Bidirectional DC-AC Converter for Isolated Microgrids with Voltage Unbalance Reduction Capabilities

Felipe S. F. e Silva , Luiz A. de S. Ribeiro, and José Gomes de Matos Institute of Electrical Energy – Federal University of Maranhao – IEE-UFMA

São Luis, Brazil e-mail: simoesfs@gmail.com; luiz_ribeiro@dee.ufma.br; gomes@dee.ufma.br.

Abstract— This paper presents a three-phase bidirectional DC-AC converter suitable for operating as an interface between an energy storage system (ESS) based on a battery bank and an isolated microgrid with distributed generation. The converter consists of two stages: a DC-DC stage implemented with a bidirectional half-bridge converter that operates on buck or boost mode (during charge or discharge of the ESS, respectively), and a DC-AC full-bridge three-phase bidirectional inverter. The two stages are connected through a DC link, which also works as a power-decoupling element. Isolation from the microgrid is obtained with a Δ-Y low frequency transformer. A control strategy is proposed where the DC-DC stage regulates the DC link voltage level while the DC-AC controls the three-phase output voltage and frequency, therefore acting as a grid-forming converter (GFC). A modified droop strategy is implemented to control the power generated inside the microgrid to avoid overcharging the ESS. Voltage unbalance reduction capabilities were implemented in order to deal with unbalanced loads. A 15kW prototype was successfully built and tested in different situations and the experimental results are shown.

I. INTRODUCTION In the past decades, the constant increase of electricity

demand has been followed closely by a growth of demand for reliability and quality of service. One of the sector’s biggest challenges has been to manage providing more energy with higher levels of quality, especially when environmental issues and reduction of oil reserves limit the part played by thermal and nuclear plants.

Renewable energy sources (mainly wind and solar) together with internal combustion engines, fuel cells and microturbines called attention to the possibility of generating electricity in smaller quantities but closer to the loads and the distributed generation (DG) concept was introduced. However, traditional electric grids were not designed to absorb a high penetration level of DG’s [1] and safety precautions require the disconnection of DG’s in case of grid fault [2]. The microgrid concept was then created in order to integrate the benefits of DG and provide actual gains in quality of service and reliability to end users [3].

Most definitions of a microgrid recognize a cluster of loads, DG units and energy storage systems (ESS) interconnected as a small-scale grid, capable of operating in parallel with the main grid or in islanded mode. This paper focuses in the ESS, more specifically its interface with the microgrid.

The ESS plays an important part providing backup power in case of energy shortage and low voltage ride through capabilities, more prominently if renewable energy resources are the main energy sources in the microgrid or during islanded operation. Isolated operation may take place in case of grid fault, when energy quality level drops below a certain threshold or in areas where the costs of connection to the main grid are prohibitive [4]. In such cases, the voltage and frequency inside the microgrid need to be controlled by a steady and reliable energy source. In modern microgrids, a power electronics converter connected to the ESS commonly performs this task and can be referred to as a grid-forming converter (GFC) [5].

This paper presents a three-phase DC-AC bidirectional converter suitable to operate as a GFC. The converter positioned between the ESS and the microgrid must be a bidirectional energy converter in order to balance the energy flow inside the microgrid between the ESS, loads and DG units. One of its features is the ability to supply unbalanced loads with voltages within the limits for unbalanced operation defined by European regulation.

Furthermore, the converter incorporates a modified droop strategy capable sharing active power with other GFC’s as well as controlling the power generated inside the microgrid to avoid overcharging the ESS, without using dump loads or wired communication between the converter and DG units.

II. THE BIDIRECTIONAL CONVERTER Bidirectional converters are used in many applications

such as hybrid electric vehicles, distribution systems, electric aircrafts and uninterruptable power supplies. It is a common practice to associate conversion stages for operation in a wide range of input/output voltage levels. The structure of

This work was supported by CNPq, and FAPEMA (Brazil)

978-1-4799-5776-7/14/$31.00 ©2014 IEEE 4985

the used converter consists of a non-isolated bidirectional DC-DC converter and a bidirectional three-phase inverter as shown in Figure 1.

For the DC-DC stage, the bidirectional half-bridge converter topology was chosen mainly due to its reduced electric stress over the power switches in comparison with other classic non-isolated DC-DC topologies [6].

The three-phase inverter controls the voltage magnitude and the microgrid frequency, while the half-bridge DC-DC converter regulates the voltage at the DC link capacitor (C2) through the current extract from/injected in the battery bank. The grid voltage controller is implemented on a synchronous dq reference frame, with an inner current loop [5]. The frequency and voltage reference values can be kept constant or they can be calculated using some specific methodology, such as a droop control strategy witch calculates these reference values as a function of the active and reactive power at the converter terminals [6].

A. Control of the microgrid voltage and frequency The microgrid voltage controller uses the traditional

configuration implemented on a synchronous dq reference frame, with an inner current loop and an outer voltage loop [5]. The frequency and voltage reference values are calculated using droop control strategy as a function of the active and reactive power respectively at the grid former converter terminals. The dq model of the LC filter in the delta side of transformer T1 is used to design the control loops of the GFC. The block diagram of this model is showed in Figure 2, where: Rfo is the equivalent series resistance of the filter inductor Lfo; Cfy is the per phase equivalent capacitance of the LC filter and is equal to 3Cfo; ωe is the microgrid frequency, in rad./s; the superscript “e” denotes variables in the dq synchronous reference frame; the variables defined as are complex vectors where denotes any current or voltage. For the model presented in Fig. 2, is the current vector for the currents in the delta side of the output transformer; is the voltage vector in the capacitors of the LC filter. All the block

diagrams showed in this paper use the operator p = d ⁄ dt.

Based on the model presented in Figure 2, an inner current loop and an outer voltage loop were designed, as illustrated in Figure 3. In this figure, “^” denotes estimated parameters, GDID1 is the transfer function used to decouple at the sample instants the effect of the disturbances due to the load current vector and the cross coupling due to . ZOH means zero order hold (latch). Fundamentally, the current on the inductance Lfo is controlled in order to regulate the voltage on the capacitance Cfo, independently whether the power flux is from the PWM inverter to the microgrid or vice-versa.

The voltages reference values for the voltage controllers can be constant, generally equal to the nominal value of the microgrid voltage, or can be calculated based on a droop control strategy. In this work, the voltage reference was fixed in 220 V (RMS line voltage in the delta side of the transformer). By considering that the dq synchronous reference frame is aligned with the microgrid voltage vector, the reference values of the dq voltages are 0 and 179,6 179,6 .

The frequency reference value is calculated by using the power control strategy proposed in this work, and will be explained in section C.

Figure 1. Chosen topology for the proposed converter.

Figure 2. Block diagram of LC filter implemented in a synchronous reference frame.

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B. Control of the bi-directional dc-dc converter The DC-DC converter is used to control the voltage in

the capacitor Cdc. The action of the controller of the DC-DC converter can be considered equivalent to connecting a controlled voltage source, with mean value Vct, between the xy terminals of the converter circuit, as shown in the

Figure 4(a) and Figure 4(b). If the losses in the converter are not

considered, the voltage on Cdc depends only on the difference between the power at the battery bank terminals (Pb) and the power at the inverter terminals (Pinv), as shown in

Figure 4(c). Therefore, the dynamic equation for vdc can be written as in (1), where wdc is an auxiliary variable defined by wdc=vdc

2. (1) From (1) and

Figure 4(c), the DC bus voltage controller of the inverter can be designed with an inner current loop to control the battery bank current (ib) and an outer voltage loop to control the voltage over the capacitor Cdc, as illustrated in Figure 6. GDID is used to decouple the power disturbance from the output of the inverter over the DC bus voltage.

The output of the voltage controller (Vct) is the reference value for the PWM block used to generate the control signal for Q1 or Q2 switches, as shown in Figure 5. Pinv is the

electrical power at the terminals of the delta side of the isolation transformer, being positive when the power flux is from the inverter to the grid and negative on the contrary. When Pinv is positive, the battery bank supplies the load and the DC-DC converter functions on the boost mode using the Q2 switch and D1 diode. On the other hand, when Pinv is negative, the DC-DC converter functions on the buck mode using the Q1 switch and D2 diode.

C. Variable Frequency Operation – Modified Droop Strategy In normal standalone operation, the ESS provides energy

to the microgrid in case the power generated by the DG units cannot match the load power and absorbs the extra energy in case generation exceeds this value. However, the generated power needs to be controlled when ESS reaches its storage limit to avoid premature failure. The use of resistive dump loads to burn the excess of generated power has the disadvantage of using additional components, with rated power comparable to the renewable energy sources, therefore increasing implementation and O&M costs. This problem can be solved with a modified droop control strategy [7]. According to this control strategy the GFC verifies the battery bank voltage to know if it reached the maximum allowed charging voltage and, if so, change the microgrid frequency to inform the other sources that they must reduce their generated power. Based on the microgrid frequency, the control systems of the power generation sources connected to the microgrid decide whether or not to restrict the power generated by each of them. This control strategy can be explained based on Fig. 7. While the terminal voltage of the battery bank is below its maximum limit, the microgrid frequency (f) is determined according to the

Figure 3. Block diagram of the microgrid voltage controller.

Figure 5. DC-DC converter average model: a) original circuit, b) equivalent average circuit of inductor and battery bank, and c) average

model of the bus DC.

Figure 4. Block diagram of the voltage controller of the DC-DC converter.

Voltage Controller

vct

PWM C1

CdcLb

+

-

+

-

Vo

Vi

Q1

Q2

Figure 6. Block diagram of the commands of switches of the DC-DC

converter.

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conventional droop control strategy, described by line in Fig. 7. On this situation, there are no restrictions about the amount of power that can be generated and the existing renewable energy sources can function on their maximum power point. On the other hand, if the maximum voltage of the battery bank is reached, the microgrid frequency is imposed to be always higher than the value , which is the maximum frequency of operation of the conventional droop control strategy. This is illustrated by hatched area in Fig. 7. Now the value of the frequency ( ) is a variable that changes dynamically with the terminal voltage of the battery bank ( ), the power generated internally in the microgrid ( ), and power of the GFC ( .

The value of the grid frequency was implemented as shown in Fig. 8. A PI controller is used to regulate the battery terminal voltage equal or below its maximum allowed value ( ). The output of this controller is the increment of frequency (∆ ) that must be added to the value

to form the new reference value of the microgrid frequency. The value of ∆ is proportional to the amount of

power that must be decremented from the generated power in order to control the battery bank terminal voltage.

D. Voltage Unbalance Control Voltage unbalance in a microgrid can happen for several

reasons. The nature of the unbalance includes unequal voltage magnitudes at the fundamental system frequency, fundamental phase angle deviation, and unequal levels of harmonic distortion between the phases and normally an uneven distribution of single-phase loads is the most common cause.

During load unbalance, the converter should operate with unbalanced currents and balanced voltages. In the stationary reference frame unbalanced currents means that there are positive and negative sequence current vectors at positive and negative fundamental frequencies and its harmonics when the load is nonlinear. In a dq synchronous reference frame, the negative sequence fundamental component of the current vector, present during unbalanced operation, has 120 Hz frequency (considering only the fundamental component

Figure 7. Conventional and modified droop curves.

Figure 9. Control structure of the bidirectional converter.

Figure 8. Block diagram of the frequency control at the GFC.

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of a 60Hz system). This component will be present in the current vector reference. This means that the current controller must respond to an alternated reference. Due to the poor response of PI controllers to alternated references, the traditional synchronous frame current regulator is not capable to regulate the current vector with zero steady state error. To solve this problem a resonant branch was added to the current controller to mitigate the effects of unbalanced load operation. The high gain around the resonance frequency makes the resonant controller capable of eliminating the steady-state error of the alternated signal. The continuous time expression for the new current controller can be seen in (2).

(2)

The tuning procedure adopted in this paper for the

resonant controller takes into account its relation with integrative controllers. The expression for the resonant controller in a given reference frame can be obtained by adding two integrative controllers in reference frames rotating with symmetric/opposite angular velocities [8]. If one examines the output LC filter model in Fig. 2, it can be seen that the transition between reference frames introduces cross coupling terms that have no impact in steady state response and, if these terms are decoupled, there is no alteration in the plant model. This means that the resonant controller can be tuned as follows: first a PI controller is tuned for a desired bandwidth (assuming a DC reference signal) then the integrative gain is used as a resonant gain together with the desired resonance frequency. To implement the controller in (2) in a digital platform, the resonant was discretized using the Tustin method with resonance and prewarping frequencies set to 120 Hz.

III. EXPERIMENTAL RESULTS This section show some experimental results obtained

with a 15kW bidirectional converter prototype. The prototype can be seen in Figure 10 and the control system, DC-AC and DC-DC stages are indicated. The converter was tested in a small microgrid with only one wind generator emulator as a DG unit and a set of incandescent light bulbs as loads. The ESS consists of a battery-bank formed by 20 lead-acid batteries of 220 Ah, with a rated voltage of 12V each. The battery-bank’s rated and maximum voltage are 240V and 280V, respectively.

Figure 10. Bidirectional converter prototype.

The current and voltage controllers’ bandwidths of the DC-DC converter were set to 400Hz and 50Hz, respectively, whereas the current and voltage controllers’ bandwidths of the DC-AC converter were set to 750Hz and 240Hz. Figs. 11 and 12 show the response of the converter for a load step and a generation step, respectively. Phase voltage, phase current on Y-side of the transformer, line current on Δ-side of transformer, and DC link voltage are displayed. These results are for balanced loads/generation. The experimental results presented in Figs. 11 and 12 show that the basic functionality of a bidirectional converter was achieved, that is the ability to operate with both direct and reverse energy flows. During those situations, the voltage of the DC link and the output of the converter were kept under control with negligible variations.

Fig. 13 presents experimental results for the modified droop strategy. Normal droop operation takes place with frequency values between 59,4 and 60,6Hz, and generated power control is implemented at frequency range between 60,6 and 61,2Hz. Fig. 13 shows the electric power processed by the converter (a), the battery-bank voltage (b), and the microgrid frequency (c) through time.

Figure 11. Load step response of microgrid: phase voltage (yellow),

converter phase current in Y-side of transformer (blue), Δ -side (purple) and DC link voltage (green).

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Figure 12. Generation step response of microgrid: phase voltage (yellow), converter phase current Y-side of transformer (blue) and DC link voltage

(green).

Figure 13. Experimental results for control of SOC of the ESS.

Initially, a fully charged battery bank supplies only system losses and has a 255V voltage. Five important points in time are then highlighted. At t1, a wind-generator starts to deliver approximately 5kW to the AC bus, which is absorbed by the ESS through the GFC. The battery voltage (Vb) rises and reaches its maximum limit of 280V at t2. The frequency of the GFC is then shifted to above 60,6Hz and the generation begins to decrease, to keep Vb controlled in 280V. At t3, a 7,05kW load is turned on and the ESS starts to supply 2kW to the load and its voltage drops. The frequency is then shifted back to normal droop range. At t4 the load is disconnected from the AC bus and power flows to the ESS, increasing its voltage. At t5, Vb reaches 280V and the power control strategy is once again activated. The battery bank voltage remains regulated in 280V as generation is gradually decreased.

The voltage unbalance control strategy is analyzed though Figs. 14 to 17, that show the three line voltages on the delta side of the output transformer for different situations. The voltage unbalance factor (VUF), used to assess the effectiveness of the adopted strategy , is defined by European regulation as the ratio between the negative and

the positive sequence components of the output line voltages [9], and it’s limited to 2%.

Fig. 14 shows the output voltages for operation with no load and without the resonant branch. The VUF is 1,26% and therefore within the established limits.

Fig. 15, on the other hand, shows the output voltages when a 4 kW load is connected to one phase of the converter, on the Y side of the output transformer. The VUF is 6,8% and exceeds the 2% boundary, pointing out the necessity of the voltage unbalance control strategy.

When the resonant branch is used, the situation changes drastically. Fig. 16 shows the output voltages with no load, and the VUF already drops to 0,55%.The biggest impact of the proposed strategy, however, can be seen in Fig. 17 where the results for a 4 kW load connected to one phase of the converter. In this situation, a VUF of 0,7% was obtained and the converter was able to maintain the VUF under the allowed limits.

Figure 14. Three line voltages on the delta side of the output transformer while operating with no loads and without resonant branch on the current

controller. VUF = 1,26%.

Figure 15. Three line voltages on the delta side of the output transformer while operating with a 4kW unbalanced load and without resonant branch

on the current controller. VUF = 6,8%.

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Figure 16. Three line voltages on the delta side of the output transformer

while operating with no load and with resonant branch on the current controller. VUF = 0,55%

Figure 17. Three line voltages on the delta side of the output transformer while operating with a 4kW unbalanced load and with resonant branch on

the current controller. VUF = 0,7%

IV. CONCLUSIONS In this paper, a bidirectional grid-forming converter for

operation in isolated microgrids was presented. A functional prototype was successfully built.

Experimental results shown that the basic functionality of a bidirectional converter was achieved, that is the ability to

operate with both direct and reverse energy flows. During those situations, the voltage of the DC link and the output of the converter were kept under control with negligible variations.

The converter was able to interact with a DG unit though a modified droop strategy to limit the amount of energy generated inside the microgrid in order to protect the ESS, without the need of burning the surplus of energy.

Finally, the converter was able to keep its output voltages within the acceptable levels of VUF, even under a severe load unbalance situation. The resonant branch added to the current controller of the DC-AC conversion stage proved to be an effective alternative to deal with this problem.

Future work includes load sharing with other GFC’s and the operation with nonlinear load profiles.

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