INCREMENTAL PASSIVITY BASED PARALLEL OPERATION OF UNINTERRUPTIBLE POWER SUPPLIES WITHOUT COMMUNICATION –

TOWARDS A DIGITAL IMPLEMENTATION

Marcelo de Azevedo Ávila, Leonardo A. B. Tôrres and Paulo Fernando Seixas Programa de Pós-Graduação em Engenharia Elétrica – PPGEE

Universidade Federal de Minas Gerais – UFMG Av. Antônio Carlos, 6627 – Pampulha – Belo Horizonte, Minas Gerais

marceloavila87@gmail.com

Abstract – The digital implementation of an approach to the parallel operation of uninterruptible power supplies (UPS) is investigated. The method is developed in time domain and it relies on the natural tendency to synchronization of interconnected incrementally dissipative nonlinear oscillators. Simulations of two interconnected UPS systems to a given resistive load are carried out, taking into consideration specific problems associated with the practical implementation in a Digital Signal Processor (DSP) based system.

Keywords – Parallel Operation, Uninterruptible Power

Supplies, Passivity Based Control, Digital Implementation.

I. INTRODUCTION

The interconnection of multiple power supplies in parallel to provide energy to a common load arises, mainly in Parallel Connected Uninterruptible Power Supplies, as an alternative to increase the total power capacity or improve the system reliability through redundancy. In this application type, moreover, it is highly desirable that the synchronization strategies do not use any kind of communication between the UPS connected to the power bus, since this communication channel would be a critical single point of failure.

As mentioned in [1], [2], [4] and [5], to accomplish this parallel operation without communication in a reliable fashion, the power units should use control strategies for voltage synchronization that rely solely on variables that can be measured locally.

Among existing synchronization solutions, the most popular is the so-called Droop Method [3], whose stability analysis is discussed in [1]. The Droop Method is based on well known active and reactive power analysis commonly found in the Electrical Power System Stability area, and explicitly uses the inverter controller to impose to the UPS a behavior similar to that naturally exhibited by synchronous machines [1].

Several works in power electronics propose improvements and simplifications of the classical Droop Method [4], [8]. The aim is to incorporate specific details of the UPS parallel operation problem that are not well represented in the theory originally developed for Electrical Power Systems. For example, in reference [2] stability problems related to different connecting impedances that impact the parallel operation of UPS is investigated and new control design guidelines are proposed.

However, the Droop Method relies on frequency domain considerations to effect the parallel operation of UPS systems without communication, i.e. the method is heavily based on concepts that are not well-defined when the operational frequency is variable, e.g. active and reactive power. In reference [4] a new implementation of the Droop Method is considered where a simpler way to compute quantities based on active and reactive power estimation is used.

One the other hand, recently it was proposed in reference [5] a new parallel operation strategy that is based on power dissipation inequalities in time domain, instead of frequency domain related analysis tools. Simulation results not considering aspects associated with the practical implementation of the strategy pointed to interesting improvements when compared to the Droop Method, such as fast phase synchronization.

Following the work in [5], the main goal of the present paper is to investigate the digital implementation of the strategy proposed in [5] and [6], but considering practical aspects such as the digital control of the inverter itself and the computation of the parallel operation strategy by numerically integrating a set of differential equations using a DSP based system. Moreover, a strategy to properly connect an additional UPS to the power bus, when it is being fed by other UPS systems, is proposed and evaluated in simulation. The authors expect to have experimental results by the time of the final paper submission.

II. INCREMENTAL PASSIVITY BASED PARALLEL OPERATION OF UPS SYSTEMS

As an alternative to the Droop Method, a new parallel operation strategy rooted on time-domain considerations associated with incrementally dissipative systems was proposed in [5].

The general idea is that interconnected nonlinear oscillators can achieve the synchronization condition without relying on exchange of information between them if properly designed to be incrementally dissipative, i.e. they can reach a synchronized behavior only as a byproduct of being connected to the same electrical network because this is the minimum dissipation condition for the overall dynamical system composed by the interconnected oscillators.

On the other hand, nowadays it is possible to program a DSP-based controlled inverter to behave as an electronic nonlinear oscillator. Actually this approach follows the same

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rationale commonly used to justify theDroop Method, namely to make the Uapproximately as a simplified synchronosince this leads to some mathematical UPS systems will synchronize. The difinstead of mimicking the behavior generator, the dynamical behavior of a oscillator is emulated.

A. NONLINEAR OSCILLATORS ASYNCHRONIZATION

Figure 1 shows three nonlinear oscill

electronic circuits interconnected to a resof resistive connecting impedances.

Fig. 1. Nonlinear oscillators represented ainterconnected to a resistive

It is possible to proof that a finite n

oscillators can naturally achieve thcondition for small enough intercoimpedances. The theoretical developmenproof that support these affirmatives are d

Each nonlinear oscillator surrounded Figure 1 is numerically implemented as differential equations that have to be integ

Where:

- Inductor current [ A ]. - Capacitor voltage [ V ].

- Inductor of RLC circuit [ H ]. - Capacitor of RLC circuit [ F ]. - Resistor of RLC circuit [ Ω ].

- Total current entering the RLC From (1), the total current is given b

e correctness of the UPS system behaves ous power generator,

guarantees that the fference here is that

of a synchronous nonlinear electronic

AND

lators represented as istive load by means

as electronic circuits

load.

number of nonlinear he synchronization onnecting resistive nt and mathematical described in [6]. by a dashed line in the following set of grated:

(1)

C circuit [ A ].

by:

(2)

Where is the current floload and is the nonlinfeedback loop.

To simulate the UPS ssoftware were used in ordermore realistic system depictdigital control of the invertepass LC-filter, is taken into c

Fig. 2. A controlled inverter

The final objective is to

behaves as much as possible oscillator represented as a Rfeedback loop through a stalike the one represented in Fi

Fig. 3. The static saturatiofeedback loop of th

It is important to note tha

dashed line in Figure 1 will bin Figure 2, and in Figure 2what will be computed asdifferential equations, i.e. it i

Nonlinear Function

owing from the oscillator to the near current calculated by the

systems, Matlab and Simulink r to represent for each UPS the ted in Figure 2. Notice that the er, together with its output low

consideration.

r driven by a nonlinear oscillator.

o make the controlled inverter like the corresponding nonlinear

RLC circuit with a destabilizing atic saturation-like nonlinearity, igure 3.

on-like nonlinearity present in the he nonlinear oscillator.

at each system surrounded by a be replaced by the system shown 2 the dashed red line surrounds s the integration of a set of s not a physical circuit.

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B. AMPLITUDE CONTROL The amplitude of the interconnected oscillators’ output

voltages depends on the value of the breakpoint in the feedback loop (Figure 3).

If the value of the parameter in Figure 3 is properly chosen, the output voltage of the nonlinear oscillator will not vanish. This is accomplished because the energy dissipated by the resistor in the RLC circuit is smaller than the energy re-injected by the positive feedback loop. However, it is necessary to limit the maximum energy injected in the RLC circuit by the feedback loop, which is obtained using the saturation value , in order to have bounded oscillations.

To find the relation between the values of the saturation parameter and the amplitude of each oscillator output voltage it was used the so-called Describing Function Method [7]. Since saturation is a single-valued nonlinearity type, its Describing Function is purely real and independent of the input frequency. To find the output voltage amplitude that corresponds to a certain limiting value , is necessary to solve the following equation:

sin 1 0 (3)

Where:

- Feedback loop gain, related to the re-injected energy [ A V ].

- Feedback loop breakpoint [ A ]. - Desired oscillator output voltage [ V ]. - Resistance value of RLC circuit [ Ω ].

It is possible to calculate the values of the breakpoint

parameter by considering the oscillator connected to a resistive load. In this case, it is necessary to substitute the value of in (1) by , which is the parallel combination of

and that represents the total load connected to the oscillator output.

Figure 4 shows the values of breakpoint necessary to maintain an output voltage of amplitude in three different cases: oscillator without load, oscillator with nominal load of 25Ω and oscillator with load of 50Ω.

Fig. 4. Curves vs. for three different situations.

To control the oscillator’s output voltage amplitude is necessary to modify properly the breakpoint dynamically

as pointed out in [5]. This is done using an external loop that implements a PI controller that, based on the error value between a desired RMS reference voltage ( ) and the estimated RMS value of the oscillator output voltage, changes the breakpoint in order to correct the deviation and cancel the amplitude error between the desired nominal amplitude voltage and the oscillator's output amplitude voltage. This amplitude control loop is described by the following set of equations:

| |max 0, (4)

Where:

- Oscillator output voltage [ V ]. |ξ| - Estimated root-mean-square output voltage of the oscillator [ V ].

- Time constant of a low-pass filter [ s ]. - Estimated RMS Amplitude Error signal

[V].

III. TOWARDS THE DIGITAL IMPLEMENTATION

A. NONLINEAR OSCILLATORS AS NONLINEAR DIFFERENCE EQUATIONS

The nonlinear oscillators are actually implemented as

difference equations associated with the numerical solution of the differential equations using the Fixed Step Fourth Order Runge-Kutta method [9].

B. STRATEGIES TO CONNECT ADDITIONAL UPS

SYSTEMS TO THE POWER BUS Practical methods to add a UPS to a bus that has already

one or more UPS connected to it have to take into account the transient perturbation resulting from this new connection.

It is necessary that the connection of the new UPS to the bus affects the system as minimum as possible, in such a way that the transient voltages and currents are smooth and have short duration.

Considering the case where there is one UPS – called UPS-1 – system already connected to the power bus, and another UPS – called UPS-2 – is about to be added, to achieve smooth transients, it is necessary to guarantee that all states of the UPS-2 are very close to the states of the UPS-1 that is already connected to the bus.

By using only the voltage value measured at its own connection point with the bus, the values of inductor current and capacitor voltage of the virtual nonlinear oscillator (implemented as a set of differential equations to be integrated) are estimated by a Luemberger observer.

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The breakpoint is defined based on the curves vs. presented in section II. B.

At this pre-synchronization phase, if the electric current drained by the resistive load and the number of UPS connected to the bus are known, these informations can be used to predict the output current of each UPS and, thus, to obtain better estimated states by the observer and to properly set the breakpoint .

IV. SIMULATED AND EXPERIMENTAL RESULTS

The system described in Section II (see Figure 2), was

implemented using the DSP-based development kit Texas Instruments model TMS320F28335, together with a half H-bridge, following the approach described in Section III. In Figures 5 and 6 experimental results are shown.

Figure 5 shows the steady-state inverter output voltage and the time variation of the breakpoint value of the saturation function (see Figure 3) for nominal operation with a 25Ω resistive load. Considering the time variation of the saturation function breakpoint, one can see that the average value (dashed line in the second graph on Figure 5) of 2.77V is close to the theoretical value of 2.75V given in Figure 4 and calculated using the Describing Function Method (Section II.B).

Fig. 5. Output voltage and breakpoint value for nominal

operation with resistive load.

Figure 6 shows experimental results associated with abrupt load variation for an isolated system. Initially the inverter operates without load. At approximately 0.1 sec, a nominal resistive load of 25Ω was connected at the inverter output. It can be seen that the amplitude control was effective in keeping a nominal amplitude voltage of 25V.

Fig. 6. Output voltage and current for a load variation test.

The next results, relative to the parallel operation of two UPS systems connected to a resistive load by means of resistive connecting impedances, were obtained from simulation tests, because, by the time this article was written, only one UPS system was operational. All the simulations were done using Matlab/Simulink software together with the SimPowerSystems toolbox to model the PWM-based controlled inverter. Table I shows all the parameters used in simulations.

TABLE I

Simulation Parameters Parameter Value Information

Controlled Inverter L 1.8 H Filter inductor C 3.6 F Filter capacitor

20100 Hz PWM frequency

11 Proportional gain of current loop

0.0745

Proportional gain of voltage loop

205.7301

Integral gain of voltage loop

60 Hz Output voltage frequency

25 V Nominal output voltage amplitude

1 A Nominal output current amplitude

Nonlinear Oscillator 10 Resistance

0.001 Inductance

12 60

Capacitance

α 4 Feedback loop gain

2 Proportional gain of amplitude control loop

10 Integral gain of amplitude control loop

First Order Low Pass Filter

τ 0.1s Time constant Resistive Load

25 Ω Nominal resistive load From 0 until 1 only one UPS (called UPS-1)

feed the load. During this time interval, the output current amplitude of UPS-1 equals 25 25 1 A.

At 1 , the observer is enabled and remains until 2.49 . At this time instant the output voltage of UPS-1 passes through zero and UPS-2 is connected to the system. During this interval the estimation error tends to zero and the estimated states (inductor current and capacitor voltage of the oscillator) follows the states of UPS-1.

The difference between the two simulations is that in the first case is considered that there is no prior information about the load. That is, the observer estimates the states considering that there is no load connected to the inverter and the breakpoint is set using the curve vs. obtained for the load-less case (blue curve in Figure 4).

In the second simulation case it is considered that the load value is known before the connection of UPS-2, such that the observer based strategy to prepare UPS-2 to be added to the bus is more effective.

Figures 7 and 8 show the voltages and currents, respectively, for the first test scenario.

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Fig. 7. Output voltages of UPS 1 and 2 for the test case that

was not considered prior information about the load.

Fig. 8. Output currents of UPS 1 and 2 for the test case that was not considered prior information about the load.

From Figure 7 it can be seen that, before the connection

instant, the output voltages are almost synchronized. This make that voltages transients after the connection small and of short duration.

As shown in Figure 8, the phase synchronism is fast, but the convergence of amplitudes is much slower. This behavior may be improved with a better choice for the amplitude control parameters ( and in Table I).

Figures 9 and 10 show the voltages and currents, respectively, for the case test corresponding to the known load value.

Fig. 9. Output voltages of UPS 1 and 2 for the test case that

was considered prior information about the load.

Fig. 10. Output currents of UPS 1 and 2 for the test case that

was considered prior information about the load.

Comparing Figures 9 and 10 with Figures 7 and 8, mainly the currents, it is clear that using prior information about the load to better define the states of UPS-2 have improved the transient behavior.

To better illustrate the synchronization achieved with this parallel operation strategy, Figures 11 and 12 shows the error between voltages and currents for UPS-1 and UPS-2 for the two test cases.

Fig. 11. Errors between voltages and currents of UPS 1 and 2

for the test case that was not considered prior information about the load.

Fig. 12. Errors between voltages and currents of UPS 1 and 2

for the test case that was considered prior information about the load.

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V. CONCLUSION

A DSP-based digital implementation of a new parallel operation without communication strategy for UPS systems was proposed and tested in simulation, including the proposition of a strategy to incrementally add new UPS systems to the power bus.

The simulation results have shown that the new parallel operation strategy seems to be indeed feasible. In addition, experimental results for only one UPS system have shown that the oscillator with nonlinear dynamics and the proposed amplitude control law were effectively implemented in a DSP-based hardware architecture, and the obtained results were in agreement with the theory.

The next step is to implement the two UPS systems case presented in Section IV in an experimental setup.

ACKNOWLEDGEMENT

The authors are grateful to the Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq and to the Fundação de Amparo à Pesquisa de Minas Gerais - FAPEMIG, whose financial assistance has made this work possible.

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