Control of Active and Reactive Power Ripple to Mitigate Unbalanced Grid Voltages

Transcription

1 Control of Active and Reactive Power Ripple to Mitigate Unbalanced Grid Voltages R. Kabiri D. G. Holmes B. P. McGrath School of Electrical and Computer Engineering RMIT University, Melbourne, Australia Abstract Managing power delivery from distributed generation systems is challenging when the grid voltages are unbalanced, since the negative sequence voltage causes power oscillations at twice the fundamental grid frequency. Current regulation using sequence components can be used to manage these real and reactive power oscillations, and thus help mitigate the unbalanced network voltages. This paper presents a consolidated control scheme using double sequence frame current regulators that can readily adjust between eliminating real or reactive power oscillations created by unbalanced grid voltages, or alternatively can simply balance the three phase currents. The mitigation influence of these alternative control strategies on unbalanced grid voltages is then experimentally examined for a distribution feeder with a resistive and/or reactive series impedance. Keywords distributed generation, power oscillation control, unbalanced voltages, double synchronous frame I. INTRODUCTION Across the world, the paradigm of an electricity supply grid is changing as increasing levels of renewable generation are connected to the power grid at the distribution network level [1]-[3]. Since these small-scale distributed generation (DG) sources (PV solar, wind turbines and fuel cells) are generally interfaced through power electronic converters, they can also assist with the operation and control of the electrical grid network by varying both their real and reactive power injection in response to network needs [4][5]. DG systems are commonly interfaced through a power electronic Voltage Source Inverter (VSI), operating in closed loop current regulation mode [6]. Under balanced network voltage conditions, the real and reactive power injection from such systems is controlled by commanding from the current regulator, a current phasor that has the appropriate magnitude and phase angle with respect to the measured grid voltage (i.e. Point-of-Common Coupling - PCC). Synchronous frame current regulation is typically used for convenience and ease of implementation [7]. When the network voltages become unbalanced (because of unbalanced loads or short term disturbances), current regulation becomes more challenging, since the negative-sequence component of the unbalanced voltage causes double fundamental frequency oscillations in both the real and reactive power injections. Various strategies have been proposed to address this issue, looking to either balance the three phase AC currents, or to minimise the real and/or reactive power injection oscillation, depending on the identified target objective [8][12]. For example, the approach presented in [10] develops independent control strategies for the ripple content of the real and reactive power based on two simple gain parameters, and then combines them into a joint stationary frame PQ controller. Other approaches use a dq synchronous frame current regulator for unbalanced power control [13]-[15], recognizing the natural link that exists between real/reactive power and dq frame current references. DG systems can influence their feeder PCC voltage by virtue of the control strategy that they employ, and in fact several studies have shown how to integrate ride-through and voltage support functions into a DG controller architecture [16]-[18]. However for oscillating power flow regulators such as [10], there has so far been little exploration of the impact that these control strategies may have on a PCC voltage, particularly with varying feeder impedance characteristics. This paper presents a consolidated control strategy that uses a double sequence frame current regulator to continuously adjust between eliminating real power oscillations, balancing the inverter three phase currents, and eliminating reactive power oscillations, when connecting to an unbalanced grid voltage. This continuous control capability allows the effect of these alternative objectives on unbalanced PCC voltages to be readily investigated under different levels of P and Q injection. In particular, it allows the response of feeders with either inductive or resistive line characteristics to be explored. The results provide new understanding as to the influence of real/reactive power ripple mitigation on unbalanced network voltages for grid connected DG systems. II. THREE-PHASE DG CONVERTER MODEL The DG converter arrangement used in this paper is a standard three phase VSI, connected to the grid network at its PCC through an LCL filter, as shown in Fig. 1. Typically, such systems are controlled by a three level control structure a high level power control scheme, which feeds into a mid-level current regulation system, and which then in turn calculates voltage commands for the lowest level PWM controller [19], as shown in Fig. 2. For this paper, only a three-wire system has been investigated. However since [10] has shown that results from a three-wire scenario are consistent with a four-wire system when a current regulator is used that eliminates zero sequence currents, the conclusions from this paper can also be readily applied to a four-wire system.

2 Fig.1. Structure of a three phase VSI used for a DG system. For an unbalanced system, there are three possible reference strategies for the higher level controllers. The first approach is to operate in the αβ stationary frame, using resonant regulators to control the inverter currents since all quantities are sinusoidal [6]. The second approach is to operate in the positive synchronous rotating dq reference frame, using simple dc regulators to control the positive sequence currents. However, in this frame the negative sequence currents oscillate at twice the fundamental frequency, and hence two resonant regulators are still required in this rotating frame [12]. The third alternative is to use the positive rotating synchronous frame to control the positive sequence currents only, and to introduce a negative rotating sequence frame to control the negative sequence currents only. This arrangement requires only two simple PI control structures in each rotating frame of reference, which is straightforward to design and conceptually easy to implement [14][15]. However, it does require the measured αβ frame voltages and currents to be separated into positive and negative sequence components before the rotating frame transformation. For this paper, this third approach has been used, since calculation of the real and reactive power steady state and oscillatory quantities is much easier using dc representations of the positive and negative sequence voltages and currents in their respective rotating frames of reference [15]. To operate in the synchronous rotating frames, the converter voltages that are measured in the stationary abc frame must be appropriately transformed. This is done by transforming firstly to the stationary αβ frame using (voltage transformation shown) = 0 3/2 3/2 (1) Next, the positive and negative sequence αβ quantities are extracted using = 1 1 = 1 (2) 1 where i denotes a 90 o phase shift operator in the time domain. While various methods have been proposed to generate this phase shifted signal, the standard approaches are to use a time delay operator, which has dynamic response limitations, or a Phase Locked Loop (PLL) based on a second order generalized integrator [20]-[22]. This second approach is used in this paper. Finally, the extracted stationary frame sequence quantities are transformed into their respective positive and negative sequence rotating frames using = cos() sin() sin() cos() =() (3) = cos() sin() sin() cos() = ( ) (4) Note that the LCL output filter system that is typically used with a DG system will introduce a resonance peak into the plant frequency response which can cause current regulation stability problems [23]-[29]. While various Fig. 2. Proposed DG converter system with double synchronous frame controllers and actively damped LCL filter system.

3 techniques can be used to manage this instability, active damping using a capacitor current compensation term is usually preferred [26]-[27]. Hence for this system, four separate capacitor current feedback signals are required for active damping one for each of the dq currents in each of the two synchronous rotating frames, as shown in Fig. 2. III. CONSOLIDATED POWER CONTROL FOR A THREE-PHASE DG SYSTEM The primary objective of the top level power control system is to regulate the average real and reactive power that is injected into the grid system. The secondary objective under unbalanced voltage conditions is to either 1) eliminate the active power ripple, or 2) eliminate the reactive power ripple, or 3) simply balance the grid injected currents, as required. The power control aims to generate commanded values for the current regulators that form the next level down control system. For this purpose, these commanded values are calculated based on the target real and reactive power commands and which are either commanded from a remote controller, or set to constant values for a desired level of PQ control. The power injected into the grid is measured using = + (5) = where and are the measured grid voltages and currents in the dq frame. For unbalanced PCC voltage conditions, the real and reactive power flows can be calculated from the positive and negative sequence voltage and current components [13] using = where the and terms in (6) are the average real and reactive powers injected into the grid, and the P,P,Q,Q terms define the magnitude of the double fundamental frequency oscillating real and reactive powers as quadrature components referenced to the synchronous rotating frame. Eqn. (6) can then be used to create commanded references for the current regulators from the required grid power injections: = By deleting unnecessary rows, inverting the remaining reduced matrix and replacing the calculated powers with known reference values, commanded currents for the three (6) (7) different ripple control strategies can be determined as described in the following sections. A. Active Power Ripple Control For control of active power ripple only, the last two rows of (6) can be deleted, since the reactive power ripple is uncontrolled. The reduced matrix is then inverted, the average and injections are set to known values of and, and the target quadrature active power ripple magnitudes are set to zero, i.e. = =0, to give: = = (8) (9) where =( ) +( ) ( ) ( ) =( ) +( ) +( ) +( (10) ) With the reference currents set by commanded average power injections and zero real power oscillations only, reactive power oscillations will now occur, since their magnitude is uncontrolled. The quadrature component magnitudes of these oscillations can be obtained by combining (9) with the last two lines of (6), to give =2 (11) B. Reactive Power Ripple Control For control of reactive power ripple only, the middle two rows of (6) can be deleted, since active power ripple is uncontrolled. The reduced matrix is then inverted, the average and injections are set to known values of and, and the quadrature reactive power ripple magnitudes are set to zero, i.e. = =0, to give: = = (12) (13) Similarly to (11), the quadrature magnitudes of the oscillating real power can be obtained from (13) and (6) as =2 (14)

4 C. Balanced Current Control For balanced grid currents, only the top left hand four elements of (6) are required, since both the active and reactive power ripple are uncontrolled, and the negative sequence current references are forced to zero, so that: = + + = + ( ) ( ) ( ) ( ), = =0 (15) ( ) ( ) ( ) ( ) (16) Balanced currents are obtained at the expense of both active and reactive power oscillations. The oscillating power magnitudes can be calculated by substituting (16) into the last four lines of (6), to give = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (17) Comparing the oscillating power magnitudes of (11), (14) and (17), it can be seen that the factor of 2 has disappeared when balanced currents are generated. This is because the power oscillations are shared between both the real and reactive powers for this third case. D. Combined Power Ripple Control Eqns (9), (13) and (16) can be combined as follows: = + (18) where =( ) +( ) ( ) +( ) =( ) +( ) +( ) +( ) (19) and K is a real number in the range of 1,1 that defines the required power ripple control strategy. When = +1, (18) and (19) revert to (9) and (10) to control active power ripple only at the expense of unbalanced grid currents and oscillatory reactive power. Similarly, when = 1, (18) and (19) revert to (12) and (13) to control reactive power ripple only at the expense of unbalanced grid currents and oscillatory active power. Finally, when =0, (18) and (19) revert to (15) and (16), and the injected grid currents only are balanced. The consolidated oscillating power control concept has been verified initially using a detailed PSIM simulation representation of Fig. 2, feeding into an unbalanced grid supply where one phase voltage sags to 50%. The filter and current regulator gain parameters of the simulated system have been matched those of the experimental system presented later in this paper. For the 50% sag unbalanced grid voltage condition shown in Fig. 3, the controller performance is shown in Fig.3. Faulty grid voltages, where one phase sags to 50% (created by grid simulator). Fig. 4. For the period 0.0 t < 0.1s, the Active Power Control strategy ( =+1) is implemented and no oscillation is present in the real power. As expected, oscillations appear in the reactive power, and the threephase currents are also not balanced. For the period 0.1 t < 0.2s, the Current Control strategy is used with =0. Balanced currents are then generated to feed into the grid, but with both real and reactive power oscillation as a consequence. Finally, for the period 0.2 t < 0.3s, is changed to = 1 to enable the Reactive Power Control strategy. In contrast to active power control, no reactive power oscillations are now present, but there is now real power oscillation, and once again the grid currents are unbalanced. IV. POWER FLOW RIPPLE CONTROL AND ITS EFFECT ON PCC GRID VOLTAGE The combined power ripple control strategy is now used to investigate the effect of eliminating the active or the reactive power ripple, or just balancing the grid injected currents, when the DG feeds into a grid distribution system with a significant voltage unbalance at the PCC. For this investigation, the DG system is Fig.4. Oscillating Power Controller Performance (PSIM simulation). Three-phase currents(upper trace). Real and reactive powers (lower trace)

5 TABLE I. SYSTEM PARAMETERS Fig. 5. Three-phase grid-connected DG inverter. Symbol Nominal Value Inverter rating 5 Inverter inductor 3 Grid-side inductor 1 Filter capacitance 7.5 Switching frequency 10 khz Sampling frequency 20 khz Grid voltage V 100 V (rms) Grid frequency f 50 Hz Line resistance 1.5/ Ω Line reactance 1 (0.314 Ω) DC bus voltage V connected to the main grid through a feeder with different line characteristics ( ) as shown in Fig. 5. The effect of the three different power ripple control strategies on the voltage quality at the point of common coupling is then explored as the grid feeder impedance varies from resistive to reactive. For this part of the work, the effect of the proposed strategy has been explored with experimental investigations, using a 5 kva three-phase inverter that is connected to the grid via a LCL filter and an isolation transformer. The parameters of the system are listed in Table I. A fixed point DSP (TMS320F2810) was used as the system controller for all measurement, control and PWM functions. DC bus voltage compensation was included into the PWM processes to ensure that variations in the DC bus voltages caused by real power ripple did not affect the quality of the regulated AC currents. The three-phase unbalanced grid voltages were created by a programmable California Instrument MX30/45 grid simulator. The grid-side impedances ( ) were made up from a series combination of isolation transformer, discrete inductors and resistors. The controller gains used for this experimental system are listed in Table II. The current regulation method is based on the proposed method in [15] which uses a Double Synchronous Reference Frame (DSRF) current regulator without sequence current separation. While a LCL filter is used, the maximum current regulator gains can be calculated using the same approach as [26], the maximum possible proportional gain becomes = (20) = 0.36 = (21) while the integral reset time can be set to: 10 = 1 2 = (22) The maximum and minimum possible damping gains can also be calculated for an LCL resonant frequency below critical frequency, which gives damping limits of _ = and _ = The damping gain used in this study, =0.09, was set to maximize the closed loop system damping in accordance with the methodology detailed in [26]. TABLE II. For this study, the voltage unbalanced n-factor [30], which is the ratio between negative and positive sequence voltage amplitudes, is used as the performance parameter to quantify the system voltage unbalance at the PCC. The n-factor is defined by n= = CONTROLLER PARAMETERS Symbol Value Proportional gain Time constant Damping gain 0.09 (23) and is calculated from measurements at the PCC. The influence of the oscillating power control strategies is then evaluated by comparing the n-factor of the unbalanced grid supply voltages against the n-factor of the DG connected system at its PCC. In addition, the voltage magnitude of the sagging phase is compared against the main grid phase voltage sag, to see what improvement has been achieved by the DG power compensation injection. For each investigation, the voltage sag at the PCC was measured with no active power ripple, balanced grid current, and no reactive power ripple, respectively, for commanded average power injections of P only, Q only, and a combined PQ command. The power ripple objective was set by varying K over the range =+1,0, 1 at 0.1sec steps, for each average PQ test condition. Results are presented here for the three cases of resistive, inductive and combined RL grid network impedances, for the three operating conditions of: 800 W average P only injection 800 VAr Q only injection combined 566 W P and 566 VAr Q injection (apparent power equal to 800 VA). A. Case I: Grid with resistive feeder impedance Fig. 6 shows the results for a grid with a resistive line impedance, where for each average PQ condition the ripple power objective is changed at 0.1 second intervals during the experiments, from no active power ripple, =+1, to balanced currents, =0, to no reactive power ripple, = 1. From this figure, it can be seen that irrespective of the average PQ injection levels, the power ripple control scheme always achieves the commanded ripple objective, which confirms the

6 capability of the strategy. Furthermore, it is clear that for this resistive grid network, eliminating real power ripple achieves the lowest n-factor outcome, and hence this ripple objective provides the best grid voltage negative sequence mitigation irrespective of the average power injection conditions. It should be noted also for the PQ injection case that n-factor has only been reduced to (compared to for the P only injection case). This is because the injected real power is only 566W for this case, which further confirms that only real power injection achieves mitigation of the PCC voltage unbalance for a resistive only feeder impedance. Fig. 9 shows how the different ripple objectives influence the absolute voltage magnitude of the sagging phase voltage at the PCC. From this figure it can been seen that while all power ripple injection alternatives improve the sagging phase voltage, real power ripple elimination always achieves the best outcome. B. Case II: Grid with inductive feeder impedance Fig. 7 shows the results for a grid with an inductive line impedance, once again with the same change in ripple power objective from no active power ripple to balanced currents to no reactive power ripple at 0.1 second intervals, for each average PQ injected condition. These results show that injecting active power into the system has no significant impact on the voltage unbalance n-factor, as shown in Fig. 7 (left). Furthermore, whenever average reactive power is injected, the n-factor increases unless the reactive power oscillation is eliminated ( = 1). So for a grid with an inductive characteristic, not only is the best unbalanced voltage mitigation always achieved when reactive power ripple is eliminated, but it can only essentially be restored to the uncompensated grid n-factor. This is in sharp contrast to the improvement in voltage unbalance n-factor that can be achieved with a resistive line impedance by eliminating real power ripple. Fig. 10 shows that for an inductive grid impedance, real power injection still achieves the best absolute sagged phase voltage increase. Hence if real power is to be injected into the grid, the best DG performance is achieved with =+1, since this will maximize the increase in the sagged phase voltage without increasing the overall voltage n-factor. However, with average reactive power injection, the no reactive power ripple strategy is the best alternative to avoid increasing the n- factor. C. Case III: Grid with resistive/inductive impedance Fig. 9 presents results for a grid with a mixed resistive/inductive characteristic, where the grid impedance has an impedance angle of 45 degree ( = ). As could be expected, for active average power injection and the three different control strategies, the system performance is similar to the case of a grid with resistive characteristics, Fig. 10 (left). However, the reduction in the n-factor is less than for a purely resistive grid impedance. When average reactive power is injected into the grid the results are the same as for reactive power injection into an inductive grid, as shown in Fig. 10(middle). Hence the no reactive power ripple strategy is best for this average power injection condition. Finally, the performance with mixed average power injection is essentially the same irrespective of the power ripple objective, i.e. no significant change in the voltage n-factor compared to a grid without DG injection. Fig. 11 shows that once more, real power injection achieves the best increase in the absolute sagged phase voltage magnitude for the mixed impedance feeder irrespective of the ripple power objective. The conclusion from these studies is that regardless of the type of grid impedance, active power injection always achieves the best absolute unbalanced voltage mitigation. Furthermore, a no active power ripple strategy ( = +1) is always the best approach unless reactive power is injected into the grid. In this case it is better to proceed to a no reactive power ripple strategy (K = -1) to keep the voltage unbalance n-factor at least no worse than that of the unbalanced grid supply. V. CONCLUSION This paper has presented a strategy to vary between eliminating the real power ripple, the reactive power ripple, or to just balance the grid currents, for a DG inverter operating into a grid network with unbalanced voltages at the PCC. The strategy calculates positive and negative sequence current references from the required average power injection and power ripple objectives, and feeds these references to synchronous frame closed loop current regulators. 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8 Fig.7. Experimental results for grid with inductive characteristic. (left) Real power injection. (middle) Reactive power injection. (right) combined PQ injection. Fig. 8. Experimental results for grid with mixed RL characteristic. (left) Real power injection. (middle) Reactive power injection. (right) combined PQ injection.

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