Catalyzes the reversible oxidation of 3-phospho-D-glycerate to 3-phosphonooxypyruvate, the first step of the phosphorylated L-serine biosynthesis pathway. Does not catalyze the reversible oxidation of 2-hydroxyglutarate to 2-oxoglutarate and the reversible oxidation of (S)-malate to oxaloacetate. (2R)-3-phosphoglycerate + NAD(+) = 3-phosphooxypyruvate + H(+) + NADH Amino-acid biosynthesis; L-serine biosynthesis; L-serine from 3-phospho-D-glycerate: step 1/3. Homotetramer. Liver, kidney, brain, testis. Belongs to the D-isomer specific 2-hydroxyacid dehydrogenase family.