This article investigates mean risk hedging with respect to limited liquidity and studies the impact of different risk measures on the hedging strategies. For motivation and application purposes hedging in electricity markets is chosen, because the relevant hedging markets are characterized by limited liquidity. We enhance the approach in Woll and Weber (2015) to a mean-risk optimization under limited liquidity, including the risk measures absolute and relative Value and Conditional Value at Risk (VaR and CVaR). It can be shown that for position independent measures (Variance, relative VaR, relative CVaR) liquidity has no influence on the minimum risk hedging strategies, whereas for position dependent measures (absolute VaR, absolute CVaR) liquidity has an impact on the minimum risk hedging strategies. The article gives the mathematical formulations of the problems and discusses the economic relevance of the different models. In addition, we apply the analyzed concepts to the German Electricity markets.