Reference-Feedforward Power-Synchronization Control

In this letter, an enhancement of power-synchronization control is proposed, whereby pole–zero cancellation in the closed-loop system is achieved. An effect thereof is that step-response ringing and overshoot are eliminated. For strong grids, the closed-loop bandwidth increases, allowing a shorter step-response rise time.


Letters
Reference-Feedforward Power-Synchronization Control Lennart Harnefors , Fellow, IEEE, F. M. Mahafugur Rahman , Marko Hinkkanen , Senior Member, IEEE, and Mikko Routimo , Member, IEEE Abstract-In this letter, an enhancement of powersynchronization control is proposed, whereby pole-zero cancellation in the closed-loop system is achieved. An effect thereof is that step-response ringing and overshoot are eliminated. For strong grids, the closed-loop bandwidth increases, allowing a shorter step-response rise time.

I. INTRODUCTION
P OWER-SYNCHRONIZATION control (PSC) [1] is based on emulating the dynamics of a synchronous machine by a grid-connected voltage-source converter (VSC). The scheme was originally conceived to allow a stable interconnection with a very weak grid [2]. Its properties have been studied in detail over the years. Two recent examples are the large-signal transient stability analysis presented in [3] and the analytic selection of the power-control gain derived in [4]. In addition, in [4], an empirical selection recommendation for the so-called active resistance (which resembles the proportional gain of a current controller) is given. A robust design, with guaranteed stability margins of the power control loop, is obtained irrespective of the grid strength.
The great majority of papers on PSC consider weak-grid connections and/or grid-forming control, e.g., [5]- [8]. For robustness it is desirable that PSC should perform well also in a strong-grid connection. Unfortunately, even with the robust design in [4], the performance of PSC is inferior to that of traditional vector current control with cascaded outer loops. The closed-loop bandwidth is inherently limited and typically the step response exhibits overshoot and/or ringing.
This shortcoming is here rectified by the enhancement reference-feedforward PSC (RFPSC). In addition to using the Manuscript  power reference in the power control law, it is fed forward to the active-resistance part [9]. It is shown that this places the zeros of the closed-loop system so that they (near-exactly) cancel a complex pole pair, reducing the system order from three to one. The pole-zero cancellation occurs irrespective of the grid inductance, thus ensuring robustness. Design and analysis of RFPSC are presented in Section II, followed by experimental verification in Section III.

A. Design
In PSC, the converter voltage, expressed in the stationary αβ frame, is given as v s = ve jθ (1) assuming operation in the linear pulsewidth-modulation region, controller latency neglected, and switching harmonics disregarded. With current and power direction out of the converter, angle θ-which defines the synchronously rotating dq frame-is governed by the (active) power control law where ω 1 is the fundamental angular frequency, K p is the powercontrol gain, and P ref is the power reference is the active output power, and K is the space-vector scaling constant. For per-unit (p.u.) normalization of the quantities or power-invariant vector scaling (K = 3/2), κ = 1. Moreover, PSC gives the dq-frame converter voltage as , although in practice it may be varied via a closed control loop for the pointof-common-coupling voltage or the reactive power [1], [10]. The second term is that of the active resistance R a , expressed as a proportional control law. In conventional PSC, i ref is selected as a filtering of the converter current i = i d + ji q by the low-pass filter H( In the steady state,  which constitutes the invention in RFPSC [9]. The block diagram shown in Fig. 1 is obtained.
Remark: Being a voltage-stiff control scheme, PSC gives injection of negative-sequence current as response to an unbalanced grid. The d component of i ref has low negative-sequence content; for conventional PSC because of filtering and for RF-PSC due to its selection as a quotient of two references. Hence, the two PSC variants have virtually identical unbalanced-grid responses.

B. Analysis
The closed-loop system from P ref to P resulting from RFPSC is analyzed here. In accordance with [1] and [4], a purely inductive grid impedance, with inductance L, behind an infinite bus with the stiff voltage V g is assumed.
where s = d/dt. Since the coordinate transformation in (1) and the active-power expression in (3) both are nonlinear, smallsignal analysis is required. Identically to [4], the involved variables are expressed as perturbations (denoted by the prefix Δ) about operating points as follows: where i 0 = i d0 + ji q0 . With (7), (6) is transformed to the dq frame as follows: . This allows approximating H(s) = 0 without significantly impairing the accuracy of the results, yielding the following perturbation form of (4): Straightforward comparison of the two variants, conventional PSC and RFPSC, is thereby permitted. Substituting (9) in (8), approximating e −jΔθ ≈ 1 − jΔθ, and neglecting cross terms between perturbation variables yields where the last three terms on the right-hand side must sum up to zero, giving V g e −jθ 0 = V − jω 1 Li 0 . Solving for Δi yields the following relation: Introduction of perturbation variables in (3) gives, after linearization Substitution of (9) in (12) yields in which (11) is substituted, giving The real part is evaluated for s real, resulting in Combining (14) with the power control law (2), expressed in perturbation variables as Δθ = (K p /s)(ΔP ref − ΔP ), the closed-loop system, shown in Fig. 2, is obtained. As G p (s) is invariant of ξ, RFPSC does not affect the feedback loop in Fig. 2, and consequently not the poles of the closed-loop system G c (s). This motivates adopting the gain selection in [4] which gives ample stability margins.

III. EXPERIMENTAL RESULTS
RFPSC is here experimentally compared with conventional PSC, using the same back-to-back (grid and dc source) two-level VSC system as in [4]-see the schematic depicted in Fig. 4whose data are given in Table I. Control is implemented on a dSPACE DS1006 processor board. The dc link is controlled from the dc source.
Figs. 5 and 6 show results for four successive steps in P ref , respectively, for a weak and a strong grid, with conventional PSC as well as with RFPSC. (The subfigures for conventional PSC are repeated from [4], for clarity.) The following can be observed.
1) The step-response rise times in the weak-grid case are similar for conventional PSC and RFPSC. This was to be expected, since, for a weak grid, the real pole of the closedloop system is dominant. Cancellation of the complex pole pair only gives a slight increase of the closed-loop bandwidth. On the other hand, the tendency to ringing in the step response is eliminated. 2) In the strong-grid case, RFPSC gives shorter rise times than conventional PSC and, perhaps even more importantly, eliminates the overshoots. In addition, the voltagemagnitude transients are significantly reduced. 3) In accordance with the model in (20) resulting from the pole-zero cancellation, all step responses for RFPSC resemble first-order exponentials.

IV. CONCLUSION
In this letter, the enhancement RFPSC of conventional PSC was presented. It involves feeding the power reference forward to the active-resistance part of the control law. When observing the robustifying gain selection in (18), the complex pole pair of the closed-loop system is (near-exactly) cancelled. Compared with conventional PSC, this was shown to eliminate step-response ringing for weak grids. For strong grids, a shorter step-response rise time is obtained and overshoot is avoided, allowing performance similar to that of vector current control. The design was shown to be robust in the sense that, irrespective of the grid inductance L, the step response resembles a first-order exponential whose rise time is proportional to L. Knowledge of L is not required for the robust design, as fundamentally shown by the gain selection given in (18). A suitable topic for further research is performance analysis for a generic grid impedance.