Cart.php

<?php

class Cart extends \yii\base\Object {
  
  /**
   * @var integer
   */
  public $id;
  
  /**
   * @var Item[]
   */
  public $items = [];
  
  /**
   * @var integer
   */
  public $userId;
  
  /**
   * @var string
   */
  public $sessionId;
  
  /**
   * @return Storage
   */
  public static function getStorage() {
    return Yii::$app->cartStorage;
  }
  
  /**
   * @return static
   */
  public static function load($id) {
    return static::getStorage()->load($id);
  }
  
  /**
   * @return boolean
   */
  public function save() {
    return static::getStorage()->store($this);
  }
  
  /**
   * @return integer
   */
  public function getItemQuantity() {
    return array_sum(array_map(function(Item $item) {
      return $item->quantity;
    }, $this->items));
    //Or array_sum(\yii\helpers\ArrayHelper::getColumn($this->items, 'quantity'));
  }
  
  public function isEmpty() {
    return count($this->items) == 0;
  }
  
  public function getTotalPrice($withDiscount = true) {
    return array_sum(array_map(function(Item $item) use ($withDiscount) {
      return $item->quantity * $item->price * ($withDiscount ? $item->discount : 1);
    }, $this->items;));
  }
}

DbStorage.php

<?php

class DbStorage extends Storage {
  
  /**
   *@param array|\yii\db\Connection
   */
  public $db = 'db';

  public $table = 'Carts';
  
  public function init() {
    $this->db = \yii\di\Instance::ensure($this->db, \yii\db\Connection::class);
  }
  
  public function store(Cart $cart) {
    //store in database
  }
  
  public function load($id) {
    //load from database
  }
  
}

Item.php

<?php

class Item extends \yii\base\Object {
  
  public $price;
  
  public $quantity;
  
  public $discount;
  
}

SessionStorage.php

<?php

class SessionStorage extends Storage {
  public function store(Cart $cart) {
    //store in database
  }
  
  public function load($id) {
    //load from database
  }
}

Storage.php

<?php

abstract class Storage extends \yii\base\Object {
  
  /**
   * @return boolean
   * 
   */
  abstract public function store(Cart $cart);
  
  /**
   * @return Cart
   */
  abstract public function load($id);
  
  /**
   * @return string
   */
  public static function serialize(Cart $cart) {
    return serialize(['items' => $cart->items]);
  }
  
  /**
   * @return Cart
   */ 
  public static function unserialize($object) {
    return new Cart(unserialize($object));
  }
  
}