Sun

Channel Training Design in Amplify-and-Forward MIMO Relay Networks

This paper is on the channel training design for distributed space-time coding (DSTC) in multi-antenna relay networks. DSTC is shown to achieve full diversity in relay networks. To use DSTC, the receiver has to know both the channels between the relays and the receiver (Relay-Rx channels), and the channels between the transmitter and the relays (Tx-Relay channels). For the Relay-Rx channels, by sending pilot signals from the relays, the training problem can be solved using multi-input-multi-output (MIMO) training schemes. Given the knowledge of the Relay-Rx channels, to obtain estimations of the Tx-Relay channels at the receiver, DSTC is used. The linear minimum-mean-square-error (LMMSE) estimation at the receiver and the optimal pilot design that minimizes the estimation error are derived. We also investigate the requirement on the training time that can lead to full diversity in data transmission. An upper bound and a lower bound on the training time are provided. A novel training design whose training time length is adaptive to the quality of the Relay-Rx channels is also proposed. Simulations are exhibited to justify our analytical results and to show advantages of the proposed scheme over others.

Real-Time Power Balancing in Electric Grids With Distributed Storage

Power balancing is crucial for the reliability of an electric power grid. In this paper, we consider an aggregator coordinating a group of distributed storage (DS) units to provide power balancing service to a power grid through charging or discharging. We present a real-time, distributed algorithm that enables the DS units to determine their own charging or discharging amounts. The algorithm accommodates a wide spectrum of vital system characteristics, including time-varying power imbalance amount and electricity price, finite battery size constraints, cost of using external energy sources, and battery degradation. We develop a modified Lyapunov optimization framework for real-time power balancing and provide a fast iterative method for distributed implementation. The two components interact through a novel cost cushion parameter that tunes the trade-off between system performance and convergence speed. We show analytically that the algorithm converges quickly and provides asymptotically optimal performance as the capacity of DS units increases. We further study through simulation the algorithm performance over a wide range of parameter values and demonstrate that it is highly competitive over a greedy alternative.

Distributed Real-Time Power Balancing in Renewable-Integrated Power Grids With Storage and Flexible Loads

The large-scale integration of renewable generation directly affects the reliability of power grids. We investigate the problem of power balancing in a general renewable-integrated power grid with storage and flexible loads. We consider a power grid that is supplied by one conventional generator (CG) and multiple renewable generators (RGs) each co-located with storage, and is connected with external markets. An aggregator operates the power grid to maintain power balance between supply and demand. Aiming at minimizing the long-term system cost, we first propose a real-time centralized power balancing solution, taking into account the uncertainty of the renewable generation, loads, and energy prices. We then provide a distributed implementation algorithm, significantly reducing both computational burden and communication overhead. We demonstrate that our proposed algorithm is asymptotically optimal as the storage capacity increases and the CG ramping constraint loosens. Moreover, the distributed implementation enjoys a fast convergence rate, and enables each RG and the aggregator to make their own decisions. Simulation shows that our proposed algorithm outperforms alternatives and can achieve near-optimal performance for a wide range of storage capacity.

Channel Training and Estimation in Distributed Space-Time Coded Relay Networks with Multiple Transmit/Receive Antennas

This paper investigates the channel training and estimation problems for distributed space-time coding (DSTC). To use DSTC in multi-antenna relay networks, the receiver needs to know the channels between the relays and the receiver (Relay-R channels) and also the equivalent channels between the transmitter and the receiver (Equ-T-R channels). By sending pilot signals from the relays, the training of the Relay-R channels is equivalent to that of a multi-input-multi-output (MIMO) system. The training of the Equ-T-R channels can be conducted directly using DSTC; but it requires a long training period. Thus, a separate-training method is proposed, in which an estimation on the Equ-T-R channels is obtained from estimations on the channels from the transmitter to the relays (T-Relay channels) and the Relay-R channels. The pilot code designs that minimize the trace of the error covariance matrix are investigated. The requirements on the training period are also derived, from which an adaptive training-period design is proposed. Simulation shows that in some networks, even with shorter training period, the separate-training scheme can achieve better performance than the direct-training scheme.

Training and Decodings for Cooperative Network with Multiple Relays and Receive Antennas

In this paper, channel training and coherent decodings under channel estimation error are investigated for relay networks with one single-antenna transmitter, R single-antenna relays, and one R-antenna receiver. A two-stage training scheme is proposed to estimate both the relay-receiver and the transmitter-relay channels at the receiver, which are commonly required in amplify-and-forward (AF) relay networks. We use distributed space-time coding (DSTC) for data transmission and investigate the effect of channel estimation errors on network performance. Two coherent decodings are considered: mismatched decoding in which channel estimations are treated as if perfect, and matched decoding in which estimation error is taken into consideration. We show that for full diversity, with mismatched decoding, at least 3R symbol intervals are required for training; while with matched decoding, R+2 symbol intervals for training are enough. The complexities of the decoding schemes are investigated. To achieve a balance between performance and complexity, an adaptive decoding scheme is proposed. Simulated error rates are shown to justify the analytical results.

Real-time welfare-maximizing regulation allocation in aggregator-EVs systems

The concept of vehicle-to-grid (V2G) has gained recent interest as more and more electric vehicles (EVs) are put to use. In this paper, we consider a dynamic aggregator-EVs system, where an aggregator centrally coordinates a large number of EVs to perform regulation service. We propose a Welfare-Maximizing Regulation Allocation (WMRA) algorithm for the aggregator to fairly allocate the regulation amount among the EVs. The algorithm operates in real time and does not require any prior knowledge on the statistical information of the system. Compared with previous works, WMRA accommodates a wide spectrum of vital system characteristics, including limited EV battery size, EV self charging/discharging, EV battery degradation cost, and the cost of using external energy sources. Furthermore, our simulation results indicate that WMRA can substantially outperform a suboptimal greedy algorithm.

Distributed regulation allocation with aggregator coordinated electric vehicles

Electric vehicles (EVs) are promising alternatives to provide ancillary services in future smart energy systems. In this paper, we consider an aggregator-EVs system providing regulation service to a power grid. To allocate regulation amount among EVs, we present both synchronous and asynchronous distributed algorithms, which align each EVs interest with the systems benefit. Compared with previous works, our algorithms accommodate a more realistic model of the aggregator-EVs system, in which EV battery degradation cost, EV charging/discharging inefficiency, EV energy gain/loss, the cost of external energy sources, and potential asynchronous communication between the aggregator and each EV are taken into account.We give sufficient conditions under which the proposed algorithms generate the optimal regulation amounts. Simulations are shown to validate our theoretical results.

Phase Balancing Using Energy Storage in Power Grids Under Uncertainty

Phase balancing is essential to safe power system operation. We consider a substation connected to multiple phases, each with single-phase loads, generation, and energy storage. A representative of the substation operates the system and aims to minimize the cost of all phases and to balance loads among phases. We first consider ideal energy storage with lossless charging and discharging, and propose both centralized and distributed real-time algorithms taking into account system uncertainty. The proposed algorithm does not require any system statistics and asymptotically achieves the minimum system cost with large energy storage. We then extend the algorithm to accommodate more realistic non-ideal energy storage that has imperfect charging and discharging. The performance of the proposed algorithm is evaluated through extensive simulation and compared with that of a benchmark greedy algorithm. Simulation shows that our algorithm leads to strong performance over a wide range of storage characteristics.

On Stochastic Feedback Control for Multi-Antenna Beamforming: Formulation and Low-Complexity Algorithms

Based on the Gauss-Markov channel model, we investigate the stochastic feedback control for transmit beamforming in multiple-input-single-output systems and design practical implementation algorithms leveraging techniques in dynamic programming and reinforcement learning. We first validate the Markov decision process formulation of the underlying feedback control problem with a 4R-variable (4R-V) state, where R is the number of the transmit antennas. Due to the high complexity of finding an optimal feedback policy under the 4R-V state, we consider a reduced 2-V state. As opposed to a previous study that assumes the feedback problem under such a 2-V state remaining an MDP formulation, our analysis indicates that the underlying problem is no longer an MDP. Nonetheless, the approximation as an MDP is shown to be justifiable and efficient. Based on the quantized 2-V state and the MDP approximation, we propose practical implementation algorithms for feedback control with unknown state transition probabilities. In particular, we provide model-based offline and online learning algorithms, as well as a model-free learning algorithm. We investigate and compare these algorithms through extensive simulations and provide their efficiency analysis. According to these results, the application rule of these algorithms is established under both statistically stable and unstable channels.

Distributed real-time phase balancing for power grids with energy storage

Phase balancing is of paramount importance for power system operation. We consider a substation connected to multiple buses, each with single phase loads, generation, and energy storage. A representative of the substation operates the system and aims to minimize the cost of all buses as well as balancing loads among phases. We first consider ideal energy storage with perfect charging and discharging efficiency, and propose a distributed real-time algorithm taking into account system uncertainty. The proposed algorithm does not require any system statistics and can ensure a certain performance guarantee. We further extend the algorithm to accommodate non-ideal energy storage. The algorithm is evaluated through numerical examples and compared with a greedy algorithm.