Design and Practical Investigation of a Model Predictive Control for Power Grid Converter

In recent years power electronic converters play a major role in the grid integration of renewable energy systems [1]. These converters are used to regulate and shape an electrical signal in the required form. Among these converters, AC–DC converters, commonly known as rectifiers, are used extensively in renewable energy systems such as grid-connected DC microgrids, grid-connected solar photovoltaic energy conversion systems, etc. [2, 3].

Model Predictive Control (MPC), which was developed in the process control industry in the 1970’s, has received significant attention from industry and academia due to its fast dynamic response, conceptual simplicity and the ability to include nonlinearities and constraints in the design of the controller [1].

Several MPC-based strategies have been proposed for grid-connected converters, with a number of these directly regulating the active and reactive powerdelivered to (or drawn from) the grid by selecting the switching state of the converter.

DPC selects an optimal converter state in a similar manner to DTC by utilizing a switching table and hysteresis bounds. The Virtual Flux (VF) technique was first proposed for DPC. The VF technique makes the assumption that the grid voltage and AC- side resistance and inductance are quantities which can be related to an AC machine. The use of VF vectors in DPC enables the elimination of grid voltage sensors and a simple power calculation [4].

In the same way that MPDTC extends on DTC, Model Predictive Direct Power Control (MPDPC) can be viewed as an extension of DPC, replacing the switching table with an online optimization stage. This paper presents a VF-based MPDPC scheme for three-phase grid-connected VSCs. Under steady-state conditions, the key performance indicators are the converter switching losses, P sw, and the Total Demand Distortion (TDD) of the grid current, TDD. Under transient conditions performance is judged by the response time of the output following reference steps. In order to benchmark the performance of MPDPC, it has been compared against Pulse Width Modulation (PWM) and Optimized Pulse Patterns (OPP). The different schemes have been compared through simulation of a three-level, three-phase Neutral Point Clamped (NPC) converter.

This paper presents Model Predictive Direct Power Control (MPDPC), a new approach to the control of grid-connected converters, which regulates the instantaneous avtive and reactive power delivered to the grid within a set of symmetrical bounds, whilst minimising the device switching frequency of the converter.

This article is organized as follows: in section 2, the description of the proposed circuit is defined, this section display the physical modeling of different part with their equations model. Control strategy applied to the whole system with their step and equations model are shown in section 3. In section 4,we validated the theoretical study part and the proposed control algorithms and a dynamic model of the system is modeled and simulated in Matlab/Simulink. The description of the setup bench is detailled in section 5. Section 6, shown the obtained experimantal result tested on the platform board. Finally, conclusions are drawn in section 7.

Three-phase two level grid connected VSI is a very well-known topology in power electronics. Simplified circuit diagram of the system has been illustrated in Figure 1. It has been composed of six IGBT modules and connected to the filter inductor, resistor, and grid voltage. The mathematical equation of the system model can be described by the space vector analysis as follows [7]:

$v={{L}_{g}}\frac{di}{dt}+{{R}_{g}}i+{{v}_{g}}$     (5)

where, v, i and e are the representations of the inverter voltage vector, grid current vector and grid voltage vector, respectively; R and L are the filer resistance and filter inductance.

${{i}_{g}}\left( k+1 \right)=\left( 1-\frac{{{R}_{g}}{{T}_{s}}}{{{L}_{g}}} \right)i\left( k \right)+\frac{{{T}_{s}}}{{{L}_{g}}}\left( v\left( k \right)-{{v}_{g}}\left( k \right) \right)$     (6)

Since the MPC method is based on the discrete-time equation, the system model should be discretized with sampling period (Ts) in order to predict the future value. By using the forward Euler method on (1), the discrete-time model of the system will be expressed as follows:

$g=i_{g}^{*}\left( k+1 \right)-i_{g}^{p}\left( k+1 \right)$     (7)

where,

k is the presentation of the instant that the last switching state has been applied to the inverter and k+1 represents the next sampling instant, i(k) and v_g(k) is measured from the hardware sensors and v(k) can be obtained by using switching state of the inverter. Considering all the possible combinations of the switching state, eight voltage vectors (V₀~V₇) are obtained as shown in Figure 2(a). Therefore, the eight future grid current vectors i₀(k+1)~i₇(k+1) are predicted from (2). To determine the optimum voltage vector among the possible voltage vectors v₀(k)~v₇(k), the cost function is defined asfollows [8].

3.2 Measured voltages and current

The measured three-phase grid voltages and currents, and DC link voltage ${{v}_{dc}}$ are supplied as input signals to the control scheme [9]. The PCC scheme generates switching signals S_ai, S_bi, and S_ci for the GCC. For a balanced three-phasegrid, it is not necessary to measure phase-c grid voltages and currents because:

${{v}_{cg}}(k)=-{{v}_{ag}}(k)-{{v}_{bg}}(k)$     (8)

${{i}_{cg}}(k)=-{{i}_{ag}}(k)-{{i}_{bg}}(k)$     (9)

The control algorithm of the conventional MPC method can be described to the following steps [10];

1. Applying the switching state S(k)

2. Measure the i(k) and e(k)

3. Predict the i(k+1) for all the possible switching states.

4. Calculate the cost function with the i*(k+1) and i(k+1)

5. Determine the optimum voltage vector

6. Store switching state according to the optimum voltage vector

3.3 Prediction step

From i(k+1) on the controller can use any possible output to bring the controlled currents that closer to their reference. In the next step i(k+2), the prediction step, the controller thus calculates the measured currents at k+2 for all possible switch states at k+1. With long prediction horizon (nsteps) the output current with RL-Load can be expressed as [11]:

$\begin{align}  & \left[ \begin{matrix}   {{i}_{d}}(k+n)  \\   {{i}_{q}}(k+n)  \\\end{matrix} \right]=\left[ \begin{matrix}   1-{{T}_{s}}\frac{{{R}_{g}}}{{{L}_{g}}} & 0  \\   0 & 1-{{T}_{s}}\frac{{{R}_{g}}}{{{L}_{g}}}  \\\end{matrix} \right]\left[ \begin{matrix}   {{i}_{d}}(k+n-1)  \\   {{i}_{q}}(k+n-1  \\\end{matrix} \right] \\ & \text{                    +}\left[ \begin{matrix}   \frac{{{T}_{s}}}{{{L}_{g}}} & 0  \\   0 & \frac{{{T}_{s}}}{{{L}_{g}}}  \\\end{matrix} \right]\left[ \begin{matrix}   {{v}_{d}}(k+n-1)  \\   {{v}_{q}}(k+n-1)  \\\end{matrix} \right] \\\end{align}$     (10)

3.4 Cost Minimization Function

The main objective of the model predictive control algorithm is to minimize the error with fast dynamic response between the predicted and reference values of the discrete variables. In order to achieve this objective, an appropriate cost function e is defined with the reference and predicted value of current vector [12]. Hence, the cost function for the rectifier and inverter can be expressed with the absolute error between the predictive and reference values of input and load current for the rectifier and inverter modes as:

$g=\left| {{i}_{ref}}(k+1)-{{i}_{p}}(k+1) \right|$     (11)

where, g is the cost function. The reference input and predicted current are i_ref(k+1) and i_p(k+1).

3.5 Proposed control schema

The power control block diagram in dq-frame for a grid-connected two-level voltage source converter (2L-VSC) is shown in Figure 2. The 2Level VSC control system performs the following functions: grid active power control through the d-axis current control, grid reactive power control through the q-axis current control, and grid synchronization [13].

The proposed control strategy was further validated by experiment using a laboratory setup bench, as shown in Figure 7.

7.png

Figure 7. Experimental test bench

It consists of the following devices:

A three phase Semikron Electronic power converter composed of three IGBT modules, a dc power supplies source, and a three-phase isolated transformer, DC Link capacitor 1000 µF, a dSPACE card (model DS1104) with a PowerPC 604e at 400 MHz and a floating-point digital signal processor (DSP) TMS320F240 with control panel, electronic card with voltage sensors (model LEM LV 25-P) and current sensors (model LEM LA 55-P) for monitoring the instantaneous values of the stator phase voltages and currents, voltage sensor (model LEM CV3-1000) for monitoring the instantaneous value of the dc-link voltage.

During the real-time operation of the control algorithm, the supervision and capturing of the important data can be done by the Control Desk software provided with the DSP board.

This work outlines the steps to be followed in simulating and practical investigation of a predictive control model algorithm for a two-level voltage source converter connected to a three-phase electrical power grid.

Four steps are used to design procedure of the proposed technique in terms of estimation of grid voltage angle, calculation and extrapolation of reference currents, prediction of future grid currents and selection of optimal switching signals through the cost function minimization.

The simulation results obtained are identical and similar to those obtained with the experimental tests. A fast-dynamic response is obtained for the grid currents in different operating conditions without the use of the conventional regulators PI and without the use of a modulation stage in the internal regulation loop. Despite the abrupt and extreme change in operating conditions, our experimental system remains stable and converges towards signature results.

The obtained results show the feasibility of the implementation of the proposed control technique that proved as a simple and powerful tool in controlling grid power with excellent performance indices.