passive filters.

Figure 1 

Multibus industrial power system.

Some simplifications will be considered: the transformers and induction motors will be represented by inductances only, passive filters considered as ideal ones, without resistances, and ground capacitances of the lines and cables will be neglected as well. The rectifiers will be represented by ideal harmonic current sources 𝐼_IL with harmonic magnitudes determined by respective apparent powers, overload capacities, and by the so-called magnitude law. On the basis of the diagram of this system an equivalent circuit may be determined and the parameters of circuit elements calculated.

The potential places for APFs are bus-bars with the voltage level of 6 kV, that is the bus-bars 2–6. APFs will be represented here by voltage-controlled current sources, that is by the vector 𝐼_IF of reference currents of the individual APFs. The agreement between the real and reference APF currents depends on an inner control strategy of the real APF that is not analyzed here. Especially for dominant harmonic orders this agreement is reported to be quite well, though.

In the following analysis all quantities will be recalculated to the 6 kV level and expressed in the p.u. system with 𝑆_𝐵=1 MVA (the maximum power of the major rectifier, which is connected to the bus 6), 𝑉_𝐵=6 kV, 50 Hz.

3. Control Strategies

The voltage and current detection feedback control strategies belong among control strategies very often used for parallel APFs applied in simple power distribution systems. We proposed an application of these strategies in multibus industrial power systems with a few harmonic power sources [4, 5]. The effectiveness of the connection of the APF at a specific bus may be assessed by the degree of the voltage harmonic mitigation at selected buses and by the demanded value of the APF current 𝐼_IFRMS; but, the values of the controller gains should be taken into consideration as well, with regard to problems with stability of the whole control system.

We will analyze an application of the voltage detection feedback control strategy in multibus industrial power systems with a few harmonic power sources and several APFs.

Let the current vector 𝐼_IF of APFs be generated by using a feedback of the node voltage vector 𝑉_𝑁𝐼_IF=𝑌_𝐺𝑉_𝑁, (3.1) where 𝑌_𝐺 is the feedback gain matrix.

4. Multiple Harmonic Problem

For the multiple APF-multiple harmonic problem the objective function may be written 𝑔_𝐻=^𝐻_ℎ=2^𝑛−1_𝑖=1𝑎^ℎ_𝑖𝑉^ℎ_𝑁(𝑖)², (4.1) where the weighting factor 𝑎_𝑖(0≤𝑎_𝑖≤1,𝑖=1,…,𝑛−1) reflects the different importance of the harmonic voltage mitigation at different nodes.

The formulae for the ℎth harmonic of the voltage 𝑉^ℎ_𝑁(𝑖) at the node 𝑖, which include the parameters of the controllers of APFs, should be formulated. The optimum values of the controller parameters may be determined by finding the minimum of 𝑔_𝐻 (4.1) for 𝑉^ℎ_𝑁(𝑖) declared.

Here, the objective function (4.1) will be used for solving the multiple APF-multiple harmonic problem in case of applying the node-voltage-detection control strategy. For finding optimum parameters of the controllers of the APFs, the relation for the ℎth harmonic of the voltage 𝑉^ℎ_𝑁(𝑖), determined in [5] for the single APF, must be reformulated to be valid for more than only one APF placed at the node 𝑓.

Because𝑉^ℎ_𝑁=𝑉^ℎ_𝑁0+𝑍^ℎ_NIF𝐼^ℎ_IF, (4.2) where 𝑍^ℎ_NIF is a transfer impedance matrix of the injected APF currents, 𝑉^ℎ_𝑁0 is the node voltage vector without any compensation, and𝐼^ℎ_IF=𝑌^ℎ_𝐺𝑉^ℎ_𝑁 (4.3) determines the node-voltage-detection control strategy, the node voltage vector may be expressed by𝑉^ℎ_𝑁=−𝑍^ℎ_NIF𝑌^ℎ_𝐺−𝐸⁻¹𝑉^ℎ_𝑁0. (4.4) The elements of this voltage vector enter the objective function (4.1).

In the process of minimization of the objective function the optimum parameters 𝑌_𝐺𝑖, 𝑖=1,…,𝑚_𝐹 for the 𝑚_𝐹 controllers can be found.

But, in most of real cases the minimum value of the objective function, which is the power of the global value of THD of voltages (in p.u. system and over the whole number of bus-bars in question), is not necessary to reach. The attaining of predefined values of THDs of the voltages at the bus-bars where the APFs are placed seems to be a more practical aim. Then, the harmonic currents generated by the APFs may be remarkably lower than those needed in case of the mentioned global optimization obtained by the minimization of the objective function (4.1).

But, a question still remains whether THDs of voltages at the other bus-bars (where the APFs are not placed) will be sufficiently low to conform to our demands. Thus, comparing these THDs of voltages at remaining bus-bars of the industrial power system for different combinations of APFs places may be a key to find the best places for the APFs in this case.

For finding the parameters of the controllers for two APFs, which ensure that the predefined values of THD^∗_{𝑉𝑁(𝑖)}, 𝑖=𝑓1,𝑓2 at the bus-bars 𝑓1, 𝑓2 are attained, the objective function (4.1) should be modified as follows𝑔_𝐻𝑓1,𝑓2=_{𝑖=𝑓1,𝑓2}^𝐻_ℎ=2𝑎^ℎ_𝑖𝑉^ℎ_𝑁(𝑖)²−THD^∗_{𝑉𝑁(𝑖)}². (4.5)

5. Self-Tuning Controller of APF

By using the strategy presented in the previous paragraph we can find a proper place and controller parameters, or at least to identify places unsuitable for the APF. The analysis assumes that the system parameters and harmonic current sources are known. Such an analysis may be done as the first step of the solution of the problem with some nominal system parameters and operating modes of harmonic current sources (mostly rectifiers).

But, the parameters in a real system are not precisely known and, especially, the harmonic spectra of the current sources are changing due to changes in a manufacturing process. Thus, a simple and efficient way to tune the controller parameters of the APF is very desirable.

We have two indicators to be checked, namely the current 𝐼_IFRMS that should not exceed its nominal value for the APF used and the real value of THD_{𝑉𝑁(𝑓)} that should not be much higher than its prescribed limit THD^∗_{𝑉𝑁(𝑓)}, because in such a case there is a real danger of an increase of THD_{𝑉𝑁(𝑖)} at the remaining bus-bars and of the global index THD_𝑉𝑁 all over the system too. On the other hand, an operation of the APF with 𝐼_IFRMS≤𝐼_IFRMSnom, if THD_{𝑉𝑁(𝑓)}≤THD^∗_{𝑉𝑁(𝑓)}, is not very economical either, and it is possible either to switch the APF off or to decrease THD^∗_{𝑉𝑁(𝑓)} and, as a consequence, the values of THD_{𝑉𝑁(𝑖)} and THD_𝑉𝑁 as well.

Figure 2 shows the scheme of a self-tuning controller of the APF. The input variables are the reference THD^∗_{𝑉𝑁(𝑓)} and 𝐼^∗_IFRMS. The required value of THD^∗_{𝑉𝑁(𝑓)} is compared with the real value THD_{𝑉𝑁(𝑓)}, and the error enters a block where the gain 𝑌_GP of the APF controller is determined.

Figure 2 

Self-tuning controller.

A possible configuration is that the basic value 𝑌^∗_GP of the gain is modified by the output of the I-type controller with fairly low gain. Because the higher the negative value of the control error −(THD^∗_{𝑉𝑁(𝑓)}−THD_{𝑉𝑁(𝑓)}) is, the higher the absolute values of the gain 𝑌_GP and 𝐼_IF are; a limiter of the presented type should be used.

The real value 𝐼_IFRMS of the AFP current is compared with its required (nominal) value 𝐼^∗_IFRMS and the error is proceeded in a nonlinear block, whose output (let us call it as constant 𝐶) modifies the reference value THD^∗_{𝑉𝑁(𝑓)} of the voltage at the bus where the APF is placed. Thus, the reference THD^∗_{𝑉𝑁(𝑓)} is modified in order that it may be obtained without exceeding the required (nominal) value 𝐼^∗_IFRMS of the current generated by the APF.

If the error 𝐼^∗_IFRMS−𝐼_IFRMS is positive up to some specific value, the reference THD^∗_{𝑉𝑁(𝑓)} is not modified because the output of the nonlinear block has the value 1. But, for (𝐼^∗_IFRMS−𝐼_IFRMS)<0 the output of the block is going up quickly and increases the value of THD^∗_{𝑉𝑁(𝑓)}, which leads to a decrease of the APF current 𝐼_IFRMS and the error 𝐼^∗_IFRMS−𝐼_IFRMS becomes lower. On the other hand, a big positive error 𝐼^∗_IFRMS−𝐼_IFRMS can result in that the lower value THD^∗_{𝑉𝑁(𝑓)} is required and achieved. Another option is that this big positive-error value may be the impetus for switching the APF off.

It is evident that the control loop of the APF current 𝐼_IFRMS is superior to the control loop of THD_{𝑉𝑁(𝑓)} of the voltage where the APF is placed.

6. Simulation

Let us verify some key results, conclusions, and also the function of the controller proposed in the previous chapter by the simulation in the time domain.

The industrial power system shown in Figure 1 was simulated by using Matlab-Simulink.

The APFs were placed at the bus-bars 3 and 4 and equipped with the controller presented in Figure 2. Time and all variables are expressed in p.u. related to the nominal frequency 50 Hz, the voltage 6 kV, and to the maximum power of the biggest rectifier connected at the bus-bar 6.

The reference variables were set like this: THD^∗_{𝑉𝑁(𝑗)}=0.009; 𝐼^∗_IFRMS=0.15p.u.; 𝑌^∗_GP=−0.5p.u. for both the APFs.

Figure 3(a) shows transient processes following after increasing twice the currents withdrawn by the rectifiers at the buses 7 and 8 and decreasing to zero the currents withdrawn by the rectifiers at the buses 9, 10, 11, and 6. The responses of the following variables are shown from up to bottom: 𝐼_IFiRMS, constant 𝐶_𝑖 at the output of the nonlinear block modifying the reference value THD^∗_{𝑉𝑁(𝑗)}, THD_{𝑉𝑁(𝑗)}, 𝑌_GP𝑖, 𝑖=1,2 (number of the APF), and 𝑗=4,3 (the place of the APF). The control loops of 𝐼_IFiRMS are disconnected now, so changes of the constants 𝐶_𝑖 do not affect THD^∗_{𝑉𝑁(𝑗)}=0.009.

(a)

(b)

Figure 3 

Transient processes following after increasing twice the current withdrawn by the rectifiers at the buses 7 and 8 and decreasing to zero the currents withdrawn by the rectifiers at the buses 9, 10, 11, and 6; (a) control loops of 𝐼IFiRMS are disconnected, (b) control loops of 𝐼IFiRMS in function.

We can see that the APF2 placed at the bus 3, which lies upstream the buses 9–12, goes out of the operation 𝐼_IF2RMS=𝑌_GP2=0, while the current 𝐼_IF1RMS=0.181 p.u. of the APF 1 becomes higher than its nominal value. The reason is that the value of THD_𝑉𝑁(3)=0.0081 is lower than its reference THD^∗_𝑉𝑁(3)=0.009 in the final steady state.

Figure 3(b) shows the similar transient processes, but the 𝐼_IFiRMS control loops of the APFs are in function now. The result is that both the APFs remain in operation with 𝐼_IF1RMS=0.133 p.u. and 𝐼_IF2RMS=0.060 p.u., that is under the nominal value 𝐼^∗_IFRMS=0.15p.u., and with THD_𝑉𝑁(4)=0.0090 and THD_𝑉𝑁(3)=0.0078.

7. Experimental Verification

The function of the proposed control strategy of several APFs in the power system without their mutual communication has been experimentally verified. Figure 4 shows an experimental setup that consists of two pairs of a nonlinear and linear load.

Figure 4 

Experimental setup with two APFs working without communication.

These loads are connected to the source voltage via different impedances 𝑍_LINE1 and 𝑍_LINE2 that represent impedances of the lines, cables, and transformers of a real power system. Two APFs are placed in parallel with these load pairs. The control algorithm presented in Figure 2 is implemented into both dSPACE DS1103 control systems of APFs.

Figures 5–7 demonstrate the function of the control loop of THD_𝑉𝑁(1) of the APF1. Figure 8 shows how the superior current control loops prevent overloading of the APFs.

(a)

(b)

(c)

Figure 5 

Waveforms of the load current (a), grid current in branch 1 (b), and line-to-line voltage (c) after switching load in this branch 1 on.

(a)

(b)

(c)

Figure 6 

Details of the load current (a), grid and APF currents (b), and THD of line-to-line voltage (c) after switching load in this branch 1 on.

Figure 7 

Waveforms of the load, APF, and grid current in the branch 1 in steady state.

(a)

(b)

Figure 8 

Transient processes following after: (1) increasing nonlinear load 1 by 50% and (2) disconnecting nonlinear load 2; (a) control loops of 𝐼IFiRMS are disconnected, (b) control loops of 𝐼IFiRMS in function.

Figure 5 shows the waveforms of the load current (a), grid current in the branch 1 (b), and line-to-line voltage (c) after switching the load in this branch 1 (Figure 4) on.

Figure 6 presents the respective details of the load current (a), grid and APF1 currents (b), and THD of line-to-line voltage (c) after switching the load in the branch 1 on. The current 𝑖_su=𝑖_fu in Figure 6(b) before the load in the branch 1 is switched on is generated by the APF1 to hold THD_𝑉𝑁(1) equal to THD^∗_𝑉𝑁(1)=0.06, because the full load in the branch 2 is applied. In Figure 6(c) two waveforms are shown: the first one is the signal THD_𝑉𝑁(1) in the APF digital controller, the second one is a result of analysis of the captured voltage 𝑣_luv from Figure 5(c) made a posteriori the experiment. Both the curves feature a very good agreement.

Figure 7 shows the waveforms of the load, APF, and grid current in the branch 1 in steady state. It is evident that load current harmonics are effectively mitigated by the respective APF1.

Figure 8 shows transient processes following after: (1) increasing nonlinear load 1 by 50% and (2) disconnecting nonlinear load 2.

It is evident that the APF 1 is overloaded and the APF 2 is switched-off if the APF control loops of 𝐼_IFiRMS, 𝑖=1,2 are disconnected and only the control loops of THD_𝑉𝑁(1), THD_𝑉𝑁(2) are in function. Contrary to that, both the APFs remain in operation if the superior control loops of 𝐼_IFiRMS, 𝑖=1,2 of both the APFs are in function. The values of 𝐼^∗_IF1RMS=𝐼^∗_IF2RMS were set at 1 A and THD_𝑉𝑁(1)=THD_𝑉𝑁(2)=1.5%. The experimental results are in a good agreement with those obtained by simulation, Figure 3.

8. Conclusion

The procedure for calculating controller parameters of the APFs implemented into the multibus power system has been presented. The node-voltage-detection control strategy was applied and the controller parameters were found by solving the modified multiple APF-multiple harmonic problem under the condition that demanded THD factors at the buses where the APFs are placed will be obtained.

A cooperative control of several APFs without any communication has been proposed and simulated as well. By tuning the controller gains without considering the power circuit parameters, all APFs used tend to share harmonic load currents approximately equally regardless of the operation modes of the nonlinear loads in different parts of the power system.

Acknowledgments

The financial support of the Grant Agency of the Academy of Sciences of the Czech Republic (project no. IAA200760703), Institutional Research Plan Z20570509 of the Institute of Thermomechanics of the ASCR, v.v.i., and of the Ministry of Education, Youth, and Sports (Research Plan MSM 6840770017 of the Czech Technical University) are highly acknowledged.